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Thermodynamic Database of the La-Sr-Mn-Cr-O Oxide System and Applications to Solid Oxide Fuel Cells
DISSERTATION for the degree of DOCTOR OF SCIENCES of the SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH
presented by ERWIN POVODEN-KARADENIZ Mag. rer. nat. born on March 18, 1973 Citizen of Austria
accepted on the recommendation of Prof. Dr. Ludwig J. Gauckler, examiner Prof. John T.S. Irvine, co-examiner Dr. Ming Chen, co-examiner
Zurich, 2008
Dedicated to my parents
Whatever creates or increases happiness or some part of happiness, we ought to do; whatever destroys or hampers happiness, or gives rise to its opposite, we ought not to do.
I am deeply grateful to my supervisor Professor Gauckler. He gave me a great chance by taking me into the boat: a boat that is not only sailed to scientific success. It took me away from an insecure float wobbling in the surf and approaches a promising future. Endless gratitude belongs to my wife who stays by my side throughout highs, downs, and distances, preventing me from losing the way; she is my firm anchor. I am greatly indebted to Nicholas Grundy for open doors, his patience of a saint, great teaching, and picky reviewing. He catalyzed my way into the field of thermodynamic modeling, airing the "modeling is fun" approach at any time. I would further like to thank Ming Chen for continuing scientific support and advising; he was often motivating me to spin the wheel of accurate and fast modeling and publishing. I owe thanks to Franc and Flavia Dugal-Borsari who saved me from an unintentional outdoor adventure in Zurich during a time when it was extremely difficult to find a new accommodation. It was a very pleasant time in Zollikon. I thank Brandon Bürgler and Jennifer Rupp for their pleasing office companionship at the beginning of my work: they facilitated my jump into the ETH waters. I would also like to thank Toni Ivas for abiding collegiality, cooperation, and friendship. I thank the rest of the office crew, Thomas Ryll and Rene Tölke, for always enjoyable working hours.
Zurich, December 2008
4 1.1.1 3.2.4 Proposed strategies against chromium "poisoning" and their effectiveness 1.2.1 1.2 3.1 1.Table of Contents Table of Contents Summary Zusammenfassung 7 9 1 Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cralloy interconnects 1.3.2 1.3.2 1.1.3 Principles of SOFC The problem of chromium "poisoning" 11 11 11 13 14 17 17 22 24 24 27 28 36 36 37 45 46 46 47 47 48 49 Volatilization of Cr2O3 Literature survey 1.2 Increasing the Cr-tolerance of conventional SOFC with Cr-interconnects and LSM cathodes New ways – alternative materials 2 3 Aim of study Method 3.1 1.3.3 Stoichiometric solid oxides Solid solution phases – the Compound Energy Formalism (CEF) Vacancies and the concept of reciprocal reactions 4 .6 Degradation of SOFC caused by chromium from the interconnect The role of current load on electrical losses of degraded SOFC Impedance spectroscopy measurements and implications on the degradation process Microstructures in degraded SOFC Amounts of chromium in SOFC tested with and without current load Critical assessment of proposed mechanisms of chromium "poisoning" 1.4.1 3.3 126.96.36.199.2 1.4.2 Benefits of the thermodynamic La-Sr-Mn-Cr-O oxide database for the understanding of Cr-poisoning of SOFC Thermodynamic modeling 3.1 Introduction 1.5 1.2.
3.4 4.4 Assessment of data from the literature Modeling and optimization Results and discussion 4.Table of Contents 3.3 4.5 Conclusions 5 Thermodynamic calculations of impacts of chromium on Sr-doped 5 .2 126.96.36.199.1.1 Introduction 4.1.4 4.4 4.1 Calculation of defect chemistry using the Calphad approach 51 52 53 53 53 54 58 59 66 67 73 77 77 78 86 89 93 96 97 101 102 103 103 109 117 128 134 134 135 137 140 143 Optimization of model parameters Thermodynamic reassessment of the Cr-O system in the framework of SOFC research 4.2.3 4.1.6 Experimental data Previous assessments of the Cr-O System Thermodynamic modeling Optimization of parameters Results and discussion Thermodynamic assessments 4.2.2 Thermodynamic assessment of the Mn-Cr-O system for SOFC materials 4.1.2 4.4 Literature review of the La-Cr system Literature review of the La-Cr-O system Thermodynamic modeling and optimization Results and discussion 4.4.6 Conclusions Thermodynamic La-Sr-Mn-Cr-O oxide database for SOFC applications 4.3.4 3.7 Conclusions 4.3 4 4.5 4.3.5 4.2.1 Introduction 4.2 184.108.40.206.3 4.4.1 Technology 4.3.1 Introduction 4.3 Experimental Thermodynamic modeling Optimization of parameters Results Discussion 4.1.6 4.5 4.3 4.2 184.108.40.206.18.104.22.168 Applications on SOFC Thermodynamic assessment of the La-Cr-O system 4.
3.4 5.1 5.4 5.3.3 Introduction Method Results 5.2)0.2 5.8Sr0.9Sr0.Table of Contents manganite (LSM) cathodes for SOFC 22.214.171.124 Thermodynamic calculations of La0.3 5.9MnO3-δ contaminated by chromium Thermodynamic testing of LSM with Mn-deficiency Formation of Cr2O3 148 149 150 152 152 157 160 162 163 165 Discussion Conclusions Appendix Thermodynamic La-Cr database Thermodynamic La-Sr-Mn-Cr-O-(H) oxide database 170 169 172 Curriculum Vitae 190 6 .1 5.2 5.1MnO3-δ contaminated by chromium Thermodynamic calculations of (La0.
as well as the formation of a new spinel phase occur under thermodynamic control: decreasing concentrations of vacancies in LSM that contains chromium are calculated at decreased oxygen partial pressure reflecting SOFC operation at high current load. and some are kinetically controlled. In chapter 1 the basics of planar SOFC are briefly explained. and previous findings of chromium "poisoning" of SOFC are critically reviewed. A key role is played by the adsorption of gaseous CrO3(g) (g = gaseous) and chromiumoxyhydroxides stemming from the interconnect on LSM and reaction of chromium with LSM. some of them probably occurring simultaneously. Some of these processes are governed by thermodynamics. In the third chapter the reader learns. Furthermore spinel blocks pores and thus impedes the oxygen 7 . how thermodynamic calculations can lead to a better understanding of a system. and the aim of this study (chapter 2) is to gather a deeper understanding of these unsolved problems by using thermodynamics. Based on the findings from the literature it gets clear that several questions about the key mechanisms of the chromium "poisoning" have not been answered yet.Summary Summary The thermodynamic La-Sr-Mn-Cr-O oxide database is established by assessing oxide subsystems using the CALPHAD (Calculation of phase diagrams) approach. Chapter 4 deals with the construction of the La-SrMn-Cr-O oxide database based on the assessments of subsystems. and the modeling approach used in this study is presented. It is shown that chromium "poisoning" of SOFC cathodes is a rather complex process consisting of several steps. This has calamitous consequences for the electrochemical properties of the cathode. The chromium is known to deteriorate the electrical performance of the cathodes. The new database is applied to the problem of chromium "poisoning" of SOFC with Cr-interconnects and LSM cathodes in chapter 5: a consistent phenomenological description of the process of chromium "poisoning" of SOFC cathodes is established that is in line with both experimental findings reported in the literature and thermodynamic calculations using the presented database. The associated chemical changes of the LSM phase. even if the system is in a thermodynamic non-equilibrium state. The new database is applied to the problem of chromium "poisoning" of Sr-doped lanthanum manganite cathodes ((La1−xSrx)1-yMnO3-δ or LSM) for Solid Oxide Fuel Cells (SOFC) stemming from gaseous Cr species from the high-Cr containing alloy of the interconnect.
With this contribution the prevailing question is resolved. which of the phenomena in a chromium-"poisoned" LSM cathode are governed by thermodynamics. Appropriate measures can be foreseen preventing the long-term degradation of SOFC cathodes in combination with high-chromium containing interconnects.Summary reduction required for the function of the cell. Cr2O3(s) (s = solid) that hampers the diffusion of oxygen into the electrolyte is a metastable phase in LSM contaminated by chromium. 8 .
Die thermodynamische La-Sr-Mn-Cr-O Oxid-datenbank wird basierend auf dem Assessment oxidischer Subsysteme mit dem CALPHAD-ansatz (Berechnung von Phasendiagrammen) aufgebaut. Die neue Datenbank wird auf das Problem der "Chromvergiftung" von Srdotierten Lanthan-Manganit-kathoden ((La1−xSrx)1−yMnO3-δ oder LSM) für FestoxidBrennstoffzellen (SOFC) angewandt, welches von gasförmigen Cr spezies der hochgradig Crführenden Interkonnektor-Legierung herrührt. Es ist bekannt, dass das Crom die elektrische Leistung der Kathoden verschlechtert. In Kapitel 1 werden die Grundlagen von planaren SOFC kurz erklärt, und es wird ein kritischer Überblick über bisherige Erkenntnisse der "Chromvergiftung" von SOFC gegeben. Basierend auf den Erkenntnissen aus der Literatur wird klar, dass einige Fragen, welche die Schlüsselmechanismen der "Chromvergiftung" betreffen, noch nicht beantwortet wurden. Das Ziel dieser Studie (Kapitel 2) ist es, unter Verwendung der Thermodynamik ein tieferes Verständnis dieser ungelösten Probleme zu erlangen. Im dritten Kapitel lernt der Leser, wie thermodynamische Berechnungen zu einem besseren Verständnis eines Systems führen können, selbst wenn dieses System sich in einem thermodynamischen Ungleichgewichtszustand befindet, und der in dieser Studie verwendete Modellansatz wird vorgestellt. Kapitel 4 beschäftigt sich mit der Konstruktion der La-Sr-Mn-Cr-O OxidDatenbank, basierend auf den Assessments der Subsysteme. In Kapitel 5 wird die neue Datenbank auf das Problem der "Chromvergiftung" von SOFC mit Cr-interkonnektoren und LSM-kathoden angewandt: Eine konsistente phenomenologische Beschreibung des Prozesses der "Chromvergiftung" von SOFC-kathoden wird gegeben, welche sowohl im Einklang mit experimentellen Erkenntnissen in der Literatur als auch mit thermodynamischen Berechnungen unter Verwendung der präsentierten Datenbank steht. Es wird gezeigt, dass "Chromvergiftung" von SOFC-kathoden ein ziemlich komplexer Vorgang mit mehreren, teilweise gleichzeitig in der Zelle ablaufenden Schritten ist. Manche dieser Prozesse sind thermodynamisch kontrolliert, und manche laufen unter kinetischer Kontrolle ab. Eine Schlüsselrolle spielt die Adsorbtion von gasförmigem CrO3(g) (g = gasförmig) und Chromium-oxyhydroxiden, welche vom Interkonnektor stammen, an LSM und die Reaktion von Chrom mit LSM. Die damit verbundenen chemischen Änderungen der LSM-phase und die Bildung einer neuen Spinellphase finden unter thermodynamischer Kontrolle statt. Die 9
Berechnungen ergeben abnehmende Konzentrationen der Leerstellen in Cr-hältigem LSM unter erniedrigtem Sauerstoffpartialdruck, und somit bei Betrieb von SOFC unter hohem Laststrom . Das hat katastrophale Konsequenzen für die elektrochemischen Eigenschaften der Kathode. Weiters blockiert Spinell Poren und behindert so die für die Funktion der Zelle notwendige Sauerstoffreduktion. Cr2O3(s) (s = fest), welches die Diffusion von Sauerstoff in den Elektrolyt erschwert, ist eine metastabile Phase in Cr-kontaminiertem LSM. Mit diesem Beitrag werden einige der vorherrschenden Fragen über "Chromvergiftung" von SOFC geklärt, und geeignete Maßnahmen zur Verhinderung der Langzeitdegradation von SOFC-kathoden in Kombination mit hochgradig Chrom-führenden Interkonnektoren können vorhergesagt werden.
Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
E. Povoden and L.J. Gauckler, to be submitted to Int. J. Mater. Rev. For the use of LSM cathodes in planar SOFC a comprehensive understanding of the mechanisms of the cell degradation caused by chromium diffusing from the interconnects into the cell is needed. This "poisoning" has been intensively investigated over the last decade. In this paper the affects of Cr on the degradation of SOFC with LSM cathodes and Cr-alloy interconnects are reviewed: the suggested models of chromium "poisoning" of planar SOFC with chromium-alloy interconnects and (La1-xSrx)1-yMnO3-δ (LSM) cathodes from the literature are critically assessed. Taking into account all available experimental findings on the affects of chromium on Sr-doped lanthanum manganite cathodes in planar solid oxide fuel cells, it can be concluded that several "poisoning" processes contribute to the deterioration of the cell performance. The review of all available experimental findings on the degradation of SOFC caused by chromium allows predictions, as to how the extent of degradation caused by chromium depends on the current load, operation temperature, operation time, as well as the amount of chromium diffusing from the interconnect.
1.1.1 Principles of SOFC A fuel cell directly converts chemical energy into electrical energy. A solid oxide fuel cell consists of two porous electrodes that are separated by a dense, oxygen ion-conducting electrolyte. A simple schematic of the electrochemical process is shown in Fig. 1.1.1 (next page).
In an SOFC.2 (next page) for the widely used planar-design SOFC. The oxygen.1. cathode and electrolyte consist of refractory solid oxide ceramics. 1.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects Fig.7 to 1 V and power around 0. A single cell produces a voltage of 0. forming a cell stack to obtain higher voltage and power.5 to 1 W cm-2. The direct-current electricity is produced by the electron flow through the external electric circuit. e = electrolyte. and ceramicmetal composites are used for the anode. The electrons flow from the anode through the external electric circuit to the cathode. 12 . At the anode the oxygen ions react with hydrogen of the fuel to form water and release electrons. as shown in Fig. These ions migrate through the electrolyte to the anode. The electrodes are required to have high reactivity and the electrolyte must allow high oxygen ion diffusion. 1. All the components of the cell need to be matched in their thermal expansion in order to minimize mechanical stresses. a = anode.1 Scheme of the electrochemical processes in a fuel cell with O2 oxidant and H2 fuel. The materials for the cell components need to have a sufficient chemical and structural stability at rather high temperatures up to 1273 K that occur during cell production as well as during cell operation.1. Normally many cells are electrically connected in series by an interconnect. supplied at the cathode reacts with electrons from the external electric circuit to form oxygen ions. White circles symbolize pores. c = cathode.
stability in both oxidizing and reducing atmospheres at the high cell operating temperature (from about T = 973 K to 1273 K).1.2 The problem of chromium "poisoning" In the 1990is LaCrO3-based ceramics were intensively investigated for interconnect applications in SOFC. It is the most demanding component in a planar SOFC as it should have a high electronic conductivity.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects Fig. Nowadays the state-of-the-art interconnect is commonly a chromiumcontaining metal plate[3-5]. low permeability for oxygen and hydrogen to minimize direct combination of oxidant and fuel during cell operation. as the thermal expansions of LaCrO3-based interconnect and conventional perovskite cathode materials are similar. 1. as chromium alloys come close to all desired properties. 13 . difficulties in sintering and manufacturing and low mechanical strength[2] required the development of alternative interconnect materials. the electronic conductivity of several LaCrO3-based ceramics under SOFC operating conditions is high. a thermal expansion coefficient close to that of the cathode and the anode.2 Planar design of SOFC The interconnect separates the fuels and oxidants in adjacent cells. However high costs of these materials. and chemical compatibility (no reactions) with other cell materials.1. However high-valent gaseous Cr-oxide and Cr-oxyhydroxides diffuse from the Cr2O3(s) scale covering the interconnect into the cathode up to the cathode-electrolyte interface and cause the degradation that results in the strong deterioration of the electrical performance of SOFC. a low ionic conductivity. 1. and their thermal and redox-stability is satisfying[1].
the volatile species must be a higher oxide of chromium.6 mg at T = 1473 K at a gas flow rate of 200 ml min-1 after 20 h. it became evident that a volatile Cr-oxide was being formed[10]. the weight loss being 0. In stagnant air the volatilization was 0. This was a surprising result. as the film of Cr2O3(s) covering the alloy specimen would have been expected to act as a diffusion barrier preventing the migration of Cr that has a high vapour pressure from the alloy through the Cr2O3 layer. neither the vapour pressure of Cr2O3(s) nor its dissociation pressure is high enough to account for the quantities of deposits observed[10].6 mg at T = 1473 K. or at discontinuities such as fractures in the film and would then evaporate. 1. and at T = 1373 and 1473 K in flowing dry and wet oxygen as well as in dry and wet argon.1 mg at T = 1373 K and 5.3-2. and -diffusion processes. -reduction. and it was suggested that high-valent gaseous Cr-oxide and Cr-oxyhydroxides detrimentally affect the O2 -adsorbtion. But when it was learned that Cr2O3(s). but its formation by the reaction Cr2 O3(s) + 3 2O2(g) → 2CrO3(g) (1. Furthermore. The volatilization in wet oxygen was significantly higher after 20 h at the same gas flow rate: 2.2 cm in diameter and height were heated at T = 1273 K in stagnant air. Since weight loss takes place under oxidizing conditions. Volatilization of Cr2O3(s) was neither observed in dry nor in wet argon.2 Volatilization of Cr2O3 Early investigations[6-9] revealed that oxidation of Cr-containing alloys at high temperatures leads to the redeposition of Cr2O3(s) crystals at cooler parts of the experimental apparatus from the gas phase. The observation that no loss of Cr2O3(s) occurs in argon confirms that volatilization does neither occur by dissociation of the oxide nor as Cr2O3(g) vapor. Caplan and Cohen[10] investigated the evaporation of Cr2O3(s) by measuring the weight loss when Cr2O3(s) pellets with 1.6 mg at T = 1373 K and 2.1) 14 . Because of the high vapour pressure of Cr it was thus first considered that the metal itself would diffuse along oxide grain boundaries of the barrier film. lost weight when heated in oxygen.2.3 mg at T = 1273 K after 72 h. Appreciable volatilization occurred in dry oxygen. A known volatile oxide of Cr is CrO3. in the absence of metal.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects In the last decade a lot of effort was made to elucidate the degradation mechanisms.
1. Their formation by oxidation of Cr2O3 in wet air reads: Cr2 O3(s) + 1 2O2(g) + 2H 2 O(g) → 2CrO2 (OH)2(g) (1. As gaseous CrO3(g) was detected experimentally by mass spectrometry when Cr2O3(s) was heated under oxidizing conditions.2. 1. in a recent combined experimental and modeling study[18] these earlier findings are rejected for high temperatures: in wet atmosphere CrO2(OH)2(g) is predominant in the gas from T ≤ 1173 K.2) Cr2 O3(s) + 1 2O2(g) + H 2 O(g) → 2CrO2 (OH)(g) (1.2. and this was affirmed by thermodynamic modeling[19].2 is calculated to be −158 kJ at T = 1273 K using combined data from Opila et al. data for O2(g) from Dinsdale[12].2. The existence of gaseous Cr-oxyhydroxides as oxidation products (Eqs. and for CrO3(g) from Ebbinghaus[13]. 1.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects is thermodynamically unfavourable at high temperatures[10]. However.[18] and Ebbinghaus[13]. These findings are supported by the higher volatilization of Cr2O3(s) in wet air. Δ°G of Eq.2.3 is calculated to be +134 kJ at T = 1273 K using combined data from Kim and Belton[14] and Ebbinghaus[13].2 and 1. Ebbinghaus[13] estimated a significantly higher partial pressure of CrO2(OH)2(g) compared to CrO3(g) in wet atmosphere up to T = 1600 K based on available thermodynamic data of gaseous Cr-species. the formation of CrO3(g) occurs under kinetic control[10].1 is calculated to be +321 kJ at T = 1273 K using assessed thermodynamic data for Cr2O3(s) from Povoden et al.18] cited above.2. whereas at higher temperatures the gas phase mainly contains CrO3(g) and CrO2OH(g). and Δ°G of reaction 1. μ(O) being −300 J mol-1 referred to pure oxygen gas result from combined thermodynamic data[11-14. 15 .1 (next page): the calculated amounts of main Cr-species in the gas phase as a function of temperature in humid air of pH2O = 2000 Pa at constant chemical potential of oxygen.[11]. This tendency is shown in Fig.3) Δ°G of reaction 1.3) in wet atmosphere was experimentally proven in several studies[14-17].
57x10-3 Pa at T = 1223 K[20].1 Calculated amounts of gas molecules in Cr-gas as a function of temperature for constant pH2O = 2000 Pa at μ(O) = −300 J mol-1 referred to 100000 Pa O2(g) Transpiration experiments of Cr2O3(s) from T = 673 K to 1223 K resulted in the following partial pressures of Cr at a flow rate of 150 m min-1: pCr = 2. The Cr-vaporization rate of Cr5Fe1Y2O3 exceeds that of Crofer22APU by about a factor of 3 in the temperature range from T = 1023 K to 1173 K.12x10-5 Pa at T = 673 K and increases as a function of increasing temperature. reaching pCr = 4. 3. at T = 1073 K for a time period of about 500 h.3 μg h-1 for 25 mol% H2O in air at T = 1073 K. two high-chromium alloy interconnects widely used in SOFC.[20] to measure the vaporization rate of Cr from Cr5Fe1Y2O3 (Ducrolloy) and Crofer22APU (high-Cr ferritic steel).2. the mass loss being higher at higher water content and higher temperature: the constant rate of mass loss was 0. and 18. Cr-vaporization in SOFC: Konysheva et al. Mass loss of Cr2O3(s) at T = 973 K and 1073 K was measured in air with different amounts of water.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects Fig.2 μg h-1 for 3 mol% H2O in air at T = 1073 K. 1.[21] used a transpiration method proposed by Gindorf et al.6 μg h-1 for 3 mol% H2O in air at T = 973 K. and the 16 .
1. 18-21. this value being by about a factor of 2. Badwal et al. for an SOFC setup with a Cr5Fe1Y2O3 interconnect plate. the volatilities of gaseous CrO3(g) and gaseous Cr-oxyhydroxides are negligible under the low oxygen partial pressure at the fuel side of the cell.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects vaporization rate increases with increasing temperatures for both alloys.3 Literature survey 1.3. The amount of Cr in these degraded cells was 140 μg cm-2 with Cr5Fe1Y2O3.1 Degradation of SOFC caused by chromium from the interconnect Considering the experimental data from Caplan and Cohen[10].31. and the chromium problem is restricted to the interconnect-cathodeelectrolyte region of SOFC.1.32. 17 .35] of the degradation of SOFC with LSM cathodes caused by chromium are listed in Table 1. With increasing humidity the difference in the vaporization rates between the two alloys increases. Experimental results[21-29. an LSM cathode. an yttriumstabilized zirconia (YSZ) electrolyte and a Ni-zirconia cermet (ceramic-metallic composite) anode operated at T = 1173 K and 1273 K.[22] mentioned significant amounts of deposited Cr2O3(s) in the air exhaust of the cell. However. pp.5 higher than with Crofer22APU.34. This is in line with the experimental observation[21] that only a fraction of the chromium deposited at the cathode side contributes to the strong degradation of SOFC with LSM cathodes and Cr-alloy interconnects that were tested under a current load of 200 mA cm-2 for 393 h. thus quantitative chromium "poisoning" rates affecting the cathode are difficult to determine.3.
1 Results of chromium poisoning of SOFC with and without Cr-containing interconnects with LSM cathodes collected from the literature 18 .3.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects Table 1.
Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects 19 .
Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects 20 .
Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects The degrading effect of gaseous chromium species that form at the Cr2O3 scale under oxidizing conditions and diffuse into the cathode on the cell performance was first reported in 1995 by Taniguchi et al.9Sr0.[23].1MnO3-δ. The cell was electrochemically tested at T = 1273 K under a current load of 300 mA cm-2 for 400 h.1 V. In a test of the same setup under open circuit conditions for 21 . a YSZ electrolyte and a NiO/YSZ anode with a piece of a Ni-Cr-Fe-alloy (Inconel 600) attached on top of a Pt mesh used as current collector. and intensity measurements using electron probe microanalysis showed that Cr was concentrated at the cathode-electrolyte interface. These authors measured an increase of cathode polarization and decrease of cell voltage in an SOFC consisting of an LSM cathode with the compositions La0.7 V to about 0. The cell voltage decreased over this time from initially about 0.
holding the cells at 0. an LSM cathode. Experiments without a Cr-based interconnect plate with Pt mesh serving as current collectors were conducted at T = 1205 K and 188 mA cm-2 current density using the same electrodes and electrolyte. whereas the opposite was observed for SOFC with Cr-alloy interconnect.[29] presented cell performance data of an SOFC with LSM cathode.2 W cm-2 to 0.7 V: without the interconnect steel. whereas ohmic losses (resistance to 22 . The cell performance without interconnect plate deteriorated only little by less than 0. On the other hand the voltage of the cell with Cr-Fe-alloy interconnect decreased rapidly as a function of operation time. and to chromium deposited at the LSM-YSZ interface filling pores. Taniguchi et al.[23] thus linked the cell degradation to the time that the discharge current was applied. its power density decreasing from a maximum of 0. the voltage drop being 0. a YSZ electrolyte and a Ni-zirconia cermet anode at T = 1173 K and T = 1273 K was more related to the period of current passage and was less dependent on the time when no current was flowing through the cell: Badwal et al.4 V after only 16 h.[22]: these authors tested the cell performance of an SOFC with a Cr5Fe1Y2O3 interconnect plate.1 V during an operation time of 2500 h. the cell started to degrade severely after 20 h of testing.2 The role of current load on electrical losses of degraded SOFC Badwal et al.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects 300 h no deterioration of the cell performance was observed.48 W cm-2. and Cr was randomly distributed across the cathode.3. A comparison of measurements of the overpotentials of SOFC with LSM cathode and high-Cr alloy interconnect with measurements without interconnect[24-27] or LaCrO3-based interconnect[28] led to the following results: the overpotentials without interconnects or with LaCrO3-base interconnects consistently became less negative with time. But using a Cr-Fe-alloy interconnect. the cell performance was stable for 110 h. Simner et al. the power density being 0. 1. a YSZ electrolyte and a Pt counter electrode (in the following SOFC with Pt counter electrode are denoted as half-cell) with and without Crofer22APU interconnect at T = 1073 K. a YSZ electrolyte and a Ni-zirconia cermet anode at T = 1273 K and a current density of 250 mA cm-2. a Sm2O3-CeO2 interlayer between cathode and electrolyte. hindering the supply of oxygen gas and decreasing the number of reaction sites for the oxygen reduction. All these experimental studies[22-29] unambiguously proved that chromium stemming from the alloy interconnect causes the degradation of SOFC.[22] reported that the degradation rate of SOFC with a Cr5Fe1Y2O3 interconnect plate.05 W cm-2 after 110 h.[22] ascribed the voltage decrease to increasing losses of cathodic overpotential. Later these results were confirmed by Badwal et al. an LSM cathode.
LSM cathode and a YSZ electrolyte tested at T = 1173 K and a current density of 200 mA cm-2. At the beginning of the cell tests. with a tendency of stabilization of the cell performance after this testing period at much lower magnitude of output current.21 % Cr on top of a (La0. In earlier studies using the same setup a rapid decrease from −360 to −560 mV after 10 minutes[25. Zhen et al. in general agreement with Jiang et al.2)0. in agreement with earlier findings[22.3MnO3-δ/LSM+YSZ double layer cathode and a YSZ electrolyte confirmed the strong dependence of the voltage drop on the current density during 450 h cell tests at T = 1073 K: at 70 mA cm-1 the voltage decrease was 0.4MnO3-δ cathode and a YSZ electrolyte at 300 mA cm-2 current density. In reference tests without Cr-Fe-alloy interconnect the results were opposite to the tests with Cr-Fe-alloy interconnects: the polarization increased from −550 to −300 mV[27] or −420 to −170 mV [24.25. Matsuzaki and Yasuda[28] measured an overpotential loss from initially −500 mV to −2000 mV after 14 h in a half-cell setup with an Inconel 600 interconnect. Konysheva et al. whereas at 280 mA cm-1 the voltage dropped by 0. A plateau of degradation was reached after about 400 h of testing.32.33].Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects flow of electrons through the cathode) increased only insignificantly during the cell tests. Paulson and Birss[34] reported rapid deterioration of the performance of a half-cell setup with a stainless steel disk containing 15.8Sr0.31].26] was observed. using a half-cell with a Cr5Fe1Y2O3 interconnect. La0.5 Ohm cm2 for a thickness of 23 . a La0.6 V. Konysheva et al. However the cell degraded rapidly again when the current was switched on again.98MnO3-δ cathode and a YSZ electrolyte over 5 to 10 h at T = 1073 K applying a −0.[21]. losses increased sharply and reached their maximum values after only 15 h of cell operation.25] at 1173 K and a current density of 200 mA cm-2.5 V potential.07 V. an LSM/LSM-YSZ cathode double layer and a YSZ electrolyte tested for 400 h was markedly dependent on the thickness of the LSM-YSZ layer.28. Rpol being 0.[27] measured a rapid decrease of cell polarization from initially −350 to −750 mV after only 10 minutes in a half-cell with Cr-Fe-alloy (RA446) interconnect.23. LSM cathode and YSZ at a current density of 100 mA cm-2 at T = 1073 K and found that the rapid degradation was reversible and disappeared after switching off the current load.[24. The overpotential losses were higher and the cell deterioration was faster at higher current density.[30] tested the reversibility of degradation in a half-cell setup with CrFe-alloy interconnect.65Sr0. The polarization behavior of SOFC with Crcontaining interconnect was explained by the strong inhibiting effect of gaseous Cr-species on the oxygen reduction in LSM[27].6Sr0. The total polarization resistance (Rpol) of a half-cell setup using a Cr-Fe-alloy interconnect.
4 Microstructures in degraded SOFC Cathodic polarization: Taniguchi et al. LSM cathode and YSZ electrolyte tested at T = 1173 K and a current density of 200 mA cm-2. an LSM cathode and a YSZ electrolyte as a function of operation time. The total polarization resistance was also higher at higher current load.[32] observed less overpotential losses at lower temperatures in a half-cell with CrFe-alloy interconnect.[22] observed an increased size of the high frequency arc during the current passage in half-cell tests using a Cr5Fe1Y2O3 interconnect plate. 1.26. The degradation was higher at higher temperatures at 0. Influence of temperature on the degradation: SOFC with LSM cathodes and high-chromium 430 stainless steel were tested at T = 973 K and 1073 K for 300 h[35].[23] were the first who reported the occurrence of Cr-Mn-spinel in Cr"poisoned" SOFC with an LSM cathode by using XRD analysis.[24. This finding was confirmed 24 . Jiang et al.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects 50 μm. and 2 Ohm cm2 for 7 μm[30]. but not due to the increase in ohmic resistance. The increase of both arcs over the testing time was ascribed to the affect of Cr on the oxygen diffusion processes in the LSM cathode and across the LSMelectrolyte interface and is in line with the interpretations from Jiang[25.6Sr0. it deteriorated from 500 mA to 350 mA at T = 1073 K and from 300 mA to 150 mA at T = 973 K over the testing time of 200 h and then remained constant. from −900 to −1200 mV at T = 1073 K.32].4MnO3-δ cathode and a YSZ electrolyte operated at T=1073 K and 300 mA cm-2 current load that the degradation in the electrode caused by chromium was due to the increase in both charge-transfer resistance and surface diffusion resistance. a La0. reflecting increasing cathode resistance.3 Impedance spectroscopy measurements and implications on the degradation process Badwal et al.3. LSM cathode and a YSZ electrolyte: they measured an overpotential change from initially −300 mV to −650 mV after 10 minutes at T = 1173 K. and from −800 to −1120 mV at T = 973 K after 10 minutes.[27] reported the existence of a high frequency and a low frequency arc in impedance spectra of a half-cell with Cr-Fe-alloy interconnect. 0. Zhen et al.3.33] and Jiang et al.7 V. 1. Mazusaki and Yasuda[28] concluded from the interpretation of impedance spectra of a half-cell with an Inconel 600 interconnect.75 Ohm cm2 for 13 μm.
[22] who detected small amounts of Cr-Mn spinel after 100 h of operation of SOFC with a Cr5Fe1Y2O3 interconnect plate. LSM cathode and YSZ electrolyte Matsuzaki and Yasuda[31] reported the formation of a dense layer of Cr-deposit at the LSM-YSZ interface after a cell test at T = 1073 K and a current density of 300 mA cm-2 over 100 h of polarization. The zone of these large faceted crystals was followed by a zone of very fine grains (about 0.[27] observed dense Cr-Mn spinel-deposits exclusively at the LSM-YSZ interface after a half-cell test of an SOFC with Cr-Fe-alloy interconnect operated for 20 h at T = 1173 K and a current density of 200 mA cm-2. Zhen et al. The amount of spinel at the cathode-electrolyte interface was much larger than within the LSM cathode particularly after a period of current load. Jiang et al.36] documented spinel formation at the LSM-YSZ interface already after 4 h. an LSM/LSM-YSZ cathode double layer and a YSZ electrolyte chromium-deposits were only found in the LSM layer under open circuit conditions. in some of the experiments forming a dense layer of several microns at the cathode-electrolyte interface. The grain size of spinel was about 0. Under the same testing conditions as above. Using a half-cell setup with Inconel 600. no Cr-deposits formed after 50 h of testing under open circuit conditions[25.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects by Badwal et al. The deposition zone broadened as the polarization time increased from about 60 μm after 50 h to 89 μm after 129 h. unfortunately the specific conditions for its formation were not given in more detail.36]. On the other hand Cr-Mn spinel formed already at 25 .[22] further observed spinel in the contact region between interconnect and cathode.7 μm after 50 h. For the same setup large quantities of spinel had formed after 2000 to 2500 h of cell operation. and the cell degradation was strong[21]. On the other hand chromiumdeposits were also found in the LSM-YSZ layer and on the surface of the YSZ electrolyte on increasing the current density up to 280 mA cm-2.17 μm after 4 h of cell testing and increased to about 0. In the same setup without LSM-YSZ functional layer no chromium-deposits were detected without current at T = 1073 K over 393 h. In some cases these authors also observed Cr2O3(s) at the cathode-electrolyte interface. Badwal et al. but under anodic polarization very fine grains of Cr2O3 were forming exclusively at the LSM-YSZ interface. Very small grains of Cr-deposits formed at T = 1373 K under open circuit conditions. a YSZ electrolyte and a Nizirconia cermet anode at T = 1173 and 1273 K under current load.[25.05 μm) of Cr2O3 towards the cathode-electrolyte interface. Using the same setup as above. an LSM cathode. but further details on their spatial distribution and composition were not given. Using the same setup. and the cell-degradation was weak[21]. In a half-cell setup with a Cr-Fe-alloy interconnect.
large gaps between YSZ grains formed. dense Cr2O3-layers at the edge of LSM on the YSZ surface. and the deposition was less pronounced at T = 1073 K and 973 K. Cr2O3 was also found inside YSZ. Paulson and Birss[34] investigated the microstructures in a half-cell setup with a stainless steel disk containing 15. Influence of temperature: Microstructural changes during half-cell tests of a setup consisting of a Cr-Fe-alloy interconnect. A reference test without polarization did not lead to these features. No spinel formation was observed in these experiments. These authors observed the formation of a 500 μm broad zone of 8 individual. and the density and size of deposits increased by time. The morphology of the particles was different than the morphology of the deposits under cathodic polarization.18MnO3-δ cathode and a YSZ electrolyte were systematically investigated as a function of time and temperature at a current load of 200 mA cm-2 by Jiang et al. Jiang et al. Transmission electron microscopy analyses revealed the layered structure of the composites: a 0. exclusively covering the YSZ surface. After 160 h of testing at 100 mA cm-2 current load.5 μm thick layer directly adjacent to the YSZ containing mainly Cr2O3 is covered by a spinel layer. In direct contact with YSZ about 500 nm large Cr2O3-grains were detected.8Sr0. and spinel crystals were found on the surface of a thin Cr2O3-layer adjacent to the electrolyte.5 V and T = 1073 K. up to 10 μm away from the LSM-YSZ interface after 160 h of testing. and 30 μm from the LSM-YSZ contact after 940 h. Cr2O3 completely filled gaps between YSZ grains. After 20 h spinel formation was observed forming a 40 to 50 μm wide band at the LSM-YSZ interface.2)0.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects very low current load of 2 mA cm-2 on the surface of the electrolyte and near the LSMelectrolyte contact.72Sr0.[36] reported the formation of very fine particles of Cr2O3.98MnO3-δ cathode that rested on a 144 mm2 square YSZ electrolyte. after the half-cell was tested by a sequence of 8 chronoamperometry experiments at −0.21 % Cr attached on top of a 4 mm2 square (La0. a La0.[32]. Anodic polarization: After a half-cell test of an SOFC with Cr-Fe-alloy interconnect operated for 6 h at T = 1173 K and a current density of 200 mA cm-2. almost completely 26 . Cr-deposits consisting of Cr2O3 and Cr-Mn-spinel were concentrated in an about 2 μm broad region at the LSM-YSZ interface. After 5 minutes of testing at T = 1173 K very fine Cr-deposits (< 100 nm) already formed on the YSZ-surface.
27 . The Cr-content dropped to about 0. It further decreased slightly towards the interconnectcathode interface. a La0.5 Amounts of chromium in SOFC tested with and without current load Konysheva et al.% Cr in the Sm2O3-CeO2 interlayer.% at 14 μm distance from the contact to the electrolyte. In a half-cell with LSM cathode.% of Cr at 10 μm distance from the cathode-electrolyte interface.8 wt. although the degradation of the polarized cell was remarkably higher.vacancy within about 10 Å around Cr3+. By using molecular dynamics simulation techniques it was stated recently that only 890 ppm Cr3+ in LSM significantly increase the formation energy of O2. a Sm2O3-CeO2 interlayer between cathode and electrolyte and a YSZ electrolyte with a Crofer22APU interconnect operated at T = 1073 K.7 V for 120 h. 1. comm. The amount of Cr-deposits was significantly smaller after 20 h of testing and 200 mA cm-2 current load at T = 973 K: isolated fine particles (about 100 to 200 nm) were detected on the YSZ surface. holding the cell at 0. This was explained by the following: only under current load chromium deposits are concentrated in the functional region of LSM close to the contact to YSZ where they inhibit oxygen reduction and diffusion processes.3MnO3-δ/LSM+YSZ double layer cathode and a YSZ electrolyte after tests without current showing very small degradation. this is only 15 to 20 % higher than in the cell operated without current.3.5 wt. The amounts of chromium in the half-cell operated under a current was 100 μg cm-2 after 150 h and 150 μg cm-2 after 500 h.[35] measured about 2. Simner et al.[29] measured 5 at. associated with large grains (about 1 μm) of spinel. Krumpelt et al. but no Cr in LSM using energy dispersive scanning electron microscopy. This may lead to a dramatic drop of the oxygen diffusion coefficient in LSM by about 60%[36] and pers.65Sr0.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects covering the YSZ surface. In SOFC with LSM cathodes and a Cr-Fe-steel interconnect that were tested at T=1073 K for 300 h at 0. and under 200 mA cm-2 current density showing strong degradation as a function of testing time at T = 1073 K.[21] compared the total amounts of chromium in half-cells with Cr-Fe-alloy interconnects. The decreasing degradation at lower temperatures was ascribed to slower diffusion and lower partial pressure of gaseous Cr-species.7 V.
Badwal et al. 1.3.1) Eq.33] ascribe the mechanism of chromium "poisoning" to the reduction of gaseous CrO3(g) and Cr-oxyhydroxides at the cathode-electrolyte interface.184.108.40.206. In an LSM cathode the reduction of CrO3(g) is expected to be localized at the triple phase boundary (TPB) between LSM.3. and 2) Chemical dissociation of Crspecies on the LSM surface[24-26. This reduction reaction would compete with the oxygen reduction and would lead to blocking of the active sites at the TPB and subsequent formation of Cr-Mn spinel by the reaction of Cr2O3(s) with LSM. In particular they suggest the tight intercalation between changes of the chemical composition at the surface of LSM particles and the oxygen adsorption and surface diffusion kinetics in the early stage of chromium "poisoning". Badwal et al. described by inverse Eq.33]. 1.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects 1.37].6 Critical assessment of proposed mechanisms of chromium "poisoning" For the mechanisms of chromium "poisoning" two models have been proposed: 1) Reduction of gaseous Cr-species under polarization[21-23. Both reduction and chemical dissociation processes reflect non-equilibrium conditions.3. including changes of the chemical composition of the LSM surface. X(Cr) = 2X(Mn): La1− xSrx MnO3−δ + 3 2 y Cr2 O3(s) → La1− xSrx Mn1− y Cry O3−δ + yMnCr2 O4 + 1 4 y O2(g) (1.30-31. X(Mn)= 2X(Cr): La1− xSrx MnO3−δ + 1 2 y Cr2 O3(s) → La1− xSrx Mn1− 2 y Cry O3−δ + yMn 2 CrO4 + 5 4 y O 2(g) (1.3.31. electron-donating LSM and oxygen-accepting YSZ are available[38].[22] ascribe a key role for the late stages of cell degradation to the formation of Cr-Mn spinel that would block pores and lead to substantial decrease of the TPB area. YSZ. and gas. and blocking of pores by Cr-Mn spinel and Cr2O3(s). 1) Several authors[21-23.32. where the reaction partners for the reduction.2 is a possible reaction for the formation of spinel with a higher amount of Mn.2.2) 28 . 1. Cr-Mn spinel is interpreted by these authors to form in a solid-solid reaction between Cr2O3(s) and LSM that may have the simplified form of Eq.[22] emphasized that chromium "poisoning" would consist of several processes.1 when solid solubility of Cr in LSM[39] is considered and spinel contains the molar fraction of Cr. reduction of CrO3(g) at the cathode-electrode interface competing with the normal oxygen reduction reaction.
1 is a simplified illustration of possible reaction paths that lead to the end product Cr-Mn spinel. The true shape of the curves depends on the activation energy Ea and is thus not known. and this is not known. As it is not assured if spinel in fact forms in a solid-solid reaction.3.3. Fig. Fig.5) considering the main chromium molecules that interact with LSM for spinel with X(Cr) = 2X(Mn). Ea of the concerning reaction. and the mobility of the gas phase is high. 1. reactions of direct formation of spinel by the interaction between Cr-gas and LSM can be formulated (Eqs.3. 1. sp-form = spinel formation.3. and LSM gets more deficient in Mn. Which of the possible reaction paths is realized. 1.1 was chosen based on the consideration that the diffusionless reduction of Cr-gas may have a lower activation energy than the solid-solid reaction between LSM and Cr2O3(s). Such gas-solid reaction can be split into two reaction steps: formation of 29 .2 less Cr2O3 is needed for the formation of Mn2CrO4.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects For equal y in Eqs. more oxygen is produced.3. However the formation of spinel can also be interpreted as a direct solid-gas reaction. thus assuming a lower activation energy for the LSM-Cr-gas reaction. Oxygen production stems from the reduction of Mn3+ in perovskite to Mn2+ in spinel.3. depends on the activation energy.3. These assumptions would mean that fast reduction of Cr-gas to Cr2O3(s) occurs as one process. and the LSM-Cr-gas reaction occurs as a parallel process leading to the formation of spinel. The shape of the curves in Fig. 1.3 to 1.1 and 1.1 Possible reaction paths for the spinel formation as a function of Gibbs energy. On the other hand it may last a long time for the Cr2O3(s) that was formed by the reduction reaction to transform into spinel in the solid-solid reaction with LSM. red = reduction. 1.
3) La1− xSrx MnO3−δ + 3 yCrO2 (OH)2(g) → La1− xSrx Mn1− y Cry O3−δ + yMnCr2O4 + 3 yH 2O(g) + 5 2 y O2(g) (1. and consequently to Cr-Mn spinel and Cr2O3(s). The differences of oxygen contributions to respective reactions stem from the reaction step of Cr2O3(s) formation: La1− xSrx MnO3−δ + 3 yCrO3(g) → La1− xSrx Mn1− y Cry O3−δ + yMnCr2 O4 + 5 2 y O2(g) (188.8.131.52. 1. On the other hand the measured oxygen tracer diffusion coefficient in LSM strongly increases when the oxygen partial pressure is decreased from pure oxygen to pO2 = 200 Pa[44].33.37]: Mn2+ on the surface of LSM at reduced oxygen partial pressure close to the cathode-electrolyte interface would react with gaseous Crspecies to Cr-Mn-O nuclei. However they did not discuss the dependence of oxygen diffusion upon pO2 .3.3. Huang et al.37] oxygen diffusion is inhibited by the nuclei-formation. Thus the pO2 at the locations of the spinel formation is expected to increase. This in turn will also lead to less Mn2+ in LSM[40] and consequently lower oxygen diffusion in LSM.5 that oxygen is produced during the formation of spinel. It can be seen from Eqs.32.5) 2) The chemical dissociation of gaseous Cr-species on the LSM surface for the cell degradation was proposed as the key process for the degradation of SOFC caused by chromium by another research group[24-27.4) La1− xSrx MnO3−δ + 3 yCrO2 (OH)(g) → La1− xSrx Mn1− y Cry O3−δ + yMnCr2 O4 + 3 2 y H 2 O(g) + 3 4 y O2(g) (1.[43] confirmed these early suggestions by evaluating the ionic conductivity of LSM from pure oxygen to pO2 = 300 Pa at temperatures from 953 K to 1153 K using YSZ as blocking electrode. As Mn2+ is associated to vacancy formation in LSM that is necessary for the oxygen diffusion. The role of the oxygen vacancy diffusion mechanism in an LSM cathode has been considered controversially: Mogensen and Skaarup[41] concluded from the low oxygen self-diffusion coefficients of the order of 4×10-14 cm2 s-1 at T = 1173 K[42] that long range bulk migration of oxygen ions cannot play a significant role for the cathode performance. The ionic conductivity was lower at lower oxygen partial pressures.[24-27.32. Yasuda et al.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects Cr2O3(s) from the gas and subsequent spinel formation from Cr2O3 + LSM. opposite to the trend that would be expected under the control of the vacancy diffusion mechanism.1 to 1.3.[44] concluded that 30 .
This phenomenon was well explained by continuous feeding of an initial 31 . The activation energy for the diffusion of oxygen for LSM is in the range of 250 to 300 kJ mol-1. η = −0.4x10-6. The electrochemical reduction of CrO3(g) was rejected by the authors favoring the chemical dissociation approach[24-27. It was also mentioned in the early paper of Caplan and Cohen[10] that substantial precipitation of Cr2O3(s) from CrO3(g) occurred in the cooler part of the experimental setup. Based on the findings from the literature it can be summarized that in LSM oxygen diffuses through grain boundaries at high pO2 . This strong tendency for the precipitation of Cr2O3(s) makes a rejection of the reduction of CrO3(g) as a possible process contributing to the cell degradation doubtful.090 V) using isotopic oxygen exchange and secondary ion mass spectrometry it was found that oxygen ions can only diffuse through dense LSM at the high overvoltage of η= − 0. The calculated amount of oxygen vacancies (δ) in La0. It is necessary to test the arguments for this claim of exclusive validity: a strong tendency exists for CrO3(g) to get reduced to Cr2O3(s) at the TPB.2.8Sr0.[21] observed the extension of dense Cr2O3layers into YSZ. when the oxygen partial pressure at the cathode-electrolyte interface is decreased significantly.94x10-9 in air[23].33. Contradictory interpretations[43] from the dependence of the ionic conductivity on pO2 need to be judged with care due to the difficulty of controlling the numerous factors that can influence the results of the blocking electrode method used.9Sr0. 1. In an investigation of active sites for the oxygen reduction at the O2/LSM/YSZ interface[46] for three different overvoltages of cathode polarization (η = −0. as Δ°G of the reduction being the inversion of reaction Eq. as well as Konysheva et al.32.336 V corresponding to pO2 = 10-4 Pa[46]. Paulson and Birss[34].2MnO3-δ at 973 K and pO2 = 10-4 Pa is δ = 2. and η = −0.1CoO3-δ in which oxygen ions are transported by the vacancy mechanism. This indicates that a vacancy diffusion mechanism also applies to LSM[45]. This confirms the suggestion that the formation of oxygen vacancies in LSM contributes to the oxygen diffusion at high current loads[22].1 has a large negative value. We believe that the oxygen vacancy diffusion mechanism contributes to the oxygen diffusion under high current loads.37]. compared to δ = 3. as it was directly proven by isotopic and tracer diffusion[44] experiments. This is close to 270 kJ mol-1 for La0.336 V. Reduction of CrO3(g) to Cr2O3(s) was such predominant as to make sampling of gaseous CrO3(g) difficult.185 V.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects oxygen ions in the bulk of LSM diffuse by the vacancy diffusion mechanism. as oxygen vacancies are simply not available under these conditions.
Thus it is obvious that the explanation of the "poisoning" process by the chemical dissociation approach alone is not without doubt. which was definitively not observed.37]: the two phases formed in the scope of a polarized LSM cathode exhibit distinctive microstructures: spinel forms large grains. Cr2O3(s) deposition should also occur under open-circuit conditions. Furthermore. which both seemed to be inhibited by chromium poisoning. and the degradation can be associated to the dissociation process[24-27. In this case the contribution of reduction to the Cr-"poisoning" has to be rejected.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects Cr2O3-layer with CrO3(g).34].32. whereas an explanation by the chemical dissociation approach is not satisfying. and it is also in line with the observed temporary reversibility of the cell deterioration[22.23. Some indications for two independent chromium poisoning mechanisms can be found in the work from Jiang et al.[24.31]: by switching off the polarization the competing reduction of CrO3(g) no longer occurs. If CrO3(g) is electrochemically reduced to Cr2O3(s) in a cell. The region of spinel formation extends several microns from the TPB into the cathode. and the normal charge transfer can take place by switching it on again. and the second with a higher rate on the YSZ electrolyte surface. In this case no chromium will be deposited at the cathode-electrolyte interface under open-circuit conditions. which is increasing as a function of increasing polarization. the latter becoming reduced at the new TPB consisting of YSZ and electron-donating Cr2O3(s)[21. However the situation changes if the reduction of CrO3(g) is under the main control of the oxygen partial pressure gradient towards the cathode-electrolyte interface. whereas the phase that was most likely identified as Cr2O3 occurs in fine-grained.33. From the occurrence of finegrained Cr2O3 the existence of a large number of nuclei for its formation is concluded. But how can one explain the strictly localized deposition of Cr2O3 that also occurs under anodic polarization[37]? Under oxidizing conditions little Mn2+ is expected to be present in LSM[40].26. Also two different diffusion processes were distinguished. whereas in a polarized cathode the reduction of CrO3(g) takes place and competes with the oxygen reduction leading to Cr2O3(s) deposition. from impedance spectra analyses it was in fact possible to distinguish two distinctive depositions of Cr-species. which does not seem to be the case for the spinel phase. This explanation is in line with the microstructural features of tested cells both under open circuit voltage and under current load. This is in contrast with the complicated mechanism for the formation of Cr2O3(s) under anodic 32 . one with a lower rate on the LSM surface.28. partly layered structures.37] and subsequent formation of spinel. whereas Cr2O3 is always located directly at the cathode-electrolyte interface. thus the formation of nuclei by the proposed LSM-Cr interaction won't occur.30.
[37] that includes diffusion of Mn3+/Mn2+ driven by the oxygen evolution reaction at the cathode/electrolyte interface. This is indeed true for the case of CrO3(g) and Cr-oxyhydroxide reduction being the only Cr-poisoning mechanism.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects polarization established by Jiang et al. Oxygen deficiency is negligible in LSM under high pO2 [40]. However. but several processes may lead to the deterioration of cell 33 . This is an indication against one unique "poisoning" mechanism. based on an early finding that LSM behaves like a metallic electrode at low polarization potentials[47] that was not quantified. contrary to the situation of a strong pO2 gradient under cathodic polarization. and thus lack of spinel formation. This is a simple and consistent explanation for a strict localization of Cr2O3(s) formed by reduction of gaseous Cr-species even under anodic conditions. In this context experimental results of a half-cell test with Cr-Fe-alloy (RA446) interconnect. It was further mentioned that the existence of Cr-containing products away from the TPB would be in disagreement with the reduction approach. opposite to the situation with a platinum cathode. the number of the latter being less than under cathodic polarization. In cell tests of a polarized platinum electrode using a Cr-containing interconnect no Cr was observed. contrary to an LSM electrode. This different behavior of Pt and LSM electrodes under Cr-poisoning was used as an evidence for the exclusive validity of the dissociation approach. if both the chemical dissociation as well as the reduction of gaseous Cr-species is occurring with different proportions. This once again may favor the reduction of CrO3(g) and gaseous Croxyhydroxide resulting in Cr2O3(s) deposition at the cathode-electrolyte interface in LSM. and in LSM a pO2 gradient is expected under polarization. which is indeed not the case in a platinum cathode. and thus under these conditions LSM has no tendency at all to accept oxygen. However this conclusion was not tested in the light of the oxygen partial pressure gradient towards the electrode-electrolyte interface: contrary to platinum. again with Mn2+ acting as agent for the formation of Cr-Mn-O nuclei. LSM cathode and a YSZ electrolyte at T = 1173 K and a current density of 200 mA cm-2 from Zhen et al. electron-donating LSM and oxygen-accepting yttrium-stabilized zirconia (YSZ) are available[38]. vacancies are expected to form in LSM under increasing polarization. 4 b[27]) as a function of time reveals an inflection point after about 6 1/2 h. this apparent antagonism is abolished. Alternatively.[27] are particularly interesting: the slope of the cathode polarization curve (Fig. where the reaction partners for the reduction. the following simple explanation for strictly localized Cr2O3(s) formation under anodic polarization can be given: in an LSM cathode the reduction of gaseous Cr-species is expected to be localized at the triple phase boundary.
From the considerations in this chapter we conclude that no sustainable arguments exist for the rejection of the reduction of gaseous Cr-species as one of the controlling mechanisms of Cr-"poisoning" of SOFC. even though the decrease is expected to be less due to less LSM/YSZ active sites caused by the first degradation. Under polarization. the oxygen ions from this new.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects performance. the lower is the oxygen partial pressure at the contact between LSM and YSZ. The deposition of chromium followed by its reduction near this interface blocks direct oxygen access to the electrochemically active sites.[30] give the following explanation. The higher the current density under SOFC operation. This results in a lower oxygen partial pressure at the interface as compared to that in air.8 S m-1 in air[48]).[23]. 34 . the LSMCr interaction is again favored in the region close to YSZ as pO2 decreases at the TPB. and their respective influence on the cell deterioration may vary as a function of time. thus the remaining TPB/YSZ active sites are almost unaffected under open current circuit. the oxygen ions formed at this interface are transported from the cathodeelectrolyte interface through the electrolyte. The important role of decreased oxygen activity at the LSM-YSZ interface under current load for the cell degradation was already suggested by Taniguchi et al. Reduction already takes place at higher pO2 at the beginning of the current load operation. and the chemical activity of the cell is furthermore deteriorating due to the lack of oxygen supply through the rather dense Cr2O3 layer to the new TPB. The small area close to the new TPB that was strongly depleted of oxygen under current load is filled with air leaking through remaining pores between LSM and Cr2O3. as electronic conductivity of Cr2O3 is significantly higher at higher pO2 (1. Oxygen is mainly reduced at the new TPB between Cr2O3(s) and YSZ. Applying a current load.8 S m-1 at T = 1282 K[48] and pO2 = 1 Pa. under open circuit the LSM-Cr interactions occur randomly throughout the cathode. Konysheva et al. and oxygen cannot access the TPB. thereby still more decreasing the oxygen partial pressure at a newly formed Cr2O3(s)/electrolyte interface[30]: the TPB between LSM and YSZ diminishes more and more by the blocking of Cr2O3(s). why the strong oxygen partial pressure gradient in the LSM cathode under high current densities plays a key role for the degradation: the LSM cathode has a low electrochemically active area (TPB) near the interface with the electrolyte only. As Cr2O3(s) has a small electronic conductivity of 0. weak catalytic reaction diffuse into YSZ. The temporary reversibility of the deterioration by switching the cell off and on again can also be explained: in contrast to current load operation.
1 leading to the redeposition of Cr2O3(s) at the cathode-electrolyte interface. The reported dependence of structural features of the degraded cell on the operation temperature.3. current load.5. 35 . and number 3 denotes the reduction of gaseous Cr-species by the reverse of Eq. 1.2. Fig.2 is a visualisation of the microstructural consequences of chromium in an LSM cathode.2 denotes the interconnect-cathode interface region where oxidation of Cr2O3(s) to gaseous Cr-oxides and Cr-oxyhydroxides by Eqs.2. 1. Active LSM/YSZ sites further diminish by ongoing formation of spinel and Cr2O3 deposits.3.3. and the degradation increases as a function of time.3. Number 2 denotes the region of interactions between LSM and chromium leading to spinel formation by solid-solid reaction. 1.3.3 to 1. 1. and chromium content is schematized in the picture.1 to 1. 1.3 occurs. Eqs. or gas-solid reaction. 1. Eqs. followed by diffusion of the gaseous products into the cathode. Numbers refer to locations of processes that are decisive for the degradation Number 1 in Fig.3.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects Oxygen ions diffuse into YSZ. Fig.2.2. but new oxygen is not supplied to the new TPB.1 to 1.2 Model of chromium poisoning of an SOFC with Cr-interconnect and LSM cathode based on the findings in the literature.3. 1.
5O3-δ[66].05Mn1. La0.Sr)CoO3[63]. Application of the following coatings upon the interconnect has been shown to considerably reduce the diffusion of chromium into the cathode thus decreasing the cell degradation: Electroplated metallic Co[49. more active sites for the oxygen reduction will result in a higher Cr-tolerance. La0. as Cr in the ppm range significantly influences the oxygen diffusion in the LSM cathode[36]. two-segment Cr-Al-Y-O nanocomposite and (Mn. so far volatilization could not be suppressed completely. sputtered Co.2Mn0. thereby improving the electrical conductivity of the interconnect-cathode interface[49-69]. Ni.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects 1.54]. or Cu[52].475O4[62].8Sr0. or Mn2CrO4[52]. or Cu-Mn[51]. La0. La0. Furthermore such a buffer layer may act as a sink for CrO3(g) thus diminishing nuclei formation on LSM. coating alone does not solve the problems associated to chromium poisoning completely.1 Increasing the Cr-tolerance of conventional SOFC with Cr-interconnects and LSM cathodes More than ten years ago Badwal et al. However.4Mn1. Mn.50].[22] proposed that coating of the Cr-interconnect with a protective electrically conductive dense layer would be an effective strategy against the diffusion of Cr-species into the cathode. MnCo2O4[54-61].8Sr0.6O4[53.5Co0. La0.67Sr0.8Fe0. Co3O4[53].65]. If the buffer layer contains an ionic conductor. This was recently shown for a cell with a YSZ-LSM functional layer: a functional LSM-YSZ layer adjacent to the YSZ electrolyte led to a lower cell degradation[30]: increasing the ionic conductivity of the LSM cathode that is predominantly electronically conducting down to pO2 = 10-7 Pa[70] by admixture of YSZ results in an 36 .65Sr0. La. La0.Al)N[69].2O3[58].33MnO3[64]. Cu1. but a combination of the quoted strategies is advisable to further improve the long-time stability of SOFC performance. La0.Co)3O4[68].4Co0.3MnO3[58. (La. Several promising materials for coating applications were developed in the following years that act as chromium diffusion barrier and hinder growth of chromia scale at the alloy surface. The formation of a dense electrically isolating Cr2O3 layer is probably preventable by using electrolyte materials or a functional layer between LSM cathode and YSZ electrolyte that can incorporate Cr in solid solution without affecting the electrical conductivity.8Sr0. as well as (Ti.475Co1. Co-Mn.4.2FeO3-δ[67].85Sr0.4 Proposed strategies against chromium "poisoning" and their effectiveness 1. Ce0.2Mn0.6Sr0. However.15MnO3-δ[50].5Co0.5O3[65].
Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects expanded area of active sites for the oxygen reduction away from the TPB.2Fe0. Matsuzaki and Yasuda[31] concluded from insignificant Crdeposits in tested SOFC with Cr-Fe-alloy interconnect. contrary to LSM.71. The amount of Cr- 37 . whereas no proper nuclei were reported for LBCF. and the cell is more tolerant against chromium[30].Ba)(Co.Ba)(Co. Based on these findings they predicted that highly Cr-tolerant cathodes can be developed. Effects of Cr upon the degradation of La1-xSrxCo1-yFeyO3-δ (LSCF)[26. Thus the number of active sites is increased. The highest tolerance against the effects of chromium under SOFC operating conditions combined with high electrical conductivity has been reported recently for (La.4. The ionic conductivity can be increased by doping the B-site of ABO3 perovskite with reducible cations.2 New ways – alternative materials Badwal et al. La(Ni. leading to the formation of more scattered reduction products instead of a dense layer: thus the block of oxygen diffusion into the electrolyte can be avoided. and (La. La(Ni.72].Fe)O3-δ (LBCF)[71. In recent time it was found that new cathode materials such as La1-xSrxCo1-yFeyO3-δ (LSCF). the reduction of gaseous chromium will not be restricted to the small area at the TPB due to a smaller oxygen partial pressure gradient. Besides.Fe)O3-δ (LBCF) are more tolerant against chromium "poisoning".9 electrolyte that the ratio of the reduction of gaseous CrO2(OH)2(g) to that of O2(g) at the electrode/electrolyte interface is controlled by the electrochemical properties of the interface.Fe)O3-δ (LNF). LNF and LBCF revealed extraordinary high tolerance against chromium poisoning.4Co0. and (La.6Sr0.8Sm0.Fe)O3-δ (LNF)[71. particularly LSCF and LNF show rather high ionic contributions to the total electrical conductivity.Ni)FeO3-δ [71.2O1.8O3-δ (LSCF) cathode and Ce0. La0. 1. Ideally the selected dopants decrease the mobility of Mn2+ and thus prevent the formation of nuclei for the adsorption of CrO3(g) without influencing the formation of vacancies.75] cathodes were investigated using impedance spectroscopy.74].73]. In all these cathodes Cr-deposition was observed throughout the cathode both under polarization and without polarization.[22] already considered alternative cathode materials to reduce or stop the formation of the spinel phase. As for LSM these authors concluded that the mechanism of Cr poisoning can be explained by chemical dissociation of CrO3(g) to the perovskite-structured materials and nuclei formation in the cases of LSCF and LNF. All these perovskites are mixed electronic-ionic conductors. which makes this material a promising candidate for a steady long-term SOFC performance.
Stimming. that is towards lower oxygen partial pressures. J. Improved inhibition of the reduction of CrO3(g) is predicted for LNF. Fergus. despite rapidly developing processing techniques it is not clear at the moment if the obstacles of sinterability and low mechanical strength as well as difficult manufacturing correlated with high costs can be coped. In recent years research activities for LaCrO3-base ceramic interconnector materials were revitalized by several groups[76-78] to circumvent the problems of chromium "poisoning". As an alternative to the complicated nuclei mechanism. pp. most likely resulting in retarding or inhibiting of the reduction reaction. but their influence on the Cr deposition compared to the reduction of CrO3(g) cannot be decided yet. 2004. aging mechanisms and lifetime in solid-oxide fuel cells. Thus reduction of CrO3(g) takes place inside the whole cathode even without being promoted electrochemically by polarization of the cell. Advances. Materials Science and Engineering A. However. 2005. 271-83. 2004. the following considerations can be made using the reduction model: For the reduction reaction of CrO3(g) the presence of both an electron donor and oxygen ion acceptor is necessary. References 1. J. The higher the contribution of the ionic conduction the less complete reduction is expected due to prolonged lack of an electron donator. nuclei might form in addition. pp. which was explained by a removing effect of nuclei for the chromium deposition under polarization conditions. 171.W. The amount of deposited Cr in LSCF was even larger without polarization than under polarization. Opposite to the case of LSM no driving force for CrO3(g) to migrate to the triple phase boundary exists due to the mixed ionic-electronic conducting behaviour of the regarding cathodes.Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects poisoning of LSCF was considerable. Metallic interconnects for solid oxide fuel cells. Solid State Ionics. pp. H. Power Sources. Fergus. Tu. Lanthanum chromite-based materials for solid oxide fuel cell interconnects. J. and a typical mixed ionic-electronic conductor such as LSCF can take over both functions. 127. 284-93. 2. 397. 3. U. 38 . Even if the reduction reaction is considered to be the dominant mechanism of chromium poisoning. 1-15. However under strong polarization one can expect that LSCF gets more and more ionic conducting towards the electrode-electrolyte interface. as this phase has a particularly high ionic conductivity.W.
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which further retards the diffusion process of oxygen into the electrolyte. For a more systematic and thus more efficient combination of strategies a strong knowledge about the mechanisms of chromium poisoning of SOFC is required. this behaviour would not be expected. If the process of chromium "poisoning" were completely governed by thermodynamics. So far it was not possible to define unambiguously. but the effects of chromium would be observed only after thermodynamic equilibrium is obtained. In fact it was shown that without sufficient protection against the diffusion of chromium into the cathode the degradation of SOFC caused by chromium is not a long-term phenomenon.Aim of study 2 Aim of study Chromium poisoning of planar SOFC with LSM cathodes and Cr-alloy interconnects is a complex process consisting of several steps that may occur simultaneously inside the cell. Previous experiments have shown that the following factors: -) High temperature -) Decrease of oxygen partial pressure at the TPB under current load of SOFC and processes: -) Interaction of chromium with LSM leading to Mn-Cr-O nuclei and/or spinel formation -) Reduction of CrO3(g) to Cr2O3(s) at the TPB -) Blocking of pores at the TPB by Cr2O3 and/or spinel govern the degradation of SOFC caused by chromium. which of these processes play a dominant role for the degradation and which don't. However. and some strategies against cell degradation caused by chromium have already been successfully applied. it seems that strategies against the cell degradation have been mostly established in a rather random way so far. The causes and consequences of chromium poisoning are clear. severe degradation has been observed after several hours of testing under current load at state-of-the-art SOFC operating temperatures: from the literature findings it is obvious that the degradation of SOFC caused by chromium starts immediately after starting SOFC tests under current load. This means that the kinetic control on the mechanisms of chromium 45 . Mn2+ in LSM plays an important role for the adsorption of gaseous CrO3(g) and Croxyhydroxide on LSM resulting in blocked oxygen transport from the cathode to the electrolyte. Reduction of CrO3(g) at the TPB leads to the formation of electrically low conducting Cr2O3.
and as LSM cathodes are still considered to serve as promising cathodes due to their high electrical conductivity and stability at SOFC operating conditions. The following questions have remained unsolved so far: -) Does spinel form by a solid (LSM)-solid (Cr2O3) reaction or directly in a solid (LSM)-gas (gaseous Cr) reaction? -) Can the concentration of deposits at the cathode-electrolyte interface under current load be explained by thermodynamics? -) How does the LSM phase chemically change due to the interaction with chromium. and several studies can be found regarding the degradation of LSM cathodes caused by chromium. In recent times many materials have been tested for SOFC cathodes. and what are the conditions that favour their formation? This work aims to answer these questions by the application of thermodynamic calculations. in this study the author focuses on the effects of Cr on the degradation of SOFC with LSM cathodes.Aim of study is high.1 Benefits of the thermodynamic La-Sr-Mn-Cr-O oxide database for the understanding of Cr-poisoning of SOFC A thermodynamic La-Sr-Mn-Cr-O oxide database is highly desirable to enable fundamental understanding of the mechanisms of chromium "poisoning" of LSM cathodes for SOFC. As a degrading cell is in a non-equilibrium state. In particular LSM cathodes have been intensively investigated over the last decade. and a degrading cell is in a non-equilibrium state particularly at the early stages of the degradation. 3 Method 3. Therefore the thermodynamic La-Sr-Mn-Cr-O oxide database needs to be established based on the assessments of low-order subsystems. Thus. and can this change be explained by thermodynamics? -) Which of the phases observed in LSM contaminated by chromium form under thermodynamic control. the obvious question why the results of thermodynamic calculations should be feasible for a deeper understanding of the mechanisms 46 .
1 Stoichiometric solid oxides The stoichiometric ternary phase α.1) By calculating thermodynamic equilibria for a LSM cathode that is affected by chromium (A) in the relation above. composition of LSM. The optimization of model parameters is based on the accurate assessment of experimental thermodynamic and phase diagram data of oxide subsystems. Over time the system LSM + Cr will change from its nonequilibrium state at the beginning of the Cr-"poisoning" process towards the calculated equilibrium state. For instance. 3. one can draw conclusions on the evolution of the phase chemistry of degraded LSM cathodes. including the operating temperature. taking into account experimental data on the chromium "poisoning" of SOFC and using a thermodynamic La-Sr-Mn-Cr-O oxide database.1. It contains the optimized Gibbs energy functions of solid oxide phases: for stoichiometric phases as a function of temperature. 47 . and the rate of chromium diffusion the equilibrium state of chromium "poisoning". and for solid solution phases as a function of temperature and composition. a with the positive electrical charge r and b with the positive electrical charge q. for instance under reducing oxygen partial pressures reflecting the situation at the TPB under current load.2. and oxygen partial pressures. using the thermodynamic database one can calculate the expected thermodynamic equilibrium. From A and B.Method of chromium "poisoning" needs some explanation: from the conditions of the non-equilibrium state at the beginning of the degradation process. C in Eq.2 Thermodynamic modeling 3. can be calculated using the thermodynamic La-Sr-Mn-Cr-O oxide database: C non . temperatures.equilibrium (A) ⎯⎯ equilibrium (B) → (3.1 reflects the path the system takes towards its equilibrium state. The presented thermodynamic database of the La-Sr-Mn-Cr-O oxide system is constructed using the CALPHAD approach[1]. C can be predicted for changing cathode compositions. by choosing the starting conditions composition of LSM and defined amount of Cr at a specific temperature. containing m and n moles of two different sorts of cations.1. Hence. 3. the theoretical final state of chromium poisoning after a very long time is found by thermodynamic equilibrium calculations (B).
) w ( t . the sublattice formula of the resulting solid solution phase β(ss) reads (a r . v.2. °Gm at constant pressure is given by ° α Gm = A + BT + CT ln T + DT 2 + ET 3 + FT ( −1) (3.)w + ptv − muv − nwt ° O (g) Gm + A + BT 2tv 2 (3. another sort of cation with the positive charge q.2. D.1 is true. E.)u .2. Eq. 3.) p = q )v (O2.2.)u n ° (b G + Gm t m v r ° α Gm = °Gm ( a r )m (bq )n (O2.)u containing cation a with the positive charge r.2) A.Method respectively. 3.2. 3. For oxides c = O and charge s = −2. can be described by the sublattice formula (a r )m (b q )n (c s ) p . if it is assumed that the heat capacity of the ternary oxide composed by the two binary oxides is simply the sum of the heat capacities of the composing oxides as shown in Eq.2 Solid solution phases – the Compound Energy Formalism (CEF) If in the binary oxide Ox1: (a r )t (O2.2. the three types of ions sitting in three distinctive crystallographic sublattices. and F are model parameters to be optimized by thermodynamic and phase diagram data. E and F are optimized to heat capacity data only. w ∈ N ).5 is the criterion for charge neutrality: 48 .4: m ° ( a )t (O2. C.)u and Ox2: (b q )v (O2. c with the negative electrical charge s. 3. b q )t (O2.4) ° α Gm is the Gibbs energy of formation of the phase α relative to the oxide components. °Gm can be based on the molar Gibbs energies of existing binary oxides Ox1: (a r )t (O2. A and B are optimized by thermodynamic and phase diagram data.2. B.3) α C.2. Eq. To account for the charge neutrality criterion. mr + nq + 2 p = 0 (3. u. As Cp(α) is defined by C p = −C − 2 DT − 6 ET 2 − 2 FT −2 (3. and p moles of one sort of anions. D.1) α The molar Gibbs energy of α. bq can sit in the same sublattice as a.
The Gibbs energy of β(ss) at constant pressure reads ° β Gmss = yar °G ( a r) t (O2.Va )3 ( = ya3+ yO2.°Gma 2+ )2 (O2.)u β + tRT yar ln yar + ybq ln yar + EGmss ( ) (3.)3 ( + ya2+ yO2. The molar Gibbs energy of the phase at constant pressure reads 3+ ° A ( Gm 2 O3−δ = °Gma 2+ .7) Once again the molar Gibbs energies of all the 4 endmember compounds (a3+ )2 (O2.31451 J mol-1 K-1. a 2+ )2 (O2. and ybq is the site fraction cation b on the cation sublattice.6) where yar is the site fraction of cation a on the cation sublattice. and (a 2 + )2 (Va)3 of the phase are required for the molar Gibbs energy 49 . the charge neutrality criterion is no longer obeyed by an anionic sublattice that is completely filled with oxygen.Va )3 (3. Charge neutrality under such reducing conditions can be remained by the formation of zero-charged vacancies (Va) in the anionic sublattice resulting in the phase becoming oxygen-nonstoichiometric. the molar Gibbs energy of the solid solution phase contains the Gibbs energies of the compounds.)3 ( + ya3+ yVa °Gma 3+ )2 (Va )3 3+ ( + ya2+ yVa °Gma )2 (Va )3 ( + 2 RT ya3+ ln ya3+ + ya2+ ln ya2+ + 3RT yO2. a 2+ )2 (O2.°Gma 3+ )2 (O2.)u + ybq °G (b q )t (O2.)u .2.)3 . In the sublattice form the phase can be written as (a3+ . a 2+ )2 (O2. (a 2 + )2 (O 2. 3.Method u= t ( ya q + yb q ) 2 (3.3 Vacancies and the concept of reciprocal reactions Let us consider the case of a binary oxide phase (A)2(B)3. The second-last term accounts for the configurational entropy of mixing of t moles of a and b. R=8.)3 .2.. and B denoting the anion sublattice.. A standing for the cation sublattice. If the cation is reduced. For β(ss) the two compounds read (a r )t (O2. Va)3 . with only one cation a accepting the charge 3+ or 2+ in the cation sublattice.+ yVa ln yVa + EGma ( ) ( ) . The oxygen nonstoichiometry is denoted "O3-δ". (a 3+ )2 (Va)3 . The last term describes the excess Gibbs energy of mixing due to interactions of ions in the mixture that can be accounted for by introducing interaction parameters..2.)u and (bq )t (O2.2.ln yO2.5) Using the Compound Energy Formalism (CEF)[2-4].
3 2 Va)3 .1 The surface of reference for the Gibbs energy of the reciprocal phase (a3+ .. and (a3+ . with the neutral line and the reduced compound. a 2+ )2 (O2. The three other endmembers are charged and cannot exist. For the example of the reciprocal solid solution phase (a3+ . Va)3 the 6+ charged compound (a3+ )2 (Va)3 is chosen as reference. a 2+ )2 (O2. a 2+ )2 (O2. 3. is theoretically obtained by mixing equal amounts of either (a3+ )2 (O 2. denoted with A in Fig. Va)3 is a reciprocal phase[4].. plotted above the composition square.Va)3 . The composition square of the phase can be seen in Fig. For an unambiguous definition of the molar Gibbs energy of the reciprocal phase it is necessary to give an arbitrary molar Gibbs energy to a reference. for instance oxygen nonstoichiometry data.2.1 that is redrawn from Hillert[4].. However. Fig. denoted with R.Method of the phase. thus far off neutral compositions that can really exist. Va)3 approximating its overall Gibbs energy for Δ°Grec > 0 and Δ°Grec = 0. and its Gibbs energy can be optimized with experiments that are related to the reduction of the phase. and its molar Gibbs energy can be defined by optimization of model parameters by experiments. 3. but a line of neutral compositions connects (a3+ )2 (O2. 50 . (a3+ a 2+ )2 (3 2O2. It thus can exist. A system that obeys this relation is called a reciprocal system. the only neutral endmember is (a3+ )2 (O2.2. As the chosen molar Gibbs energy of the reference is unlikely the true value. The 2+ charged center composition of the square.)3 . the reference should favorably be a highly charged compound. 3.1.)3 with the reduced compound (a 2+ )2 (2 3O2.2. included.)3 and (a 2 + )2 (Va)3 or (a3+ )2 (Va)3 and (a 2 + )2 (O 2.)3 .
b 2 + . As no tendency of demixing was reported for the nonstoichiometric oxide solid solutions that are treated in this study.) 3 − °G ( a 3+ ) 2 (O 2.1 (page 50) only the edge of this plane is seen as bold line.)3 and the reference (a 3+ )2 (Va)3 are fixed. as long as these endmembers are charged and away from the existing composition range of the phase.4 Calculation of defect chemistry using the Calphad approach The Calphad approach is very powerful for the calculation of the defect chemistry of highorder nonstoichiometric reciprocal solid solution oxide phases[5] such as (A)(B)O3-δ perovskite with a complex sublattice formula.. Note that in order to obtain the same Gibbs energy of the reduced compound R for Δ°Grec > 0 and Δ°Grec = 0.)3 and (a 2+ )2 (Va)3 by only slightly oxidizing or reducing it. Va)(c 2 + .2.2.1 (page 50) and approximates the whole Gibbs energy of the phase. c 4 + . Anyway. 3. and oxygen partial pressure. the Gibbs energy surface is curved. d 3+ . 51 . c3+ . and without excess terms for the Gibbs energy is visualized in Fig. a 2+ )2 (O2. temperature. if Δ°Grec is zero.Method The surface of reference for the Gibbs energy of the reciprocal phase (a3+ .)3 − (a3+ )2 (O 2.. For this purpose model parameters of the reduced and oxidized compounds are optimized with experimental information on charge carriers.8) If Δ°G of the reciprocal reaction.2. for instance (a 3+ . d 4+ . it is legitimate to define Δ°Grec = 0. Va)(O 2. On the other hand. The morphology of the Gibbs energy surface depends on Δ°G of the reciprocal reaction (a3+ )2 (Va)3 + (a 2 + )2 (O 2. Va)3 for a Cr-doped LSM perovskite as a function of composition. Va)3 at very low temperatures (to make the configurational entropic contribution negligible). when the Gibbs energies of the endmember (a 3+ )2 (O 2. This is not a problem for the description of a reciprocal oxide phase.) 3 − °G ( a 2+ ) 2 (Va)3 (3. and the theoretic compound A will tend to demix to (a3+ )2 (O2. 3. the Gibbs energy surface is flat and no tendency of demixing of A exists. In Fig. and no experiments define a proper value of the reciprocal reaction parameter.2. the Gibbs energies of the remaining endmembers are significantly different for Δ°Grec > 0 and Δ°Grec = 0.)3 − (a 2 + )2 (Va)3 : Δ °G rec = °G ( a 3+ ) 2 (Va)3 + °G ( a 2+ ) 2 (O 2. 3. site fractions and oxygen content. Δ°Grec is positive. the true surface shape of a reciprocal oxide phase with charged endmembers is not known.
References 1. B. M.. 1988. Hillert. J. pp.. pp. Sundman. This weighting process is based on the accurate assessment of experimental thermodynamic and phase diagram data.J.3 Optimization of model parameters The optimization of the thermodynamic parameters was performed using the PARROT module of the Thermo Calc[6] database system. 9(2). 1985. Calphad Calculation of Phase Diagrams.-O.N. Hillert. M. Jansson. Andersson. The Thermo-Calc databank system.O. the authors selectively adjusted the relative weight of each experimental data point and excluded data that were inconsistent with the majority of the data points during the optimization procedure. 2. pp. Saunders. 34. Metallkd. N.F. A. Jansson. Grundy. PARROT can take into account all sorts of thermodynamic and phase diagram data simultaneously.P. 3. B. B. Jansson. Elsevier Science Ltd. 79(2). 33-41. Guillermet. J.. 437-445. Acta Metall. 4. 320. Calphad. B. Hillert. Sundman. A CompoundEnergy Model of Ordering in a Phase with Sites of Different Coordination Numbers. 30. pp. 52 . 479 p. Gauckler. Cmpd. 2006. 1998. Andersson. Application of the Compound-Energy Model to Oxide Systems. 153-90. 1. The Compound Energy Formalism. Vol. Z. Calphad. Calculation of Defect Chemistry Using the CALPHAD Approach. J. Ivas.Method 3. 6. Povoden. Miodownik.. A. E. B. As the use of all the experimental data in a simultaneous least square calculation often leads to divergence. pp. B. The program minimizes the sum of squared errors between calculated and experimentally determined phase diagram and thermodynamic data. A. 2001. T. Alloy. L. M. 81-87. 5. Pergamon Materials Series. Sundman. 161-76. 1986.
thus substantially reducing the triple- 53 . 5 wt. 27. Povoden. Namely a Cr5Fe1Y2O3 oxide dispersion strengthened alloy with the composition 94 wt.. Diff. ceramic and metal interconnect materials have been tested and evaluated over the years. which offers low fabrication costs. Phase Equilib. A comprehensive compilation and evaluation of experimental and thermodynamic data for the Cr-O system is presented and.1 Technology SOFC offers high fuel conversion efficiencies and. due to the high operating temperature (>1173 K). Meanwhile the use of Cr-based alloy interconnect materials has gained popularity due to their relative ease of fabrication. For the planar design SOFC. the use of this alloy as an interconnect material in SOFC leads to the degradation of the fuel cell performance especially on the cathode side of the fuel cell. and the liquid is described using the two-sublattice model for ionic liquids.J. 4. a consistent set of thermodynamic model parameters is optimized based on new experiments.1.% Cr. Grundy.% Fe and 1 wt.% Y2O3 developed jointly by Plansee and Siemens with satisfying material properties has been promoted as a suitable alternative to the earth alkaline-doped LaCrO3 ceramics interconnect. which block active sites as well as pores.Thermodynamic assessments 4 Thermodynamic assessments 4. by application of the CALPHAD method. Also the magnetic transition in Cr2O3 and the oxygen solubility in Cr are modeled. A. pp.and power-generation capability. 353-62. low manufacturing costs and high thermal conductivity[1]. Nonstoichiometry of eskolaite (Cr2+xO3) is described using the compound energy model. Microstructural analyses of the cathode of SOFC show the formation of Cr2O3 and (CrMn)3O4. 2006. and L.N.1 Thermodynamic reassessment of the Cr-O system in the framework of solid oxide fuel cell (SOFC) research E. However. combined heat. Gauckler J. Loss of performance caused by the migration of Cr originating from the alloy interconnect is well documented by several investigators. Cr3O4 is described as a stoichiometric compound.
Thermodynamic assessments phase boundary area for the normal oxygen reduction reaction at the cathode/electrolyte interface.1.1. The influence of Cr from the interconnect alloy on the strontium-doped lanthanum manganite (LSM) cathode can be modelled in terms of an equilibrium thermodynamic view to contribute to strategies for reducing the SOFC chromium poisoning process by optimizing SOFC operating conditions and refining SOFC material compositions. T (K) T (K) 2257 2317 2603 ---- 2543 ± 25 -- 54 . Eskolaite (Cr2O3) is the dominating stable oxide phase over a wide temperature range.1. 4. Results of special points in the Cr-O phase diagram from several studies are summarized in Table 4. These authors document the existence of a large miscibility gap between the metallic and the oxide melt. Table 4. X(O) ----Cr3O4 detected ----Stability range Mono- of Cr3O4. tectic T (K) ----T (K) ----Reference Kanolt[4] experimental Wilde and Rees[5] experimental McNally et al.1 Special points in the Cr-O system Eutectic Melting of Cr2O3 in Eutectic composition.1.[6] experimental Bunting[7] experimental air.2 Experimental data Phase diagram data: Experimental investigations of phase diagrams in the Cr-O system were made by Ol'shanskii and Shlepov[2] and Toker[3].
Microstructures of a quenched 55 .496 0. Concerning the pure Cr-O system. Lam[9] reported the existence of molten chromium with oxygen impurities of 1400 ppm at T = 2133 K.Thermodynamic assessments --2571 ---2539 1933 1918 1941 1929 1937 1938 ± 2 1938 0. The monotectic reaction of Cr (bcc) metal and liquid was found at T = 2083 K by Grube and Knabe[8] and by Ol'shanskii and Shlepov[2].[13] experimental This work.523 0. Investigations made by Hilty et al. Ol'shanskii and Shlepov[2] and Johnson and Muan[12] did not find Cr3O4 up to the eutectic temperature of chromium oxide. whereas Toker et al. The question of the existence of a crystalline Cr3O4 phase was discussed controversially by several authors. Mc Nally[6] measured a melting temperature of 2603 K in air using an induction furnace. Grube and Knabe[8] found that 1 wt.497 0. calculated Note: Itallicized data were used for optimization The melting temperatures of eskolaite in air reported from Kanolt[4] and Wilde and Rees[5] can be discarded as being too low. experimental Johnson and Muan[12] experimental Degterov and Pelton[39] calculated Kowalski and Spencer[40] calculated Taylor and Dinsdale[41] calculated Toker et al.[13] concluded from microstructural observations and a discontinuity in the slopes of the temperature-oxygen pressure curves for univariant equilibria involving metallic Cr and various chromium oxide phases that a Cr3O4 phase exists in a narrow temperature range between T = 1923 K and 1978 K.52 0.[10] and Hook and Adair[11] led them to postulate the existence of a crystalline Cr3O4 phase in the Cr-Fe-O system.499 0.% Cr2O3 lowers the melting point of metallic Cr from T = 2163 K to between T = 2043 K and 2063 K.513 0.497 no no yes yes yes yes yes --1923 1978 1918 1974 1923 1978 1923 ± 2 – 1978 ± 3 1918 1973 – – – – 2083 2083 -2160 2130 2083 2117 Ol'shanskii and Shlepov[2]. This value significantly deviates from the result of Bunting[7]. who measured T = 2543 ± 25 K also in air.
The obtained 56 . At T ≥ 1573 K they were confronted with the loss of a quarter of Cr in the case of oxidation. The independent results of corrected cell potentials of the two measurement series are excellent. that is. Toker et al. 1273 K. The reversibility and accuracy of the yttria-doped thoria electrolyte and the electrode was tested by measurements of a standard iron-chromium alloy at 1326 K. thus at these temperatures log( pO2 ) values were determined solely from the reduction of Cr2O3.Thermodynamic assessments chromium melt with maximum oxygen impurities of about 2930 ppm lately investigated by Lam[9] document an inner Cr3O4 phase and an outer Cr2O3 phase in dispersed oxides in large chromium grains and grain boundaries. Thermodynamic data: Oxygen Potentials: Grube and Flad[14] measured log( pO2 ) values for the Cr-Cr2O3 equilibrium between T = 1053 K and 1573 K by both oxidizing Cr to Cr2O3 and reducing Cr2O3 to Cr in a flowing H2-H2O atmosphere. Disagreement between the emf results from Pehlke et al. Novokhatskii and Lenev[15] studied the equilibrium of the reduction of Cr2O3 to Cr with hydrogen from T=1493 K to 1893 K. These authors used a flow method where thermal diffusion problems were suppressed by inserting corundum bushes into the reaction tube. causing transfer of oxygen through the cell.[17]. Davies and Smeltzer[16] determined log( pO2 ) values of Cr2O3 at T=1173 K.[17]. Holzheid and O'Neill[21] noted a deviation from the well-established trend from T = 900 K to 1300 K for high-temperature data caused by finite electronic conductivity at elevated temperatures. The data are in close agreement with the gas-solid equilibrium measurements by Jeannin et al.[17] used two separate series of emf measurements employing the solid oxide electrolyte galvanic cell technique from T = 1148 K to 1548 K.[18]. and Tretjakow and Schmalzried[20] were assigned to possible electronic conduction in the zirconia electrolyte used by the latter authors.[13] measured log( pO2 ) values of Cr2O3 by equilibrating Cr and Cr2O3 in H2-CO2 mixtures of known oxygen potentials at temperatures from T = 1773 K to 2098 K. Appreciable sublimation of metallic chromium was not observed. using an electrochemical cell with a calcia-zirconia electrolyte and a Fe/FeO reference electrode.[13] and Lam[9]. as well as transport of oxygen ions from the cathode to the Cr/Cr2O3 anode. Applying the same technique as Pehlke et al. Pugliese and Fitterer[19]. This indicates that the first phase to crystallize on solidification is Cr3O4 giving strong evidence for the stability of this phase. Pehlke et al. days for T < 1100 K. as well as the importance of sufficient time to attain equilibrium. and 1373 K. Thus in this study the authors accept the findings of Toker et al.
10 ×10−3 T 2 + 3.[27].37 J mol-1 K-1 at T = 298.53 + 2.736 ×105 T −2 (4.5 K to 340 K with mean increments of 0. data presentation. and fitting procedure are worked out very carefully.1.15 K Chase et al.1. The accuracy of this study is evident from excellent data reproduction by performing two runs in the entire temperature range.[26] relied on the calculated results from heat content measurements performed by Kelley et al.68 ≤ T ≤ 323. 4.1.56 K.1. heat Contents.736 ×105 T −1 − 9759 (4. who calculated ° S298K (Cr2O3) = 81.84 J K-1mol-1 by a graphical method of plotting the heat capacity against the logarithm of the temperature and modeling the heat capacity curves with Debye 57 . The latter authors fitted their data measured from T = 400 K to 1800 K by H T − ° H 298K = aT + b T 2 + cT −1 + d 2 ° (4.17 ± 0.2 results in C p = 28.[26] relied on the results from Anderson[23].43 K.Thermodynamic assessments dissociation pressures of Cr2O3 are in agreement with average values derived from emf studies using an yttria-doped thoria electrolyte worked out by Jacob[22] and a very high temperature gas-mixing study of Toker et al. Uncertainties of 0. Bruce and Cannell[24] applied a two-dimensional temperature wave method using a single crystal of Cr2O3 to calculate specific heat in the temperature range 290.[13]. Resulting Cp data correspond nicely to the most recent calorimetric results from Klemme et al.2) Temperature derivation of Eq.3) For ° S298K (Cr2O3) Chase et al. and fitted the data to the heat of diffusion equation that considers some material properties employing a least-mean-squares fit. Documentation of the experiments.1) yielding ° H T − ° H 298K = 28.4 % for Cp (20 K < T < 200 K) and 0.7 % for Cp (T < 20 K) were estimated.[25]. and entropies: Anderson's[23] calorimetric data set of Cp-values lacks detailed documentation of the experimental procedure. For Cp(Cr2O3) = 120. Heat Capacities.53T + 1.20 ×10−3 T − 3. The latter authors measured a consistent data set of heat capacities of synthetic eskolaite from T = 1.
42 kJ mol-1. This was circumvented by heating the combustion products to T = 1323 K.2 ± 0. Shirokov[30] estimated Δ f.[28] adopted their ° S298K (Cr2O3) value from Wagman et al.el° H 298K (Cr2O3) = –1128. The latter authors proposed a 58 .Thermodynamic assessments functions.el° H 298K (Cr2O3) = –1122.[29].el° H 298K (Cr2O3) =–1140. Mah[32]. and thermodynamic estimates for CrO from Shirokov[30].el° H 298K (Cr2O3) = –1139. Degterov and Pelton[39] reassessed the CrO-Cr2O3 subsystem for the molten slag database using a modified quasi-chemical model for the liquid phase.[27] were used. Kowalski and Spencer[40] used the associated solution model for the liquid phase based on the experimental data used by Taylor and Dinsdale[41]. calculated Δ f. who calculated ° S298K (Cr2O3) = 85. Their calculated liquidus temperature of Cr2O3 in air is T = 2571.7 ± 8.16 K. Klemme et al.06 kJ mol-1.4 kJ mol-1 from several earlier studies.3 J K-1 mol-1 from their measurements.1 J K-1mol-1 by reevaluating emf data from Holzheid and O'Neill[21].72 kJ mol-1 from Wagman et al. for example.1. using a bomb calorimetric combustion technique at 1323 K and 30 atm oxygen pressure. Some difficulty caused by moisture adsorption was encountered in weighing the combustion products.el° H 298K (Cr2O3) = –1128.7 kJ mol-1. Chase et al. Navrotsky[35] cited Garrels and Christ[36] for Δ f. Enthalpies of Formation: Roth and Wolf[31] found Δ f.98 ± 1.[26] evaluated Δ f.[25].[33] used heat capacity and entropy data from tabulations of Coughlin[34] to obtain Δ f.3 Previous assessments of the Cr-O system Banik et al.el° H 298K (Cr2O3) = –1125.el° H 298K (CrO) = –305.86 J K-1 mol-1.[25] recommended Δ f. Ramsey et al.5 kJ mol-1 (el=elements) by applying a calorimetric technique.4 kJ mol-1 by evaluating emf data from Holzheid and O'Neill[21].4 kJ mol-1 for metastable CrO.el° H 298K (Cr2O3) the heat content data given by Kelley et al.[28] adopted Δ f.[37] established a phase diagram for the Cr-O system based on a subregular solution model that is in good agreement with experimental data obtained by Ol'shanskii and Shlepov[2]. For the calculation of Δ f. 4. Klemme et al. Klemme et al. This procedure was critically documented by other authors.74 ± 1.[29]. which is in good agreement with an early finding by Bunting[7] who measured T = 2543 ± 25 K.8 ± 2. while Dellien et al. thermodynamic data for Cr-Cr2O3 from Fromm and Gebhardt[38].[25] recommend ° S298K (Cr2O3) = 83. Shirokov[30] estimated ° S298K of a metastable CrO phase to be 46.el° H 298K (Cr2O3) = –1134. Dellien et al.
and simplified by Hillert and Jarl[44]. 4. There is a large uncertainty concerning the exact melting point of Cr2O3.4) 59 . space group R3c . especially as their miscibility gap does not close on increasing temperature. Their optimization of one of the charged endpoints in their compound energy model for eskolaite and the use of six interaction parameters to describe the liquid may lead to problems on extrapolation to higher-order systems. The magnetic properties of eskolaite can be described using a magnetic ordering model proposed by Inden[43].1. Their calculated values for the enthalpy of formation and the entropy of Cr3O4 are in agreement with an estimate done by Chipman[42]. The use of six parameters for the description of the Cr3O4 phase is somewhat incommensurate with the scanty experimental information of this phase. the stability field of Cr3O4. Kelley et al. using the same thermodynamic models as the authors use in this work.[26] at elevated temperatures as a sum of magnetic and nonmagnetic contributions.Thermodynamic assessments phase diagram in good agreement with the experimental data obtained by Toker[3]. Toker[3]. Taylor and Dinsdale[41] fitted Cp data from Anderson[23] close to the antiferromagnetic to paramagnetic transition and data from Chase et al. The heat capacity of Cr3O4 was taken as 7/5 times the nonmagnetic value for Cr2O3 according to Neumann and Kopp's rule. a magnetic contribution to the Gibbs energy is added to the nonmagnetic part of the Gibbs energy given as: MAG ΔGm = RTln(β +1) f ( τ ) (4. In this model. which are the two-sublattice ionic model for the liquid and the compound energy model for the Cr2+xO3 phase. This is reflected by significant variations of the position of the eutectics.1. and the temperature of the monotectic reaction of Cr(bcc) and liquid between the assessments of the Cr-O system.5 K. and only few thermodynamic data of the Cr3O4 phase and the liquid phase exist. Experimental information on phase relations for their assessment was taken from Ol'shanskii and Shlepov[2].[27]. Eskolaite shows an antiferromagnetic to paramagnetic transition at T = 305. and Grube and Knabe[8].4 Thermodynamic modeling Solid phases: The crystal structure of eskolaite is α-Al2O3 type.
5) giving the equilibrium constant ' x [CrCr ]3 2 [Cri••• ]1 2 [Va ix ]1 4 [OO ]9 4 pO x x [CrCr ]2 [Va ix ][OO ]3 38 2 Kr = (4.6). The magnetic parameter p equals 0. To explain their experimental results Matsui and Naito[45] proposed a defect reaction that leads to the same proportionality.[46]. their equation violates the fundamentals of defect chemistry and must be rejected in favor of the defect reaction given above (Eqs.1. Tc and β are both dependent on the composition.5 and 4.6 gives the proportionalities [Cri••• ] ∝ pO2 −3 16 and [CrCr ] ∝ pO2 −3 16 .7) 60 . Assuming the defect reaction that describes the formation of oxygen vacancies: x x ' CrCr + 1 2OO → CrCr + 1 2 Va •• + 1 4O2(g) O (4. Inserting this ' into Eq.1. Tc is the critical temperature for magnetic ordering. the latter because of the large size of Cr2+. When modeling nonstoichiometry in an oxide phase. however.1. This means that reduction is accomplished by the formation of interstitial Cr3+ and not by the formation of oxygen vacancies. 4.6) ' Assuming small defect concentrations all concentrations except [CrCr ] and [Cri••• ] are ~ 1 and ' can be ignored.28.Thermodynamic assessments where β is a parameter related to the total magnetic entropy. and Cri•••• giving a slope of pO −3 20 2 . it is important to submit the experimental data to a defect-chemistry analysis. which is in agreement with Young et al.1. 4. Both are unlikely: the former because it is unlikely to get Cr4+ on reduction. Due to charge neutrality the relation [Cri••• ] = 3[CrCr ] must hold. The defect chemistry of Cr2+xO3 with the sublattice occupation (Cr2+.1. and τ = T/Tc. In the case of Cr2+xO3 modeled with interstitial Cr3+ the defect reaction reads x x ' x 2CrCr + Va ix + 3OO → 3 2CrCr + 1 2Cri••• + 1 4 Va ix + 9 4OO + 3 8O 2(g) (4.Va)1 (O2-)3 can be modeled using experimental data from Matsui and Naito[45].1.Cr3+)2 (Cr3+. The following other interstitial defects could be assumed: Cri•• giving a slope of pO2 −1 4 .
1. Fig. Cr3+ → Cr2+ + Cr4+. Only compounds along the neutral line can exist on their own. Also the defects cannot explain the electrical properties measured by Young et al. In contrast to Matsui and Naito[45] who explain this assuming that neutral Cr forms interstitially. as it would make the description quite complex. the present authors believe that the different slopes are caused by a competing defect reaction.1 is a graphic representation of the model the authors use to describe the oxygen nonstoichiometry of eskolaite.1 Compound energy model for the Cr2+xO3 phase The four corner compositions represent all possibilities to express the Cr2+xO3 phase according to the above formula for the sublattice occupation.Thermodynamic assessments ' leads to a proportionality of [Va •• ] ∝ PO2 −1 6 and [CrCr ] ∝ PO2 −1 6 .1. As the most reasonable way to model reduction is to use the reduced neutral endpoint 61 . 4. 4. for example charge disproportionation. The low nonstoichiometry data from Matsui and Naito[45] show a different slope than their higher nonstoichiometry data. This slope does not correspond O to the experimental findings of Matsui and Naito[45]. The three other corner compositions present charged compounds. similar to the case of LaMnO3 perovskites[47].[46]. The corner Cr3+:Va:O2corresponds to stoichiometric Cr2O3. where each corner of the composition square represents a °G parameter. The present authors didn't consider this by their defect chemistry model. Fig.
9) In order to avoid the inevitable formation of miscibility gaps if the energy of the reciprocal relation is large we set this energy zero.1.1. pp.8) The last term describes the configurational entropy due to mixing of Cr3+ and Va on the interstitial site.1. labeled A in Fig. by choosing an arbitrary reference.1. 4.63-64.1.Thermodynamic assessments (Cr2+)2 (Cr3+2/3Va1/3)1 (O2-)3. The function to model the reduction then reads ° GCr2+ 3+ 2− 2 (Cr 2 3Va1 3 )(O )3 = °GCr O + 2 3 °GCrSER + A + BT + RT ( 2 3ln 2 3+1 3ln1 3) 2 3 (4. 4.10) This means that without introducing interaction parameters one gets an ideal description between Cr2O3 and Cr2+xO3.10 are listed in Table 4. °G of the 3+ charged endmember (Cr3+)2 (Cr3+)1 (O2-)3 is chosen as reference and given the value °GCr3+ :Cr3+ . 62 . which leads to ° G Cr3+ :Cr3+ + °G Cr 2+ :Va − °G Cr3+ :Va − °G Cr 2+ :Cr3+ =0 (4.2. This is done by using the two equations for the stoichiometric and the reduced endpoints. The expressions for all °Gs at the corners resulting from Eq.8 to 4. one has to find functions of °G of three charged corners expressed solely in terms of the neutral compositions. and by defining a reciprocal reaction giving four equations with which all °Gs at the corners can be expressed.1. Then the reciprocal relation reads ° G Cr3+ :Cr3+ + °G Cr 2+ :Va = °G Cr3+ :Va + °G Cr 2+ :Cr3+ = ΔGr (4.1.1.
2923T 3 Cr O3 SER SER GCr 22+ :Va:O 2..Cr 3+ ) p (O 2..Va L = −709542 Tc = −311.543 102.4 β = −0.2923T 3 p = 0.)q p = 2 yO2.996 15.0 S298 23.Va)1 (O 2.− 2 H Cr − 2H O = 2GCR1O1_L Reference Cr (bcc_A2) 1 2 Mass 51. q = 2 yCr 2+ + 3 yCr3+ ° ° ° ° L SER GCr 2+ :Va q.Va)3 ° ° bcc SER GCr:Va − H Cr = GHSERCR [49] bcc SER SER GCr:O − H Cr − 3H O = GHSERCR + 3GHSEROO[49] + 243T 0 bcc Cr:O..= 121000 Solid Cr (bcc_A2) (Cr)1 (O.999 H298 .Va q.2 Thermodynamic description of the Cr-O System Element Element Cr O Liquid (Cr 2+ .5 p = 0.0 Cr3O4 ° Cr3O SER SER GCr:O 4 − 3H Cr − 4 H O = GCR3O4 Functions 63 . Cr 3+ ) 2 (Cr 3+ .6 β = 3.Thermodynamic assessments Table 4.Va q.52 mol O2 0 LCr 2+ :O2.+ qyVa .1.28 Tc = 308.Va q.)3 ° ° ° ° Cr 3 SER SER GCr 2O:Va:O 2.− 3H Cr − 3H O = GCRO0 − 2 GHSERCR [49] − 5.− 2 H Cr − 3H O = GCR2O3_L L SER SER GCr 2+ :O2.− H Cr = 2GCR_L[49] + GCR2O3_L − 3GCR1O1_L L SER SER GCr3+ :O2.0 4341.008 CrO ° Cr1O SER SER GCr:O1 − H Cr − H O = GCR1O1 Cr2O3 (Cr 2+ .− 3H Cr − 3H O = GCR2O3 + GHSERCR [49] 3+ Cr O3 SER SER GCr 22+ :Cr3+ :O 2.H0 4050.= 0 LCr3+ :O2.− 3H Cr − 3H O = GCRO0 + 1 GHSERCR [49] − 5.− 2 H Cr -3H O = GCR2O3 3+ Cr 3 SER SER GCr 2O:Cr3+ :O 2.− H Cr = GCR_L[49] L SER GCr3+ :Va q.
mol.76T GCRO0 = 108305 + GCR2O3 + 2 GHSERCR [49] 3 GCR2O3_L = GCR2O3 + 439078 − 169T GCR1O1_L = 0. Ionic liquid: The two-sublattice ionic liquid model[50. Parameters for solid Cr. 0 LCr2+ :O2.5GHSEROO[49] + 280045 − 93. Fig.2 (next page) is a graphic expression of the model.Va)3. and one can reduce the number of parameters to only two. liquid Cr.5GCR2O3 − 0. the number of parameters is kept as low as possible. and gaseous O are from Dinsdale[49] In contrast to Taylor and Dinsdale[41]. 4.Cr2+)p(O2-. Therefore a large value is given to the endmember °GCr:O (in this case 0 was a large number) and the oxygen stability is modeled with the temperature dependence of °GCr:O and a regular interaction parameter 0 LCr:O.97 × 10-3T 2 + 1050000T -1 GCR1O1 = 0. It was not possible to model the oxygen solubility using the endmember °GCr:O as this endmember turned out to be too stable and CrO3 appeared in the stability diagram at high oxygen partial pressures. Its heat capacity is given by Neumann and Kopp's rule.Va and 0 LCr3+ :O2.Va that are required to give the miscibility gap. 64 .Vaq-)q is chosen. the latter constraint is not needed in the model.. K.8T ln T −4.4T Note: All parameters are in SI units: J.. where each corner of the composition square represents a °G parameter of the liquid phase.5GCR2O3 − 0.1.Va that must of course be negative.56T − 119. literature data from Caplan and Fraser[48] are used. The Cr3O4 phase is based on the eskolaite phase. The oxygen solubility in solid Cr(bcc) can be described by an interstitial solution model of the form (Cr)1(O. who needed 4 parameters to model the Cr2O3 phase and had to arbitrarily equate the °G of (Cr2+)2 (Va)1 (O2-)3 to stoichiometric Cr2O3.31451 J mol-1 K-1. The descriptions for solid and liquid chromium metal and gaseous O2 are from Dinsdale[49]. As the experimental data on the liquid phase are scarce.82T GCR3O4 = 1.5GCR2O3 − 0.Thermodynamic assessments GCR2O3 = −1164542 + 728.5GHSEROO[49] + 255269 − 53. With this expression one is able to obtain reasonable results for the liquid phase using the positive interaction parameters. For the optimization of model parameters.51] is selected to describe the ionic liquid. Pa: R = 8.5GHSEROO[49] + 339673 − 121. The sublattice occupation (Cr3+. Metastable CrO is described in the same way.
2. Cr3+:Va must be metastable compared to Cr2+:Va. One derives the °GL functions of the oxide compositions (Cr3+:O2-) and (Cr2+:O2-) from the eskolaite phase. 4.[52] in his original assessment of the Cu-O system. Hallstedt and Gauckler[54] recently reoptimized the Cu-O liquid. One way of doing this would be to simply say that Cr3+:Va equals Cr2+:Va plus a large positive term. The °GL of liquid Cr is taken from Dinsdale[49]. for example +600000 as given to °GCu2+ :Va by Hallstedt et al. In this model description of the liquid phase metallic Cr-liquid can be described by both the corners Cr2+:Va and Cr3+:Va. This is however problematic for reciprocal systems.1.Thermodynamic assessments Fig. obtaining the parameter °GCu2+ :Va from the reciprocal relation and giving it a reciprocal energy of 0. A special feature of the Cr-O system is the occurrence of a eutectic very close to the composition of CrO. If the reciprocal energy of the system is large there will be a tendency to form miscibility gaps as pointed out by Hillert and Sundman[53].2 Two-sublattice ionic liquid model for the Cr-O system The four corner compositions represent all possibilities to express the liquid phase according to the above formula. The liquid composition changes along the hyperbolic curves in Fig.1. 4. This considerably improved the description of the Cu-O liquid and removed the inverted 65 . The eutectic temperature is mainly determined by the value of the corner Cr2+:O2-.
63-64).1.[13]. In principle.[13]. and. In the next step the authors optimized the nonstoichiometry of Cr2+xO3 using data from Matsui and Naito[45]. As the use of all the experimental data in a simultaneous least square calculation often leads to divergence.[18] and Toker et al. ΔGr = 0 (4.5 Optimization of parameters The complete set of optimized thermodynamic parameters describing the Cr-O system is given in Table 4. The first parameters to be optimized were the Cp-parameters of Cr2O3. Finally the solubility of O in solid Cr was optimized using data 66 .1.Thermodynamic assessments miscibility gap found at high temperatures in the original assessment[52].The ° G L 3+ Cr :Va = 2 °G L 2+ Cr :Va + °G L 3+ Cr :O2- − 3 °G L 2+ Cr :O2- + ΔGr . The authors optimized Tc and β using Cp data from Klemme et al. The program minimizes the sum of squared errors between the calculated and experimentally determined phase diagram and thermodynamic data. The melting temperature of eskolaite in air was taken from Bunting[7]. PARROT can take into account all sorts of thermodynamic and phase diagram data simultaneously. The data used were heat content data from Kelley et al.el° H 298. with low relative weight.[27] and Cp data from Klemme et al. An identical strategy is employed here. using experimental phase equilibria data from Toker et al. the authors selectively adjusted the relative weight of each experimental data point and excluded data that were inconsistent with the majority of the data points during the optimization procedure.[25] close to the antiferromagnetic to paramagnetic transition temperature. Thus metallic liquid is given by the corner L parameter °GCr3+ :Va is obtained by the reciprocal reaction given as ° G LCr2+ :Va . high temperature emf data from Holzheid and O'Neill [21] . The optimization of the thermodynamic parameters was performed using the PARROT module of the Thermo Calc[55] database system. These parameters were then kept fixed during the rest of the optimization. They assessed Cr3O4 and the liquid simultaneously. and experimental data on the liquidus at the oxygen rich side of the miscibility gap from Ol'shanskii and Shlepov[2]. experimental data on the liquidus at the oxygen poor side from Toker et al. To determine the parameters describing the enthalpy and entropy of Cr2O3 log( pO2 ) data from Jeannin et al.[13].[25] at T = 290 K and from T = 335 K to 338 K with a low relative weight.16 data from Holzheid and O'Neill[21] were used.11) 4.2 (pp.1.16 and ° S298. Δ f.
54-55) values that were used for our optimization are written in italic letters.1 (p.Thermodynamic assessments from Caplan and Fraser[48]. 4. 4. 184.108.40.206. In Table 4.6 Results and discussion Phase diagram: The calculated phase diagram with oxygen isobars is shown in Fig.4 (next page).1. Fig. 67 . logarithmic) given. The gas phase was not included in the calculation An enlargement of the phase diagram close to the CrO composition is presented in Fig.3 Calculated Cr-O phase diagram with oxygen isobars (Pa.1.1. 4.
Thermodynamic assessments Fig.1. 4. Fig. For the monotectic temperature of the reaction of Cr (bcc) and liquid the present authors calculate T = 2117 K. with experimental data and oxygen isobars (Pa.497. The calculated liquidus temperature of eskolaite in air is T = 2539 K.5 (next page) shows the calculated oxygen potential phase diagram of the Cr-O system with experimental log( pO ) data included. At a mole fraction of oxygen > 0. in good agreement with the measurement from Bunting[7].4 Enlargement of the calculated Cr-O phase diagram close to the CrO composition. 2 68 .1. Cr3O4 is formed at T = 1918 K by the eutectoid reaction Cr2 O3 + Cr + 1 2O2 → Cr3O4 . 4.[13] and an earlier experiment from Ol'shanskii and Shlepov[2] is slightly deviating from former optimizations. logarithmic) included The shape of the liquidus at the oxygen poor side of the miscibility gap resulting from the authors' optimization relying on a single experimental datum from Toker et al. and for the eutectic one gets T=1938 K at a mole fraction of oxygen of 0.497 it decomposes in a peritectic reaction at T = 1973 K forming Cr2O3 and liquid.
4. Fig.[13] are particularly well reproduced by the authors' optimization. 4.Thermodynamic assessments Fig. 188.8.131.52. The shape and size of the miscibility gap is speculative due to the lack of experimental data.6 Stability of Cr3O4 in the log( pO2 ) versus temperature diagram 69 .1. with experimental log( pO2 ) data as a function of temperature from different studies The experimentally determined phase stabilities from Toker et al.5 Calculated oxygen potential phase diagram of the Cr-O system. The stability of Cr3O4 is shown in the log( pO2 ) versus temperature diagram in Fig.
The maximum calculated δ = 0.4.098 at T = 1918 K.Thermodynamic assessments The solubility of oxygen in Cr(bcc) is shown in Fig.8 (next page).1.7 Calculated oxygen solubility in Cr(bcc) with experimental data and oxygen isobars (Pa.1.7. The comparison of the calculated nonstoichiometry in Cr2+xO3 with the experimental data by Matsui and Naito[45] is given in Fig.1. the total charge of Cr is given by 6+2δ. Fig. 4. 4. If the commonly used – however grubby – notation "Cr2O3-δ" is applied.% at T=1938 K. but it results simply from the extrapolation of experimental data from Matsui and Naito[45] on excess Cr as a function of pO down to the oxygen partial pressure at the Cr-Cr2O3 2 equilibrium following the proportionality given by the defect chemistry analysis in section 4. 70 . 4.1. The cation overstoichiometry resulting from the presented optimization might seem somewhat high.08 at. logarithmic) included For the maximum solubility of oxygen in Cr(bcc) one calculates 0.
The low nonstoichiometry data show a different slope than the higher nonstoichiometry data. Therefore. as the introduction of an additional defect species would be required to reproduce these.8 Optimized nonstoichiometry of Cr2+xO3 with the only available experimental data from Matsui and Naito[45] included. Optimization of a temperature dependence is represented by dotted lines. Solid lines result from our accepted optimization without considering temperature dependence. Obviously the calculated results show a temperature dependence that is significantly stronger compared to the experiments.Thermodynamic assessments Fig.1. and due to existing data at only three different temperatures from a single author it was decided not to optimize a temperature dependence giving GCRO0 = 108305 + GCR2O3 + 2 3GHSERCR . The solid lines correspond to the optimization that is accepted in this work. 4. 71 .8) and leads to the reduced neutral endpoint being too stable at low temperatures. The data at low oxygen nonstoichiometries were not used. Considering a temperature dependence for the reduced neutral endpoint of the phase Cr2+xO3 gives values of GCRO0 = −202130 + 235T + GCR2O3 + 2 3GHSERCR (dotted lines in Fig. 4.1.
Fig. For Δ f. which is very close to the results from Holzheid and O'Neill[21].0. and ° S298K = −79 J K -1 mol-1 based on the estimates of Shirokov[30]. 4.9 Comparison of calculated heat capacities of Cr2O3 with experimental data For the magnetic parameter β we calculate 3. and for ° S298K (Cr2O3) we get 85 J K-1mol-1.el° H 298K (Cr3O4) we calculate –1402 kJ mol-1.el° H 298K (Cr2O3) we calculate –1123 kJ mol-1. Cp.6.1. 72 . which is in particularly good agreement with the data from Ramsey et al. These values for Cr3O4 deviate significantly from the results of Taylor and Dinsdale[41] who calculated Δ f ° H 298K (Cr3O4) = –1447.el° H 298K = −306 kJ mol-1 . and ° S298K (Cr3O4) = 150.1. 4.9) are well represented by our assessment. For Δ f.[33].685 kJ mol-1. of the solid Cr2O3 phase (Fig. and for ° S298K (Cr3O4) we get 175 J K-1mol-1.555 J K-1 mol-1.Thermodynamic assessments Thermodynamic Data: The heat capacities. and for Tc we get 308. For a metastable CrO phase we calculate Δ f.
Grube.. pp. 73 . Min. Kanolt. 1953. Lam. Solid State Ionics. Foger. 315-18. Forgeng. 2000. Thesis. S. melting points of MgO in a N2 atmosphere and of Cr2O3 in N2 and in air atmospheres. 7. 1936. Interaction between chromia forming alloy interconnects and air electrode of solid oxide fuel cells.7 Conclusions With the presented reassessment of the Cr-O system the authors are able to excellently describe available thermodynamic and phase diagram data with as few optimizing parameters as possible. pp. and that a large variation of the measured melting points of eskolaite exists. Nauk. 561-64. Bunting. Oxygen solubility and oxide phases in the FeCr-O system. 203(2). However. Phase equilibria in the system Cr2O3-Al2O3.F. pp. Ol'shanskii.D. J. Hilty. Stand. Wilde. Melting points of some refractory oxides. 4.. 6. 123-55. 1997. Shlepov. References 1.Thermodynamic assessments 4.P. 5. 947-49. 10. Zhang. 1961. 297-310. F. D. Dokl. T.. pp. The system palladium–chromium. Toker. J. Sci. 42(11).. J.T. V.I.W. Brit. Wash. 1931. Eng. W. 253-68. Rees. Z. Ceram. Acad. Bur. 42(7). 1955. R. Melting and casting of high purity chromium with controlled oxygen content. E. Metall. 3. 3. W. 44(10). it must be kept in mind that experimental data on the liquid miscibility gap are largely missing. Folkman. 6(6). 9. pp. Res. Am. The ternary system MgO-Al2O3-Cr2O3. 99. Y.P. Soc. C. Elektrochem. 2. 91(3).K. Equilibrium phase relations and thermodynamics for the systems Cr-O and Fe-Cr-O in the temperature range 1500 to 1825 °C. Sistema Cr-Cr2O3. Ceram. SSSR. Akad. pp. 1913. R.N.C.Y. 793-804 (in German). Trans. pp. R.H. 1943.1. Ramprakash. Knabe.I. pp. W.L. Pennsylvania State University. J.S. G. Deller. K. Laboratory furnace for studies in controlled atmospheres. Badwal. J. United States Patent 6039788.. R. N. Nat.N. Peters. 1978. Y. I. McNally. 491-93..J. R.K. P. 8. Ribbe.
W. 488-91. Toker. Jeannin. pp. Grube. Metall. J. 1963. 230(6). 430-33. 39. Activities and phase boundaries in the Cr–Ni system using a solid electrolyte technique. Mineral. O'Neill. F. 475-79. Novokhatskii.. T. 24. 1977. 1995. Mazandarany.A. 22(2). pp. Mannerskantz. R. J. R.. J. aluminate). Anderson.Y. F. 1997-2002. Ac. Smeltzer. T. Soc. Tretjakow. Ac.M. 14. Richardson. S.. The heat capacities of chromium. The formation and dissolution of chromium oxides in chromium. 25. Berich. M. 51(8).S. 21. B. 543-49. A. 85. Lenev. 1991. pp. 1686-93. pp. W. Electrochem. Ceram.M. 15. pp. pp. 1(7). H. Equilibrium phase relations and thermodynamics of the Cr-O system in the temperature range of 1500 °C to 1825 °C. Davies. L.N. Specific heat of Cr2O3 near the Neel temperature. 121(4). Metall..H. L. pp. Activities in iron–chromium alloys. pp. Ceram. chromous chloride and chromic chloride at low temperatures. 396-402 (in German). 11(9). Metall. Aime. Cosmochim. Flad. Am. Geochim. pp. Rev. R. The heat capacity of MgCr2O4. 1964. H. pp. Bunsen Gesell. 377-89 (in German). Soc. Hook. 59(3). C. 22. Phys. Gmelin. 74 . 1977. Adair. Trans. The thermodynamics of spinel phases (chromite. Schnelle. 59. Schmalzried. N. D.. 1942. Cosmochim. 48(7). Thermodynamic properties of Cr2O3 and FeCr2O4 at high temperatures. H. 15(9). 18. Pugliese. Soc.T.. Muan.D. L. A. Soc. Metall. J.D. 2000. Z. J. and Cr2O3 at low temperatures and derived thermodynamic properties.Thermodynamic assessments 11.E. Geochim. K. 1827-31. 1974. Am. 13. 20. pp. pp. Soc.E. 227(2). 1970. B. 69(5). O'Neill.. 1278-83. 16. Inorg. Affinity and enthalpy of the solid solution in the system Cr-Ni. 124.. 1937. 1975. Russ.S. pp. Cannell.S. Solid oxide electrolyte emf cell determination of the standard free energy of Cr2O3 and applications to chromium–bearing mineral systems. Aime. Electrochem. pp.D. chromic oxide. ferrite. Fitterer. Darken.. The Cr-Cr2O3 oxygen buffer and the free energy of formation of Cr2O3 from high-temperature electrochemical measurements. Bruce. Potentiometric determination of the Gibbs free energy of formation of cadmium and magnesium chromites. Elektrochem.R. Holzheid. Am. Jacob.S. A. 225-32. Y. Phase diagrams for the systems Si-O and Cr-O. pp.W. C.. E. 17. A. H.. 833-45. 1968. Johnson.H. 1078-80. FeCr2O4. Radzilowski. Oxygen and metal activities of the chromium–nickel–oxygen system between 900° and 1100°C. Muan. G. R. 23. A. Chem. G. R. Trans. Pehlke. 1965.T. 4451-59. 19. 12. J. Klemme. Soc. 300-5. 1966.
Janaf thermochemical tables . CrO-Cr2O3-Al2O3. pp. 43 pp. Thermodynamic consideration on the system Cr-Cr2O3. Hepler.J. 1969.L. 46. 28. Garrels and C. Springer Verlag. 31. 1996.D. 37. Thermodynamic properties of carbides of chromium. Jr.I. 32. Geochim. and tungsten: thermodynamic properties. Halow. 521-34 (in German). W. B. chemical equilibria. Am. J.H. I. Parker. Kelley. D. P. G. 30. D.R. Soc. F.. V. Thermodynamics of the oxidation of chromium. pp. Data. 662. 819-32. K. 1973. Z. NBS Tech. R. Chem. Thermodynamic properties of chromous oxide.. and standard potentials. 45-46 (in German). E. Cosmochim. pp. 1954. Contributions to the data on theoretical metallurgy. molybdenum. Metallkd. 1975. W. 1940.3rd ed. A.B. Electrochem.H. F.. 27. Chem. Mah. Lux.. The heat of formation of chromium oxide. 1976. Bangert. 1): pp. 3363-65.M.Thermodynamic assessments 26. Bur. Phase Equilib. Navrotsky. 39. Huffman. J.G. I. Harper & Row. Mines Bull. 80 pp. Rev. Nauk. N.S. Syverud. Gebhardt: Gases and Carbon in Metals. Degterov. p. Ettmayer. J.N. Coughlin. Mines Tech. Thermochemistry of chromium compounds. Banik. Ac. Wolf. Selected values of chemical thermodynamic properties. Dellien. 36. 644-45. 76(13). Chromium. R.A. 1954.D. Davies. J.K. M. Roth.. 270(4). Boericke. Burr. 1965. Schumm. Downey. 135-38. Soc. 75 . Berlin. C. Wagman. Bailey. Caplan.A. D. J.. Ramsey. W. and CrO-Cr2O3-CaO systems.. J. 38. 542. A. Ref. 33. 29. 35. J. 71(10): pp. Chase. N.. E. Metal.M. Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CrO-Cr2O3. SSSR. p. Schmitt.A. 39. New York. Tables for elements 35 through 53 in the standard order of arrangement. 283-310. 410. 103(2). 2. U. Paper. 17(6). Dokl. 1985. Minerals and Equilibria. Elektrochem. 102.A. Christ: Solutions. S.W.M. T. 476-87. Bur. 76(3). Heidelberg. pp. 1980. A.M. Z. 940-42. R. pp. Akad. E. 34. 14(Suppl. D. S.. Shirokov. Phys. Heats of formation of chromium oxide and cadmium oxide from combustion calorimetry. Chem.. L. McDonald. 1956. pp. Fromm. Flurip. Notes.H. Evans. Hall. especially oxides at high temperature. Pelton. 1944. A. 1976. pp.P.
B. M. Predicting miscibility gaps in reciprocal liquids. Burr: in Ductile Chromium. p. General treatment. 227-38.R. Ca-Cu-O and Sr-Ca-Cu-O systems. Taylor. B. 1955. A. J. The oxygen partial-pressure dependence of the defect structure of chromium(III)oxide. Existence of hypostoichiometric chromium sesquioxide at low oxygen partial pressures. Gauckler. pp. ASM. Metallkd. Fe-O and Ni-O systems: 229-43. Povoden. Sundman. Calphad.. Hillert. Hallstedt. 317-425. 51.J. Calphad. B. 42. Sr-Cu-O. Metall. J. Cr-O and Cr-Ni-O systems using the ionic liquid and compound energy models. Phase Equilib. Trans. Young. 25(4). T. Soc..T. 1957. Modification of the two-sublattice model for liquids.W. 52. J. L. E. Gauckler. 134(9). Revision of the thermodynamic descriptions of the Cu-O. Atomic interactions in molten alloy steels. Z. Inden. 599-605. 33-41. A two-sublattice model of molten solutions with different tendency of ionization. Ågren. 81(5). 44.H. pp. 177-91.. pp. 15. 354-66. SGTE data for pure elements. J. Determination of chemical and magnetic interchange energies in bcc alloys. 196. M. 48.J. Caplan.T. Jarl. Matsui.. Calphad. Grundy. pp. 76 . A. 45. Cleveland. 1991. Fraser. 1985. Calphad. Sundman. 1994. 46. Ivas. 53. de Witt. Jansson. L. T. Ag-Cu-O. K. Sundman. AgO. J. Calphad. 1985. 15(4). A. pp. Bi-Sr-O. Kowalski. 15(5). 54. 66(10). M.A. pp. Risold. Thermodynamic assessment of the copper-oxygen system. Z. 1975.J. Naito. D. pp. 261-66. 19(3). M. 43. 1995. Bi-Cu-O. pp. B. Calculation of defect chemistry using the Calphad approach. pp. Hillert. 136.. Nucl. J. 1978. Hallstedt. 50. pp. D. Thermodynamic reevaluation of the Cr-O. I.N. J. 1990. Calphad. G. 2(3). A. Hillert. Dinsdale.Thermodynamic assessments 40. 1991. M. Ohio. 2003. pp. Iron Steel Inst.. A model of alloying effects in ferromagnetic metals. E. Dinsdale. 41. B. 49. 2257-60. Gauckler. 109-19. pp. 1994.J. A. 577-82. Metallkd. Calphad. M. Electrochem. J.H. J. 30. Gerretson. pp. A thermodynamic assessment of the Ni-O. B. 16A. 78-82. 1987. 97-106.W. Remodelling of the liquid. 47. 27(2). L.J. Spencer. 2005. Mater. P. 180. bcc and fcc phases. 483-99. pp.A. Chipman. 2001.
thus substantially diminishing the triple phase boundary area for the normal oxygen reduction reaction at the cathode/electrolyte interface[4]. Gauckler Int. pp. 153-90. and L. J.% Fe.1 Introduction For the planar design of SOFC the use of heat-resistant high chromium alloys has been promoted as a suitable alternative to earth alkaline doped LaCrO3 ceramic interconnect materials[1. Chromium manganese spinel MnyCr3-yO4 and its tetragonally distorted polymorph are described using the compound energy model.% Cr.2. J.2]. Mater. Also solid solutions of the phases (Cr1-yMny)2+xO3.[8].J.[7].6 wt.N. 22. Sundman. 4. and the liquid is described using the two-sublattice model for ionic liquids. The processes by which these protective oxide scales reduce the chromium poisoning and their effect on cell degradation during long-term SOFC operation are not well known yet.Thermodynamic assessments 55. Mn2-yCryO3. However. and 0. Andersson.2 Thermodynamic assessment of the Mn-Cr-O system for SOFC materials E. 97. 4. mobilization predominantly via the gas phase[3] of Cr originating from the alloy interconnect leads to the formation of Cr2+xO3 (eskolaite) and chromium manganese spinel MnyCr3-yO4 which block catalytically active sites as well as pores. a consistent set of thermodynamic model parameters is optimized for the Cr-Mn-O system based on experimental data. We are contributing to the understanding of the underlying thermodynamics of these processes by assessing the MnCr-O system using the CALPHAD approach.% Mn resulted in an improvement of short-term SOFC operation. Calphad. Jansson. 9(2).O. B. 569-78. pp. The Thermo-Calc databank system. The thermodynamic data of the pure elements are taken from Dinsdale[6]. and (Mn1-yCry)1-xO are considered. B. and Lee [9] 77 . 1985. Cr-O. Simner et al.[5] observed that the formation of chromium manganese spinel layers on top of a Cr2O3 oxide scale on the surface of a Mn-containing ferritic stainless steel (Crofer22 APU) interconnect with 76. 2006. Grundy.45 wt.8 wt. and Mn-Cr binaries from Grundy et al. and the data for the Mn-O. Res. A. Relevance for solid oxide fuel cells is discussed. Povoden et al. By application of the CALPHAD method. Povoden..
bcc for chromium manganese alloy with bcc A2 structure. Normal spinel is given by the formula [A2+](B3+)2O4.3 (p.2. bxb for Mn2O3 (bixbyite) with dissolved Cr. and liq for the liquid phase. and 4. Spinel containing a large amount of Mn3+ becomes tetragonally distorted on lowering the temperature as a consequence of the macroscopic Jahn-Teller effect that is caused by the distortion of the octahedral sites occupied by Mn3+[11]. mgs for Mn1-xO (manganosite) with dissolved Cr.Thermodynamic assessments respectively. esk for Cr2+xO3 (eskolaite) with dissolved Mn. The most prominent oxide phase in the Mn-Cr-O system is cubic chromium manganese spinel with the formula MnyCr3-yO4. Fig. show varying degrees of mutual solid solubility. α-spl for tetragonally distorted polymorph spinel solid solution. 4.2 (p. No new ternary phases are found in the Mn-Cr-O system. whereas spinel of the formula [B3+](A2+B3+)O4 with half of B on the tetrahedral sites – marked with angular brackets in the above formulas – is called inverse spinel. 80). 4.4 (p. 79).2. In the case of cubic MnyCr3-yO4 both the trivalent cations of manganese and chromium show a remarkable preference to fill the octahedral sites marked with round brackets in above formulas[10]. 4. In this work we use the following abbreviations: β-spl for cubic chromium manganese spinel solid solution.2. β-hsm (βhausmannite) for the cubic and α-hsm (α-hausmannite) for the tetragonally distorted Mn3O4 endmember of the spinel solid solution.2 Experimental Phase diagram data: Our calculated phase diagram of the MnOx-Cr2O3 system in air is shown in Figs. 78 .1.2. 80) shows the calculated phase diagram at pO2 = 1×10-4 Pa . 4. however all the binary oxides except pyrolusite (prl).2. MnO2.
2 Calculated pseudo-binary phase diagram of the system MnOx-Cr2O3 in air. 79 .2. Fig.2. The gas phase was not included in the calculation. with experimental data.1 Calculated pseudo-binary phase diagram of the system MnOx-Cr2O3 in air.Thermodynamic assessments Fig. 4. The gas phase was not included in the calculation. 4.
2.3 Mn rich part of the calculated pseudo-binary phase diagram of the system MnOx-Cr2O3 in air. with experimental data. 4. Fig. 80 . 4.4 Calculated pseudo-binary phase diagram of the system MnOx-Cr2O3 under strongly reducing conditions ( PO2 = 1×10-4 Pa ).Thermodynamic assessments Fig. showing the expanded stability field of β-spl + mgs.2.
3. The Mn solubility in (Cr2-yMny)1+xO3 reported from Speidel and Muan[12] is significantly higher than it is found by Golikov et al. Tanahashi et al. and β-spl + esk + liq in equilibrium at T = 2243 ± 20 K.2.2. 4. next page).[13] studied the MnOx-Cr2O3 system using quenching techniques and high temperature X-ray diffractometry in air in the temperature range from T = 973 K to 1673 K. 79 and 4. but it is lower than the findings from Speidel and Muan[12].15] studied phase stabilities in the MnOx-Cr2O3 system in the temperature range from T = 1100 K to 1620 K in air by means of X-ray measurement of annealed samples. p. The solubility limit of Cr in Mn2-yCryO3 is measured by these authors to be y = 0.[14]. Golikov et al.2. They consider the solubility limit of Mn in (Cr1-yMny)2+xO3 to be negligible. p. p. This value is in agreement with the result from Geller and Espinosa[16]. Their data are shown in Figs.2. From the absence of changes of the lattice parameters of esk in equilibrium with β-spl annealed at T = 1105 K and 1620 K in air compared to pure Cr2O3 they conclude that the solubility of Mn in (Cr2-yMny)1+xO3 is low and does not depend significantly on temperature. 80. Their resulting phase diagram is in considerable disagreement with the findings of Speidel and Muan[12].14 at T = 1105 K in air.[13] and Pollert et al.[17] investigated the compositions of coexisting β-spl + mgs and β-spl + esk from pO = 2×10-6 to 2×102 Pa at T = 1873 K thus determining the range of solid solubility of 2 β-spl by quenching techniques under controlled CO-CO2 atmosphere (Fig. 4. They estimate a minimum temperature of T = 773 K for the stability of β-spl.2. Pollert et al.[14.2.[14] report a solubility limit of y = 1. They find β-spl + α-spl + bxb coexisting in equilibrium at T = 1183 ± 5 K. 79).42 at oxygen partial pressure >> 20000 Pa.5. 81 . They report a minimum temperature of β-spl stability of T = 973 K and lower solubility of Cr in tetragonally distorted MnyCr3-yO4 and of Cr in Mn2-yCryO3.Thermodynamic assessments Speidel and Muan[12] present a phase diagram of the MnOx-Cr2O3 system in air in the temperature range 873 K to 2253 K resulting from the determination of phase equilibria using quenching techniques and X-ray and microscopic examination (Fig. 4. Pollert et al.
5 Cr contents of β-spl in equilibrium with mgs. and significantly increasing Cr solubility in cubic MnyCr3-yO4 with decreasing oxygen partial pressure (Fig. As the compositions of mgs 2 solid solution are located on the line connecting Mn1-xO with CrO in the ternary phase 82 . each phase in the quenched specimens was subjected to electron probe microanalysis (EPMA). Experimental data are included. β-spl in equilibrium with esk. From this result Tanahashi et al.2. which increases slightly with increasing oxygen partial pressure.[17] conclude that Mn is dissolved in cubic MnyCr3-yO4 in the form of Mn3O4. Phase relations were verified using X-ray diffraction. and 1873 K. 4. and mgs in equilibrium with β-spl in the pseudo-binary MnOx-Cr2O3 system as a function of oxygen partial pressures at T = 1073 K. 4. They report small solubility of Mn in (Cr1-yMny)2+xO3 at pO2 = 2×10-6 . esk in equilibrium with β-spl. They found increasing Mn solubility in cubic MnyCr3-yO4 at oxygen partial pressure higher than 2 ×10-2 Pa . They found almost unchanging solubility of Cr in (Mn1-yCry)1-xO from pO = 2×10-6 to 2 ×102 Pa at T = 1873 K. In order to identify the equilibrium compositions. 1473 K.2.5). The compositions of β-spl are located on a line connecting MnCr2O4 with β-hsm in the ternary plot.Thermodynamic assessments Fig.
and 1273 ± 5 K in the oxygen partial pressure range from 0. 4. 1173 K.6).[18] investigated the composition changes of the two phase equilibrium β-spl + mgs at T = 1073 K. 82).Thermodynamic assessments diagram.% at T = 1323 K performing an isopiestic experiment (Fig.2.2.2. Also the experimental result on the three phase equilibrium MnO + MnCr2O4 + bcc from Ranganathan[19] is plotted.6 Ternary phase diagram of the system Cr-Mn-O with stoichiometric single phase equilibria (points). There are no data on oxygen nonstoichiometry of MnyCr3-yO4. these authors conclude that chromium oxide dissolves in (Mn1-yCry)1-xO in the form of CrO. 4.1 to 10-13 Pa (Fig. Three-phase field boundaries are denoted with thin solid lines. 4. 83 .2 cat. p. two-phase fields and three-phase fields.5. Dotted lines are tie lines. Bobov et al. For the invariant three phase equilibrium mgs + β-spl + bcc Ranganathan and Hajra[19] measured the Mn content in bcc to be 25. Fig. single solid solution phase equilibria (heavy lines).
2.[11] investigated the martensitic α-spl → β-spl transition temperatures. 4.Thermodynamic assessments Holba et al.4 for the formation of α-spl.5×10-4 Pa from the 2 standard Gibbs free energy changes of the reactions Mn (in molten Fe) + 2 Cr (in molten Fe) +2 O2(g) = MnCr2O4 and Mn (in molten Cu) + 2 Cr (s) + 2O2(g) = MnCr2O4 (4. which is equivalent to Δf G of 1 2(Δ f GMnCr2O4 − Δ f GMnAl2O4 ) .2. From these data and the activities of CrO1.5 + Mn0. Samples with y < 1.MnyAl3-yO4 solid solutions formed from Cr2O3-Al2O3 mixtures at T = 1873 K.5CrO2 (4.2.5 + Mn0. solid Cr and oxygen at T = 1873 K in the pO range from 2×10-6 to 1.5AlO2 and AlO1.[20] derive Δ f °GMnCr2O4 = –958 ± 8 kJ mol-1 from liquid Mn.2.5CrO2 obtained from a previous study[23] they derive ΔG of the reaction CrO1.2. This means that the Gibbs energy of formation of β-spl of the composition MnCr2O4 from its 84 . Giving α-spl the formula [Mn2+](Mn3+. p. We recalculate this value using the most recently assessed Δf °GMnO [7] and Δ f °GCr2O3 [8] β-spl values at T = 1873 K giving Δ f °GMnCr2O4 = –66 ± 8 kJ mol-1. 79).3) β-spl to be –10 kJ mol-1 at T = 1873 K. enthalpies and entropies of MnyCr3-yO4 samples annealed at T = 1723 K using X-ray analysis and DTA measurement. Tsai and Muan[22] experimentally determined compositions of coexisting MnyCr3-yO4 . Tanahashi et al.8 do not show Jahn–Teller distortion at room temperatures.2) (4.Cr3+)2O4 this corresponds to a minimum concentration of [Mn3+] = 0.5 in Mn0. and remain β-spl.1) β-spl Using compiled Δf °GMnO and Δf °GCr2O3 [21] they calculate Δ f °GMnCr2O4 from its oxides to be –59 ± 8 kJ mol-1. Thermodynamic data: Cubic spinel (β-spl): Only values for the standard Gibbs energy of formation of β-spl of the composition MnCr2O4 β-spl are published.5 in Mn0. With decreasing Mn-content the temperature for the transition decreases (Fig.5AlO2 = AlO1.
Fig. Tsai and Muan[22] chose the value determined by Lenev and Novokhatskiy[24]. 85 . Δ f °GMnAl2O4 = –32. with experimental data and error bars.7 Calculated Gibbs energy of formation of β-spl of the composition MnCr2O4 as a function of temperature. Filled symbols correspond to originally reported literature data. Using other values for Δ f °GMnAl2O4 reported β-spl in the literature[25-27] leads to deviating Δ f °GMnCr2O4 of –34. 4.Thermodynamic assessments oxides using this calculation technique depends on the value of Δf °GMnAl2O4 .0 kJ mol-1 at T=1523 K.2. ΔΗ α β = 18810 J mol-1. unfilled symbols correspond to recalculated values. 4.[15] present thermodynamic data on the transition of α-spl to β-spl. Biggers[28] by using the same technique as Tsai and Muan β-spl MnO-Cr2O3 system found Δ f °GMnCr2O4 = –59.2. [22] in the CoO- β-spl The spread of Δ f °GMnCr2O4 values resulting from different studies and our recalculations is shown in Fig.7.4 ± 10 kJ mol-1.1 kJ mol-1. and ΔS α β = 13 J K-1 mol-1. Tetragonally distorted spinel (α-spl): Pollert et al. According to these authors the transition of pure α-hsm to β-hsm takes place at T=1445 K.6 kJ mol-1 β-spl giving Δ f °GMnCr2O4 = –52. –46. and –36.6 kJ mol-1 at T = 1873 K.1 kJ mol-1.
The Gibbs energy of the endmember of the formula [Mn2+](Cr3+)2O4 is given by the expression ° Cr O β-spl β-hsm G[Mn 2+ ](Cr3+ ) O = 2 3 °G[Cr32+ 4](Cr3+ ) O + 1 3 °G[Mn 2+ ](Mn3+ ) O + Aβ-spl + Bβ-splT 2 4 2 4 2 4 (4. As the degree of inversity of β-spl is very low[10]. All endmembers of our model β-spl are neutral.3 Thermodynamic modeling Cubic spinel (β-spl): There is experimental evidence on the presence of Cr2+ in β-spl as the Cr endmember of β-spl was found to be a stable phase in a small temperature range[29. so we stick to the less complex description without Mn2+ and Mn4+ on the octahedral sites.Mn2+.Mn3+)2O4 using the compound energy model[31–33]. Lu et al. To maintain electroneutrality Mn2+ is formed on the octahedral sites resulting in a charge disproportionation reaction. The Gibbs energies of the endmembers [Mn2+](Mn3+)2O4 that corresponds to β-hsm. We define this last endmember using a reciprocal relation ° Cr O β-spl β-hsm β-spl G[Cr2+ ](Mn3+ ) O = °G[Cr32+ 4](Cr3+ ) O + 1 3 °G[Mn 2+ ](Mn3+ ) O − °G[Mn2+ ](Cr3+ ) O 2 4 2 4 2 4 2 4 (4. β-spl can therefore be described by the simple formula [Mn2+. This state is denoted SER (Stable Element Reference).8]. However there is no experimental data quantifying the amount of Mn4+ in β-spl.Thermodynamic assessments 4. Considering these findings an alternative description of β-spl would read [Mn2+.2.[34] measured the electrical conductivity of β-spl. In our description we further go along with the presumption that the amount of oxygen vacancies may be neglected.Mn3+.30].Cr2+](Cr3+.Cr2+](Cr3+.5) The Gibbs energy of the reciprocal reaction is taken to be zero.2. In our CALPHAD assessment the °G values of all compounds are given relative to the enthalpy of selected reference states for the elements at T = 298. 2 4 2 4 86 . and [Cr2+](Cr3+)2O4 that corresponds to Cr3O4 are taken from the assessed binaries[7. They propose small polaron hopping between Mn3+ and Mn4+ on the octahedral sites as mechanism for the electrical conductivity.4) This endmember is considerably more stable than the endmember of the formula [Cr2+](Mn3+)2O4.15 K and p = 105 Pa[6].Mn4+)2O4.2. Thus the endmember ° β-spl β-spl G[Cr 2+ ](Mn3+ ) O becomes less stable the more stable °G[Mn 2+ ](Cr3+ ) O becomes.
The Gibbs energy of the endmember (Mn3+)2(O2-)3 is taken from Grundy et al.2.6) Bixbyite (bxb): Geller and Espinosa[16] postulate the incorporation of Cr into Mn2-yCryO3 by a simple substitution mechanism between Cr3+ and Mn3+.Mn3+.Mn3+. the two endmembers of α-spl read [Mn2+](Mn3+)2O4 and [Mn2+](Cr3+)2O4.Thermodynamic assessments Tetragonally distorted spinel (α-spl): The transformation of β-spl to α-spl is due to the Jahn-Teller distortion of the octahedral sites occupied by trivalent Mn ions leading to the tetragonal structure of α-spl[11. (Mn2+.Va)(O2-) leads to far more satisfactory 87 . Thus we may describe bxb as (Mn3+. Hence.14. Experiments[11. Due to these considerations we may write [Mn2+](Cr3+.15].15.Cr3+)2(O2-)3. Manganosite (mgs): Based on the proposed incorporation of Cr into (Mn1-yCry)1-xO in the form of CrO[15] we tested a description of mgs given by (Mn2+. The Gibbs energy of [Mn2+](Mn3+)2O4 is equal to α-hsm.Mn3+)2O4 to describe α-spl. whereas for ordering due to Jahn–Teller distortion the opposite holds.7) The experimental data could be reproduced without the optimization of a temperature dependent parameter.Cr3+. This is a reasonable assumption as the radii of these ions are very similar[35]. and the Gibbs energy of (Cr3+)2(O2-)3 is given by ° bxb esk G(Cr3+ ) O = °G(Cr3+ ) 2 3 2 (Va)1 (O 2.2.) 3 + Abxb (4.34] show that α-spl is stabilized at high Mn contents. and the Cr solubility in tetragonally distorted MnyCr3-yO4 does not extend beyond MnCr2O4.Cr2+. The Gibbs energy of [Mn2+](Cr3+)2O4 is given by ° Cr O α-spl α-hsm G[Cr2+ ](Mn3+ ) O = 2 3 °G[Cr32+ 4](Cr3+ ) O + 1 3 °G[Mn 2+ ](Mn3+ ) O + Aα-spl + B α-splT 2 4 2 4 2 4 (4.Va)(O2-). as the degree of inversity is increasing with higher temperature. It is very unlikely that trivalent cations are incorporated into the tetrahedral sites of α-spl.[7]. The incorporation of chromium of valencies other than three is mentioned nowhere in literature. Using this description the solubility of Cr in function of oxygen partial pressure experimentally determined by Tanahashi[17] could not be reproduced correctly.
[14] postulate the incorporation of trivalent Mn ions into (Cr1-yMny)2+xO3.2.)3 Gas − 1 3 °GO − 3 2 RT (1 3ln1 3 + 2 3ln 2 3) + Amgs 2 (4.Thermodynamic assessments reproduction of these data. These experiments also provide evidence against Cr being incorporated interstitially.8 Geometrical representation of the mgs phase described using the compound energy model. Eskolaite (esk): Pollert et al. The Gibbs energy of (Mn3+)2(Cr3+)1(O2-)3 is given by 88 .Mn3+)2(Cr3+. 4. 4. Fig. Agreeing with these authors we model the solubility of Mn by (Cr3+. With this description we are in agreement with O'Keefe and Valigi[36] who observe a decrease in the lattice parameter of mgs compared to undoped Mn1-xO providing strong support for the assumption that it is Cr3+ that is substituting the much larger Mn2+ ion and which is forcing the lattice to contract.2.8.Cr2+.[7]. The Gibbs energy of the neutral endpoint ( Cr 3+ 2/3 Va1/3 ) O is given by 2 3 °G mgs + 1 3 °G mgs + RT (1 3ln1 3 + 2 3ln 2 3) and based on the Gibbs energy of 1 mole of (Va )O1 3 (Cr3+ )O1 mgs Gas esk. The model description of mgs is shown in Fig. Using °G(Va)O1 = 1 °GO2 the following expression for the parameter °G mgs is obtained 3+ 2 (Cr )O1 ° G mgs = 1 2 °G esk 3+ 3+ (Cr )O1 (Cr )2 (Va)1 (O2.Va)1(O2-)3.2.8) The Gibbs energies of the three other endmembers are taken from Grundy et al.
The liquidus temperature is optimized using the interaction . and Lee[9].2. The descriptions of further alloy phases are taken from[9]. No data are reported for the oxygen solubility in pure bcc A2 manganese metal. Assuming low oxygen solubility in bcc bcc manganese metal we give a large value to the endmember °GMn:O . 90-92).Vaq-)q using the two-sublattice model for ionic liquids parameter 0 Lliq3+ Cr .Thermodynamic assessments ° G esk3+ (Mn )2 (Cr3+ )1O3 = °G bxb3+ (Mn )2 (O2.Va)3.)3 + °GCr SER + Aesk (4.Mn2+)p(O2-. Liquid: We model the liquid phase as (Cr3+.4 Optimization of parameters The complete set of optimized thermodynamic parameters describing the Mn-Cr-O system is given in Table 4.[8].2. 4.Mn3+ :O2- [38.39] . Povoden et al.2. Cr-Mn alloys: We describe the oxygen solubility in bcc by an interstitial solution model of the form (Cr. Experimental data on the oxygen solubility in pure bcc A2 chromium metal[37] were used for the description of (Cr)1(O. 89 .Va)3[8].Cr2+.2.10) We take the Gibbs energies of the other endmembers from Povoden et al.Mn)1(O.[7]. Mn3+.[8].The binary interaction parameters are taken from Grundy et al.)3 + Aesk (4.1 (pp.9) and the Gibbs energy of (Mn3+)2(Va)1(O2-)3 by ° G esk3+ (Mn )2 (Va)1O3 = °G bxb3+ (Mn )2 (O2.
938 15..Thermodynamic assessments Table 4.Va q.0 23.− H Cr = GCR_L[9] liq SER GCr3+ :Va q.52 (Cr 2+ .0 4996.− 2 H Mn − 2H O = 2GMN1O1_L[8] 0 liq Cr 2+ :O2..+ qyVa .Mn 2+ :Va q- L 0 liq Cr 3+ .Va q- L L 0 liq Cr 2+ .− 2 H Cr − 2H O = 2GCR1O1_L[9] liq SER GMn 2+ :Va q. q = 2 yCr 2+ + 2 yMn 2+ + 3 yCr3+ + 3 yMn3+ ° ° ° ° ° ° ° ° liq SER GCr 2+ :Va q.− 2 H Cr − 3H O = GCR2O3_L[9] liq SER SER GCr 2+ :O2.Va q- L L = 121000[9] = 129519[8] = −45459[8] = −33859 [8] = −15009 + 13.543 32.H0 S298 Cr Mn O Liquid (liq) BCC_A2 CBCC_A12 ½ mol O2 51.1 Thermodynamic description of the Cr-Mn-O system a) Element Element Reference Mass H298 .Cr 3+ .6 0 liq Mn 2+ :O 2.Cr)1 (Va.− H Cr = 2GCR_L + GCR2O3_L[9] − 3GCR1O1_L[9] liq SER SER GCr3+ :O2.− H Mn = 2GMN_L[7] + GMN2O3_L[8] − 3GMN1O1_L[8] liq SER SER GMn3+ :O2.2.Mn 3+ :O 2- L Bcc A2 alloy (bcc) (Mn.Va q1 liq Mn 2+ :O 2..Mn 3+ ) p (O 2.− H Mn = GMN_L[7] liq SER GMn3+ :Va q.Mn 2+ .O)3 90 .996 54..)q p = 2 yO2.6587T = 504 + 0.9479T = −188487.Mn 2+ :Va q1 liq Cr 2+ .008 102.Mn 3+ :O 2.0 4341..Va q- L 0 liq Mn 2+ .999 4050.− 2 H Mn − 3H O = GMN2O3_L[8] liq SER SER GMn 2+ :O2.
)3 ° ° ° esk SER SER GCr 3+ :Va:O 2.Va)1 (O 2.− 2 H Cr − 3H O = GCR2O3[9] + 3459 ° Eskolaite (esk) (Cr 2+ .28 esk Tcesk = 308.Mn 3+ ) 2 (Cr 3+ .− 2 H Mn − H Cr − 3H O = GMN2O3[8] + GHSERCR [7] + 39503 esk SER SER GMn 3+ :Va:O 2.− 3H Cr − 3H O = GCRO0[9] + 1 GHSERCR [7] − 5.− H Mn − H O = GMN1O1[8] − 21883.6 y esk Cr 3+ :Va:O 2- esk β esk = 3 yCr :Va:O esk β esk = 3 yCr :Cr 2+ 2+ 3+ esk Tcesk = 308.4183T [10] 1 bcc Cr.6 yCr 2+ :Va:O2- :O 22- esk β esk = 3 yCr :Va:O Cubic spinel (β-spl) 91 .Mn:Va L 0 bcc Cr:O.93265( yCr − yMn ) 4 ][10] Manganosite (mgs) (Mn 2+ .2923T 3 esk SER SER SER GMn 3+ :Cr3+ :O2.− 3H Cr − 3H O = GCR2O3[9] + GHSERCR [7] esk SER SER GCr 2+ :Cr3+ :O 2.008 yCr − 0. Cr 3+ .Cr 3+ ) 2 (O 2.7339T [10] = −9162 + 4.Mn 3+ .− 2 H Mn − 3H O = GMN2O3[8] + 39503 ° ° ° Magnetic contribution[9] p = 0.6 yCr 2+ :Cr3+ :O2esk Tcesk = 308.1533[8] 1 mgs Mn 2+ .2923T 3 esk SER SER GCr 2+ :Va:O 2.− 2 H Mn − 3H O = GMN2O3[8] bxb SER SER GCr 3+ :O 2.8766[8] = 46513.1853365T 0 mgs Mn 2+ .− H Cr − H O = 0.5 yCr − 580 yMn + yCr yMn [−1325 − 1133( yCr − yMn ) 2 − 10294( yCr − yMn ) 4 + 26706( yCr − yMn ) 6 − 28.5GCR2O3[9] + 71549.− H Mn − H O = GMN1O1[8] mgs SER SER GCr 3+ :O 2.− 2 H Cr − 3H O = GCRO0[9] − 2 GHSERCR [7] − 5. Cr 3+ .Thermodynamic assessments ° ° ° ° bcc SER GCr:Va − H Cr = GHSERCR [7] bcc SER GMn:Va − H Mn = GHSERMN[7] bcc SER SER GCr:O − H Cr − 3H O = GHSERCR [7] + 3GHSEROO[7] + 243T bcc SER SER GMn:O − H Mn − 3H O = GHSERMN[7] + 3GHSEROO[7] 0 bcc Cr.)3 ° bxb SER SER GMn 3+ :O2.93845T mgs SER SER GMn 3+ :O2.− 2 H Cr − 3H O = GCR2O3[9] esk SER SER GCr 3+ :Cr3+ :O 2.4 Tcbcc = −311.Mn 3+ :O 2- L Bixbyite (bxb) (Mn 3+ .)1 ° ° ° mgs SER SER GMn 2+ :O 2.3 − 7.27 yMn + yCr yMn [0.48643 − 0.Va)1 (O 2.72035( yCr − yMn ) 2 − 1.5213 − 22.Va L = −709542[9] p = 0.6 yCr3+ :Cr3+ :O2esk β esk = 3 yCr :Cr 3+ 3+ 3+ :O 22- T esk c = 308.Mn:Va L = −20328 + 18.Mn 3+ :O 2- L = −42104.117( yCr − yMn )8 ][10] β bcc = −0.
4 and Aα-spl and Bα-spl in Eq.) 4 ° α-spl SER SER SER GMn 2+ :Cr 3+ :O 2..4 we use the Δ f °GMnCr2O4 value derived from Tsai and Muan[23] using Δ f °GMnAl2O4 from Kim and McLean[25] and the composition of bcc in equilibrium with β-spl and mgs reported by Ranganathan and Hajra[19].105 from Speidel and Muan[12] to optimize Aβ-spl and Bβ-spl in Eq.Cr 2+ )1 (Cr 3+ . 4.2.4. mol.%) and α-spl is used to optimize Aβ-spl and Bβ-spl in Eq. The program minimizes the sum of squared errors between the experimentally determined phase diagram and thermodynamic data and the corresponding calculated data.1T a) Note: All parameters are in SI units: J.− H Mn − 2 H Cr − 4H O = GSPINEL β-spl SER SER GCr 2+ :Cr 3+ :O 2. β-spl To optimize the parameters Aβ-spl and Bβ-spl in Eq. we selectively adjust the relative weight of each experimental data point and exclude data that are inconsistent with the majority of the data points during the optimization procedure.2. The optimization of the thermodynamic parameters is performed using the PARROT module of the Thermo Calc[40] database system.5+61.Mn 3+ ) 2 (O 2.4 and 0 Lliq3+ . As the use of all the experimental data in a simultaneous least square calculation often leads to divergence.− 3H Mn − 4H O = GMN3O4[8] ° Functions GSPINEL = 2 GCR3O4+ 1 GMN3O4B[8] 3 3 −210795. 4.− H Mn − 2 H Cr − 4H O = GTSPINEL α-spl SER SER GMn 2+ :Mn 3+ :O 2.Mn 3+ ) 2 (O 2. Further we use – with lower weights – the temperature of the two phase equilibrium β-spl + liq at X(Cr) = 0.4 and 0 liq L Cr3+ .− H Cr − 2 H Mn − 4H O = GCR3O4+GMN3O4B[8] -GSPINEL Tetragonally distorted spinel (α-spl) (Mn 2+ )1 (Cr 3+ .Mn3+ :O2- . and we use data on the solubility of Cr in MnyCr3-yO4 at T=1873 K under varying 92 .7 cat. Pa: R = 8.69T GTSPINEL = 2 GCR3O4+ 1 GMN3O4[8] 3 3 −200941.Mn3+ :O2. K.9+75.2.− 3H Mn − 4H O = GMN3O4B[8] β-spl SER SER SER GCr 2+ :Mn 3+ :O 2.− 3H Cr − 4H O = GCR3O4[9] β-spl SER SER GMn 2+ :Mn 3+ :O 2. The temperature found from Speidel and Muan[12] for Cr the two phase equilibrium of Mn rich β-spl (Mn = 94.2. 4. 4.) 4 ° ° ° ° β-spl SER SER SER GMn 2+ :Cr 3+ :O2. All these data are given a high weight. PARROT takes into account all sorts of thermodynamic and phase diagram data simultaneously.31451 J mol-1 K-1.Thermodynamic assessments (Mn 2+ . 4.2. Further the melting temperature of β-spl in air found by Speidel and Muan[12] is used to optimize Aβ-spl and Bβ-spl in Eq.
2. 82). The maximum Mn solubility in (Cr1-yMny)2+xO3 is 0.2. p.2.992 at 1203 K in air.2. p.054 in air.67 in air.2.2. 82 are used. p.2.2. 4. β-spl and esk coexist from X(Cr) = 0. 4. p.2.4. prl coexists with esk at T < 513 K in air.[17] shown in Fig.7 is optimized using data on the solubility of Cr in Mn2-yCryO3 from Pollert[14].2.10 data on the solubility of Mn in (Cr1-yMny)2+xO3 from Pollert et al.% at T = 668 K in air. 4.2.2. 80) to optimize Aβ-spl and Bβ-spl in Eq. The two-phase field bxb + α-spl is only found in a very small area at about 1150 K.2.1 and 4. 4. p. 4. Temperature data from Speidel and Muan[12] and Pollert et al.2. 4.9 and 4.5.[14] on the two phase equilibrium β-spl + bxb in air (Fig. 4. 4. 4.2. In Fig.Thermodynamic assessments oxygen partial pressures from Tanahashi et al. 4. β-spl is stable in a large temperature range from T = 513 K to 2243 K and from X(Cr) = 0 to X(Cr) = 0.66 to 0.2.3. 4.3. bxb is stable from T = 694 K to 1154 K in air. Abxb in Eq.2. p.6.23 in air. 4.4.[17] are used (Fig. αspl coexists with β-spl from X(Cr) = 0 at T = 1441 K to X(Cr) = 0. 79.2. 79 shows the temperature dependence of the diffusionless transformation of α-spl to β-spl.2 cat. The dotted line in Fig. 79 to optimize Aβ-spl and Bβ-spl in Eq. At pO2 = 400 Pa it starts to form in equilibrium with β-spl in a small area at the Mn-rich side of the MnOx-Cr2O3 system around T = 1840 K. and data from Pollert et al.4.% at 2243 K in air. 4. Single phase α-spl is stable in a small T–X(Cr) range from T = 1153 K to 1441 K and X(Cr) = 0 to 0. From T = 513 K to 668 K and maximum X(Cr) = 0. This two-phase field expands under more reducing conditions which can be seen in the calculated phase diagram of 93 .65 prl and β-spl coexist in air. 22.214.171.124 Results Phase diagram data: The calculated phase diagram of the pseudo-binary system MnOx-Cr2O3 in air is shown in Figs. and Aα-spl and Bα-spl in Eq. The maximum Cr solubility in Mn2-yCryO3 is 23 cat. 4. 4. and Aα-spl and Bα-spl in Eq.[14] on the phase equilibria α-spl + β-spl and α-spl + β-spl + bxb are used to optimize Aβ-spl and Bβ-spl in Eq.[11] on the temperature dependence of the diffusionless transformation of α-spl to β-spl shown in Fig. 80 the Mn rich part of the diagram is shown in detail.2.2.6. p.2. mgs is not stable in air. prl + bxb is stable in a small area from T = 668 K to 694 K and X(Cr) = 0 to 0. 4.2.8 data on the solubility of Cr in (Mn1-yCry)1-xO from Tanahashi et al.2.175 at T = 1156 K. 79 and Fig. We use data from Holba et al. p. for Amgs in Eq. 4. and for Aesk in Eq.[14] shown in Fig.5. p. 4.
1173 K. p.[18] were not used for the optimization. and Mn in esk + β-spl are presented.2. 4.Thermodynamic assessments the pseudo-binary MnOx-Cr2O3 system at an oxygen partial pressure of 1×10-4 Pa in Fig. Isothermal sections of the Cr2O3-MnO-MnO2 system at different temperatures are plotted in Fig.2. 4.4. 94 . p. and 1273 K in function of log(pO2 ) are compared to the calculated results from this work.[17] on the solubility of Cr in the phases of the two phase equilibria mgs + β-spl and esk + β-spl at 1873 K. Experimental data from Tanahashi et al.2. The data from Bobov et al.2. 83 the stable alloy phases of the system are plotted in addition to the oxides based on the assessment of the binary Cr-Mn system from Lee[9]. p.[18] on the solubility of Cr in the phases of the two phase equilibria mgs + β-spl at T = 1073 K. In Fig. 4. and from Bobov et al.9 (next page). 4. 80.5.6. 82 experimental and calculated solubility data of Cr in mgs + β-spl. In the isothermal phase diagram of the Mn-Cr-O system at T = 1323 K of Fig.
and single solid solution phase equilibria are heavy lines. Three-phase field boundaries are denoted with thin lines. Stoichiometric single phase equilibria are points.9 Isothermal sections of the ternary system Cr2O3-MnO-MnO2 showing oxide and liquid evolution as a function of temperature and composition.Thermodynamic assessments Fig. Dotted lines are tielines.2. 4. 95 .
4. The results from Bobov et al. The oxygen nonstoichiometry of mgs is yet insignificant (Fig. Our calculated T0 line for the diffusionless transformation of α-spl → β-spl is in perfect agreement with experiments by Holba et al.2.2.15] and Ranganathan et al. 80). The calculated dependence of β-spl solid solubility on oxygen partial pressures shown in Fig. 4.[11] (Fig.7.Thermodynamic assessments Thermodynamic data: The calculated enthalpy. °SMnCr2O4 = 116 J mol-1 K-1. 4. For both cases Speidel and Muan[12] mention the speculative character of their phase diagram due to the lack of experimental data. 85. 95) represents the phase relations of the oxides and the evolution of liquid formation. 4. 4. 4.6 Discussion Phase diagram data: Our assessed phase diagram is in rough agreement with the findings from Speidel and Muan[12]. The three-phase regions prl + esk + bxb and bxb + esk + β-spl. β-spl + bxb. and β-spl Δ f °GMnCr2O4 = –1634017 J mol at T = 298.2.15 K. 4.2. Large deviations of our calculated phase diagram from the phase diagram presented by these authors concern the stability of the liquid and phase stabilities at low temperatures. At T = 1873 K we get Δ f °GMnCr2O4 = –34388 J mol-1.2.9 a to c).2. 4.2.3 (p. p.[14. Our assessed phase diagram is in excellent agreement with the findings of Pollert et al.6 (p. At this temperature small oxygen nonstoichiometry of esk is apparent. 83). ° α-spl S = 98 J mol-1K-1. entropy and Gibbs energy of formation of β-spl of the composition β-spl β-spl MnCr2O4 from the elements is Δf °H MnCr2O4 = –1599421 J mol-1.2. For α-spl of the composition MnCr2O4 we calculate Δ f °H α-spl = –1596517 J mol-1. At T=1700 K α-spl is no longer stable and the three-phase regions mgs + α-spl + β-spl and bxb + α-spl + β-spl (Fig.[17].2. Fig. 79).2.2. 82 agrees well with the results from Tanahashi et al. 79). 4.2 (p. but it increases at elevated 96 . p. and the two-phase fields prl + bxb.5. p.9 b).[19] as shown in Figs.338 T with an error of ± 0. 4. The calculated temperature dependence of the -1 Gibbs energy of formation of of β-spl of the composition MnCr2O4 from the oxides MnO and β-spl Cr2O3 is shown in Fig. and Fig. and mgs + β-spl dominate the system in a wide temperature range from T=1200 K to 1900 K (Figs.21 %.[18] on the other hand cannot be reproduced.9 (p. In the β-spl temperature range from 1050 to 1800 K Δ f °GMnCr2O4 from the oxides is given by the term –89167 + 29.2.15 K. and Δf °G α-spl = –1625681 J mol-1 at T = 298.9 a) disappear. 4.
9 d). At T = 2400 K the only remaining stable solid phases are esk and prl (Fig.7 Applications on SOFC Due to the large stability range of β-spl and esk in air it is not realistic to prevent the formation of these unwanted phases under oxidizing conditions at the cathode side of SOFC operated with high Cr alloy interconnects and LSM cathode.2. Even more three phase regions due to increasing liquid formation start to exist at T = 2000 K (Fig. p.2.9 c). and ΔSα β values for the transformation of α-spl to β-spl are very small. 4. At T = 1900 K phase relations become more complex due to incipient melting (Fig.[42] found that the electrical conductivity of chromium manganese spinel increases with increasing Mn-content.9 f). 83.[12].6.6. 84) on Crofer22 APU alloy is expected under SOFC operating conditions. Our assessed ΔHα β and ΔSα β values for the transition of α-hsm to β-hsm compare β favorably with the values reported by Holba et al. Hence. Recently Qu et al.2.9 c). The problem of the application of synthesized Mn-rich α-spl on the interconnect for the purpose of combining a decrease of Cr evaporation with enhanced electrical conductivity is that α-spl will with time tend towards its stable composition of MnCr2O4. The composition of Crofer22 APU alloy is close to the Cr-corner of the Mn-Cr-O phase diagram. 4. The occurrence of other Cr-Mn phases in the protective scales formed during thermal exposure of Crofer 22 APU interconnects is not expected thermodynamically.2. 4.Thermodynamic assessments temperatures becoming apparent at T = 2000 K (Fig.9 d).6. 4. In a thermodynamic view the formation of β-sp with the composition MnCr2O4 (Point A in Fig.2. This is obvious from Fig. Thermodynamic data: β-spl β-spl Our calculated Δ f °GMnCr2O4 value at T = 1873 K is in agreement with the Δ f °GMnCr2O4 value spl derived from Tsai and Muan[22] using Δ f °GMnAl2O4 from Kim and McLean[25].[5] must be kinetically controlled.2. 4.2.2. which is at point A in Fig. 4. 4. 4. p. p. The calculated ΔHα needed for the transformation to take place. 83 associated with decreasing 97 . indicating that only very little energy is 4. At T = 1900 K liquid is formed at the Mn-rich side of the system. and the-three phase fields bxb + β-spl + liq and mgs + β-spl + liq emerge (Fig. the formation of a protective Cr2O3 single phase layer followed by a chromium manganese spinel on Mn bearing interconnects as it is observed by Simner et al.2.
P.S. J. which is very close to the experimental findings of several authors. Lanthanum chromite-based materials for solid oxide fuel cell interconnects. Foger. 4. and the only available -1 β-spl Δ f °GMnCr2O4 values are spread over a range of 31 kJ mol .). H. Fergus. K. Deller. K. Vol. Göttingen. Solid State Ionics. There is a surprising lack of thermodynamic data on β-spl. and Δf°G data for β-spl and α-spl. Bossel (Ed. H. First European Solid Oxide Fuel Cell Forum Proceedings. Hilpert. °S. pp. Technology and Applications. 1994. Quadakkers. Lamm. J. 99. Das. M. 3. in: U.). Hilpert. All features of the system are well described with the optimization of only 8 additional optimization parameters. compositions and transformations of unwanted MnxCr3-xO4 spinel solid solution and eskolaite phases in solid oxide fuel cells under any desired temperature and oxygen partial pressure conditions. 2003. 98 . Zhang.8 Conclusions Due to the lack of inversity and oxygen nonstoichiometry of spinel we chose a model description of β-spl and α-spl without the introduction of vacancies into the spinel structure.P. Handbook of Fuel Cells – Fundamentals. Nickel. Our Thermo Calc[40] dataset resulting from the presented CALPHAD modeling of the Mn-CrO system allows the calculation of phase stabilities. 703. Miller. 1-15. 171. References 1. Kinzel. K. p. Singheiser. Ramprakash. Y.W. 2004. Solid State Ionics. pp. 4. W. Also α-spl will then transform to β-spl and on thermal cycling of the SOFC back to α-spl leading to mechanical stresses that might result in the appearance of cracks. 2.A. 297-310. p. D.Thermodynamic assessments electrical conductivity. L. A.J. John Wiley & Sons. 1037. Gasteiger (Eds. Interaction between chromia forming alloy interconnects and air electrode of solid oxide fuel cells. Recalculating old experiments using new thermodynamic data together with phase diagram data we achieved a description. 2. and we present well-founded Δf°H. Vielstich. in: W. S. R. Badwal. Chichester. Druckerei J. 1997.2.
1993. E. The system manganese oxide-Cr2O3 in air. M. 14. 38. Bull. G. Nevřiva. A 24. L. J. Ceram. Speidel. Nevriva.. B 1. E. Solids. M. Res. 46. 3763-69. A. A. Tetragonal distortion of spinel solid-solutions MnCr2O4Mn3O4. Trans. 12. J. Soc. 1309-1315. 58. Khim. Bobov.J.. 317-425. Phase Equilib. Am. Phase Equilib. G.75O4 solid-solutions. J. A. 19.. 15. Yang. 1980. pp.M. pp. pp. J. Calphad. Rev. E. S. J. Metall. Phase diagram of the Mn2O3-Cr2O3 system in air. Novak. 7.R. G. J.. B-J.. Diff. Zalazinsky. Bull. 149-58. 41. 2003. 1984. Pollert. Y. 1991. pp. pp. A. 11. Magnetic and crystallographic transitions in Sc3+. Phys. Pollert.P. A740-45. Zh.-G.. Balakirev. Cr3+. Gauckler. Chem. Dinsdale.H. J. Mater.N. A thermodynamic evaluation of the Cr-Mn and Fe-Cr-Mn systems. 6. J. pp. J. 21-39. Pollert. ISIJ Int. 2005. S. D. Phase equilibria of the MnO-SiO2CrOx system at 1873 K under controlled oxygen partial pressure. L.P. 8. Nevriva. 152.P.D. M. Stevenson. V.. J. L. Corliss. 562-65.F. 27. 17. Magnetic structure of manganese chromite. 10. Golikov. 1975. Novak. Solid State Chem.G. Tanahashi. 853-60. Rev. P.. Phys. 1919-1933. Yamauchi.I. Z. Fujisawa. pp. A. M. pp. 24.M. pp. Bull. Y. 126.. 1970. pp. 18. 99 . Lee. Ranganathan.J.N. T.W.. 556-65. T. pp. pp. 1962. 750-751 (in Russian). 9. 353-62. Geller. Gauckler. Simner. Sci. Fiz. Phase equilibrium diagram of the system Mn-Cr-O. 16. 10. Anderson. Hallstedt. 1977. B. Povoden. Balakirev. 13. Grundy. A. Xia. 2001.. Alloy oxide equilibria in the Cr-Mn-O system. 1987. S. Hajra. 2006.V.F. 1453-56. Mater. V. and Ga3+ substituted Mn2O3. E. Peculiarities of phase-diagram in the reduction of Me0. SGTE Data for Pure Elements. Mater.Thermodynamic assessments 5. Miscibility gap of MnxCr3-xO4 spinels. Assessment of the Mn-O system.P. 9. Golikov. 15. Thermodynamic reassessment of the Cr-O system in the framework of solid oxide fuel cell (SOFC) research. SOFC performance with Fe-Cr-Mn alloy interconnect. L. J. Furuta. Grundy. N. Hastings.V.. Electrochem.. 1987. Espinosa. 577-78. 1963. 15(4). Muan. M. Soc. 71. 1145-47. pp. pp. Pederson. Res. C.25Mn2. Holba. Chufarov. Phys. pp.
320. 437-445. Cmpd. 24. 89-92. pp. Fujisawa.Cr2O3 solid solution at 1873 K. pp. Steel Res. pp. Am. pp. Sundman. 225-232.M. Furuta. Tsai. Kim. 2000. Control of the manganese-oxygen reaction in pure iron melts.. 2001. Can. 33. pp. Taniguchi. Jansson. Electrical conductivity of the manganese chromite spinel solid solution. 161-76. M. M. C. University Park.. Izv. pp. L. Soc. pp. R. 1966. Weyl. Metall. Metall. The Compound Energy Formalism. Alloy. J. I. Muan. 10B.D.T. M. pp. T. C.. McLean.. B. 25. 66. 2003. 20. 87-92. Jansson. T. 1991. A. Activity composition relations in FeCr2O4-FeAl2O4 and MnCr2O4MnAl2O4 solid-solutions at 1500°C and 1600 °C. S.P. J. Parts I and II. 1979. Barin: Thermochemical Data of Pure Substances. 7-13. N. M. 27. Trans. 1995. Revised effective ionic-radii and systematic studies of interatomic distances in halides and chalcogenides. R.K. Lu. Metallkd. 21. 34. Ceram.Thermodynamic assessments 20. 75. A 32. B. A. J. 1993. J. 23. Weinheim. Soc. 43. 1412-15. Sundman. 1992. Acta Metall. 35. ISIJ Int. 3. Hillert. 1986. Zhu. Soc. Janke.. Paranthaman. VCH Verlagsgesellschaft mbH. Lenev. Biggers: Ph.-O. Activity composition relations in refractory oxide solid-solutions at high-temperatures – the system Cr2O3-Al2O3.D.T. Ceram. L. 751-67. E. Dimitrov. Thermodynamics of iron-manganese aluminate spinel inclusions in steel. 29. Q. Muan. Tsai. A CompoundEnergy Model of Ordering in a Phase with Sites of Different Coordination Numbers. Darken. pp.. Guillermet. J. 1976. 32. A.V. Novokhatskiy. Tanahashi. pp.F. pp. Ceram. H. Z. 1407-11. Met. 1981. 22. B. N. pp.. Phase diagram of system MnO-Al2O3 and thermodynamic properties of MnAl2O4. A. M. Thesis. Nauk SSSR. H.A. Akad. A. 1050-53. Yamauchi. 1966. Payzant. J. Jacob. 2nd Ed. 22. Standard Gibbs free energy of formation of MnO-saturated MnO. Am. A. K. PA.T. 575-84. Pennsylvania State University. B. 1992. 2005. 75. 79(2). Acta Crystallogr. 30. 100 . 31. Trans. Equilibrium phase-relations and thermodynamics of the Cr-O system in the temperature-range of 1500°C to 1825°C. Z. Muan. 1988. Hillert. J. Revision of thermodynamic data on MnO-Al2O3 melts.. 88..S.K.. B. 28.(in Russian). Shannon. 81-87.. 73. Andersson.A.. I. 34. Am. B.Y. Toker. Metall.F. Application of the Compound-Energy Model to Oxide Systems. 26. Hillert. pp. Lam: United States Patent 6039788. D.
Caplan. 4. 114-24. 1985. 1970. L. Ivas.N. V. Sundman. pp. In the La-Cr-O system the Gibbs energy functions of La2CrO6. Qu. The calculated La-Cr phase diagram as well as LaO1. 196. La2(CrO4)3. Cleveland. pp. Jansson. Sundman. A.Thermodynamic assessments 36. and L.5 phase diagrams in pure oxygen. Ågren. Hill. B. Chem. J. air.G. In the La-Cr system reported solubility of lanthanum in bcc chromium is considered in the modeling. Power sources. 16A. Chem. The Thermo-Calc Databank System. W. 37. O'Keefe. and oxygen solubilities in bcc and fcc metals are modeled.M. Emphasis is placed on a detailed description of the perovskite phase: the orthorhombic to rhombohedral transformation and the contribution to the Gibbs energy due to a magnetic order-disorder transition are considered in the model. 39. 153-90. Fraser. Jansson. 2006. D. J. Calphad. Russ. Ivey. 38. and perovskitestructured LaCrO3 are presented. The following standard data of 101 . 41. 40. A. ASM. Phase Equilib. Andersson. Jian. M. 261-66. Phys.J.-O. Gauckler J. V. pp. Trans.3 Thermodynamic assessment of the La-Cr-O system E. Phys. and under reducing conditions are presented.J. Burr. p. Metall. D. J. Thermodynamic properties of alloys of manganese with transition elements of fourth period (Cr Fe Co Ni) and with copper. pp. 1957. M. B. Modification of the Two-sublattice Model for Liquids.5-CrO1. M. Lukashenko. 109-19. (accepted) The La-Cr and the La-Cr-O systems are assessed using the Calphad approach. M. 42. Electrical and microstructural characterization of spinel phases as potential coatings for SOFC metallic interconnects. 1991. Sidorko. 15. Grundy. T. 42. J. Phase equilibria of the La-Cr-O system are calculated at T = 1273 K as a function of oxygen partial pressure. Valigi.A. J. 947-962. A. M. 343-. The electrical properties and defect structure of pure and chromium-doped MnO. B. Povoden. B. Sundman.M.M. A Two-Sublattice Model of Molten Solutions with Different Tendency of Ionization. B. Eremenko. pp.R. Chen . 9(2).. G. 153. Ohio. J. pp. 31. Diff. 1968. Calphad. 1985. Hillert. Solids. in: Ductile Chromium.
As the thermal expansions of LaCrO3-based interconnect and conventional perovskite cathode materials are similar. The liquid phase is modeled using the two-sublattice model for ionic liquids.2 J mol-1 K -1 . V-doped[5] and Zn-doped[6] La1-xCaxCrO3-δ have been considered as promising alternative interconnect materials for SOFC. Gibbs energy of formation from the and ° S 298 K (LaCrO3 ) = 109. The presented thermodynamic assessment of the La-Cr-O system is laying the grounding for extensions to the thermodynamic La-Sr-Mn-Cr-O oxide database that is required to understand the thermodynamics of SOFC degradation by chromium. The lattice stabilities of elements are adopted from Dinsdale[10]. aiming on minimizing the squared errors between 102 .3.oxides° H 298 K (LaCrO3 ) = −73. Diffusion of chromium from the metallic interconnect with high chromium content into the cathode leads to the formation of Mn(Cr. The assessment of the La-Cr-O system using the Calphad approach is based on the recently reassessed La-O[8] and Cr-O subsystems[9]. Δf.7 kJ mol-1 . The decomposition of the perovskite phase by the reaction 1 3 LaCrO3 → La 2 O3 + Cr + O2 (g) ↑ is calculated as a function of temperature and oxygen partial 2 4 pressure: at 1273 K the oxygen partial pressure of the decomposition. Furthermore earth alkaline-containing LaCrO3 has been proposed as a cathode material in a recent study by Jiang et al[7]. recently Sr-. pO2 (decomp) = 10-20.Thermodynamic assessments stoichiometric perovskite are The calculated: Δf.0034 T (kJ mol-1) (T = 1273 K to 2673 K) is calculated. Sr-doped lanthanum manganites (LSM) with the perovskite structure are used as cathode materials in SOFC.403–0.Mn)2O4 spinel and Cr2O3 along with a severe cell voltage decrease[1-4]. thermodynamic. and Crdiffusion into the cathode from LaCrO3-based interconnects is significantly lower than from Cr-containing metallic interconnects. Cation nonstoichiometry of La1-xCrO3 perovskite is described using the compound energy formalism (CEF). oxides. 4.1 Introduction In SOFC. and the model is submitted to a defect chemistry analysis. It is also a starting point for extensions to thermodynamic databases with additional components serving as dopants in LaCrO3 for SOFC interconnect and cathode applications.oxides G(LaCrO3 ) = –72. All available experimental phase diagram.97 Pa. and structurechemical data are critically assessed. the thermodynamic stability of the cathode is particularly important for efficient long-term operation.
[17] found La < 0. modeling of the La-solubility in bcc-structured Cr. whereas Cr is almost insoluble in La[13].13]. Small solubility of La in αCrss was reported [12. but in the graphic presentation of the phase diagram in the same paper Tm(argon) ≈ 2600 K.%[12] or 99.[15] determined the partial enthalpy of mixing in La-Cr liquid with infinite dilution of Cr.13]. Svechnikov et al.% Cr2O3 (T = 2248 K)[18] or 80 at. The solubility of La in αCrss was determined in investigations by Savitskii et al. Furthermore deviations between the data from Tresvjatskiy et al.5 quasibinary system reveal a considerable spread.3.04 at. and the exact value of the oxygen partial pressure was not specified.% in αCrss at T = 1533 K. The solubility of La in αCrss decreases towards lower temperatures.[14] reported a La solubility of 0.5-CrO1.1 at. 4. denoted as αCrss .% at 1983 K. ΔH Cr at T = 1700 K using high-temperature calorimetry. Tm(argon) = 2703 K was reported by Tresvjatskiy et al. No intermetallic phases were found in the La-Cr system[12.3 Literature review of the La-Cr-O system In the LaO1.5. and at 84 at.13] and 3. as well as a large liquidliquid miscibility gap[12.[18] and Berjoan[19] 103 . is of technological interest.% Cr2O3 (T = 2243 K)[18] or 12 at.5 at. The melting temperature of lanthanum chromite in air.% Cr2O3 (T = 2473±20 K)[19] in argon atmosphere on either side of the congruently melting perovskitestructured lanthanum chromite[18-20] (in this study oxides containing Cr(III) and Cr with higher valencies than three are denoted as chromite and chromate respectively).% at T = 2103 K.[12] from T = 1073 K up to the melting of Cr using metallographic and microhardness techniques to be 2. 4.3.4 at. Berezutskii et al.17] .[18].5 system two eutectics were found at 19 at.Thermodynamic assessments experiments and calculation during the optimization of model parameters using the PARROT module of the Thermocalc[11] software.CrO1. This is not surprising as experiments are complicated due to the high investigation temperatures and evaporation of predominantly Cr[25. and Epstein et al. As small additions of rare-earth metals essentially increase the high-temperature corrosion resistance of chromium[16].68 at. Tm(air) = 2773 K was determined by Foëx[21] and by Coutures[20] using a thermal analysis technique described in more detail in earlier publications.% Cr[13] and a monotectic at T = 1983 K[12] or T = 2103 K[14] and 96 at.2 Literature review of the La-Cr system The La-Cr system has a eutectic at T = 1138 K[12.26].% Cr2O3 (T = 2323±20 K)[19]. Experimentally determined special points in the LaO1.[22-24] The melting temperature was measured with optical pyrometers.%[14] Cr.14.
[32]. The peritectic phase diagram proposed by Cassedanne[27] is in gross conflict with the phase diagram data from the other groups. and nonstoichiometry[55-56] along with the investigation techniques used are listed in Table 4. thermodynamics[30.33-35.[9] and Grundy et al.[30] LaCrO4 has been interpreted as a mixed-valent intermediate decomposition product of La2(CrO4)3[30. phase stability[54]. Experimental oxygen solubilities in pure Cr and La were considered in thermodynamic assessments by Povoden et al. whereas experiments on oxygen Lanthanum chromates: The following lanthanum chromates were documented: Berjoan[19] reported that orthorhombic La2CrO6 forms at T > 923 K.46-53].25O2(g) ↑ → (4. solubilities in αCrss are missing.[29] to be −3961±11. The enthalpy of formation of La2(CrO4)3 from the elements at T = 298 K was proposed by Tsyrenova et al.1) at T=1055 K and pO2 =83000 Pa to be −151±8 kJ mol-1.1 (next page).3.3. 104 . La2(CrO4)3 decomposes by 890 −1030 K La 2 (CrO4 )3 ⎯⎯⎯⎯⎯ 2LaCrO3 + 0.43.3.31].5Cr2 O3 + 2. The perovskite phase: Existing experimental data of lanthanum chromite perovskite structure[33-45].2) An enthalpy change of 231 kJ mol-1 was determined for this reaction at the average temperature of T = 960 K.7 kJ mol-1.Thermodynamic assessments may partly originate from differences of the oxygen partial pressure. However these were in significant disagreement with later results obtained by the same author[19]. [28] . which in both studies was not exactly specified. Using differential scanning calorimetry (DSC) he determined the enthalpy change of the reaction 3 2La 2 O3 + Cr2 O3 + O2(g) → 2La 2 CrO6 2 (4. Stoichiometries and thermal stability ranges of lanthanum chromates with complex formulae were reported by Berjoan et al.
4[30] HT (high temperature) .4(kJmol −1 ).1× 10−5[53] Knudsen mass spectrometry La CrO6 = −73.elements ° H 298K = −3845 kJmol−1 this work. 700 . calculated Enthalpy of the formation reaction La 2 O3 +1.5O 2(g) → La 2 CrO6 2 Δ f.2 kJmol-1 this work.oxides ° H 298K aCr2O3 = 1. calculated[29] 2 Δ f.38 kJmol −1[52] CaF2 .2[30] HT .elements ° H 298K ° 2 S 298K La (CrO4 )3 = 516 Jmol−1K −1 this work.oxides ° H 1078K ° LaCrO3 Standard entropy S 298K LaCrO3 = 109. calculated = −62.45 + 0.3. 1273 .based emf Δ °G = −94.1 × 10−4 ± 1.2 Jmol-1K -1 this work. calculated = −3961 ± 11.oxides ° H 298K Δ f.403 − 0. calculated = −73. calculated Enthalpy of the dissociation reaction La 2 (CrO 4 )3 → 2LaCrO3 + 0.29 ± 0.emf Δ °G = −42.9 ± 1.75 kJmol−1 this work. calculated Δ °G = −78.35 kJmol-1 this work.oxides ° H 298K La (CrO4 )3 = −372 kJmol−1 this work.758 + 0. (kJmol−1 ) T = 1090 K 98.5 kJmol −1[49] solid oxide electrolyte .5Cr2 O3 + 2.52 kJmol −1 this work. calculated 139. calculated La (CrO4 )3 La (CrO4 )3 La 2 (CrO 4 )3 2 Δ f.1 Calculated and experimental thermodynamic data of La-Cr oxides Rhombohedral LaCrO3 Standard enthalpy Δ f.oxides ° H 975K LaCrO3 = −1368.elements ° H 298K Δ f.0034T (kJmol−1 ). calculated Δ °G = −44.08530T (kJmol−1 ). this work.1 ± 1.0 kJmol−1 this work.1 kJmol −1[53] Knudsen mass spectrometry Δ G = −72. calculated T = 1273 K T = 1273 K T = 2100 K T = 2100 K ° Δ °G = −30.5Cr2 O3 + 2.06 ± 2.5Cr2 O3 +1.25O 2(g) → La 2 (CrO 4 )3 2 Δ f.calorimetry T = 1350 K 133.calorimetry Activity of Cr2 O3 in LaCrO3 T = 2100 K T = 2100 K La 2 CrO6 Enthalpy of the formation reaction La 2 O3 + 0.7 kJmol-1 this work.05 this work.25O 2(g) 2 ΔH 298K La (CrO4 )3 = 231 kJmol−1[30] and this work. calculated ° 2 S 298K La CrO6 = 330 Jmol-1K -1 this work. fitted 105 .19. calculated Gibbs energy of formation by 1 3 La 2 O3 + Cr2 O3 → LaCrO3 2 4 T = 1273 K Δ °G = −76.based emf Enthalpy increments H − H 298 K .7 kJmol−1 .79 kJmol-1 Drop solution calorimetry in 2PbO × B2 O3[46] LaCrO3 LaCrO3 Δ f.Thermodynamic assessments Table 4. 855 -1073 K[50] CaF2 .11 × 10−4 this work. calculated 94. calculated aCr2O3 = 1.885 K[51] CaF2 .based emf Δ °G = −79.2673 K this work. calculated = −73.002115T ± 0.
simultaneous DSC .XRD 540 ± 2[40] a) HT . HT . this work.25 at 536 K[35] a) calculated from adiabatic shield calorimetry 340 ± (10 .XRD 528 − 533[38] a) HT . DSC. DSC 533 ± 5[40] a) HT .84 at 503 − 583 K [33] calculated from adiabatic calorimetry 277 at 544 ± 1 K[34] a) DSC 403.XRD 523[42] a) starting transition.75[35] a) calculated from adiabatic shield calorimetry a) used for optimization The reported transformation temperatures lie between T = 503 K and 583 K. HT . dilatometry. HT . XRD Enthalpy change of transition (Jmol−1 ) 340.XRD 533[43] estimated from neutron powder diffraction 509[44] DSC.XRD. Table 4. this work.08 J mol-1 and 0. enthalpy and entropy changes of this first-order[44] transition taken from the literature are listed in Table 4.XRD.2 Calculated and experimental data of the orthorhombic to rhombohedral transition of LaCrO3 Transition temperature (K) 540.96 at 503 − 583K[33] calculated from adiabatic calorimetry 0.Thermodynamic assessments Crystal and magnetic structure: LaCrO3 is orthorhombic (o-prv) at room temperature and transforms to rhombohedral structure (r-prv) at higher temperatures[20. calculated 502.microscopy.3.2 along with the investigation techniques used. DSC 550[41] HT . dilatometry 545[41] heating.08 ± 41. The temperatures. The determined enthalpy and entropy changes vary from 277 J mol-1 to 502.40) at 533 ± 5[40] a) DSC 380 at 550 K[41] DSC 310 at 509 K[44] DSC Entropy change of transition (Jmol-1K −1 ) 0.5 J mol-1 to 106 . this work. dilatometry 536 [35] a) adiabatic shield calorimetry. simultaneous DSC .XRD 541[42] a) completed transition.ray photography 550[37] HT .x . HT .3. calculated 0.33-42].63.XRD (air and vacuum) 563 ± 5[36] DTA. thermogravimetry. DSC 535[41] cooling.XRD 533 ± 3[38] a) DTA 543[39] XRD 533[20] HT . calculated 503 − 583[33] adiabatic calorimetry 544 ± 1[34] a) DTA.XRD.5[34] a) calculated from DSC 0.
Höfer and Kock[34] (480 to 610 K) and Satoh et al. and Dudek et al. On the other hand Geller and Raccah[38] as well as Höfer and Kock[34] did not observe the rhombohedral to cubic transition up to T = 1873 K and T = 1823 K respectively using differential thermal analysis (DTA).96 J mol-1 K-1. Gibbs energy of formation: in order to obtain the Gibbs energy of formation of LaCrO3.% in furnace-cooled LaCrO3 annealed at T = 1773 K in air was reported from Khattak and Cox[55]. Enthalpy of formation: Cheng and Navrotsky[47] determined the enthalpy of formation of LaCrO3 by oxide melt solution calorimetry at T = 1078 K.1 Pa using thermogravimetry combined with X-ray diffraction (XRD). Berjoan[19] further reported prevailing of the cubic structure at T = 2173 K. Heat capacity and enthalpy increment data: the heat capacities of LaCrO3 were measured by Korobeinikova and Reznitskii[33] from T = 340 K to 900 K using adiabatic calorimetry.76 cat. This means that the perovskite phase does not decompose within this oxygen partial pressure range.[51]. Chen et al. and Sakai and Stølen[43] (T = 272 K to 1000 K) using adiabatic shield calorimetry.[45] (150 to 450 K) using DSC. LaF3/CaF2/LaF3.% to 1. T = 700 to 885 K.[50]. Sakai et al. Single phase lanthanum chromite with 0.Thermodynamic assessments 0.[53] derived the Gibbs energy of formation of LaCrO3 from the determination of the thermodynamic activity of Cr2O3 in LaCrO3 for the Cr2O3-poor phase boundary of LaCrO3 in the temperature range from T = 1887 K to 2333 K using Knudsen effusion mass spectrometry. LaCrO3. 289 K[45]. Cr2O3/O2. and T = 1273 K respectively. O2/La2O3.[35] (T=100 K to 1000 K) using laser-flash calorimetry.28 cat.[45] (T = 77 K to 280 K) using alternating current calorimetry. La2O3.% excess 107 . Satoh et al. in agreement with Berjoan[19] (T = 1923 ± 20 K) using dilatometry. Chemical stability: Nakamura et al.[49] measured electromotive force (emf) of the solid oxide galvanic cell Pt/Cr.38 cat. whereas Coutures et al. and its oxgen nonstoichiometry is negligible. Peck et al. Cr/Pt at 1273 K.[54] reported no weight loss of lanthanum chromite at T=1273 K from pure oxygen to pO2 =10-16. or 295 K[46]. A magnetic order-disorder transition was documented to occur at T ≈ 287 K[35]. Azad et al. Cation nonstoichiometry and defect chemistry: Maximum excess Cr in single-phase La1-xCrO3 of 0.[37] and Momin et al. LaCrO3/MgO-stabilized ZrO2/Cr2O3.[20] reported T = 1923 K using high-temperature x-ray diffraction (HT-XRD). A transformation from rhombohedral to cubic structure at a temperature close to T = 1300 K was reported by Ruiz et al. Enthalpy increments of LaCrO3 at T = 1090 K and 1350 K were measured by Suponitskii[30] using a high-temperature heat-conducting calorimeter.[41]. Chen et al. Pt in pure oxygen from T = 855 K to 1073 K.[52] measured emf of Pt.
58-60]. However n-type conductivity was not approved by any further study. thus the presence of interstitial Cr in reduced chromite was proposed.[56] observed an intensity decrease of the high frequency band in a Raman spectrum of lanthanum chromite measured after annealing the phase in vacuum at T = 1273 K.0 ×103 Pa to pO2 = 2. The transition from reduced to stoichiometric chromite was accompanied by a decrease of about 0.59] agree that the electrical neutrality is maintained by holes and lanthanum vacancies.1% in weight. Ruiz et al. the same as reported in an earlier study[25].[58] measured the isothermal electrical conductivity of an equilibrated La1-xCrO3-Cr2O3 mixture with 5 vol. Iliev et al. They observed an extraordinarily slow equilibration of the samples: More than four months were required to measure the electrical conductivity at equilibrium state. On the other hand a slope of pO2 1 4 from T=700 K to 1300 K and purely intrinsic conductivity > 1600 K stated by Shvaiko-Shvaikovskii et al. This feature was assigned to a reduced number of Cr4+ due to partial removal of oxygen during the annealing of the originally lanthanum-deficient perovskite phase.% excess Cr2O3 from T = 1573 K to 1673 K from pO2 = 1. Several groups[58.[37] reported that the ionic transport number in lanthanum chromite is less than 0. in line with the results from thermogravimetry[54]. and that the carrier is the hole in lanthanum chromite[25. Interpretations of the defect chemistry of the perovskite phase were made from electrical conductivity measurements: the electrical conduction in lanthanum chromite is almost purely electronic[37. the electrical conductivity being 2 proportional to pO2 −3 8 .57]. In contrast to the other authors Shvaiko-Shvaikovskii et al. resistivity and thermo-emf at pO2 = 1Pa and pO = 102 Pa . Akashi et al.0 ×104 Pa .[58] reported that concentrations of lanthanum vacancies and holes slightly increase from T = 1550 K to 1700 K. affirming the lack of oxygen vacancies in the structure.Thermodynamic assessments Cr was prepared at T = 1773 K in a pure oxygen atmosphere[56]. 108 .[57] is inconsistent with the findings from Akashi et al.[57] deduced n-type conductivity from measurements of transport number. The conductivity was proportional to pO2 3 16 . Akashi et al.[57] and Meadowcroft[25] proposed the occurrence of chromium vacancies instead of lanthanum vacancies.05 % up to T = 1250 K.[58] ShvaikoShvaikovskii et al.
and to optimize their model parameters with phase diagram data[19. Cr2O3.15 K and 10 Pa.3) SER H x is the standard enthalpy of the stable state of element x at 298. we reassess the oxygen-solubility in Cr(bcc) using the model (Cr)(O.3. These chromates can be interpreted as intermediate products in the 109 . Due to the lack of experimental data the oxygen solubility in αCrss was modeled as an ideal extension of the oxygen solubilities in pure La and Cr. The Gibbs energy of the end-member (Cr)(O)1.Va)1. and αCrss is then given by the two-sublattice description (La.O)3. the zeroth-order.5 is defined as 3 2 3 ° gas[10] G + A + BT 4 O2 ° SER SER G(Cr)(O)1.La:Va was given a positive value. mixedvalent chromates mentioned above. and B and a regular interaction parameter 0 LCr:O. The formation of chromates that contain mixed Cr valences may be explained by gradual reduction of Cr6+ in La2CrO6 as the temperature increases.32].3.5. Eq. We chose the solubility values from Svechnikov et al.4 Thermodynamic modeling and optimization Metal phases: In order to account for the solubility of La in αCrss . and O2 in proper stoichiometries and A + BT parameters that were fitted to the enthalpy of formation from the oxides.3.Va were optimized with the same experimental data[9].O)1. using the PARROT module of the Thermocalc software[11] A was given the fix value 0 for the reasons discussed in an earlier paper[9]. 5 [10] A and B are adjustable parameters.[14] for its optimization. For the reasons discussed recently[62].5 − H Cr − H O = °GCr(bcc)[10] + (4.Thermodynamic assessments 4. The thermal stability of La2CrO6 is slightly influenced by the thermodynamics of the intermediate. Solid oxides: Lanthanum chromates: The Gibbs energy function of La2CrO6 was based on the sum of the Gibbs energy functions of La2O3.[9] described the solubility of oxygen in Cr(bcc) using the model Cr(Va. Povoden et al. compositionindependent interaction parameter[61] 0 Lbcc Cr.Cr)(Va. In order to refine the model parameters of La2CrO6. 4. as these data are more comparable to solubilities in other rare earths-transition elements systems.1 as well as thermal stability data. it was thus necessary to consider these mixed-valent chromates in a provisional version of the thermodynamic La-Cr-O database in spite of their arguable stoichiometries.5.
[35] and enthalpy increment-data 110 .(1. GVCR4O and GLCR4O stand for the Gibbs energy functions of the completely oxidized neutral endmember. GRPRV denotes the Gibbs energy function for stoichiometric rhombohedral perovskite. The enthalpy of formation from the elements[29] was not used as it is a calculated value.Thermodynamic assessments scope of a sluggish decomposition of La2CrO6. We go along with the interpretation of LaCrO4 being an intermediate reaction product during the decomposition of La2(CrO4)3 by Eq.5 x) La 2 O3 + La1. The simplified decomposition reaction reads 1+ x 1. and C are optimized using the enthalpy of formation from Cheng and Navrotsky[47].3. GVCR4O and GLCR4O are set equal for orthorhombic and rhombohedral perovskite.5) The parameters A. heat capacity-data obtained by adiabatic calorimetry from Sakai and Stølen. °GLaCrO3 is given by ° r-prv SER SER SER GLaCrO3 − HLa − H Cr − 3H O = °GLa3+ :Cr3+ :O2− = GRPRV = 1° 1 GCr2O3 [9] + °GLa2O3 [8] + Gmag + A + BT + CT ln T 2 2 (4. and consequently ambiguous stoichiometries of mixed-valent intermediate chromates. The superscripts o-prv and r-prv stand for Gibbs energy expressions that have different values for orthorhombic and rhombohedral perovskite. These lanthanum chromates with conflicting stoichiometries[19.3.32] are not included in the presented thermodynamic database. The perovskite phase: The following denotations are used in this section: the superscript prv is written if the regarding Gibbs energy expression is the same for both orthorhombic and rhombohedral perovskite.3. which starts at T = 1153 K[19.2 and do not include this phase in the modeling. activity-data of Cr2O3 in LaCrO3 from Peck et al.32] (4. The Gibbs energy function of La2(CrO4)3 was formulated using the same strategy as for La2CrO6.x CrO3 + O2 (g) ↑ 2 2 mixed-valent chromates → La 2 CrO6 ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ [19.5 .32] and is completed at T = 1473 K[32] or 1523 K[19].[53]. B. The model parameters were fitted to the experimental enthalpy and temperature of decomposition[30]. Stoichiometric perovskite: The Gibbs energy function of stoichiometric rhombohedral r-prv LaCrO3 with the sublattice formula (La3+)(Cr3+)(O2-). 4.4) Slight differences of the oxygen partial pressure during experiments may be reflected by a variable extent of Cr-reduction.
A phase diagram with congruent melting of lanthanum chromite and two eutectics[18.40.Va)(Cr3+.5 system required for SOFC applications due to diversities between the model descriptions of lanthanum chromite and lanthanum manganite[65]. The rhombohedral to cubic transformation at high temperatures is not considered in the model.40] and entropies[34.35] of transition having been obtained by combined investigation techniques and being internally most consistent. Thus these data were excluded from the optimization.42].58] measurements.Cr4+)(O2-)3.35.5-MnO1. as there is no existing thermodynamic data for this transition. 112-114) resulted in negligible concentrations of Va on the B-site and the anion sublattice.3 (pp.19] cannot be reproduced by using the emf-experiments[49-52]. While this model results in a satisfying reproduction of experimental data. 111 .5-CrO1.38. Thus the defects in n-type conducting[57] lanthanum chromite are ambiguous and were not considered in the model. Cation-nonstoichiometric perovskite: To choose a proper model for nonstoichiometric perovskite the following considerations are made: the formation of interstitial Cr in lanthanum chromite proposed by Shvaiko-Shvaikovskii et al.Va)(Cr3+.Cr4+. The optimization of selective model parameters listed in Table 4.Va)3.64]. and the perovskite formula essentially remains La1-xCrO3.Thermodynamic assessments measured at high temperatures[30].Va)(O2-. A+BT parameters of the low-temperature orthorhombic perovskite phase were optimized with those temperatures[34. and oxygen nonstoichiometry can be excluded from thermogravimetry[54] and electrical conductivity[37. This means that the simplest sublattice model to describe cation nonstoichiometric La1-xCrO3 reads (La3+.3.35. enthalpies[34.[57] is unlikely due to the densely-packed perovskite structure. B-site vacancies are energetically less favored than A-site vacancies in the perovskite structure[63. irreconcilable trouble is encountered at the extension to the LaO1. These are solved by allowing Va on the B-site and the anion sublattice of lanthanum chromite just like in lanthanum manganite[65] leading to the appropriate sublattice formula (La3+.
Va q.Thermodynamic assessments Table 4.La3+ :O2.La:Va = 83500 p = 0.5 yCr [9] β bcc = −0. q = 3 yLa3+ + 2 yCr 2+ + 3 yCr3+ ° ° ° ° ° ° liq SER GLa3+:Vaq.4[9] Tcbcc = −311. Cr 3+ ) p (O 2.− 2 HLa − 3H O = GLA2O3LIQ[8] liq SER GCr 2+ :Vaq. Cr 2+ .5T [28] 2 4 Lbcc Cr:Va.− 2 H Cr − 3H O = 5GCROLIQ − 179638 + 79.La3+:O2..− H Cr = GCRLIQ[10] liq SER GCr3+:Vaq.Vaq.3.+ qyVa . Cr)(Va.23T + (65393 − 23T )( yCr 2+ − yLa3+ ) Cr Lliq 2+ .− HLa = GLALIQ[8] liq SER SER GLa3+:O2..Vaq.O = −355151.= 121000[9] Cr Cr Lliq 2+ .− 2 H Cr − 2H O = 2GCR1O1_L[9] Interaction terms Lliq 2+ :O2.= −101850 − 39016( yCr3+ − yLa3+ ) Cr Bcc A2 phase (La. O)1.= −101850 − 39016( yCr 2+ − yLa3+ ) Cr Lliq 3+.)q p = 2 yO2.923T [9] liq SER SER GCr 2+ :O2.5 ° ° bcc SER GCr:Va − HFe = GHSERCR [10] bcc SER GLa:Va − HLa = GLABCC[10] 3 SER 3° bcc SER GCr:O − H Cr − H O = GHSERCR [10] + G (O 2(g) )[10] + 113..− H Cr = 2GCRLIQ[10] − GCR2O3_L[9] − 3GCR1O1_L[9] liq SER SER GCr3+:O2.3 Model descriptions and Gibbs energy functionsa) Liquid (liq) (La 3+ .= 61397 − 5.422 ° Lbcc Cr.La3+ :Vaq.= Lliq 3+ :O2.17755T 2 4 3 SER 3° SER ° bcc GLa:O − HLa − H O = GLABCC[10] + G (O 2(g) )[10] − 855000 + 142.008 yCr [9] 112 .
5 °G(O2(g) )[10] + Gmag o-prv SER SER GLa3+:Cr4+ :Va − HLa − HCr = 5 6GS4O[72] − GS3V[72] +1 6GS4V[72] +GOPRV − 1. Va)3 ° ° ° o-prv SER SER SER GLa3+ :Cr3+:O2.Thermodynamic assessments La1-xCrO3 perovskite (La 3+ .5 °G(O2(g) )[10] + Gmag ° o-prv SER SER GVa:Cr3+:O2.5GVVV[65] − 2GLCR4O − 0.Va:O2.)12 ° SER SER SER 4 3 2 GLa3+ :Cr6+:O2.35056T + Gmag ° o-prv SER r-prv SER GVa:Cr4+:Va − HCr = °GVa:Cr4+:Va − HCr = = 2GVCR4O + 1 3GVVV[65] − 4 3GLCR4O − °G(O2(g) )[10] + 4.− HLa − HCr − 3HO = 5 6 GS4O[72] +GOPRV − GS3V[72] + 1 6GS4V[72] + Gmag ° r-prv SER SER SER GLa3+ :Cr4+:O2.− HLa − HCr − 3HO = GRPRV + Gmag o-prv SER SER SER GLa3+ :Cr4+:O2.Va:O2.5GVVV[65] − 2GLCR4O + 0.75 °G(O2(g) )[10] − 1.− HLa − HCr − 3HO = 5 6GS4O[72] +GRPRV − GS3V[72] + 1 6GS4V[72] + Gmag ° ° ° o-prv SER SER GLa3+:Cr3+ :Va − HLa − HCr = GOPRV − 1.75 °G(O2(g) )[10] − 1.− 2HLa − HCr − 6HO = GLA2CRO6 6+ La CrO La 2 (CrO4 )3 (La 3+ )2 (Cr 6+ )3 (O2.5GVCR4O +0.41263T + Gmag ° o-prv SER SER r-prv SER SER GVa:Cr4+:O2.5GVVV[65] − 2GLCR4O + 0.41263T + Gmag ° r-prv SER SER GVa:Cr3+:O2.= Lprv3+:Cr4+.75 °G(O2(g) )[10] − 1.5 °G(O2(g) )[10] + 4.Va)(Cr 4+ .5GVCR4O +0.Cr3+ k = O-2.= 250000 La La Magnetic contribution Tco-prv = Tcr-prv = 291.75 °G(O2(g) )[10] − 1.894 yi:j:k SER SER SER 2 GLa3+ :Cr6 :O2.− HLa − HCr − 3HO = GOPRV + Gmag r-prv SER SER SER GLa3+ :Cr3+:O2.− HCr − 3HO = = 2GVCR4O + 1 3GVVV[65] − 4 3GLCR4O + 0.35 yi:j:k i = La 3+ ..5 °G(O2(g) )[10] + Gmag r-prv SER SER GLa3+:Cr3+ :Va − HLa − HCr = GRPRV − 1.5 °G(O2(g) )[10] + Gmag ° r-prv SER SER GLa3+:Cr4+ :Va − HLa − HCr = 5 6GS4O[72] − GS3V[72] +1 6GS4V[72] +GRPRV − 1.35056T + Gmag Interaction term Lprv3+:Cr3+.Cr3+ .− HCr − 3HO = GRPRV + 1.5GVCR4O +0.5GVCR4O +0.5GVVV[65] − 2GLCR4O − 0. Va)(O2.)6 ° prv β o-prv = β r-prv = 0.− 2HLa − 3HCr − 12HO = GLA2CR3O12 La (CrO ) 113 . Va La .− HCr − 3HO = °GVa:Cr4+:O2.41263T + Gmag ° o-prv SER GVa:Cr3+:Va − HCr = GOPRV + 1.Va j = Cr 4+ .Chromates La 2CrO6 (La 3+ )2 (Cr 6+ )(O2.41263T + Gmag ° r-prv SER GVa:Cr3+:Va − HCr = GRPRV + 1.− HCr − 3HO = GOPRV + 1.
5GCR2O3[9] + 0.38T − 47.Thermodynamic assessments Functions Perovskite Stoichiometric orthorhombic perovskite GOPRV = 0. and yk is the site fraction of O2.5T La 2 (CrO4 )3 GLA2CR3O12 = GLA2O3A[8] + 1.31451 Jmol K −1 −1 Using the compound energy formalism (CEF)[66-68] the molar Gibbs energy of La1-xCrO3 reads ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ° prv prv Gm = ∑∑∑ yi y j yk °Gi: j:k + RT ⎜ ∑ yi ln yi + ∑ y j ln y j + ∑ yk ln yk ⎟ + EGm + Gmag (4. K.5GCR2O3 − 1.01T − 0.00307T 2 + 190000T −1 +0.31451 J mol-1 K-1.7186T − 47.68T ln T Neutral nonstoichiometric perovskite endmembers GS4O[72] = −597648 + 213.5GCR2O3[9] + 0.5GCR2O3[9] + 2.25 °G(O2(g) )[10] GS3O[72] = −472704 + 191. mol.5GLA2O3A[8] + 0. The second-last term describes the excess Gibbs energy of mixing due to interactions of ions in the mixture.6) i j k i j k where yi is the site fraction of Va and La3+ on the A-sublattice.5GCR2O3[9] − 73591 + 2. R = 8.56T ln(T ) − 0.5GCR2O3[9] + 0.9T − 47.68T ln T Stoichiometric rhombohedral perovskite GRPRV = 0. Cr4+ and Va on the B-sublattice.25 °G(O2(g) )[10] − 371557 + 205T a) All parameters are in SI units : J. R = 8. The third-last term accounts for the configurational entropy of mixing.5GLA2O3A[8] + 0.56T ln(T ) − 0. These are accounted for by the 114 .3.38T − 0. yj is the site fraction of Cr3+.75 °G(O2(g) )[10] − 72615 − 4.25 °G(O2(g) )[10] − 200000 Perovskite reference[72] GS4V[72] = −607870 + 268.5GCR2O3[9] + 0.00307T 2 + 190000T −1 +0.25 °G(O2(g) )[10] La 2CrO6 GLA2CRO6 = GLA2O3A[8] + 0.5GCR2O3[9] GVCR4O = 0.00307T 2 + 190000T −1 +0.25 °G(O2(g) )[10] − 291802 − 250T GLCR4O =1 3GLA2O3A[8] + 0.56T ln(T ) − 0.5GCR2O3[9] − 73931 + 3.and Va on the anion sublattice of the perovskite A1-xBO3.
) and °G(La3+ )(Cr 4+ )(Va) from Povoden et al. For the magnetic part of the Gibbs energy a magnetic ordering-model proposed by Inden[69] and simplified by Hillert and Jarl[70] was used. A short summary of this model can be found in Chen et al.[71] The magnetic parameters Tc and β were fitted to the C p data around the magnetic transition temperature from Sakai and Stølen[35]. Fig. with the 8 Cr-containing compounds being the corners of the cube.1 Representation of the Cr-containing part of the model for nonstoichiometric lanthanum chromite.Thermodynamic assessments optimization of interaction parameters. These endmembers of 3 3 nonstoichiometric perovskite have been fixed firmly by a sufficient number of consistent experiments in 3 the LaO1.3.[72].3. Fig.3 (pp. 112-114). The thin lines margin the neutral plane. The parameters of the compound energy formalism are the Gibbs energies of the not necessarily neutral 12 end-member compounds °Gi: j:k . 4. The last term designates the magnetic contribution to the Gibbs energy.5 3 system [72] . The neutral compounds used for the optimization are marked by the black spots. 115 .) and °G(La3+ )(Cr 4+ )(Va) are given in Table 4.3. Only compounds inside the neutral plane can exist on their own. ° prv prv G(La3+ )(Cr 4+ )(O2. Thus the authors prv prv adopted °G(La3+ )(Cr 4+ )(O2.1 is a visualization of the Cr-containing part of the model the authors use to describe the cation nonstoichiometry of lanthanum chromite.5-SrO-CrO1. 4.
°G(Va)(Va)(O2. and °G(Va)(Va)(Va)3 from Grundy et al. As cation diffusion in La1-xCrO3 is extremely slow even at high temperatures.3.3. Furthermore the temperature dependence of lanthanum vancancy and hole concentrations from Akashi et al.3. °G(Va)(Cr 4+ )(O2. 4.r-prv SER SER o-prv. ° prv G(La3+ )(Cr3+ )(Va) results from a reciprocal relation which was set zero in analogy to Grundy et 3 al.Thermodynamic assessments The neutral Cr4+ -containing endmembers 2° 1 ⎛ 2 2 1 1⎞ GVa:Cr 4+ :O2− + °GVa:Cr 4+ :Va + 3RT ⎜ ln + ln ⎟ 3 3 ⎝ 3 3 3 3⎠ 1 1 gas = GVCR4O = °GCr2O3 [9] + °GO2 [10] + Gmag + A + BT 2 4 prv SER SER GVaCrO2 − H Cr − 2 H O = ° (4.with Va on the anion sublattice.r-prv GLaCrVa3 − HLa − H Cr = °GLa3+ :Cr3+ :Va = GLaCrO3 − (4. °G(Va)(Cr3+ )(Va) . the 12 endmembers of the compound energy formalism of the perovskite phase are defined.[65] were used to obtain ° prv prv prv prv G(Va)(Cr3+ )(O2. [65] : 3° G (O2(g) )[10] 2 ° o-prv.) .3. 3 3 3 [65] .3. The configurational entropy3 3 3 3 term in Eq.5 to 4.7 describes random mixing of O2.7 and A of Eq.8 and adopting the Gibbs energies of the remaining endmembers ° prv prv prv prv G(La3+ )(Va)(O2.) . The parameters A and B of Eq. and °G(Va)(Cr 4+ )(Va) . 4.8) 1 1 1 gas = GLCR4O = °GCr2O3 [9] + °GLa2O3 [8] + °GO2 [10] + Gmag + A 2 3 4 prv GLa2 3CrO3 − ° and reciprocal relations which were set zero in analogy to Grundy et al.3.3.[58] was considered in the optimization. 4. In Eq. The 116 .8 are optimized using experimental data of excess Cr in perovskite[56].) .) . 4. 4.3.7) and 2 SER 2 1 ⎛ 2 2 1 1⎞ SER SER H = °GLa3+ :Cr 4+ :O2− + °GVa:Cr 4+ :O2− + RT ⎜ ln + ln ⎟ − H Cr − 3H O 3 La 3 3 ⎝ 3 3 3 3 ⎠ (4. the Croverstoichiometry in a furnace-cooled specimen reported by Khattak and Cox[55] does most likely not represent the overstoichiometry at an intermediate temperature and was not used for the optimization.8 it describes random mixing of La3+ and Va on the A-site.9) Using Eqs.3. °G(La3+ )(Va)(Va) .
as were the two sub-regular interaction parameters.Va:Cr4+ :O2.La3+ :O2.= 0 Lliq 2+ . Furthermore the two regular interaction parameters 0 Lliq 3+ .and the two subregular 1Lliq 3+ .14. and the congruent melting temperature of the perovskite phase from Coutures et al.5 Results and Discussion The La-Cr system: The calculated phase diagram of the La-Cr system is presented in Fig.3. The liquid phase: The two-sublattice model for ionic liquids[73.Thermodynamic assessments introduction of positive interaction parameters 0Lprv3+ .Vaq-)q. the temperature of the eutectic at the Cr-rich side from Berjoan[19].2 (next page).13. Using the following data for their optimization led to the lowest error between experiments and calculation: the composition and temperature of the eutectic at the La-rich side and the composition of the eutectic at the Cr-rich side in the oxide LaO1. ΔH Cr [15] in La-Cr liquid were used to optimize the temperature-dependent regular 0 Lliq 2+ . Higher oxidation states are unlikely to exist in the liquid at normal oxygen partial pressures.5 system from Tresvjatskiy et al. 4.and 0Lprv3+ . Berjoan[32] and Tresvjatskiy et al. It was assumed that the interactions between Cr2+-La3+ and Cr3+-La3+ are of the same order of magnitude in the oxide melt. thus the two regular interaction parameters were set equal to each other.14] at the eutectic and monotectic in the metallic La-Cr system and the partial enthalpy of mixing of Cr. 117 .CrO1.La3+ :O2.[18].= Cr Cr Cr 1 liq Cr 2+ .5.La3+ :Va Cr Cr interaction parameters to account for interactions between La and Cr.[18] did not specify the value of the prevailing oxygen partial pressure during their phase diagram experiments conducted in an argon atmosphere. It was based on the liquid descriptions of the binary subsystems.[20] and Foëx[21]. The chromium species considered in the liquid are Cr2+ and Cr3+.La3+ :O2- L were optimized.3. The liquid is thus given by the model description (La3+.La3+ :Va and subregular 1Lliq 2+ .Cr2+. we defined pO2 = 1 Pa. 4.Cr3+)p(O2-. As a value of the oxygen partial pressure is required for the optimization. The experimentally determined temperatures and liquid compositions[13.Va:Cr3+ :O2.that were given La La the same values circumvents too high Cr4+ contents at low temperatures that would be in conflict with the experiments.17]. together with experimental phase diagram data[12.La3+ :O2.74] was used for the description of the liquid phase of the La-Cr-O system.
The calculated enthalpies of mixing are shown in Fig. of 2 ×10-3 at.Thermodynamic assessments Fig. the lowest temperature of stable γ La ss . The model description of the bcc phase results in a tiny solubility of Cr in La(bcc). denoted as γ La ss . which is tantamount to a small solubility of La in αCrss in agreement with the experiments [14.3.% at 1134 K.3 (next page) together with the experimentally determined value[15] that is well reproduced by the calculation. 118 . The positive value of 0Lbcc Cr.2 Calculated phase diagram of the La-Cr system with data from the literature included (symbols). which further decreases as a function of increasing temperature. 4.17] .La:Va used to model the bcc phase results in a large miscibility gap between the La-rich and Cr-rich metals. 4.3.
4. The higher value was favored by Dinsdale[10] and is adopted in this study. The La-Cr-O system: Phase equilibria: Calculated LaO1. in air at 119 .3 Calculated partial enthalpies of mixing of La and Cr in La-Cr liquid. A satisfying reproduction of the experimental data was obtained by considering a moderate temperature dependence of 0 liq Cr 2+ . whereas the lower melting temperature was chosen by Savitskii et al.Thermodynamic assessments Fig.25 and T ≈ 5000 K that is of course unphysical.5.[12] and Svechnikov et al.La3+ :Va L and 1Lliq 2+ . Considerable deviations of the calculated liquidus from experiments at the Cr-rich side of the system can be ascribed to the problem of two different melting temperatures for Cr cited in the literature.CrO1.5 phase diagrams in pure oxygen at pO2 =105 Pa. which are T = 2180 K and 2130 K.La3+ :Va .[15] at T = 1700 K included (symbol with error-bar). with the experiment from Berezutskii et al.[14]. This is unfortunately associated with Cr an inverse liquid-liquid miscibility gap with a minimum at X(Cr) = 0.3. and integral enthalpies of mixing as a function of composition.
air atmosphere.[56] Be it that the reported thermodynamic data of La2CrO6[19] and La2(CrO4)3[30] are correct. and the liquid stability increases considerably at the Cr-rich part of the system 120 .Thermodynamic assessments pO2 = 21278 Pa. On the other hand a significant amount of Cr3+ in the ionic liquid is reduced to Cr2+ under reducing conditions. A decrease of Cr4+ during annealing of an originally lanthanum-deficient perovskite phase under reducing conditions is predicted by the model. Due to the ambiguous oxygen partial pressure of phase diagram experiments[18. lanthanum chromite is expected to be metastable at room temperature. and orthorhombic perovskite is stable only at pO2 ≤102 Pa.4 Calculated phase diagrams of the LaO1. La2CrO6 is stable within a wide temperature-range in pure oxygen. Fig.5 system in pure oxygen. Analogous to Fe in the La-Fe-O system[62] this oxidation of Cr2+ to Cr3+ governs shifts of eutectic compositions and temperatures and the increase of the melting temperature of the perovskite phase on increasing the oxygen partial pressure. and under reducing conditions at pO2 = 1 Pa representing the typical oxygen partial pressure in argon atmosphere are shown in Fig. whereas it does not form in air and argon atmosphere.19] and the conflicting data on the melting temperature of lanthanum chromite in argon atmosphere[18] the presented liquid description is rather tentative.4 together with experimental data[18-21]. and under reducing conditions representing argon atmosphere at pO2 = 1 Pa with experimental data included (symbols).3.5-CrO1. 4. reflected by the disappearance of Cr overstoichiometry. 4.3. Excess Cr in lanthanum chromite is favored at high oxygen partial pressures. This is in line with the interpretations of Raman spectra from Iliev et al. Under oxidizing conditions Cr3+ is favored over Cr2+ in the liquid.
[9] was obtained using the new model description (Cr)(O.3. In Fig.Va)1. At pO2 = 10-34.3.3 (pp. Despite this discrepancy we did not go for an alternative liquid model for the sake of consistency with our previously assessed systems. 4.5 Calculated phase equilibria of the La-Cr-O system at T = 1273 K as a function of oxygen partial pressure.3. The liquid description using the twosublattice model for ionic liquids also resulted in a significantly larger decrease of the melting temperature of lanthanum chromite at pO2 ≈ 1 Pa than the given values in argon atmosphere[18].3.2 (p. 106). 4.3.5 calculated phase equilibria of the La-Cr-O system at T = 1273 K are shown as a function of oxygen partial pressure. 105-107) is a compilation of the Gibbs energy functions and model descriptions of the phases in the La-Cr-O system obtained in this study. 105). Fig.Thermodynamic assessments leading to a considerably lowered eutectic temperature. 121 . The same oxygen solubility in Cr as in the assessment by Povoden et al. Calculated and experimental data on the orthorhombic to rhombohedral transition of LaCrO3 are listed in Table 4.1 (p. Table 4. Thermodynamic data: Calculated thermodynamic data of solid oxides are listed together with experimental data from the literature in Table 4.04 Pa metallic liquid forms at the lanthanum-rich side of the phase diagram.5. It is obvious that no mutual solubilities of La and Cr in bcc metal in equilibrium with oxides are expected.
Fig. whereas the calculated standard enthalpy of formation from the elements[29] was rejected. The use of C p -data from Sakai and Stølen[35] along with enthalpy increment-data from Suponitskii[30] to optimize the 122 . and/or by significant deviations between the thermodynamic standard data used for the calculation of the enthalpy of formation from the elements[29] and assessed values[8-10].3.Thermodynamic assessments Lanthanum chromates: Testing an optimization of model parameters of La2(CrO4)3 by using all available thermodynamic data[29. bearing in mind the high degree of uncertainty of the resulting description. The perovskite phase: the calculated heat capacities of LaCrO3 are compared with experiments from the literature in Fig. 4.6. Anyway the model parameters were fitted to the experimental data[30]. The dashed line marks the temperature of the o-prv ↔ r-prv transition. The considerable error might be explained by experimental difficulties to reach equilibrium at the low investigation temperatures. The calculated C p -curve extrapolates well to high temperatures.3.31] resulted in gross disagreement between optimized and reported values.6 Calculated heat capacities of LaCrO3 (solid curve) as a function of T with experimental data included (symbols). 4.
p. Due to the consistency between both groups of calorimetric experiments[30. p. In this case the emf depends on the activity 123 . The calculated C p -peak at T = 290 K reflects the temperature of the magnetic order-disorder transition. The C p -anomaly is equally well reproduced by the model[69.3.3. It needs to be clarified why all of the emf-measurements are problematic: Azad et al. For the sake of compatibility with the recent assessment of the La-Fe-O system[62] we chose p = 0. Yet it is obvious that the CaF2based emf-technique is neither suitable for the determination of thermodynamic data of lanthanum chromite.4.70] using p = 0. 105). A possible explanation is found in a study by Akila and Jacob[75]: Fine precipitates of CaO can form on the surface of CaF2 in water. 4. 105. and hcp is not available in the literature. As CTlnT was set equal for o-prv and r-prv. Experimental enthalpy increments[30] are well reproduced by the calculation (see Table 4. Two values for the magnetic parameter p are possible depending on the crystal structure.10) are listed as a function of temperature together with data from the literature [49-53] in Table 4.1.28 and p=0.[50] stated that the Gibbs energy of formation of LaCrO3 cannot be studied properly using the solid oxide electrolyte method due to experimental difficulties in measuring the low oxygen potentials encountered in a mixture of coexisting LaCrO3-La2O3-Cr. p=0.35] the term CTlnT is fixed firmly. fcc. The calculated Gibbs energies of the formation of LaCrO3 from the oxides 1 La O + 1 Cr O → LaCrO 3 2 2 3 2 2 3 (4.or oxygen-containing atmosphere. The experimentally determined C p -peak around 545 K caused by the first-order transition o-prv ↔ r-prv is in fact a discontinuity which cannot be implemented in the model. whereby the proper p-value for structures other than bcc.184.108.40.206 or p = 0. A small peak which was found around 855 K can be explained most likely by the decomposition of an undetected impurity phase[35]. The resulting Gibbs energies of formation from emf-measurements are remarkably less negative than the Gibbs energies of formation derived from Knudsen mass spectrometry[53]. their C p is the same. as it unavoidably leads to emf that are too low.1.3. The calculated transition temperature of T = 540 K is shown by the broken line in Fig.Thermodynamic assessments parameter CTlnT of the Gibbs energy of stoichiometric perovskite resulted in the lowest error between experiments and calculation. Only the use of the latter data for the optimization resulted in the proper phase diagram with congruent melting of the perovskite phase and two eutectics.28. the transition temperature being in agreement with the experiments.
3. Fig.3.7.97 at 1273 K. 4.3.3. 4.Thermodynamic assessments of CaO at the electrode/electrolyte interface.11 is plotted as a function of temperature and oxygen partial pressure in Fig.7 Calculated decomposition of lanthanum chromite as a function of temperature and oxygen partial pressure. Defect chemistry of the perovskite phase: 124 . The calculated decomposition of the perovskite phase by Eq. Chemical stability of the perovskite phase: The calculated oxygen partial pressure for the decomposition of lanthanum chromite by the reaction 1 3 LaCrO3 → La 2 O3 + αCr + O2 (g) ↑ 2 4 (4. and changing activity of CaO at the electrode/electrolyte interface can alter the chemical potential of fluorine at this electrode and thus the emf across the electrolyte.11) is pO2 = 10-20. 4.
and charge neutrality is maintained by 1 • [Va ′′′ ]= [CrCr ] La 3 (4. and CrCr in La1-xCrO3 correspond to the site 3 fractions yprv 3+ . yprv 3+ .3.3. CrCr . yprv . yprv 3+ . La x x • ′′′ The concentrations of the defects LaLa . 4. [CrCr ] ∝ PO2 16 .Thermodynamic assessments Applying a defect chemistry analysis of La1-xCrO3 in equilibrium with Cr2O3 the following defect reaction for its oxidation can be written in the sublattice form.)3 2 4 (4. if [Va ′′′ ] and [Va •• ] are O Cr assumed to be negligible according to Akashi et al.12) Using Kröger-Vink notation this defect reaction reads 1 2 x 1 x x x • x La La +CrCr +3OO + O2(g) → La La + Va ′′′ + CrCr +3OO 4 3 3 La (4. Va La . [CrCr ] . 4.3. A La A Va B Cr B Cr A La A Va B Cr y prv 4+ and the tiny fractions y prv and y prv are plotted logarithmically as a function of B Cr B Va O Va log pO2 at T = 1073 K and 1673 K in Fig. yprv 3+ .)3 + O2(g) → (La 3+3 Va1 3 )(Cr 4+ )(O2.3.[58]: 1 (La 3+ )(Cr 3+ )(O2.14) x x x For small oxidation extent [La La ] .15) • Substituting this into Eq. and yprv 4+ in the compound energy formalism. yprv .13) and the equilibrium constant of the oxidation reaction is x • x [Va ′′′ ]1 3[La La ]2 3[CrCr ][OO ]3 La x x x 3 14 [La La ][CrCr ][OO ] pO2 K ox = (4. and [OO ] can be considered to be ~ 1.8 (next page) for lanthanum chromite in equilibrium with Cr2O3.3. The line for yprv 3+ at 1073 K cannot be seen as it is very close to 1. A La 125 .14 gives the proportionalities [Va ′′′ ].3.
[58].3. The calculated slopes of [Va ′′′ ] and [CrCr ] are equal to the slope of the electrical La conductivity from 1573 to 1673 K between pO2 = 1.[57] may be explained by problems of reaching equilibrium due to extraordinarily slow cation diffusion in • ′′′ lanthanum chromite.0 ×104 Pa determined by Akashi et al.0 ×103 Pa and pO2 = 2.3. 4. pO 2 . In Fig. The conflicting data from Shvaiko-Shvaikovskii et al.9 (next page) the calculated slopes of VaLa and CrCr are 126 . This slope is • fixed by the defect reaction Eq.3. At T = 1673 K the slope of 3/16 of [Va ′′′ ] and [CrCr ] is La reproduced by the calculated slope using the compound energy formalism at 105 Pa > pO > 2 10-8 Pa. The slope • At T=1073 K a constant slope of 3/16 of the defect concentrations [Va ′′′ ] and [CrCr ] shown in La the triangle. hence oxidation of LaCrO3 to La1-xCrO3 governs the electrical conductivity of perovskite with fixed activity of Cr2O3 at unity between pO2 = 105 Pa and 10-8 Pa at this • temperature. 4.Thermodynamic assessments Fig. 4. is calculated from very high to very low oxygen partial pressures.12.8 Calculated site fractions of species in La1-xCrO3 in thermodynamic equilibrium with Cr2O3 logarithmically plotted at T = 1073 K and 1673 K as a function of of 3/16 of the calculated defect concentrations is indicated in the triangle.
Eq.3. 127 .[58] derived from electrical conductivity measurements (symbols with error-bars. as calculated [Va ′′′ ] and [Va •• ] are very small.3. 4.15. The calculated amount of [Va ′′′ ] relative to [CrCr ] is fixed by the criterion for La charge neutrality. Fig. as the temperature and oxygen partial pressure dependence of excess Cr in La1-xCrO3 has not been investigated systematically so far.9 Calculated defect concentrations in La1-xCrO3 in thermodynamic equilibrium with Cr2O3 (solid lines) logarithmically plotted as a function of reciprocal temperature along with the data from Akashi et al.[58]. The calculated O Cr relative defect concentrations are in line with those proposed by Akashi et al. The presented defect chemistry calculations are still rather tentative.Thermodynamic assessments • compared with slopes of [Va ′′′ ] and [CrCr ] determined by Akashi et al. The calculated concentrations agree well with the data derived from electrical conductivity • measurements[58]. 4.[58] as a function of La reciprocal temperatures. broken lines).
References 1. pp. I. and further work on the temperature dependence of excess Cr as a function of temperature and oxygen partial pressure would allow a more accurate quantification of the defect chemistry of lanthanum chromite. pp. 147(11).).P. First European Solid Oxide Fuel Cell Forum Proceedings. Proceedings of the 26th Risoe International Syposium on 128 . J. Nickel. Göttingen. S. Zhang. Foger. 3.-M. 4013-22. Interaction between chromia forming alloy interconnects and air electrode of solid oxide fuel cells. Das. Larsen. Using the new database the stability limits of lanthanum chromite in function of temperature and oxygen partial pressure can be quantified. 297-310. as the use of these data for the optimization of model parameters resulted in a proper reproduction of the phase equilibria derived from experiments. P. Foger. Kinzel. 4. Carlsson. The proposed existence of lanthanum vacancies and holes to maintain charge neutrality in lanthanum chromite with excess Cr is reproduced by the model. Deposition of chromium species at Sr-doped LaMnO3 electrodes in solid oxide fuel cells. M.H. Kjaer and J. Vol. Hilpert. Cr-Mn deposition at the three-phase boundary observed by TEM. and K. 2000.[53] and Cheng and Navrotsky[46]. Bossel (Ed. Solid State Ionics. J.. Y. The thermodynamic modeling of lanthanum chromite was based on experimental thermodynamic data reported by Peck et al. Ramprakash and J.3. U. The orthorhombic to rhombohedral transition in lanthanum chromite and the magnetic order-disorder transformation are well reproduced by the model. Zhang. Deller. 1994. p. R. Electrochem. 703. A. Druckerei J. and the calculated slopes of defect concentrations in function of oxygen partial pressure and temperature are in line with the slopes derived from electrical conductivity measurements.Thermodynamic assessments 4. 2. 99. Jiang.G. K. 1997.P. However the amounts of excess Cr in La1-xCrO3 used for the optimization of the cation nonstoichiometry are preliminary. The thermodynamic descriptions of lanthanum chromates and the liquid phase are rather tentative due to humble or sketchy experimental information.6 Conclusions Model parameters of the presented thermodynamic La-Cr-O database were optimized with assessed thermodynamic and phase diagram data. S. H. 2. P. Mechanism and kinetics. D. A. Soc. K. Miller. S. Badwal.
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M. 20. 29.. Coutures. 45(2). 25. 119-35 (in French). 28.B.A. A. Solubility limits of yttrium and the lanthanide rare-earth elements in chromium and chromium-iron alloys.. An. 9(1). Anorg. Bras. J. Lopato. pp. 45-50. 8..B. V. Badie. Tsyrenova. 2705-07. Ceram. pp. 2004. C. 30. Sol. 105-13. R. Rev. Foёx. Thermodynamic assessment of the lanthanumoxygen system. 18. Khim. Allg. 1966. pp. Berjoan. R. 313-24 (in German). Cassedanne. Energy. 24. 48(11). Temp. 26. 23. J. Refract. A. 2005. Temp. Phase correlation in the systems formed by oxides of rare earths and by oxide of chromium. Energy Comm. Paris. Flamand. 1980. Foёx. Epstein.. U. Gauckler. Suponitskii. pp.G.A. At. Cienc.. 1969. Coutures.Thermodynamic assessments 17. Examination of freezing points of rare earth oxides and chromites. 1965. 33136. Comments on the allotropic transformations of the rare earth sesquioxides. 19. S.S. 61-67. A. Suvorov. Ed.. Shevchik. L. Phys.K. Ind. pp. Sci. Chem.. 1968. S. D.R. Thermochemical properties of lanthanum chromates(VI). Sc. Acad. M. scandium and yttrium. or lanthanum chromite. Acad.M. 54(2). Russ. Measurement of the solidification points of several refractory oxides. Zh. 6389-92 (in French). pp. Karapetyants. Rev. Hautes. pp. 337. 1974. pp. M. 40(1). Appl.G. B. S. 260. O. 2001. 309-26 (in French). Some properties of strontium-doped lanthanum chromite. M. pp. Int. R. Brit. R. Hallstedt. Examination of the equilibrium diagram La2O3-Cr2O3. J.. Phase Equilib. L. High Temp.-P.L. M. pp. 57-60 (in French). Rouanet. BMI-1376.P. 21. A. J. 1965. 1976. Contribution to the study of interactions between oxygen and mixed lanthanum oxide and chromium oxide(III). Foёx.. Temp. 22. 94-99. Hautes. Grundy.L. Fiz. B. Stability and thermodynamic properties of rare earth perovskites. Gr. Measurement of the freezing points of refractory oxides. 27. Chem.F. Int. Hautes. Shevchenco. Meadowcroft.. 1225-33. Z. 1959.. 1968. 2(2).N. Thermal properties and thermochemistry of lanthanide chromates. Comparison of thermal properties of oxygen-containing compounds of rare-earth elements.V. 130 . S. Rev.N. Yu. 3. Int. A. Tresvjatskiy.. pp. Bauer.. 2. 1963. Dickerson. Berjoan. Foёx. Int. J. 13. 294-99. Pavlivov. 22(2). Suponitskii. pp. 5. Y. J. Chemical equilibria involving lanthanum chromite.J. pp.M. 13.
493-506. Izv.. Anorg.-M. 679-82 (in Russian). pp. 43. K. J. Neorg. pp. 1985. pp. Structural Phase Transition of Orthorhombic LaCrO3 Studied by Neutron Powder Diffraction. N. T.Thermodynamic assessments 31. Lopato.A. Y. 5-8 (in French). pp. 27(5). S. 38.R. 309-16 (in French). Kamiyama. pp.P. Kamiyama. Traverse.S. A. at Temperatures from 298. and Entropy of Lanthanum Chromite between 298 and 900 °K. Tsuda. LaCrO4. Kishi. Phase Transformations of Certain Chromites of the Rare Earth Elements. Hashimoto. 36. Heat Capacity and Thermodynamic Properties of Lanthanum(III) Chromate(III): LaCrO3. 23(9).. 40. 1973. C. Tanaka. Acad. Korobeinikova. Chim. Mirza. 35. Tsuzuki.M.. Izv. J. Soc. M.. Höfer. Solid State Ionics. Nauk SSSR.F. W. pp. 264. J. Crystal Chemistry and Thermal Behavior in the La(Cr. Anthony. K. Acad. Dokiya. 132. Rev. 2(4). 1-14 (in German). LaCrO3 at Room Temperature. Phase Transitions in Perovskitelike Compounds of the Rare Earths. L. N. Lyutsko. Phys. 10. Z.M. T. Miner. 2000. 524-29. K. Chem.G.E..G. Sc. Paris B. Sakai K. 1966. 39. Oikawa. Mater. B. Schwarz. K. 1167-72. 183-90. Nauk SSSR. 322(1-2). 41. On the chromates(V) of the rare earths. Tresvyatskii.V. R. Y. Analysis of Crystal Structure and Phase Transition of LaCrO3 by Various Diffraction Measurements. E. N. 1246-48. Ni)O3 Perovskite System. 1967. pp. Takagi. D.P. T. 33. P. Zonov. N. J. Reznitskii. Foëx. Structural study and thermal decomposition of lanthanum based chromate. Shimojyo. Morii. 131 . Chem. Kononyuk. Tolochko. 1973.R. C.F. A. Some Observations on the Formation and Structure of Lanthanum Chromite.B. pp. H. pp. High-Temperature X-ray Diffractometric Studies of LaCrO3.15 K. A. 2000. 37. Evaluation of the Thermal Conductivity. pp. pp. Geller. Neorg.N. 1976. 2889-94. A. pp. 34. Raccah. Allg. Akad. 276. J.. 1991. T. Mater. 1520-24 (in Russian). Pavlikov. 10. Tagawa. Akad. Mathews. V. Sci. I.C.. H. Terao. 32. Coutures. High Temp. Yoshida. 805-06. 14(4). 1995. Enthalpy. A. 140(10). Solid State Chem. 2(4).P. 154. 42. Electrochem. M. J. Paris C. Rev. Stølen. Berjoan. Thermodyn. Ruiz. Sc.. Yu. 1963. Oikawa. 1993. I lanthanum chromate(V). Specific Heat. 1271-74 (in French). Sakai.. Kock. J. 1970. Lett. H. S. Momin. S. Phase Transitions in Solid Solutions Based on Lanthanum Chromite. On the Semiconducting Properties of Lanthanum Chromite. Mater. M. Hashimoto. pp. V. S.
Experimental Results. 1979.J. Less-Common Met. Róg. Khattack and D... Heat Capacities of LnCrO3 (Ln=Rare Earth). Iliev. Solid State Commun. Nakamura. N. A. Larssen. 2007. Zhou.. Alloys Compt. Vaporization of LaCrO3: Partial and Integral Thermodynamic Properties. Murakami. Peck. pp. Takahashi. pp. M. Sakai.. Mater. Cox. N. Mat.M. 79(12). G. W. Xing. M. pp. 1996. Kikegawa. Stability of the Perovskite Phase LaBO3 (B=V. N. Fe. 3266-72. 166(1). Kamegashira. Enthalpies of Formation of LaMO3 Perovskites (M=Cr. Matsushita. Litvinchuk. Sreedharan.E. J. X.M. pp. Dudek. 259. pp. 81. Abstracts of the 27th Symposium on Thermal Analysis and Calorimetry. Satoh. Kawada. J.Y. 48.-H. 1990. Kolev. Electron Paramagnetic Resonance and Antiferromagnetism in LaCrO3. 214301-1214301-7. 25(5). H. T. 19-24 (in Chinese). Raman Spectroscopy of Low-Temperature (Pnma) and High-Temperature (R 3 c) Phases of LaCrO3. K. X. 2005. 50. pp. A. K. Petzow. Yokokawa.. Phys. 74. 51. O. Chem. N. pp. Nickel. November 1991. 7677 (in Japanese). Nature. 132 . Yuan. pp. 463-72. A. I. Li. 23-29. Ceram. 55. Sun. Am. Sudha. R. S. 562-66. Thermodynamic Properties of LaCrO3. L. Chen. Determination of the Standard Free Energy of Formation of LaCrO3 at 1273 K. J. 1987. G. H. pp. Y. Tagawa. M.Sr)CrO3 System. Japan. R.P. Res.. Meng.. pp. 45.. 649-59. D. 53. M. Mater. Y. G. M. 57-62. 1961. 1997. Cheng. V. Res. Fe. A. Ni) in Reducing Atmosphere I. 56. Hao. 46. 191-200. Bull. 12. Thermodynamic Stability of LaCrO3 and CaZrO3 Using a Solid-State Galvanic Cell Method. Abrashev. Yoshida. T. 47. Hilpert. Z. Chen. J. 54. M. 2006. J. T. Hashimoto. Wang. 2006. H. Li.-L.N. H. Miller. Bull. Z. Co. 14. Structural Studies of the (La. W. C. Rev. Kyoto. Res. Kojima. 5(3). 49. M. Co.G.Thermodynamic assessments 44.F. Soc. Huang. Chung. Navrotsky. 108(9). 20(1).P. Polish J. N. H. B. 445-46. Dokiya. Zhongguo Xitu Xuebao. Cmaidalka. Takagi. Koseki. 1998. 176-82. pp. J. Weinberg.-Q. Hadjiev. Cr. Mn. P. Thermodynamic Stability of LaCrO3 by a CaF2Based E. Azad. Dokiya. Rare Metals. pp. Pressure-Induced Structural Phase Transition of LaCrO3. D. F. T. Kobertz. 1977.-Y. Method. Y. S. and Ni). M. 192(4). Heat Capacity Measurement of Lanthanum Chromite by Laser Flash Method. Kozlowska-Róg. Gauckler. pp.V. 52. 691-94. Y.
Jarl. T. Hillert.N. Grundy. pp. 2001. 61. A Model of Alloying Effects in Ferromagnetic Metals. T.N. Diff. Grundy. Povoden. 66(10). C. 2003. A. B. Calphad Calculation of Phase Diagrams. Metallkd. Andersson. K.. T. Gauckler. Solids. C. 1982. 70. Rao. pp. Alloy.. E. 30. Pergamon Materials Series. Thermodynamic Assessment of the Co-O System. Mater. Thermodynamic Assessment of the La-Fe-O System.. 212-27. Gopalakrishnan. 1971. Hillert.J. Electrical Transport in Light Rare-Earth Orthochromites. Advances in Catalysis. 68. Cmpd. Chen. Maruyama.J. 24(3). -Manganites and -Ferrites. Popov.F. A CompoundEnergy Model of Ordering in a Phase with Sites of Different Coordination Numbers. M. J.V. Ivas. A. 1441-45 (in Russian). 437-45. pp.L. Shvaiko-Shvaikovskii.P. Nauk SSSR. Jansson.K. 15(8). J.J. 1975. Calphad. J.G. Vidyasagar..G. 1989. Z. Saunders. 62. Phase Equilib. 33-41. 79(2). Gauckler.. T. A. Rao. Chen. 71. G. 1988. Vol.E.-O. Metallkd. Acta Metall. Lal. 133 . Wanklyn. 320. pp. B. 2006. L. Sci. M.N.B. H. pp. 66. Izv. B. Calculation of Defect Chemistry Using the CALPHAD Approach. 1978. N.. A.M. T. 1. 23A. L. 1998. 36. Akashi. Mater. 2(3). pp. General Treatment. Sundman. J. 243-. 32. L. 265-84. Influence of the Synthesis Conditions on the Electrical Properties of LaCrO3. 60. Gordon. 65. 34.G. pp. Tripathi. pp. 81-87. Transport of Lanthanum Ion and Hole in LaCrO3 Determined by Electrical Conductivity Measurements. Phys. Tejuca. Povoden-Karadeniz. 58. p 161-76. 345-58. 577-82. Determination of Chemical and Magnetic Interchange Energies in BCC Alloys. 67. p 227-38.. B. V.S. 1984. Hallstedt. M. 1979. pp.. E. pp. Akad. Guillermet. V.. Rao. Superstructures. 164. Phase Equilib. J. Elsevier Science Ltd. Indian J. L.Thermodynamic assessments 57. Inden. 1986.R. Structure and Reactivity of Perovskite-Type Oxides.. pp. Ordered Defects & Nonstoichiometry in Metal Oxides of Perovskite & Related Structures. J. I. 94-96. accepted 63. M. Solid State Ionics.N. Hillert. 17. Application of the Compound-Energy Model to Oxide Systems. 2003. Chem. B. Goto. pp. M. 1595-1609. 64. The Compound Energy Formalism. Calphad. V. A. Neorg. Z.R. 69. J. B. G. Hillert. M. M. Chem. 59. J. 177-83. Miodownik. Sundman. Jansson. Gauckler. Ivas. Fierro. Electrical Transport in Rare Earth OrthoChromites.P.
Sr2. 294-300. Sr2CrO4. pp. J. Sundman. K. M. Sundman.. M. Calphad. The Mobility of Oxygen Ions in CaF2. 16A. 4.1 Introduction Sr-doped lanthanum manganite (LSM) with the perovskite structure ABO3-δ is used as cathode materials in SOFC. B. Chen. Grundy. Gibbs energy functions of SrCrO4. Modification of the Two-sublattice Model for Liquids. 109-19. pp. 1991. Chen. A.J.T. M. Experimental solid solubilities and nonstoichiometries in La1-xSrxCrO3-δ and LaMn1-xCrxO3-δ are reproduced by the model. 74. Povoden. A. A thermodynamic La-Sr-Mn-Cr-O oxide database is highly desirable for the development of endurable SOFC: thermodynamic calculations set an important base for the optimization of cathodes aiming to avoid long-term degradation due to chromium poisoning.4. E. Appl.N. Akila. Thermodynamic La-Sr-Mn-Cr-O oxide database for solid oxide fuel cell applications. J. Grundy.2]. and SrCr2O4 are presented. 4. L. pp. 75. 1985.4 Thermodynamic La-Sr-Mn-Cr-O oxide database for SOFC applications E. B. 261-66.Thermodynamic assessments 72. Jansson. and L. Gauckler. Povoden. as well as defect concentrations of the cathode contaminated by Cr at different temperatures and oxygen partial pressures. B. The database should meet the demand to calculate stable and metastable phase equilibria. submitted to Scripta Mater. Hillert. 15. Electrochem. R. 1990.N. 20.67Cr2O8. Jacob. Ågren. Trans.J. 73. A Two-Sublattice Model of Molten Solutions with Different Tendency of Ionization. However diffusion of chromium from the metallic interconnects into the cathode leads to a severe cell voltage decrease that was linked to the formation of Crcontaining phases[1. Gauckler to be submitted The thermodynamic La-Sr-Mn-Cr-O oxide database is obtained as an extension of thermodynamic assessments of oxide subsystems using the Calphad approach. thermodynamic driving forces and activities. Metall. These requirements are conformed by using the CALPHAD approach. For the construction of the 134 . A.
0. and the LaSr-Mn-O oxide database is taken from Grundy et al.15-19]: for the stabilities of SrCr2O4 and Sr2CrO4 we trust the accurate study of Jacob[11].785 Å for at maximum 6-fold coordinated Mn3+)[7] we omit Mn3+ on the A-site. 4. Limited solution of Sr in La1-xSrxCrO3-δ perovskite[18] was confirmed by a later investigation[20]. Cr-O.67Cr2O8 by using microprobe analysis[18]. No quaternary phases or solid solutions were found in the Sr-Mn-Cr-O oxide system[8].4. On the other hand the conflicting phase equilibria presented by Kisil[16] lack experimental details.2 Assessment of data from the literature Previous assessments of the La-O.5 Å for 12-fold coordinated La3+. Calculation of the oxygen nonstoichiometry of perovskite + MnO instead of metastable single phase perovskite[6] leads to a good agreement between experimental and calculated nonstoichiometries. We propose optimized thermodynamic functions for oxide phases of the Sr-Cr-O oxide system resulting from the assessment of all available experimental data: agreement exists between Gibbs energies of formation of SrCrO4 determined by emf technique using a Y2O3 stabilized ZrO2 electrolyte[11. Sr-Cr-O oxide: Thermodynamic functions for Sr-Cr-oxides in the SSUB database[9] are based on estimates[10].Thermodynamic assessments La-Sr-Mn-Cr-O oxide database La-Mn-Cr-O oxide and La-Sr-Cr-O oxide systems are assessed. La-Sr-Cr-O oxide: In the La-Sr-Cr-O oxide and La-Mn-Cr-O oxide systems no quaternary stoichiometric compounds were reported. Sr-Mn-Cr-O oxide is treated as ideal extension from the subsystems. whereas emf measurements using CaF2-based emftechnique[13] led to conflicting results likely caused by competing reactions[14]. and La-Cr-O databases are adopted[3-5]. The stoichiometry of a phase defined as Sr3Cr2O8[15] was later corrected to be essentially Sr2. Differences concern the reported stabilities of further compounds[11. Sr3Cr2O7[12] was approved as high pressure phase only[17].12. Phase equilibria in the La-Sr-Cr-O oxide system in air at 1223 K and under vacuum at 1873 K were determined by using solid state technique[18]. which is in agreement with Negas and Roth[15]. Due to large differences between the ionic radii of La3+ and Mn3+ and possible coordination numbers (1.[6] allowed Mn3+ on the A-site of LSM to reproduce experimental oxygen nonstoichiometries under low oxygen partial pressures. The 135 . in agreement with Hartl and Braungart[19].[6] with a slight modification: Grundy et al.12].
1373 K. and 0. −0.Sr)CrO4 is omitted in the modeling.25.8Sr0.Sr)CrO4 were stable in air[10].Sr)CrO4 is ambiguous. 0.1.2.1. and 0. Peck et al.[21] determined the Gibbs energy of formation of La1-xSrxCrO3 with x = 0. δ of LaMn0.9Cr0.1. and 0. 0. and 1573 K[23].3 at T = 1173 K that Cr4+ were absent in the latter. Thus its extension to the quinary database would not be reliable. Complete solid solution between the LaMnO3 and the LaCrO3 perovskites was affirmed[8]. Cheng and Navrotsky[22] measured enthalpies of formation of La1-xSrxCrO3-δ with x = 0. Cr4+ and oxygen vacancies are regarded as the major defects[23.2. and the solubility of Cr is unknown. −0.04.2MnO3 and Cr2O3 at 1073 K was reported after 1000 h of heat treatment in air[28]. 1473K.3 at T = 1273K. and δ = 0.1O3-δ was measured using thermogravimetry[26].5O3-δ with x = 0.24]. La-Mn-Cr-O oxide: In the La-Mn-Cr-O oxide system no quaternary stoichiometric compounds were reported.1. Nonstoichiometry data for La1-xSrxCrO3-δ with x=0. 0.2. 0.2. Plint et al. solely Sr(La. 136 . La-Sr-Mn-Cr-O oxide: In the La-Sr-Mn-Cr-O oxide system complete solid solubility of Mn and Cr is reported for La1-xSrxMn1-yCryO3-δ perovskite[8]. Sr(La.3 as a function of temperature and oxygen partial pressure using XRD analysis.3.2. Positive δ in the perovskite formula reflects oxygen deficiency.3 using Knudsen mass spectrometry.2CrO3-δ at 1273 K[24] were measured as a function of oxygen partial pressure using thermogravimetry. thermodynamic data are missing. and 0. and La0.09.Sr)CrO4 showed reproducible stoichiometry[18]. Myoshi et al. As Ruddlesden-Popper phases have not been reported to form during SOFC operation with LSM cathodes. Perovskite+MnCr2O4 spinel equilibrium of a powdered mixture of La0. whereas negative δ essentially stands for cation nonstoichiometriy. and −0.8Sr0.[18] it was proposed earlier that Sr(La.[20] investigated the single phase region of La1-xSrxCrO3 with x = 0. An isothermal section of the La-Mn-Cr-O oxide system at 1073 K in air and pure oxygen has been published without further commenting of experimental evidences[25]. The exact temperature and oxygen partial pressure range of Sr(La. In contrast to Peck et al.5Cr0.Thermodynamic assessments existence of several Ruddlesden-Popper phases is restricted to reducing conditions. and 0. 0.[27] concluded from the similarity between X-ray absorbtion spectra of Cr K of LaCrO3 and La1-xSrxMn0.11 using drop calorimetry at T = 1080 K.
75.41] were reported. Sr2.Thermodynamic assessments The perovskite phase: Magnetic and structural transitions of La1-xSrxCrO3-δ [29−35]. As the magnetic transitions are low temperature features.and perovskite layers of the latter.67Cr2O8 following the proposed formula[19] and for the Ruddlesden-Popper phase Sr2CrO4. in terms of the applicability of the new database for SOFC the authors omit structural transitions in the modeling. accounting for the structural feature of alternating rocksalt. Transitions of LaMn1-xCrxO3-δ are complex as they depend on temperature. 0. H a is the standard enthalpy of the stable state of element a at 298.67Cr2O8+SrCrO4+Cr2O3 as a function of temperature and oxygen partial pressure[11. Gibbs energy functions of Sr-Croxides were formulated as 1 2 ° SER SER SER gas G(Sr)x(Cr)y(O)z − xH Sr − yH Cr − zH O = x °GSrO[44] + y °GCr2O3[4] + v °GO2 [45] + A + BT (4. 4. their modeling was omitted without consequences for the applicability of the database for SOFC.4. All 137 . most likely due to interactions that cannot be reproduced by the model.36−40]. A and B are adjustable parameters. Thus. and 0. and Sr2CrO4 respectively. Consistency among transition data for La1-xSrxCrO3-δ and LaMn1-xCrxO3-δ prevails. Magnetic transitions have been well reproduced by an ordering-model[42. However we did not obtain satisfying results in higher-order perovskites. (Sr2+)8/3(Va)1/3(Cr6+)2/3(O2-)8/3(Cr5+)4/3(O2-)16/3 and (Sr2+)(O2-)1(Sr2+)(Cr4+)(O2-)3 were chosen for Sr2.15 K and 105 Pa[45]. composition and oxygen partial pressure. and the equilibrium Sr2. LaMn1-xCrxO3-δ [26.67Cr2O8. and La1-xSrxMn1-yCryO3-δ [8. 7/6.4. their optimization with the following experimental phase diagram and thermodynamic data using the PARROT module of the Thermocalc software[46] resulted in the lowest error between model and experiments: Gibbs energies of formation of SrCrO4[11.1) SER v = 0.3 Modeling and optimization Sr-Cr-O oxide: The sublattice models (Sr2+)(Cr6+)(O2-)4 and (Sr2+)(Cr3+)2(O2-)4 are employed for the descriptions of SrCrO4 and SrCr2O4.25 for SrCrO4.43] for LaCrO3[5]. whereas diversities exist regarding the transitions in La1-xSrxMn1-yCryO3-δ . SrCr2O4.12] and phase stabilities of SrCr2O4 and Sr2CrO4 investigated by equilibration experiments of different mixed oxide compositions under controlled atmospheres[11].12].
2.1.15 kJmol-1[21] x = 0. calc. δ = 0.1 Optimized model parameters Sr .2 Calculated and experimental thermodynamic data SrO +1 2 Cr2 O3 + 3 4 O 2 = SrCrO 4 Δ °G = −273.3 kJmol-1 this work.15832T kJmol-1 this work. Δ ° H = −20. calc. δ = 0.050 + 0. Δ ° H = −34. Δ °G = −109.04. δ = 0.7 kJmol-1[20] x = 0.13152T kJmol-1 this work. calc. T = 298 K. Table 4.4. ° Δ ° H = −67. Δ ° H = −55.54 kJmol-1[21] x = 0. Δ °G = −102. δ = 0.767 + 0.3.340 + 0.72 kJmol-1[21] x = 0.88 kJmol-1[21] x = 0. T = 298 K.Cr oxides ASrCrO4 = −273771 J.859 + 0.67 Cr2 O8 + SrCrO 4 + Cr2 O3 Δμ O 2 = −265. calc.106904T kJmol-1 .67Cr2O8 = −508507 J.6 kJmol-1 this work. BSrCr2O4 = −95.5 J ASr2.825 ± 0.1073 − 1473 K[11] Δμ O 2 = −276.1 kJmol-1 this work.8 kJmol-1 this work. Δ ° H = −20. Δ °G = −93. Δ ° H = −50. calc. ° Δ ° H = −36. Δ ° H = −34. Δ °G = −213. Δ °G = −85. Δμ O 2 = −262.4 kJmol-1 this work. Δ °G = −88.166T kJmol-1 .48 kJmol -1[21] 138 . T = 298 K.3 kJmol-1 this work. T = 298 K. Δ H = −65.4. T = 2000 K.4 kJmol-1 this work.15553T kJmol-1 .950 − 1280 K[10] Sr2.2 + 0. T = 298 K. calc.4.0 kJmol-1 this work.2 kJmol-1 this work.6 J ASr2CrO4 = −145000 J.1.1080 − 1380 K[10] (1 − x) 2 La 2 O3 + xSrO + 1 2 Cr2 O3 + x 4 O 2 − δ 2 O2 = La1− xSrx CrO3−δ x = 0. calc. δ = 0. calc.2.2. δ = 0. BSr2. Optimized parameters and calculated and experimental thermodynamic data are listed in Table 4. δ = 0. calc.3.= 5 6GS4O − GS3V + 1 6GS4V + GRPRV[5] GSr 2+ :Cr 3+ :O2.5 kJmol-1[20] x = 0.774 + 0. BSr2CrO4 = 50 J ASrCr2O4 = 98000 J. calc.= GS3V + 1 6GS4O − 1 6GS4V GSr 2+ :Cr 3+ :Va = GS3V − 5 6GS4O + 5 6GS4V Table 4. δ = 0.Thermodynamic assessments reported phase equilibria[11] are correctly reproduced by the model. Δ ° H = −56.5 °GO2 [45] ° ° ° GLa3+ :Cr 4+ :O2. Δ °G = −93.76 kJmol -1[21] x = 0.11.3.1.4.7 kJmol-1[20] x = 0. calc. BSrCrO4 = 131.851 − 1116 K[12] Δ °G = −273.13157T kJmol-1 .09.2.67Cr2O8 = 219 J La1 − xSrxCrO3 − δ ° gas GLa3+ :Cr 4+ :Va = 5 6GS4O − GS3V + 1 6GS4V + GRPRV[5] − 1. T = 2000 K. T = 2000 K. Δ H = −48.1 and 4. T = 298 K. Δ ° H = −59. δ = 0.
(La3+)(Cr3+)(Va)3. e.8Sr0. and A and B parameters of °G of two neutral compounds 139 .4. The parameters of the compound energy formalism are the Gibbs energies of the end-member compounds °Gi: j:k .Va)3 with A. °G(Sr2+)(Cr4+)(Va)3 1° 5 gas GCr2O3 [4] − °GO2 [45] 2 4 ° SER SER GSrCrVa3 − H Sr − H Cr = °GSr2+ :Cr 4+ :Va = GS4V = °GSrO[44] + (4. (Sr2+)(Va)(O2-)3. It can be accounted for by introducing interaction parameters.Va)(Cr3+. La0.Sr2+.and Va on the anion sublattice.4.Thermodynamic assessments The perovskite phase: It is essential for a consistent description of the perovskite phase that defects that occur in the structure in low-order systems remain on the same sites at the extension to higher order.2MnO3-δ are rhombohedral at SOFC operating temperatures (T=1073 K to 1273 K).3) is chosen as reference. (La3+)(Va)(O2-)3.Va)(B.48].Va)(O-2. Thus it is reliable to take the Gibbs energies of the compounds of rhombohedral perovskite from [5] for the model. We adopt the description (A.2) where yi is the site fraction of each cation and Va on the A-sublattice. Typical compositions of Sr-doped lanthanum manganites used for SOFC cathodes.Va)3. and small amounts of Cr brought into the cathode unlikely lead to a change of the structure. The molar Gibbs energy of the perovskite phase then reads ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ° prv prv Gm = ∑∑∑ yi y j yk °Gi: j:k + RT ⎜ ∑ yi ln yi + ∑ y j ln y j + 3∑ yk ln yk ⎟ + EGm i j k i j k (4. (Sr2+)(Va)(Va)3. and (Va)(Va)(Va)3 and ternary interaction parameters are adopted[5. this is achieved by using the same model. B = cations and Va = vacancies[6] using the compound energy formalism[47]. (Va)(Va)(O2-)3.6.Va)(O2-.31451 J mol-1 K-1. Using the above model and the proposed defect chemistry[22-24] the sublattice formula for La1-xSrxCrO3-δ reads (La3+.Cr4+. The molar Gibbs energy °G of La1-xSrxCrO3-δ is uniquely defined as follows: °Gs of the endmembers (La3+)(Cr3+)(O2-)3. yj is the site fraction of each cation and Va on the B-sublattice. R = 8. (La3+)(Va)(Va)3. The last term describes the excess Gibbs energy of mixing. The second-last term accounts for the configurational entropy of mixing. and yk is the site fraction of O2.g.
0L(La3+:Cr3+.Sr . 4.24] of La1-xSrxCrO3-δ. 4.2 (next page).6.4.1 and 4.Cr3+.Va)3.Cr .4.Cr4+.20].4. 4.4.5 − H Sr − H Cr − 2.5Va0. and phase equilibria in the La-Sr-Cr-O oxide system by the modeling is satisfying as shown in Table 4.Va)3.Va)(Mn2+.Mn3+. (Sr2+)(Cr3+)(O2-)3.5. All endmembers have been defined in the assessed subsystems.5 in Eq. All endmember compounds have been defined in the assessed subsystems.2 (p.Cr . 140 . Thus for LaMn1-xCrxO3-δ we propose the sublattice formula (La3+.5) are optimized with all available experimental data of the perovskite phase.Va)(Mn . 3+ 4+ (La3+)(Cr4+)(O2-)3. and in Figs.4. A = 136453 and B = −91.4. Though structure-chemical information of site occupancies in LaMn1-xCrxO3-δ perovskite is missing.Mn4+.5H O = GS3V = 5° 1 1 ⎛5 5 1 1⎞ GSr2+ :Cr3+ :O2− + °GSr2+ :Cr3+ :Va + RT ⎜ ln + ln ⎟ = °GSrO[44] + °GCr2O3 [4] + A + BT 6 6 2 ⎝6 6 6 6⎠ (4.1 (p.Va)(O . The regular interaction parameter 0L(La3+:Cr3+. 138).2 for ° GSrCrO2.4 denotes °G (Sr2+)(Cr4+)(O2-)3. and nonstoichiometries[23.4 Results and discussion The reproduction of experimentally determined Gibbs energies[21] and enthalpies of formation[22]. solid solubilities[18.Mn . 4.Va)(O2-.Mn3+:O2-) accounting for interactions between Cr and Mn cations is fitted to experimental nonstoichiometries[26]. Eq. it is reliable to allow Cr4+ on the B-site: as Cr4+ exists in nonstoichiometric lanthanum chromite perovskite[5].4) ° SER SER SER GSrCrO2.Thermodynamic assessments ° SER SER SER GSrCrO3 − H Sr − H Cr − 3H O = °GSr2+ :Cr 4+ :O2− = GS4O = °GSrO[44] + 1° 1 gas [4] G + °GO2 [45] + A + BT 2 Cr2O3 4 (4.Mn3+:O2-) = +9421 J.4.4. it is expected that it is not removed from the structure if the phase is doped. 138).5Va0. and (Sr2+)(Cr3+)(Va)3 are obtained by conversions of reciprocal equations that are set zero[48] and are listed in Table 4. °Gs of the remaining endmembers (La )(Cr )(Va)3. The 3+ 2+ sublattice 2+ 3+ formula 4+ 3+ of 4+ the 2- quinary perovskite reads (La . with A = 27027 and B = −69.Mn .4.
4. Filled circles.5-SrO-CrO1.4. blank circles. and three phase equilibria.5 system calculated at T = 1223 K in air atmosphere (solid lines) with experimental data[17] included (symbols).Thermodynamic assessments Fig. two phase. prv = La1-xSrxCrO3-δ. 141 . Calculated phase equilibria are the same as in[17]. and circles with crosses denote single phase.1 LaO1.
The calculated isothermal section of the La-Mn-Cr-O oxide system at T = 1273 K in air is presented in Fig.25.3. 0.2. as shown in Fig. However it was not possible to reproduce the nonstoichiometries at T = 1073 K and 973 K.3 LaO18.104.22.168-MnOx-CrO1. Fig. 141 Calculated (lines) and experimental (symbols)[22. p. 0. Deducing from the change of δ from T = 1273 K to 1173 K the measured increase of δ from T = 1173 K to 1073 K might be too small. prv = LaMn1-xCrxO3-δ.4. The calculated nonstoichiometries of La1-xSrxCrO3-δ are in good agreement with the experimental values at higher temperatures. 142 .4 (next page). α-spl = tetragonally distorted Cr-Mn-spinel. 4. possibly caused by equilibration difficulties due to slow diffusion. 4.Thermodynamic assessments Fig.4.2. and 0.3 as a function of oxygen partial pressure. β-spl = cubic Cr-Mn-spinel.4. 4.5 system calculated at T = 1273 K in air atmosphere. 4.23] nonstoichiometries of La1-xSrxCrO3-δ at different temperatures for x = 0.
and the conclusion of missing Cr4+[27] is not based on a direct chemical analysis of Cr valencies.1O3-δ at different temperatures as a function of oxygen partial pressure.Mn3+:O2-) and L(Sr2+:Cr4+.4 Calculated (lines) and experimental (symbols)[27] nonstoichiometries of LaMn0.5 Conclusions The thermodynamic La-Sr-Mn-Cr-O oxide database has been obtained by combining thermodynamic assessments of oxide subsystems.4.Va)3 for the quinary perovskite phase.Thermodynamic assessments Fig.Mn3+.Mn4+. it would be necessary to give large positive values to the regular interaction parameters 0 0 L(Sr2+:Cr3+. Optimized by experiments in pseudoternary and pseudoquaternary oxide subsystems.28] are in line with our calculations.9Cr0. Experimentally determined nonstoichiometry of LaCrO3 indicates the existence of some Cr4+. To approximate the absence of Cr4+[27] in quinary perovskite.Cr4+. temperature. We believe that complete removal of Cr4+ from the perovskite structure is unlikely. 4.Sr2+. Experimental findings[8. this model allows the quantitative calculation of defects as a function of composition.4. and oxygen partial pressure.Cr3+. We propose the model (La3+.Mn3+:O2-).Va)(O2-. 4.Va)(Mn2+. Thus we stick to a model without interaction parameters. The new database is adapted for quantitative calculations of 143 .
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N. 27.S. A. Matter.. A. K. K. 474. Cabeza. Brito. pp. Electronic transport in the novel SOFC anode material La1-xSrxCr0. 2005. T. 2006. P. 2003. Yamaji. M. J. Solid State Chem. 32. H. K. Hashimoto. C. 4151-60.00 ≤ 3+δ ≤ 3. M. Ohba. 2005-08. 3193-98. Y. Y. Inami. 222-29.12) compound. Matsunaga.. S. 28. Shimojo. F. Takahashi. Muirhead. Matter.: Condens.: Condens. Tezuka. 463-71. Solid State Chem. Sato.P.95Sr0.15). Y. J. Matsunaga. Tyagi. Morales. Matsubara. Y. pp. Tezuka. M. 2008. Thermodynamic considerations on Cr poisoning in SOFC cathodes. Tao.05CrO3 and La0.85Sr0. Thermochim. Acta. pp. N. T. T.13. Greaves. Nakamura.E. Structural study of La0. Ramanadham. Res. 31. Analysis of relationship between magnetic property and crystal structure of La1-xSrxCrO3 (x=0. Solid State Comm. pp. Connor. Acta. 1999. Yusuf.9Cr0. H.-P. Chakraborty.S. Hinatsu.K. Xiong. Evolution of crystal structure with the oxygen content in the LaMn0. H. Shimojo.5O3±δ. Chiba. K. Y. pp. 145. J. Hashimoto. Studies on magnetic properties of La0. Y. 2000. Hashimoto.G.R. 2006. 2006.1O3+δ (3. T. Nakamura. Oikawa. 34. Takahashi. F. T. Matter.A. Magnetic and neutron diffraction study on perovskites La1-xSrxCrO3. Magnetization and resistivity in chromium doped manganites. Atake.M. 177. A. C. 29. Kishimoto. J.75Sr0. 33. 57-. 404-10. Arai. Matsunaga. 36. Irvine. Y. H. 141. Structural studies of (La. 176. S. Hinatsu. 146 . Phys. Y.Sr)CrO3 system. Komatsu. 0.. Solid State Ionics. pp. Phys. T. D. K. Morii. Horita. T. Arai. C. Y. Pomjakushin. Plint. Bull. 177. 2008. M. 12. V.25CrO3 at high temperatures. 404-10. Bari. Morii. Cox. L. Yokokawa.E. J. Nakamura. P.M. pp. 502-06.: Condens. pp. K. Phys. H. 170. J. Long. Mat.Thermodynamic assessments 25. 30. Sakai. 18. 11. 35. H. K. J. H. xSrxCrO3 Analysis of magnetic and structural phase transition behaviors of La1- for preparation of phase diagram. 2569-78. R. 435. S. 12. 2008. 1977. Y. Khattak. Kawaji.R. Solid State Ionics.15CrO3 by means of powder neutron diffraction. Krishna.5Mn0. Francesconi.T. H. Thermochim.M. 26. Power Sources.. Caneiro. 132-. Takahashi. M. 1998. O.A. 8661-72.
B. Calphad.1. Rundlöf. 45. 2001. Preliminary data on solid solubility between LaCrO3 and LaFeO3 or LaMnO3. 16. 10. 75. El-Fadli. Mater. 319-25. Dhahri. Calphad.. 153-90. 15(4). 143-46. P. 44.25) using the Rietveld method of analysis. 161-76. Holc. 457. S. pp. Z.. Andrè. 1996. Ceram. Sol. pp. S. Hrovat. and 0. Sci. Folgado. 26. pp. Anderson.J. Z. Kallel. Sundman. Soc. 0.. Vincent. F. 20. 47. Ghedira. Stat. E. The strontium-oxygen system. J. 39. G. D. Alloy Compd. SGTE data for pure elements.V. 1997. Bourèe. Yau. Beltrán. Phys. N. M. Assessment of the La-Mn-O system. Hillert. 131-51 147 . 532-40. Lett. pp. 2(3). J. Metallkd. Beltrán. 2005. 227-38. 1685-87. Calphad.5. H. The thermo-calc databank system.A. 184. Metni.T. J.. 9. J. Gauckler. Mater. pp. R. S. Determination of chemical and magnetic interchange energies in bcc alloys. H. M. Hillert and M. Sapiña. J.N.3). L. and magnetic properties of LaCr1-yMnyO3 (y=0. 1978. E. 577-82. 0.. Nordblad. A. B. L. 40. Structural effects of Co and Cr substitution in LaMnO3+δ. Gauckler. 46. J. M. J. G. J. General treatment. J. pp. 1992. J. M. 2000. Chen. Dinsdale. 2001. M. Tellgren.J. M.2. Grundy. Inden.Thermodynamic assessments 37. D. Kolar. Synthesis.-K. 48..3Mn1-xCrxO3 with 0 ≤ x ≤ 0. Risold. pp. Jansson. D. Effect of Cr doping in La0. M. 1985. Howard. Phase Equilib. 41. Jarl. Chem. Am. M. 66(10). A. 38. (a).U. X-ray-powder diffraction structural phasetransition study of La(Cr1-xMnx)O3 (x=0 to 0. Alloy. A model of alloying effects in ferromagnetic metals. B. Martinez. H. Diff. 437-43. Oumezzine. Bernik. Hallstedt. J. 43. B. Tseggai. 1975. 320. Calphad. Andersson. D. 317-425. Kuscer.7Sr0. Cmpd. pp. pp.. 42.-O. 2008. Hallstedt. The compound energy formalism. Dhahri. A. nuclear structure. 353-61.R. Zemni. 1991. I. F.
whereas Cr2O3 is metastable. the deterioration of the cell performance is expected to be less pronounced when the cell is operated at lower temperatures and current loads. 148 .J. In particular the concentrations of cation and oxygen vacancies are smaller than in an LSM without chromium under decreased oxygen partial pressure at 1273 K. From the thermodynamic calculations structural chemical changes in the cathode perovskite caused by the interaction with chromium can be predicted: it is shown that the interaction of chromium with the LSM cathode leads to a change of the defect chemistry of the perovskite phase. to be submitted A new thermodynamic database is used for thermodynamic equilibrium calculations in a Srdoped lanthanum manganite cathode (LSM) affected by chromium at typical operation temperatures of 1073 K and 1273 K as a function of oxygen partial pressure. M. From the results of these calculations it is concluded that the processes of chromium poisoning of solid oxide fuel cells (SOFC) are partly explicable by thermodynamics. Povoden. Chen. and L. This has consequences for the electrochemical properties of the cell: the electronic conductivity of the cathode will decrease. Ivas. and partly they occur under kinetic control: at the cathode/electrolyte interface of a Cr-"poisoned" cell Cr-Mn spinel exists in thermodynamic equilibrium with LSM. The spinel formation goes along with increasing Mn2+ in LSM under decreasing oxygen partial pressures.Thermodynamic calculations of impacts of chromium on LSM cathodes 5 Thermodynamic calculations of impacts of chromium on Srdoped lanthanum manganite (LSM) cathodes for solid oxide fuel cells (SOFC) E. Proper strategies to prevent the problem of chromium "poisoning" are proposed. T. Gauckler. Even though the chromium problem cannot be solved satisfactorily by varying the cathode composition or the SOFC operating conditions. and the contribution of a vacancy mechanism for the oxygen diffusion in LSM is thermodynamically hampered in the presence of chromium at high temperature and high current loads.
-reduction. and -diffusion process[1]. as well as low fabrication costs. thermal stability. 149 . The chemical dissociation approach is coherently based on the interpretation of a large number of impedance spectra. Consequently Cr-Mn spinel and Cr2O3(s) would form. In the last decade a lot of efforts were made to elucidate the degradation mechanisms. though partly with conflicting results.1 Introduction Chromium-containing metallic interconnects are commonly used in planar-design solid oxide fuel cells (SOFC) due to their high oxidation resistance. This affinity would be linked to the creation of free Mn2+ on the surface of LSM due to the oxygen partial pressure gradient caused by the polarization. electron-donating LSM and oxygen-accepting yttrium-stabilized zirconia (YSZ) are available[15]. where they cause the degradation of the cell by detrimentally affecting the O2adsorbtion.Thermodynamic calculations of impacts of Cr on LSM cathodes 5. Both groups of researchers agree that without polarization Cr is randomly deposited inside the cathode. associated to these nuclei. However high-valent gaseous Cr-oxide and chromium-oxyhydroxides can diffuse under fuelcell operation conditions from the interconnect into the cathode up to the cathode-electrolyte interface. and no Cr2O3(s) is formed. This reduction reaction would compete with the oxygen reduction and lead to blocking of the active sites at the triple phase boundary (TPB). For the mechanism of chromium poisoning two models have been proposed: 1) reduction of gaseous CrO3(g) in dry atmosphere or chromium oxyhydroxide(g) in wet atmosphere under polarization[2-6] and 2) chemical dissociation of Crspecies on the LSM surface[7-14]. good electronic and negligible ionic conductivity. mechanical strength. Ad 2) In contrast to 1) it was proposed that gaseous Cr-species would be chemically dissociated to LSM under the polarization of the cell. Mn2+ would serve as agent for the formation of Cr-Mn-O nuclei that would be able to migrate to the triple phase boundary and further into the electrolyte. Consequences of Cr poisoning have been investigated specifically in (La1-xSrx)MnO3-δ (LSM) perovskite-structured cathodes. On the other hand the electrochemical reduction of CrO3(g) was rejected by the authors favoring the chemical dissociation approach. Ad 1) In an LSM cathode the reduction of CrO3(g) is expected to be localized at the triple phase boundary. where the reaction partners for the reduction.
Thermodynamic calculations of impacts of Cr on LSM cathodes
In the critical assessment in chapter 1.3.6 it was concluded that doubtless reasons to reject the reduction approach do not exist. One critical point concerns the extension of dense Cr2O3layers into the YSZ electrolyte[6]: this phenomenon can be explained best by continuous feeding of an initial Cr2O3-layer with CrO3(g), the latter becoming reduced at a new TPB consisting of YSZ and electron-donating Cr2O3(s). On the other hand this process cannot be explained satisfactorily by using the chemical dissociation approach. Even though particularly the early stages of chromium "poisoning" occur in thermodynamic non-equilibrium, the system SOFC develops towards thermodynamic equilibrium by time. This is reflected by a flattening of the curves that reflect the performance deterioration as a function of time, such as the curves of voltage drop and overpotential loss. Thus thermodynamic calculations allow interpretations of the phase equilibria that result from the interactions between LSM and chromium, as well as changes of the phase chemistry that are associated with the chromium contamination of LSM cathodes.
The La-Sr-Mn-Cr-O oxide database is used for the following thermodynamic calculations: phase equilibria in Cr-contaminated LSM (in the following denoted as LSM(Cr)), phase compositions of LSM(Cr) and Cr-Mn spinel, defect concentrations of LSM(Cr), as well as driving forces for the formation of Cr2O3 were calculated with the poly-module of the ThermoCalc software[16]. The following model descriptions were used: for the Cr-contaminated cathode perovskite with the
4+ 3+
2+ 4+ 3+
sublattice for cubic
description spinel,
reads AB2O4,
(La ,Sr ,Va)(Mn ,Mn ,Mn ,Cr ,Cr ,Va)(O ,Va)3, for tetragonally distorted spinel (Mn2+)(Mn3+,Cr3+)2(O2-)4 was chosen[17], (Mn2+,Cr2+)(Mn3+,Cr3+)2(O2-)4 was used[18], and for Cr2O3 (Cr2+,Cr3+)2(Cr3+,Va)(O2-)3 was taken[18]. Uptake of Cr in LSM is expected, as a complete solid solubility of Cr in LSM has been shown experimentally[19]. For proper thermodynamic calculations of phase equilibria thermodynamic conditions need to be set that reflect the conditions of the chromium contamination of SOFC: the bulk pressure (room pressure, 101325 Pa), the operation temperature (typically from T = 1073 K to 1273 K), the oxygen partial pressure, the cathode composition, and the amount of chromium.
Thermodynamic calculations of impacts of Cr on LSM cathodes
The oxygen partial pressure at the interconnect-cathode interface is air. Under current load it is expected that the oxygen partial pressure will strongly decrease close to the cathodeelectrolyte interface in the triple phase boundary (TPB) region where the oxygen reduction in LSM takes place: the oxygen partial pressure at the cathode-electrolyte interface, pO2(i) can be approximated from the measured cell voltage of a Pt/LSM/YSZ/Ni-Cermet/Pt solid oxide cell and the fuel composition by using the equation for the overall electromotive force E of the cell:
pO RT 2(i) ln 4 F pO
R = 8.31451 J mol-1 K-1, F = 96485.309 C mol-1 and pO2(an) is given by the ratio of H2-H2O in
the fuel. From a measured cell voltage of 0.7 V[2] at T = 1173 K (fuel: 97 vol.% H2, 3 vol.% H2O) and a high current load of 300 mA cm-2 a strong decrease of the oxygen partial pressure at the oxygen reduction sites is expected, pO2(i) ≈ 0.01 Pa. As we are interested in the influences of chromium throughout a cathode under realistic operation conditions of SOFC, results of the thermodynamic calculations are presented for pO ≤ 21278 Pa ≥ 0.01 Pa.
Several LSM cathode compositions can be found in the literature. Part of them is cation stoichiometric, and part of them has excess Mn that is known to prevent unwanted formation of electrochemically isolating zirconate at the cathode/electrolyte interface. In this study two cathode compositions are used for the thermodynamic calculations: La0.9Sr0.1MnO3-δ and (La0.8Sr0.2)0.9MnO3-δ. The sublattice model for this perovskite phase[20] allows the formation of vacancies on each site and changing valencies of Mn as a function of temperature and oxygen partial pressure. The amount of chromium in the system is defined by the partial pressure of the Cr-gas phase:
⎛ μ Cr ⎞ ⎟ ⎝ RT ⎠
pCr = exp ⎜
This means that by knowing the partial pressure of the Cr-gas phase in the TPB region, it is possible to calculate the thermodynamics of the chromium contamination. The problem is that the definite amount of gas that contributes to the degradation phenomena is not known
Thermodynamic calculations of impacts of Cr on LSM cathodes
exactly, as only a fraction of the Cr-gas that evaporates from the Cr2O3 scale on the Cr-alloy interconnect interacts with LSM or is reduced. Fortunately the amount of deposited Cr in a degraded LSM cathode has been analyzed as a function of distance from the cathode/YSZ electrolyte interface[21], and the combined data of X(Cr) and the oxygen partial pressure at the TPB fix the chemical potential of Cr. The amount of deposited Cr close to the LSM(Cr)/YSZ interface was about 3 wt.% after a long cell test of 300 h at T = 1073 K. If one assumes that the pO2 under the test conditions was 1 Pa at the the LSM(Cr)/YSZ interface (normal cell performance), the chemical potential of the Cr-gas phase can be calculated. Even though it is clear that the chemical potential of Cr will change if the amount of evaporated Cr from different interconnect materials is different, the Cr-gas reservoir is assumed to be in a saturated state due to "unlimited" supply from the interconnect during the cell performance, and thus its chemical potential is fixed in the thermodynamic calculations. This simplification is reasonable, as in all investigated cell tests with LSM and Cr-alloy interconnects the degradation was similar, so that changing chromium amounts due to different interconnect alloys are obviously not detrimental for the cell degradation. H2O (operation of SOFC in humid air) is not considered in the calculations, as neither hydroxides nor solubilities of hydrogen or OH− were included in the La-Sr-Mn-Cr-O oxide database.
Thermodynamic calulcations of La0.9Sr0.1MnO3 contaminated by chromium
Fig. 5.3.1 (next page) shows phase fractions in Cr-"poisoned" La0.9Sr0.1MnO3-δ at constant chemical potential of CrO3, μ(CrO3) = −300000 J mol-1 referred to 100000 Pa of CrO3(g) as a function of oxygen partial pressure at T = 1273 K and 1073 K, and in Figs. 5.3.2 (next page) and 5.3.3 (p. 153) phase equilibria are indicated: the cathode remains single phase at pO2 > 102.75 Pa. By decreasing the oxygen partial pressure, tetragonally distorted Mn3O4 spinel (t-sp), the manganese endmember of the Cr-Mn spinel solid solution phase forms.
Cr)O3-δ as a function of oxygen partial pressure at T = 1273 K and μ(CrO3) = −300000 J mol-1. 5. with A and B standing for the cation sublattices and C standing for the oxygen sublattice. 5. and C denote sublattices of the perovskite phase.1(Mn. A.Thermodynamic calculations of impacts of Cr on LSM cathodes Fig. Vertical lines indicate boundaries between different phase equilibria 153 .9Sr0.3.9Sr0. B.1MnO3-δ and defect concentrations of La0.1MnO3-δ as a function of oxygen partial pressure at T=1273 K and 1073 K at μ(CrO3) = −300000 J mol-1 Fig.2 Phase equilibria in Cr-"poisoned" La0.3.1 phase fractions in Cr-"poisoned" La0.9Sr0.
Thermodynamic calculations of impacts of Cr on LSM cathodes
Fig. 5.3.3 Phase equilibria in Cr-"poisoned" La0.9Sr0.1MnO3-δ and defect concentrations of
La0.9Sr0.1(Mn,Cr)O3-δ as a function of oxygen partial pressure at T = 1073 K and
μ(CrO3)= −300000 J mol-1. The vertical line indicates the boundary between phase equilibria
At T = 1273 K (Figs. 5.3.1, p. 153 and 5.3.2, p. 153), tetragonally distorted spinel remains stable to pO2 = 10-0.4 Pa. At lower pO2 cubic Mn-Cr spinel forms. At 1073 K (Figs. 5.3.1, p. 152 and 5.3.3), tetragonally distorted spinel remains stable to pO2 = 100.75 Pa, followed by the formation of cubic spinel at lower pO2 . This means that by decreasing the oxygen partial pressure from pO2 = 104.3, the pressure of air, to 10-1.5 Pa, the amount of spinel in the contaminated cell increases. At 1073 K Cr-Mn spinel formation is less pronounced, and CrMn spinel formation starts at lower pO2 than at 1273 K. To find out about the structural chemical changes in the cathode perovskite caused by reaction with chromium, the fractions of species in a specific sublattice (site fractions) are calculated at
T=1273 K and 1073 K (plots in Figs. 5.3.2, p. 152 and 5.3.3) as a function of pO2 The results .
are compared with the calculated site fractions in a cathode with a very small chemical
Thermodynamic calculations of impacts of Cr on LSM cathodes
potential of Cr, μ(CrO3) = −106 J mol-1 that means with practically no Cr (Figs. 5.3.4 to 5.3.5).
Fig. 5.3.4 Defect concentrations in La0.9Sr0.1MnO3-δ
as a function of oxygen partial pressure at T=1273 K.
Fig. 5.3.5 Defect concentrations in La0.9Sr0.1MnO3-δ
as a function of oxygen partial pressure at T = 1073 K. 155
Thermodynamic calculations of impacts of Cr on LSM cathodes
In general defect concentrations of the Cr-contaminated LSM differ from the defect concentrations in LSM without Cr at a high temperature of 1273 K: with Cr the concentrations of vacancies on the A- and B-sublattices decrease stronger by decreasing the oxygen partial pressure. The increase of oxygen vacancies by decreasing the oxygen partial pressure on the other hand is weaker when chromium is present. At T = 1273 K and pO2 = 1 Pa, which is the expected pO2 at the LSM/YSZ interface at 250 mA cm-2 current load, the site fractions of cation vacancies on the A- and B-sublattices for LSM(Cr) are y(Va)A = 1.98x10-6, y(Va)B=4.3x10-6, whereas in LSM y(Va)A = 3.086x10-6 and y(Va)B = 7.096x10-6 are calculated. The concentration of oxygen vacancies at 1 Pa and T = 1273 K in LSM(Cr) is slightly higher than in LSM, y(Va)C = 3.01x10-5 in LSM(Cr),compared to y(Va)C = 2.57x10-5 in LSM. A pronounced drop of cation and oxygen vacancies is calculated at 1273 K and pO2 = 10-1 Pa, the expected oxygen partial pressure at the TPB under a high current load of 300 mA cm-2: the concentration of oxygen vacancies in LSM(Cr) is y(Va)C = 3.39x10-5, compared to
y(Va)C = 9.48x10-5 in LSM. This means that if the oxygen partial pressure at the LSM/YSZ
interface strongly decreases the vacancy concentrations will drop significantly. The concentrations of Cr3+ and Cr4+ in LSM(Cr) increase when the temperature increases and the oxygen partial pressure decreases. The calculated compositions of tetragonally distorted spinel (Fig. 5.3.6 a, next page) and cubic spinel (Fig. 5.3.6 b) formed during chromium "poisoning" show a strong dependence upon the oxygen partial pressure: only under low oxygen partial pressures a significant amount of chromium is found in the spinel phase, whereas at higher oxygen partial pressures the spinel phase has a composition close to Mn3O4. At T = 1073 K the spinel phase contains less chromium than at T = 1273 K.
tetragonally distorted Mn3O4 (t-sp) is expected to form.2)0.Thermodynamic calculations of impacts of Cr on LSM cathodes Fig.9MnO3-δ as a function of oxygen partial pressure at T = 1273 K and 1073 K and μ(CrO3) = −300000 J mol-1 157 . 5.3. 5.6 Calculated site fractions of ions in cubic spinel (6 a) and tetragonally distorted spinel (6 b) formed during chromium "poisoning" at T = 1273 K and 1073 K 5.2 Thermodynamic calculations of (La0. 5. Fig. At T = 1073 K Mn2O3 is stable in a Cr-contaminated LSM cathode with excess Mn in air.9MnO3-δ contaminated by chromium From Fig.7 phase fractions in Cr-"poisoned" (La0.3.7 it is obvious that in this widely used LSM composition Cr-"poisoning" leads to the formation of additional phases already at high oxygen partial pressures: A small amount of about 5 mol% of the pure spinel endmember.3.2)0.8Sr0.8Sr0.3.
5. Fig.9MnO3-δ cathode are shown in Fig.8Sr0.3. In general.8 Calculated site fractions of ions in cubic spinel formed during chromium "poisoning" at T = 1273 K It is interesting whether the consequences of chromium for the concentrations of defects in LSM(Cr) with excess Mn are more or less pronounced than in cation-stoichiometric LSM(Cr): Phase equilibria and defect concentrations in a (La0. 5. the compositions of the spinel phases formed during chromium "poisoning" become richer in Cr under more reducing conditions.8 the compositional changes of cubic spinel are plotted as a function of oxygen partial pressure at T = 1273 K.2)0.9 (next page).3. 5.Thermodynamic calculations of impacts of Cr on LSM cathodes In Fig. as in the case of cation-stoichiometric LSM.3. 158 .
In LSM(Cr) the concentrations of these cation vacancies drop strongly at low pO2 . 159 .2)0.2)0. 5.9(Mn.220.127.116.11(Mn.8Sr0.8Sr0. and the concentration of oxygen vacancies is lower in LSM(Cr) than in LSM at relatively high and low pO2 . The vacancy concentrations on the A-sites and B-sites of the Cr-contaminated perovskite phase are basically in the middle between these vacancy concentrations in LSM.Cr)O3-δ as a function of oxygen partial pressure at T = 1273 and μ(CrO3) = −300000 J mol-1.2)0.10) at 1273 K.Thermodynamic calculations of impacts of Cr on LSM cathodes Fig.3.9 Phase equilibria in Cr-"poisoned" (La0.10) and without Cr (solid lines in Fig. Mn2+ is higher in LSM(Cr) than in LSM at higher pO2 . 5.9MnO3-δ with Cr (broken lines in Fig. 5.10 (next page) is a comparison of defect concentrations of (La0.8Sr0. The vertical line indicates the boundary between different phase equilibria Fig.Cr)O3-δ and defect concentrations in (La0. 5.
Calculated concentrations of all species in LSM(Cr) and tetragonally distorted spinel in equilibrium are listed in Table 5.1 Pa. next page.3.9(Mn.Cr)O3-δ (dashed lines) and (La0.Thermodynamic calculations of impacts of Cr on LSM cathodes Fig.3. 160 .8Sr0.9MnO3-δ (solid lines) as a function of oxygen partial pressure at T = 1273. 5.3.148Mn0. 5.11.2)0.3.3.2)0. Table 5.1 Compositions of LSM(Cr) and spinel in equilibrium at different T at pO2=1 Pa with and without Cr.947O3-δ spinel formation becomes important only at pO2 < 0.8Sr0.1. 5. as it is illustrated in Fig.10 Defect concentrations in (La0.871Sr0.3 Thermodynamic testing of LSM with Mn-deficiency Only in a cathode with Mn-deficiency it is possible to push the formation of additional phases towards a lower oxygen partial pressure: for the case of La0.
148(Mn.11 Phase fractions in a Cr-"poisoned" Mn-deficient LSM as a function of oxygen partial pressure at T = 1273 and 1073 K and μ(CrO3) = −300000 J mol-1.2)0.8Sr0. 161 . 5.3.Cr)0.871Sr0.947O3-δ is illustrated in Fig.8Sr0. The influence of chromium on defect concentrations in La0. after reaching a plateau at pO2 = 103 Pa.9MnO3-δ at high oxygen partial pressures.871Sr0. and the concentration of oxygen vacancies is almost an order of magnitude lower then in (La0.2)0. next page: The concentration of oxygen vacancies in La0. However.148(Mn. y(Va)C even decrease slightly towards lower pO2 .947O3-δ is half of an order of magnitude higher than in (La0.9MnO3-δ at pO2 = 10-1 Pa.Cr)0.Thermodynamic calculations of impacts of Cr on LSM cathodes Fig.12.3. 5.
2)0.Cr)0. the phase is thermodynamically stable.3.12 Phase equilibria in Cr-"poisoned" Mn-deficient LSM and defect concentrations in La0.3. 162 .4 Formation of Cr2O3 This phase was not found in the thermodynamic calculations.148(Mn. The more negative the driving force.8Sr0. This is the amount of energy that is needed to bring the phase to its stable state. Vertical lines indicate boundaries between different phase equilibria 5.947O3-δ as a function of oxygen partial pressure at T = 1273 K and μ(CrO3) = −300000 J mol-1 (solid lines).9MnO3 without chromium. the more energy is needed to stabilize the phase. In Fig. 5. and the driving force for the formation of the phase is low.13 (next page) the driving force of Cr2O3 is plotted as a function of temperature at two different pO2 in a LSM cathode with excess Mn under Cr-"poisoning". One can get an idea about the degree of metastability of a phase by calculating its thermodynamic driving force. 5.Thermodynamic calculations of impacts of Cr on LSM cathodes Fig.871Sr0. If the driving force is 0.3. and thus its formation is kinetically controlled. Dashed lines indicate the defect concentrations in (La0.
Thermodynamic calculations of impacts of Cr on LSM cathodes
Fig. 5.3.13 Driving force of Cr2O3 as a function of temperature
at different pO2 at μ(CrO3) = −300000 J mol-1. The driving force for the formation of Cr2O3 is less negative at higher oxygen partial pressures.
In the following the results of the thermodynamic calculations are compared to experimental findings on chromium poisoning from the literature. Interpretations are given, which of the chromium poisoning mechanisms occur under thermodynamic control. By carrying out equilibrium calculations of state-of-the-art LSM cathodes with the compositions La0.9Sr0.1MnO3-δ and (La0.8Sr0.2)0.9MnO3-δ at constant chromium in the gas phase it was tested if spinel formation would be favored thermodynamically under low oxygen partial pressure, i.e. close to the electrode-electrolyte interface under polarization conditions. The calculations showed that this is indeed the case. As the A-sublattice of the spinel is completely filled by Mn2+ under the cell operation conditions, and the only source for this species is LSM, it is obvious that spinel formation will be associated with increasing Mn2+ in LSM. Thus, as Mn2+ in LSM increases as a function of decreasing pO2 , also the amount of
Thermodynamic calculations of impacts of Cr on LSM cathodes
spinel formed is higher at low oxygen partial pressure. Cr-gas reveals increasing affinity to LSM towards the electrode-electrolyte interface: both Cr solid solution in LSM and spinel formation increase under decreasing the oxygen partial pressure. From the calculation it is interpreted that the spinel phase that forms under Cr-"poisoning" of the cathode will contain a high amount of Mn, if the oxygen partial pressure at the cathode/electrolyte interface is about 1 Pa. Only at lower pO2 significant Cr is incorporated in the spinel phase, with the stoichiometric MnCr2O4 phase forming at about pO2 = 10-1 Pa. Though spinel formation is thermodynamically driven in Cr-contaminated SOFC, it seems that spinel formation per se is not one of the keys of severe cell degradation due to chromium, but the affinity of Cr-gas to the LSM surface, as even very small Cr contamination in the ppm range apparently leads to a dramatic decrease of the oxygen diffusion in LSM[22]. From impedance spectroscopy analyses it was consistently concluded that the oxygen diffusion is severely influenced by chromium. The thermodynamic calculations showed that Cr interacting with LSM leads to a change of the defect chemistry of the perovskite phase, and particularly to a decreasing amount of oxygen vacancies at high temperatures and low oxygen partial pressures. As the formation of oxygen vacancies in LSM is inhibited, oxygen diffusion to the triple phase boundary is retarded. The results of the thermodynamic defect chemistry calculations of LSM(Cr) thus indicate that the deterioration of the oxygen diffusion is higher under at decreased oxygen partial pressures reflecting high current loads. Cr2O3 is found in degraded SOFC, particularly under high current load. However this phase was not found in the thermodynamic calculations, and its driving force remains negative under SOFC operating conditions. This means that its formation is kinetically controlled. Even though Cr2O3 is not a thermodynamically stable phase in Cr-contaminated SOFC, a strong tendency exists for CrO3(g) to be reduced to Cr2O3(s) at the TPB, as the reduction reaction has a large negative ΔG. It was also mentioned earlier that a high tendency for the precipitation of Cr2O3(s) from CrO3(g) exists[23]. In addition to the adsorption process it is expected that a great many of Cr-gas molecules are driven further to the energy valley for their reduction, namely the TPB. Thus it is non-contradictory that coupling of Cr-gas to LSM and subsequent spinel formation at the LSM surface, and the reduction of CrO3 (g) at the TPB leading to the metastable reduction product Cr2O3(s) occur simultaneously. An alternative way to form Cr2O3 was discussed by Konysheva et al.[24]: The kinetic decomposition of the spinel phase may occur in an oxgen partial pressure gradient due to different mobilities of Mn2+ and Cr3+.
Thermodynamic calculations of impacts of Cr on LSM cathodes
In addition to the inhibiting of oxygen diffusion to the TPB and blocking of active triple phase boundary sites by the thermodynamically controlled formation of spinel and the kinetically driven formation of Cr2O3(s) and thus retarded diffusion of oxygen ions into the electrolyte, further unwanted consequences of chromium poisoning can be ascribed to the low electrical conductivity of Cr2O3[25]. Also Cr-Mn-spinel and Cr-doped LSM are significantly less conductive than pure LSM[26-29]. The electrical conductivity of Cr-Mn spinel decreases as its Cr-content increases. From the thermodynamic calculations it can be predicted that increasing the current load will lead to the formation of a spinel phase with a low electrical conductivity. The ohmic resistance of spinel will also increase due to more Cr dissolved in spinel as the amount of deposits of chromium in the cathode increases as a function of time. Furthermore it is expected that the electrical conductivity of LSM is influenced by chromium particularly under high current loads, as chromium leads to decreased concentrations of cation and oxygen vacancies in LSM(Cr) relative to LSM under such operating conditions of SOFC.
Thermodynamic calculations of LSM contaminated by chromium showed that the formation of spinel is thermodynamically driven, whereas Cr2O3 is a metastable phase that forms under kinetic control in degraded SOFC. The formation of spinel is favored under low oxygen partial pressures, thus in an SOFC under current load this phase is found predominantly at the LSM/YSZ interface. The interaction between chromium and LSM leads to changes of the defect chemistry of the LSM perovskite phase. Particularly diminished concentration of oxygen vacancies relative to LSM without chromium may be a reason for the inhibited oxygen diffusion in degraded SOFC at high temperatures and high current loads . This is also true for Mn-deficient LSM compositions, though the formation of spinel can be restricted to lower oxygen partial pressures. Its defect chemistry is particularly problematic at low oxygen partial pressures, the concentration of oxygen vacancies being strongly diminished relative to LSM with excess Mn. Anyway the use of a Mn-deficient LSM cathode for SOFC is not recommended due to the formation of electrically isolating zirconate.
Y. pp. pp. Soc. Tu. chromium "poisoning" of SOFC with an LSM cathode and Cr-alloy interconnect can only be prevented by applying effective coatings that act as diffusion barrier in combination with additional functional layers. Kadowaki. 99. Saitoh. Y. pp. Electrochemical properties of a SOFC cathode in contact with a chromium-containing alloy separator. Deller. Zhang.P. pp.I. H. Dependence of SOFC cathode degradation by chromiumcontaining alloy on compositions of electrodes and electrolytes. Foger.C. S. R. Soc. K. Degradation phenomena in the cathode of a solid oxide fuel cell with an alloy separator. M. A1961-68. Paulson. References 1. L. Interaction between chromia forming alloy interconnects and air electrode of solid oxide fuel cells. Solid State Ionics. Thus it is expected that in this case the consequences of Crpoisoning will persist particularly at high current loads. 4. interaction between Mn from LSM with Cr may be cumbered by proper doping of the perovskite with further B-site cations. Ramprakash. J. aging mechanisms and lifetime in solid-oxide fuel cells. Even though the deterioration of the cell performance due to chromium is expected to be less pronounced when the operation temperature and current load is decreased. Jiang. Advances. Chromium poisoning of LSM-YSZ SOFC cathodes. pp. Mechanisms and kinetics. From the thermodynamic point of view it can be summarized that there are neither optimized SOFC operating conditions nor optimized LSM compositions that eliminate the chromium problem in SOFC with LSM cathode and Cr-alloy interconnect. Yasuda. 73-9. I. 3.. Akiyama. J. H. 284-93. 2. Birss. 166 . Foger. A126-31. 271-278. S. Power Sources. I.P. 2001. Yasuo.. Yasuda. T. Kawamura. Miyake. Taniguchi. Y.P. J. pp. T. Apateanu.Thermodynamic calculations of impacts of Cr on LSM cathodes By lowering the operation temperature of SOFC additional phases are expected to form at lower oxygen partial pressures. 297-310. Y. 148. Electrochem. Stimming. Matsuzaki. S. Furthermore.P. Matsuzaki. 151(11). Soc. J. Badwal. Power Sources. Zhang.S. J. 7. 6. 132. S. J. 2004. 5. pp. K. 2004. 127. 2000. J.. Electrochem. V. Deposition of chromium species at Srdoped LaMnO3 electrodes in solid oxide fuel cells I. 1995. Electrochem. U. Solid State Ionics. 1997. Y. 147(9). 55. 3195-3205. 2000.
16.W. Mater. 353-62. J. Li. 22. J. S. The Thermo-Calc databank system. pp.P. Apateanu. 108. A comparison of O2 reduction reactions on porous (La. L. Europ. pp. 695-703.. 2002. Jiang. Solid State Ionics. 2004. 18. A.N. J. L. 39-43. Filonova. B. 23.Sr)MnO3 and (La. 1961. 14. 9. 2001. Y..P. J. Power Sources. pp. pp. Gauckler. J. J. S. 13. Int. Grundy. E. Characterization and performance of (La. Grundy. A. pp. A. Fergus. 4013-22. 153-190. pp. 2004. Jansson. 771-774. 9. 56978. Mater. Sci. pp. 438-442. Y. 20. 2006. 1043-1052.J. Gauckler. 2008. Use of gaseous Cr species to diagnose surface and bulk process for O2reduction in solid oxide fuel cells.Fe)O3 cathode for solid oxide fuel cells with iron-chromium metallic interconnect. Soc.P. Soc.N. L. Jiang. J. B (119) (2005) 80-86. Zhang. Petrov. Electrochem. D.P. pp. 2000.. J. Eng. pp. 15. 28.P. 31.Sr)(Co. Diff.. Power Sources. Calphad. Oxygen reduction on strontium-doped LaMnO3 cathodes in the absence and presence of an iron-chromium alloy interconnect.J. Deposition of chromium species at Srdoped LaMnO3 electrodes in solid oxide fuel cells.N. pp. Wu. comm. Zhang. E. 146. The volatilization of chromium oxide. pp. I. Inorg. J.Thermodynamic calculations of impacts of Cr on LSM cathodes 8. 21. J. J. Jiang. Sundman. Grundy.P.. M.D. Soc. Int. Chem. 3664-71. 2007. Zheng. 2006. Caplan and M. Russ. 19. 4th international symposium on solid oxide fuel cells and pers. J. Cohen. Demina.P. J. Hydrogen Energy. FY Annual report. S.-O. Phase equilibria in the system LaMnO3SrMnO3-SrCrO4-LaCrO3. E.N. 2006. 32. J. Gauckler. 1-22. Krumpelt et al.G. Hallstedt. Applied Electrochem. 27. 12. 11.P. 181-192. 52. X. 97. B.J. Effect of cathode and electrolyte transport properties on chromium poisoning in solid oxide fuel cells.Ba)(Co. Zhang. S. Zhen. pp. 147. 17. A.D.P. S. Jiang. 2002. S. 1985. Thermodynamic assessment of the Mn-Cr-O system for solid oxide fuel cell (SOFC) materials. 361-73. B. J. J. Andersson. S. 162. L..Fe)O3 electrodes. Ceam. A. Zhen. Assessment of the La-Sr-Mn-O system. 167 . Jiang. Mechanisms and kinetics. Zheng and P. 10. Zhen.. S. Phase Equilib.. Y. Thermodynamic reassessment of the Cr-O system in the framework of solid oxide fuel cell (SOFC) research. Jiang. 2007. 22. K. Povoden. pp. 191-201. Electrochem. Povoden. Res. Foger.N. Jiang. pp. A comparative investigation of chromium deposition at air electrodes of solid oxide fuel cells. 180. Calphad.A.
Yokokawa. Kishimoto. 114-24. Electrocatalytic properties and nonstoichiometry of the high-temperature air electrode La1-xSrxMnO3.. Maruyama.C.M. Qu. J. Singhal. L. Pennington. J. 176. D. The Electrochemical Society Proceedings Series. Koc. 2006. p. 26. Structure and transport property of manganese-chromium-iron oxide as main compound in oxide scales of alloy interconnects for SOFCs. Chromium poisoning of the porous composite cathode. Penkalla. H. Sakai. Solid State Ionics. Brito. NJ (1995). Eds. Sammes. Soc. Soc. 681-686.. A. S. Singheiser. M. pp. M. Siebert. 1212-16. Electrical and microstructural characterization of spinel phases as potential coatings for SOFC metallic interconnects. Hammouche.P. J. in SOFC-IV. Yamamoto. 472. T. 154 (12). Electrochem. Anderson.U. 29. 2005. E. Tagawa. Hammou. 28.G. E. 168 . Howard. T. Horita. pp. S. PV 95-01.. H. Mertens. J.A. 220.. Jian. Hilpert. 1991. p. Xiong. A. Power sources. 153. W. Hill. pp. R. PV 89-11. H. Kleitz. S. pp. Y. M. 27. 2007.E.B. N. Caneiro. Singhal. Konysheva. A. H. Dokiya. H. O.M. in SOFC-1. K. Ivey. K. Phillips. B1252-B64. NJ (1989). 25.Thermodynamic calculations of impacts of Cr on LSM cathodes 24.C. N. Electrochem. The Electrochemical Society Proceedings Series. Ed. L. Pennington. M. Effect of cathode thickness and current density. J. Yamaji. 138.
072353*T-21. 1134 Y -16377.6651E+03 4.15 -8856. bcc ENTER-SYMBO FUNCTION GLABCC 298. 800 Y +321682. Dinsdale 1991 @@ La.9547989E-05*T**3-36581228*T**(-1).882+181.15 -7968.8932E-07*T**3-399448*T**(-1).387295093*T**2 +4..06113*T-17.908*t*LN(T)+0. 6000 N @@------------------------------------------------------------------@@ Solid metals.0*T*LN(T)-2. 2000 Y -15608.284604*T-26.08252*T+513.15 -3952.492988*T-39.988+174. @@ ---------------------------------------------------------@@ Functions @@ ---------------------------------------------------------@@ Standard data for elements. Dinsdale 1991 @@ La.056395E-06*T**3+21167204*T**(-1).1996E+01 2.25865E-07*T**3.34*T*LN(T)-.008371705*T**2 +6.1659411*T*LN(T)-.15 169 . 1193 Y -136609.004045175*T**2 -5.48*T-26.18*T-50.673-3565..47721E-06*T**3+139250*T**(-1).3088*T*LN(T).053968535*T**2 -4. 2180 Y -34869.34397*T-163.001295165*T**2. bcc ENTER-SYMBO FUNCTION GHSERCR 298.7919*T*LN(T)-0.161+88.88526E+32*T**(-9).413074*T*LN(T)+0..0500E+03 0 S0 0. STATE ATOMIC MASS AMEND-ELEMENT LA DOUBLE_HCP(ABAC) 1.894+218.413+59.Appendix Appendix La-Cr databasea) @@ Database La-Cr. AMEND-ELEMENT CR BCC_A2 5.94+157. 4000 N @@ Cr. 2000 Y -8205.344+344.390071*T-34.3891E+02 5.836315*T-34.6902E+01.403+120. fcc ENTER-SYMBO FUNCTION GLAFCC 298.440708*T*LN(T)-0.35429E+01. double hcp ENTER-SYMBO FUNCTION GHSERLA 298. 550 Y -3381. Povoden-Karadeniz 2008 @@ GO G ENTER-ELEMENT LA CR VA @@ELEMENT NAME REF.5388*T*LN(T).3088*T*LN(T). AMEND-ELEMENT VA VACUUM 0 H0 6.00189435*T**2 -1.91+1123. 4000 N @@ La.
4000 N @@ ---------------------------------------------------------------------@@ Liquid metal functions. from SGTE @@ La(g) ENTER-SYMBO FUNCTION F12026T 298.331-31.042032405*T**2 -3. 3200 Y +497751.36083*T*LN(T)+7.3088*T*LN(T).5353212*T-40.0037094435*T**2 -2.908*T*LN(T)+.020171603*T**2 +2. from SGTE ENTER-SYMBO FUNCTION F7491T 298.059775*T-26.403+41. 2180 Y -16459. 1134 Y -124598.004961847*T**2 -1.232-104.588679E-07*T**3+10285. Dinsdale 1991 @@ La ENTER-SYMBO FUNCTION GLALIQ 298.005444405*T**2 +4.007085085*T**2 -4.25865E-07*T**3.018431*T-34.016725*T-42. 4000 N @@ Cr ENTER-SYMBO FUNCTION GCR_L 298.30043383E-07*T**3-34158815*T**(-1).928-44.004+171. 1400 Y +642608.085237*T+2.7643*T*LN(T)-.70261E-07*T**3+2891891*T**(-1).976+955. 6000 N @@-----------------------------------------------------------@@ Gas functions @@ La gas.653+18.54399*T-34.85*T**(-1).7919*T*LN(T)-0.797+89.0188*T*LN(T)+0.00406*T*LN(T)+0.878375*T-139.82257667E-08*T**3+5. 1300 Y +404460.843-369.93775E-06*T**3-133541*T**(-1). 600 Y +426628. from SGTE ENTER-SYMBOL FUNCTION F7763T 298.791973*T*LN(T)-0.0037862445*T**2 -2.3347881*T-22.23012*T-11.02767321*T**2 170 .4786162*T-13.33826017E-06*T**3-312130. 2000 Y -12599.747-246.83676*T*LN(T)-0.15 +5332.616317*T-50*T*LN(T). 8200 Y -92343.5*T**(-1).2*T**(-1). 800 Y +613345.015+146.1074654*T-19.69883E-07*T**3-1738066.011938995*T**2 +1.386+178.253215E-04*T**2 -1.004045175*T**2 -5.5192158*T-21.Appendix -6109.71447833E-07*T**3+102710.06299*T*LN(T)-0.0441+773.17+114.56798*T*LN(T)+.61216717E-06*T**3+154422.905-85.955-30.001513089*T**2 -4.3088*T*LN(T).28626*T+17.96003*T*LN(T)+. 10000 N @@ Cr gas.15 +422273.006002155*T**2 +1.64743*T*LN(T)-.066199E-06*T**3+20994153*T**(-1).15 +15483.207991*T-19. 1134 Y -3942.15 +390765.47721E-06*T**3+139250*T**(-1)+2. 1100 Y +393886.878761*T-21.418475E+08*T**(-1).15 +598511.984+335. 6000 N @@ Cr2 gas.1*T**(-1).15*T**(-1).00189435*T**2 -1.23648333E-07*T**3-722515*T**(-1).338363*T-111.37615E-21*T**7.0188191*T*LN(T)-0.346741*T*LN(T)+0.
. AMEND-PHASE-DESC BCC MAGN -1 0. 6000 N @@ -------------------------------------------------------------------@@ Phases @@ ------------------------------------------------------------------@@ Metals @@ La.15 +GLALIQ.028597625*T**2 -4.7145*T*LN(T)+. 2 1 1 LA CR..0) 298...0) 298..15 +GHSERLA..15 +GHSERCR.. ENTER-PAR G(GAS...... ideal extension from lower-order systems ENTER-PHASE LIQ.CR:VA.15 +F7763T+RTLNP.15 64573-23*t. ENTER-PAR BMAGN(BCC..0) 298.tcm 171 .. ENTER-PAR G(GAS. VA.. @@ GO PAR SET-OUT-LEVEL. VA...Appendix +1....0) 298.9699545E-04*T**2 +1.. @@ ----------------------------------------------------------------@@ Alloys @@ BCC_A2 ALLOY ENTER-PHASE BCC.5 LA . ENTER-PAR G(LADHCP..15 -0. @@-----------------------------------------------------------@@ Gas ENTER-PHASE GAS G 1 LA CR CR2.....CR.LA.CR:VA.LA:VA...0) 298.15 83500. 2 1 3 LA CR...CR:VA.CR:VA..15 60713-5.0428*T*LN(T)+3..LA...CR:VA.. 3900 Y +347492.LA:VA... ENTER-PAR G(LIQ. fcc ENTER-PHASE LAFCC.15 +GLABCC..1) 298.. ENTER-PAR G(BCC.4 ENTER-PAR TC(BCC.15 +GCR_L..CR:VA.. ENTER-PAR G(BCC. 5800 Y -484185..137623*T-105. @@ La.25559*T-334...0) 298. 2 1 1 LA.97520167E-07*T**3+7.0) 298... 2300 Y +553119. dhcp ENTER-PHASE LADHCP..5939925E-07*T**3+14793625*T**(-1).895+159..LA:VA. ENTER-PAR G(GAS..LA:VA.0) 298.0) 298.07969*T*LN(T)-.51783483E-07*T**3+1.0) 298.004229401*T**2 +1..0) 298.5. AMEND-PHASE LIQ COMP 2... ENTER-PAR L(LIQ.15 +F12026T+RTLNP.055+2598..LA. @@ Interaction parameters from binaries ENTER-PAR L(LIQ.15 +GLAFCC..0) 298...4843765E+08*T**(-1).LA. 2 1 0..008.0) 298..CR:VA. @@ ------------------------------------------------------------------------@@ Liquid... N...49*t.15 -311..135805E+08*T**(-1).34+623....605906E-06*T**3-5831655*T**(-1). ENTER-PAR G(LAFCC. ENTER-PAR L(BCC.188555*T-52........ ENTER-PAR G(LIQ. VA.15 +F7491T+RTLNP. set-interactive a) databases scripts can be used in Thermocalc with the extension . VA.CR2..
1996E+01 4.1008E+01 0 0.5694E+01... as only few phase @@ diagram data exist! @@ -------------------------------------------------------------------GO G ENTER-ELEMENT LA SR MN CR O VA H @@ELEMENT NAME REF. AMEND-ELEMENT VA VACUUM 0 0 0.65340E+02. AMEND-ELEMENT CR BCC_A2 5. @@ Actual version: Dec2008 by Povoden-Karadeniz @@ @@ COMMENTS @@ @@ Sr-Cr-O liquid: simple description. Povoden-Karadeniz @@ @@ Database La-Sr-Mn-Cr-O-(H).3410E+03 1.5680E+03 5.2008E+01.. @@ @@ -------------------------------------------------------------------@@ Species @@ -------------------------------------------------------------------ENTER-SPECIES LA+2 LA/+2 ENTER-SPECIES LA+3 LA/+3 ENTER-SPECIES SR+2 SR/+2 ENTER-SPECIES MN+2 MN/+2 ENTER-SPECIES MN+3 MN/+3 ENTER-SPECIES MN+4 MN/+4 ENTER-SPECIES O2 O2 ENTER-SPECIES O3 O3 ENTER-SPECIES O-2 O/-2 ENTER-SPECIES SRO SRO ENTER-SPECIES SRO2 SRO2 ENTER-SPECIES CR+2 CR/+2 ENTER-SPECIES CR+3 CR/+3 ENTER-SPECIES CR+4 CR/+4 ENTER-SPECIES CR+6 CR/+6 ENTER-SPECIES CR1O1 CR1O1 ENTER-SPECIES CR1O2 CR1O2 ENTER-SPECIES CR1O3 CR1O3 172 .4938E+01 4.0252E+02.. associate at composition SrCrO4 can @@ help for better fit to experiments – future work @@ @@ No data exist for Sr-Mn-Cr-O. Solubility of Cr in SrMnO3 not known @@ --> Subsystem Sr-Mn-Cr-O is a purely ideal extention @@ @@ no oxygen solubility in La-oxide description (taken from Zinkevich et @@ al. AMEND-ELEMENT SR SR_FCC_A1 8.3891E+02 6.) considered @@ @@ Quinary Ruddlesden popper phase is very tentative. AMEND-ELEMENT H 1/2_MOLE_H2(G) 0.0500E+03 2. first version: Feb2006 by Povoden. AMEND-ELEMENT MN CBCC_A12 5.5999E+01 4..Appendix La-Sr-Mn-Cr-O-(H) oxide database @@ LA-SR-Mn-CR-O-(H) oxide. STATE ATOMIC MASS H0 S0 AMEND-ELEMENT LA DOUBLE_HCP(ABAC) 1.6902E+01. AMEND-ELEMENT O 1/2_MOLE_O2(G) 1.7620E+01 6.9960E+03 3..35429E+01.6651E+03 5..
5028601*T-11. 1000 Y 173 . (1/2 O2) ENTER-SYMBO FUNCTION GHSEROO 298.15 -8115.908*t*LN(T)+0. 820 Y -13380.251266E-3*T**2 +1. double hcp ENTER-SYMBO FUNCTION GHSERLA 298. fcc ENTER-SYMBO FUNCTION GHSERSR 298.008371705*T**2 +6.0*T*LN(T)-2.8932E-07*T**3-399448*T**(-1).1*T**(-1).47721E-06*T**3+139250*T**(-1). cbcca12 ENTER-SYMBO FUNCTION GHSERMN 298.18*T-50.656847E30*T**(-9).0905432*T*LN(T)-3. Dinsdale 1991 @@ La.94+157. 550 Y -3381.001295165*T**2. 1519 Y -28733.15 -7968.4582*T*LN(T)-0.00189435*T**2 -1.00734768*T**2 +69827.88526E+32*T**(-9). bcc ENTER-SYMBO FUNCTION GHSERCR 298.196104*T-30.005098873*T**2 +6.8742*T**(-1).15 -7532.6184604E-07*T**3-38364.48*T-26.367+107.15 -8856.41+312.102+153.06113*T-17.61225E-3*T**2 -1.403+120. 2000 N @@ Cr. 2180 Y -34869.84189E-07*T**3+850134*T**(-1).34*T*LN(T)-.882+181. 2000 Y -15608.2648*T-48*T*LN(T)+1.3088*T*LN(T).67477E-07*T**3-2055*T**(-1). 3000 N @@ Mn.183879*T-23.15 -3480.1659411*T*LN(T)-.905*T*LN(T)-4.284604*T-26.390071*T-34. 6000 N @@ O1.059572*T-23.Appendix ENTER-SPECIES CR2O3 CR2O3 ENTER-SPECIES CR3O4 CR3O4 ENTER-SPECIES CRH1 CRH1 ENTER-SPECIES CRH1O1 CRH1O1 ENTER-SPECIES CRH1O2 CRH1O2 ENTER-SPECIES CRH1O3 CRH1O3 ENTER-SPECIES CRH2O2 CRH2O2 ENTER-SPECIES CRH2O3 CRH2O3 ENTER-SPECIES CRH2O4 CRH2O4 ENTER-SPECIES CRH3O3 CRH3O3 ENTER-SPECIES CRH3O4 CRH3O4 ENTER-SPECIES CRH4O4 CRH4O4 ENTER-SPECIES CRH4O5 CRH4O5 ENTER-SPECIES CRH5O5 CRH5O5 ENTER-SPECIES CRH6O6 CRH6O6 ENTER-SPECIES H2 H2 ENTER-SPECIES H2O1 H2O1 ENTER-SPECIES H1O1 H1O1 ENTER-SPECIES H1O2 H1O2 ENTER-SPECIES H2O2 H2O2 @@ @@ ---------------------------------------------------------@@ Functions @@ ---------------------------------------------------------@@ SER Lattice stabilities.27966+130.872255-25. 4000 N @@ Sr.1355068*T*LN(T)-0.413+59.344+344.
...778*T**(-1)...54747566E+02*T*LN(T) -1. BETA-MN3O4 (CUBIC) ENTER-SYMBO FUNCTION GCMN3O4 298.96393E+05+5.8138015*T*LN(T)-5. ENTER-SYMBO FUNCTION GLA2O3H 298.5*GCR2O3-0. MN1O2 ENTER-SYMBO FUNCTION GMN1O2 298...2856E+02*T-119.89567858E+02*T-1.75120338E+02*T-1..59355626E+02*T-4. Grundy 2006 ENTER-SYMBO FUNCTION GMN2O3 298.164542E+06+7. @@ CR-SPINEL CR3O4 ENTER-SYMBO FUNCTION GCR3O4 298..15 -1. 6000 N @@-----------------------------------------------------------@@ Binary oxides.056E-02*T**2 +6. optimized @@ La-oxides....15 -1..43703676E+06+8. 3300 Y -13986..9*T-47.. @@ SrO2 ENTER-SYMBO FUNCTION GSRO2SOL 298..15 +108305+GCR2O3+0. Risold 1996 @@ SrO ENTER-SYMBO FUNCTION GSROSOL 298..82*T.Appendix -6568.9579637E-04*T**2 +6..... @@ Sr-oxides.5*GCR2O3-0.629*T*LN(T)-0. Grundy 2003 @@ MANGANOSITE..85001409E-03*T**2+2.986*T+GLA2O3D.15 +0.95379396E+02*T-6.86138663E+05*T**(-1).5*GHSEROO+280045-93.. @@ @@ MN2O3-FUNCTION. @@ ESKOLAITE..9536*T*LN(T)-4.12922234E+05*T**(-1)...66000166*T-16.74079033E-02*T**2+9.66666666667*GHSERCR.006854*T**2 +808000*T**(-1)-1E7*T**(-2). ENTER-SYMBO FUNCTION GLA2O3X 298. @@ reduced neutral endmember of CR2O3 ENTER-SYMBO FUNCTION GCRO0 298.15 -607870+268. Cr2O3 ENTER-SYMBO FUNCTION GCR2O3 298.41618912E+06+8.25243E-04*T**2 +1. Povoden 2005 @@ METASTABLE CRO ENTER-SYMBO FUNCTION GCR1O1 298.74079033E-02*T**2+9. @@ PYROLYSITE.54747566E+02*T*LN(T) -1..86138663E+05*T**(-1).64955386E+05*T**(-1)..15 43192-18...05E+06*T**(-1).15 -5..76*T.555*T+GLA2O3D. @@ Cr-O oxides... MNO ENTER-SYMBO FUNCTION GMN1O1 298.15 -1.15 32350-13..76015+12.. @@ -------------------------------------------------------------- 174 .8*T*LN(T)-4. @@ BETA-HAUSMANNITE.728+31.15 -4.52766201E+01*T*LN(T) -7.56*T*LN(T)-0.259625*T-18.15 -9.00307*T**2 +190000*T**(-1).15 +GSROSOL+GHSEROO-43740+70*T... ALPHA-MN3O4 (DISTORTED) ENTER-SYMBO FUNCTION GTMN3O4 298..15 -1833257+692. MODIFIED.0721E-08*T**3+4383200*T**(-1).0822E+05*T**(-1)..68352649E+01*T*LN(T) -3.5*GHSEROO+255269-53. @@ Mn-oxides. @@ ALPHA-HAUSMANNITE.45091278E+05+3.97E-03*T**2 +1..80284521E-03*T**2+6.15 +1. Zinkevich 2006 ENTER-SYMBO FUNCTION GLA2O3D 298.6846E+02*T-9.78055555E-09*T**3+262904...02477557E+05+2.911E+01*T*LN(T)-2.9664*T-120.
Grundy et al.5E+04.5*GHSEROO-154101-2..71704891E+01*T.Appendix @@ Ternary oxides....5*GLA2O3D+0.. @@ SrMn3Oz as SrMnO3_Mn2O3 ENTER-SYMBO FUNCTION GSM4OZ 298.. @@ LA7 @@ ENTER-SYMBO FUNCTION GLA7 298.15 +2*GSROSOL+2..15 +4*GSROSOL+3*GMN1O2-3.15 @@ 8*GLA2O3D+3.15 +GSROSOL+0. ENTER-SYMBO FUNCTION RE_ALPHA 298..19200000E+04..5*GCR2O3+4.15 +GSROSOL+GLA2O3D+GMN2O3-137400...5*GMN2O3-7.5*GHSEROO-73045-4.15 GLA2O3D+0. ENTER-SYMBO FUNCTION RE_BETA 298.15 +GMN2O3+GSM3_HEX-2...15 +2*GSROSOL+GMN1O2-1..55*T..158E+04.32830000E+05.. @@ LA2CR3O12 ENTER-SYMBO FUNCTION GLA2CR3 298.15 +GLA2O3D+2..73000000E+03 -1..15 GLA2O3D+1.. @@ @@ Functions of the La-Cr-O system..15 0..79100000E+03.. ENTER-SYMBO FUNCTION SRX_ALPH 298.14*T....15 @@ 3. ENTER-SYMBO FUNCTION GSM3OZ 298.. @@ RP1 ENTER-SYMBO FUNCTION GS4O_RP1 298.5*GHSEROO-540404-9.. @@ Sr7Mn4O1 175 .....799*T. Povoden 2008 @@ LA2CRO6 ENTER-SYMBO FUNCTION GLA2CRO6 298..15 +2*GSROSOL+2. @@ RP2 ENTER-SYMBO FUNCTION GS4O_RP2 298.5*GCR2O3+9. optimized (except perovskite functions) @@ @@ Functions of the La-Sr-O system.26029731E+04-3....5E+04. @@ intermediate La-chromates @@ LA16 @@ ENTER-SYMBO FUNCTION GLA16 298. Grundy 2004 @@ HEX Phase ENTER-SYMBO FUNCTION GSM4_HEX 298.15 +2*GSROSOL+2.5*GLA2O3D+GCR2O3+2..70000000E+01*T...... ENTER-SYMBO FUNCTION GSM3_HEX 298....15 +GSROSOL+0.5*GMN2O3-68300..5*GCR2O3+1. Grundy 2004 ENTER-SYMBO FUNCTION SR_ALPHA 298..15 +GMN2O3+GSM4_HEX-8.15 +GLA2O3D+GMN1O1+6.. ENTER-SYMBO FUNCTION LA_BETA 298.78500000E+05.11300000E+05.5E+04..15 +3*GSROSOL+2*GMN1O2-8... 2005 ENTER-SYMBO FUNCTION GL2MNO4 298..15 +GSROSOL+GMN1O2-1. ENTER-SYMBO FUNCTION SRH_ALPH 298...15 0....99100000E+04-90*T. ENTER-SYMBO FUNCTION GL3O_RP2 298.. @@ @@ Functions of the La-Mn-O system. @@ RP3 ENTER-SYMBO FUNCTION GSM4_RP3 298... @@ @@ Functions of the Sr-Mn-O system. ENTER-SYMBO FUNCTION GL3O_RP1 298.5*GHSEROO-371557+205*T..
ENTER-SYMBO FUNCTION GLCR3O_RP1 298..15 +7*GSROSOL+4*GMN1O2-6.77*T-7..15 +GLACRO3+GSROSOL+7000-25*t...15 +2..44550000E+04 176 .72*t....5*GHSEROO-273771 +131. ENTER-SYMBO FUNCTION GVVV 298.15 0.. Povoden 2005 @@ CUBIC SPINEL ENTER-SYMBO FUNCTION GSPINEL 298.5*GMN2O3-63367+51.1*T. Povoden 2008 @@ Ruddlesden Popper phase ENTER-SYMBO FUNCTION GREFRP 298..666666667*GCR3O4+.5*GMN2O3-63367+51.15 +0... @@ @@ Functions of the La-Sr-Cr-O oxide system. @@ SR2CRO4 ENTER-SYMBO FUNCTION GS2CO4 298.5*GMN2O3-63367+51. @@ @@ Functions of the Sr-Cr-O system.5*GLA2O3D+0.15 +0.5*T.75*GMN1O2-91857+20. @@ TETRAGONALLY DISTORTED SPINEL ENTER-SYMBO FUNCTION GTSPINEL 298.666666667*GCR3O4+.15 0.. @@ SRCR2O7 ENTER-SYMBO FUNCTION GSC2O7 298. @@ ENTER-SYMBO FUNCTION GL3OL 298..5*GHSEROO.73000000E+03-1...66666667*GSROSOL+GCR2O3+2..15 +2*GSROSOL+0.. ENTER-SYMBO FUNCTION GMS3O 298.3+61. ENTER-SYMBO FUNCTION GL4O 298.5*GLA2O3D+0.333333*GLA2O3D+GMN1O2-53760. @@ ---------------------------------------------------------------@@ Perovskite functions @@ Grundy 2005 @@ Charge compensated by Mn+4 (correct) ENTER-SYMBO FUNCTION GL3O 298..77*T-7.....15 +0.6*T.5*GLA2O3D+0..5*GLA2O3D+0.5*GMN2O3-7..5*GCR2O3+1.15 +0.5*GCR2O3+0.. @@ SRCRO4 ENTER-SYMBO FUNCTION GSCO4 298. Povoden 2008 @@ SRCR2O4 ENTER-SYMBO FUNCTION GSC2O4 298.15 +GSROSOL+GCR2O3+3*GHSEROO-325047+196*T.. @@ ENTER-SYMBO FUNCTION GL3OR 298.15 2*GSROSOL+0.15 +6*GL2O+4*GL4O+3*GV4O-12*GL3O-254212.......... ENTER-SYMBO FUNCTION GL2O 298. @@ @@ Functions of the Mn-Cr-O system.33333333334*GCMN3O4-210795..Appendix ENTER-SYMBO FUNCTION GS7M4 298.69*T..333333333333*GHSEROO -508507+219*T..77*T-7. ENTER-SYMBO FUNCTION GV4O 298.12450000E+05+50*T..19*T*LN(T) +232934*T**(-1)-3429+4..4*t...15 +GSROSOL+0..5*GCR2O3+0..19*T*LN(T) +232934*T**(-1)+400-0.5*GHSEROO-145000+50*T.15 +GSROSOL+0.15 +0..15 +GSROSOL+GCR2O3+98000-95.19*T*LN(T) +232934*T**(-1).5*GLA2O3D+GMN1O1+27672.33333333334*GTMN3O4-200942+75....31*T. @@ SR3CR2O8 ENTER-SYMBO FUNCTION GS3C2O8 298...15 +0.
63*t.5*GCR2O3+0. ENTER-SYMBO FUNCTION GALACRO3 298....5*GHSEROO-200000..908*T*LN(T)+.15 0. 1519 Y +GHSERMN+18739.41929E-21*T**7.2288*T-1..15 +GLACRO3-340+0. @@ Function for neutral endmember SR(CR+3.52*t... 1134 Y -3942..Appendix -1.15 +GSROSOL+GMN1O2-1.37615E-21*T**7....33333*GLA2O3D+..015+146.15 GSROSOL+0.5*GCR2O3+0.15 GSROSOL+0.91-12.616317*T-50*T*LN(T).406219*T-39..2386*T+135166-88. 3000 N @@ Cr ENTER-SYMBO FUNCTION GCR_L 298.018431*T-34....6208*T-4..51-13.653+18.70000000E+01*T.23012*T-11. @@ ---------------------------------------------------------------------@@ LIQUID FUNCTIONS @@ ---------------------------------------------------------------------@@ Liquid metal functions. @@ (LaSr)CrO3+/-delta-Perovskite @@ Reference SrCrVa3 ENTER-SYMBO FUNCTION GS4V 298.020171603*T**2 +2..118994*T-5.5*GHSEROO+10222-55.15 +GHSERMN+17859. 1050 Y -10855. 6000 N @@ --------------------------------------------------------------------- 177 .47721E-06*T**3+139250*T**(-1)+2.981237E-06*T**3-265559*T**(-1).15 0.38*T-0..5*GHSEROO.5*GCR2O3+0..059775*T-26. @@ Reciprocals: all 0!!!!! @@ @@ Povoden 2008 @@ LaCrO3-PEROVSKITE ENTER-SYMBO FUNCTION GLACRO3 298..997-10.26500000E+04 -7.1840595E-2*T**2 +4...004+171.29+213. @@ Function for neutral endmember SrCrO3 ENTER-SYMBO FUNCTION GS4O 298.42*t..15 +GSROSOL+0.5*GLA2O3D+0. Dinsdale 1991 @@ La ENTER-SYMBO FUNCTION GLALIQ 298.15 +15483.984+335. 2180 Y -16459...0668978*T*LN(T)-3.15 +5332.5*GCR2O3+11..5*GHSEROO-291802-250*t.93775E-06*T**3-133541*T**(-1).VA)O3 ENTER-SYMBO FUNCTION GN 298.15 +2194. @@ Functions for defect chemistry ENTER-SYMBO FUNCTION GVCR4O 298. 3000 N @@ Mn ENTER-SYMBO FUNCTION GMN_L 298...0188191*T*LN(T)-0. ENTER-SYMBO FUNCTION GMS4O 298.00189435*T**2 -1.5*GCR2O3-73591+2..15 0.3088*T*LN(T).11300000E+05+2. ENTER-SYMBO FUNCTION GLACR4O 298. 4000 N @@ Sr ENTER-SYMBO FUNCTION GSRLIQ 298.69000000E+00*T. ENTER-SYMBO FUNCTION ANTI 298.463*T*LN(T).5*GCR2O3-2.68*T* LN(T).656847E30*T**(-9).15 +547422.
2897*T*LN(T)-.15 +390765. from T.R.14296167E-05*T**3+978019*T**(-1).15 0.2320948*T**2-9..237405*T+14.001513089*T**2 -4.083*T-30.15 +176483. @@ liquid Mn oxides. @@ liquid Cr oxides.5*GHSEROO+339673-121...15 -332319.A.S Class: 5) ENTER-SYMBO FUNCTION F7705T 298. 4000 Y +307209.00607059*T**2 +9.006854*T**2 +808000*T**(-1)-1E7*T**(-2)+141329-56.. REASSESSED BY MING CHEN (2006) BASED ON EBBINGHAUS (1993) ENTER-SYMBO FUNCTION GCR1O1_G 298.00119977*T**2 -1.0063*T**2 +31300*T**(-1)+9.1304*T*LN(T) -. 1100 Y +393886.555*T*LN(T)+0.6220*T. 1000 Y +167489.48508*T**2-.9664*T-120.C.19*T*LN(T) +27.629*T*LN(T)-0.41*T*LN(T). 6000 N @@ CR1O1 Gas (SGTE 1998.15 +173449.15 GMN1O1+4. source: Thermocenter of russian academy @@ of science (T..178604*T-117.8669*T*LN(T) +.1074654*T-19. ENTER-SYMBO FUNCTION GCR2O3_L 298..504926*T**2+4.63356E+08*T**(-1).502-414.45*T-22596.135*T**(-1).331-31. Risold ENTER-SYMBO FUNCTION GSROLIQ 298.59563*T-186.003139382*T**2 -1.35563E+08*T**(-1).928-44.S. Grundy ENTER-SYMBO FUNCTION GMN1O1_L 298..48744*T*LN(T)-.39465890E+04-2.1684007*T-39. @@------------------------------------------------------------------@@ LIQUID WATER. 500 Y -62418..69E-7*T**3.15 -1833257+692.00148*T**2 +873600*T**(-1)+1.4*T.671+1078.31*T-40..00631160667*T**3+5.A.5567E-7*T**3.869-31.5192158*T-21. 10000 N @@ CR1O1 Gas.9513659*T-30.8788-3288.708+805.49525609E+04+4.9+142414.31437957E+01*T.74749*T*LN(T)+.1*T*LN(T). 540 Y -8528143.. optimized @@ liquid La2O3.96003*T*LN(T)+.C.097*T*LN(T)-0. Zinkevich 2006 ENTER-SYMBO FUNCTION GLA2O3LIQ 298.C.52515733E-07*T**3+682877*T**(-1).06284295E+01*T.36083*T* LN(T) +7..62+32.282+741.18729*T+495. from T.. 601 N @@ -----------------------------------------------------------------------@@ GAS FUNCTIONS @@ --------------------CHROMIUM GAS---------------------------------------@@ CR Gas: SGTE v 3. 900 Y +170853.008463125*T**2 +1..3+37.15 GCR2O3+439078-169*T.588679E-07*T**3+10285. @@ liquid SrO.5*GCR2O3-0.722975E-07*T**3-64209900*T**(-1).A.224944*T-121.. 8400 Y -403765.Appendix @@ Liquid oxide functions.917665E-05*T**3-18523425*T**(-1). 600 Y -331037. Class: 4 @@ SGTE=scientific group thermodata Europe @@ ENTER-SYMBO FUNCTION F7491T 298.36845867E-08*T**3+6.5329*T*LN(T)+.15*T**(-1).S)... ENTER-SYMBO FUNCTION GMN2O3_L 298. 178 .R.15 +2*GMN1O1+GHSEROO-6.253215E-04*T**2-1... Class: 4 ENTER-SYMBO FUNCTION GH2O_L 298.0 (1998).15 -566346+449*T-73.229905E-07*T**3+35263.23648333E-07*T**3-722515*T**(-1).4-33.R. Povoden ENTER-SYMBO FUNCTION GCR1O1_L 298.
01555*T*LN(T)+1.21188*T*LN(T)-5.621+24.84857*T*LN(T)-0.64520667E-09*T**3-3973170.15 -109942.075-3566.526*T*LN(T)-0.17486667E-07*T**3+1572175*T**(-1).01526167E-08*T**3-64163. based on Ebbinghaus 1993 ENTER-SYMBO FUNCTION GCR1O2_G 298.108664-15.01667E-8*T**3.2*T*LN(T)-. 2800 Y 179 . 6000 N @@ O3 Gas (SGTE 1998.879+30.80563*T+421.89*T-82. 4900 Y +97590. 1300 Y +49468.C. from T. reassessment Chen 2006. 2100 Y -18840.00012*T**2 +932050*T**(-1)-8.0216*T**2 +428900*T**(-1)+3.C.5*T**(-1).15 +243206.99+130.401E-6*T**3.00016*T**2 +1814700*T**(-1)+7.S Class: 4) ENTER-SYMBO FUNCTION F10963T 298.944-37.10457667E-06*T**3+12362250*T**(-1).0922361*T**2 +4.46390667E-07*T**3+56582.A.4989821*T-20.00206456*T**2 -5.8612582*T-21.61*T-57. 6000 N @@ H2O1 Gas (SGTE 1998. reassessed by Ming Chen 2006.15 -341231. 3000 N @@-------------------OXYGEN GAS------------------------------------@@ O Gas (JANAF 1982.44768833E-06*T**3-2.45*T**(-1).2687055E-04*T**2 -1.A.33E-9*T**3.14281783E-08*T**3+3561002.3*T**(-1).555105E-07*T**3-2.434+4. 1000 Y +180.15 +130696.09*T**(-1).35707*T*LN(T)+0.0847281*T-17.78+10. 6000 N @@ H Gas (JANAF 1982.59784667E-06*T**3+9. assessment dated 3/77 from SGTE) ENTER-SYMBO FUNCTION HGAS 298.01283575*T**2 -3.5*T**(-1).1663+92.43E-6*T**3.007055445*T**2+3.15 -250423.59*T-39.15 +211801.1894682*T-31.R.696*T*LN(T)-0.5*T**(-1). 6000 N @@ -------------O-H GAS----------------------------------@@ H2 Gas (JANAF THERMOCHEMICAL TABLES SGTE) ENTER-SYMBO FUNCTION H2GAS 298. 1100 Y -256145.4437*T*LN(T)-.81*T-56.383-1950.60539333E-06*T**3+99530.23131283E-08*T**3-42897.798361*T-149. 700 Y +114760. 1000 Y -354716.45*T**(-1).0010728235*T**2 +1.3956+710.43044*T*LN(T) -.78611*T*LN(T). 3000 N @@ CR1O3 Gas.610855E+08*T**(-1).0027589925*T**2 -7.R.05535833E-07*T**3+1246309.Appendix 3000 N @@ CR1O2 Gas.09482*T-134. 2950 Y +252301.569*T*LN(T)-0.40916*T*LN(T) -.09+299. 2800 Y +409416.13383*T-764.00584168*T**2 +3. assessment dated 3/77 from SGTE) ENTER-SYMBO FUNCTION F13349T 298. 3500 Y -1866338.039707355*T**2 -4. from T.6+6101.423-52.05082*T*LN(T)-0.00623741*T**2-6.626737*T-60.6128262*T-17.494-20.3696*T*LN(T)+.8435*T*LN(T)+.306855E-06*T**3-21589870*T**(-1).70834*T+223.1699975E+08*T**(-1).623+176. 2100 Y +866367.15 -9522.09852775*T**2 -2.10286*T*LN(T)+.97393+78.9608*T*LN(T)+.1284109*T**2 +5.413565E-04*T**2 +7.5273873*T-31.S Class: 4) ENTER-SYMBO FUNCTION F14021T 298. based on Ebbinghaus 1993 ENTER-SYMBO FUNCTION GCR1O3_G 298.02763076*T**2 +4. 1000 Y -118120+123.3120249*T-32.043+890.14618667E-07*T**3-1280036*T**(-1).45470312*T-28.2001*T*LN(T)-.1304835E+08*T**(-1).0155*T**2 +245800*T**(-1)+2.9096643*T-27.58118*T*LN(T)-.
8400 Y -489068. 18000 Y -165728.690197*T-42. 6000 N @@ H2O2 Gas (JANAF SECOND EDIT SGTE) ENTER-SYMBO FUNCTION F10983T 298.15 -497678+273.52*T-74.97594167E-08*T**3+2458230.15 +30698.65*T**(-1). 20000 N @@ H1O1 Gas (SGTE 1998.6898+15.5127-12.S Class: 1) ENTER-SYMBO FUNCTION F10666T 298.771+239.05*T**(-1).A.15 -274384.4+195.242048*T-24. 3000 N @@ CR(OH)2 Gas.418+116.0016703495*T**2-1.52+180.001713168*T**2-6.R. from T.2E-7*T**3.799205E-07*T**3-25503.0018*T**2+1338300*T**(-1)+9. 3000 Y +31735.12331E-04*T**2-6.1931655E+08*T**(-1).30298483E-10*T**3-8.882+553.007931945*T**2+4.191295*T-50.00501027*T**2+2.259882*T-92.927*T*LN(T) -0. 1000 Y -276268.45435*T*LN(T) -.24542*T*LN(T) +.0023107985*T**2+5.0783-20.94271*T*LN(T) -.7343256*T-24.96842*T*LN(T) -.39E-6*T**3.65*T**(-1). 20000 N @@ H1O2 Gas (SGTE 1998.659505E-06*T**3+65357.0146*T**2+715900*T**(-1)+2.15E-8*T**3.0015*T**2+938850*T**(-1)+5. 700 Y -156470.15 +1075.036948065*T**2+6.2921095E-09*T**3-4.1497212*T-26.953+370.9096451*T-29. 18000 Y -154907.64106-55.15 -351288.406716*T-68.77872*T*LN(T) +2.334E-8*T**3. 1000 Y -492562+351.S Class: 4) ENTER-SYMBO FUNCTION F10729T 298. 3000 N @@ CRO2(OH) Gas.257*T*LN(T) -0.002*T**2+185600*T**(-1)-1.053*T*LN(T) -0. 1000 Y 56684+136.8961+275.42186*T*LN(T) -.573855E-09*T**3+26048030*T**(-1). based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH2O2_G 298.32+190. 8600 Y +41016.87*T-46. 3000 N @@ CRO(OH)1 Gas REASSESSED BY MING CHEN (2006) BASED ON EBBINGHAUS (1993) ENTER-SYMBO FUNCTION GCRH1O2_G 298.77*T-83.47*T-96.97699*T*LN(T) +.2768*T*LN(T) +6.003069987*T**2+6.5*T**(-1).4391015E+08*T**(-1). combined assessment Chen 2006 @@ based on Ebbinghaus 1995 @@ and from Povoden based on Kim and Belton 1974 @@ (data suggested by Opila 2007) ENTER-SYMBO FUNCTION GCRH1O3_G 298.32333233E-08*T**3+1. 1000 Y 180 .5*T**(-1).29733833E-07*T**3+684985.15 -147258.0792741*T-24.47539017E-08*T**3+1.505+120.0018*T**2+2218000*T**(-1)-2.0019361405*T**2-1.R.91863E-08*T**3-6415210*T**(-1).36297E-06*T**3-29469.292415E+08*T**(-1).0007*T**2+243850*T**(-1)-9.175*T*LN(T) +0.551*T*LN(T) +0.765625E+08*T**(-1). 3600 Y -67875. assessment Chen 2006.Appendix -268423. 800 Y -7932.82*T**(-1).122915E-07*T**3+925845*T**(-1).34404917E-07*T**3+116618.326117*T-69.1173*T*LN(T) +6.15 +68260+52.0031*T**2+266750*T**(-1)-9. 1500 N @@-------------------CR-O-H GAS---------------------------------------@@ CR(OH)1 Gas REASSESSED BY MING CHEN (2006) BASED ON EBBINGHAUS (1993) ENTER-SYMBO FUNCTION GCRH1O1_G 298.213599E-04*T**2-1.75E-7*T**3.86*T-75.645643*T-59.2016233*T-40.C.42189E-05*T**2-1.99164+54.94216*T*LN(T) -.971-37.7*T-72.10636*T*LN(T) -.53*T-57.018507875*T**2+2. from T.686636*T-25.775*T*LN(T) -.9*T*LN(T) -.51E-7*T**3. +326722.277-65.C.003149545*T**2+1.A.135E-7*T**3.724*T*LN(T) -0.4077*T*LN(T) +.
01*T**2+4151100*T**(-1)+5. based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH6O6_G 298.Appendix -359644+228.0096*T**2+4.45*T-229. 3000 N @@ CRH1 Gas (SGTE 1998. based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH3O4_G 298.7+464.545E-7*T**3.15 -578683+391. from T.713-424.386334*T-22.60191*T+219.15 -902751.83+534.97*T-180.098*T*LN(T) -0.5*T-163*T*LN(T) +0.006*T**2+2525450*T**(-1)+2.3*T-137.18913267E-06*T**3-77266.36214*T+18.15 -650064.004*T**2+2094950*T**(-1)+1.65*T*LN(T) -0.006*T**2+498450*T**(-1)-2.6+712.026-56.37019*T*LN(T) -.05+820.15 -1029121.002*T*LN(T) -0. 1000 Y -991549.9*T-190.525*T*LN(T) -0. 3000 N @@ CRO(OH)3 Gas.7467E-7*T**3.C.049*T*LN(T) -0. 1000 Y -582354+394.S Class: 4) ENTER-SYMBO FUNCTION F7586T 298.973194012145*T-158.4+51.77E-6*T**3.2*T*LN(T) -0.8867E-7*T**3.34E-7*T**3.3*T-121. 1000 Y +421602.25*T*LN(T) -0.15 -976204+672.457*T*LN(T) -0.15 -787712+400*T-107.019*T**2+513600*T**(-1)+1. 3000 N @@ CR(OH)3 Gas. assessment Chen 2006 based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH2O3_G 298.35E-07*T**3+665100*T**(-1).9865812*T-37.86+694. 1000 Y -909897.12+967.89*T-216.6*T-162.0054*T**2+1023500*T**(-1)-1.15 -978211.0086*T**2+3058600*T**(-1)+4. 3000 N @@ CR(OH)5 Gas. 1000 Y -997791.16*T*LN(T) -0.15 +432449. based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH3O3_G 298.15 -851590. based on Ebbinghaus 1993 ENTER-SYMBO FUNCTION G_CRH4O5 298.2*T-109.97*T-79.004*T**2+785800*T**(-1)-2.3E-7*T**3.0099*T**2+770750*T**(-1)+5.355E-6*T**3.00056*T**2+663150*T**(-1)-5.67833E-07*T**3.35E-7*T**3. assessment Chen 2006. assessment Chen 2006.11767E-6*T**3.008*T**2+840600*T**(-1)-1.455*T*LN(T) -0.9391*T*LN(T) 181 . assessment Chen 2006. assessment Chen 2006. 5500 Y +1270342. based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH4O4_G 298. 3500 Y +587860. 3000 N @@ CRO(OH)4 Gas.99681*T*LN(T) +3.74*T-146.46-2142.819*T*LN(T) -0.13133917E-07*T**3+1368173*T**(-1).014*T**2+1.86*T*LN(T) -0.9958E-06*T**3.014*T**2+6008850*T**(-1)+7.91E-7*T**3. 3000 N @@ CRO2(OH)2 Gas.6*T-195.R.93E-7*T**3.A. 3000 N @@ CR(OH)4 Gas. 1000 Y -656538+448. 1000 Y -806262+567*T-131. 1000 Y -1053466+1080.007723995*T**2+7. 3000 N @@ CRO(OH)2 Gas. combined assessment Chen 2006 @@ based on Ebbinghaus 1995 @@ and from Povoden-Karadeniz based on Opila 2007 ENTER-SYMBO FUNCTION GCRH2O4_G 298.5*T*LN(T) +0.76+600.8967E-07*T**3+1688150*T**(-1). 3000 N @@ CR(OH)6 Gas. assessment Chen 2006.41*T*LN(T) -0. assessment Chen 2006.1+867.004*T**2+1.349852E-04*T**2-1.37*T-125.00994042*T**2+1.0049*T**2+3311450*T**(-1)+2.945E-07*T**3+4671850*T**(-1).378E-6*T**3.05*T**(-1). based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH5O5_G 298.874*T*LN(T) -0.99444833E-08*T**3-86705500*T**(-1). 1000 Y -861477.8+813.524*T*LN(T) -0.6022*T*LN(T) -.6*T-109.0065*T**2+2669300*T**(-1)+3.
ENTER-PAR L(LA2O3_HEXSS. +GLA2O3X-3*GHSEROO...87691*T.LA+3...SR+2:O-2.87691*T....0)...... +SRH_ALPH+GHSEROO+15. ENTER-PAR G(LA2O3_HEXSS..SR+2:O-2. 2 2 3 LA+3 SR+2. ENTER-PAR G(BETA.87691*T.Appendix -. +GLAO-GHSEROO. ENTER-PAR L(LA2O3_CUBSS.15 +193600-78....0).SR+2:VA. ENTER-PAR L(LA2O3_CUBSS..SR+2:O-2..LA+3.. ENTER-PAR G(LA2O3SS...LA+3.149E+05-7.81E+01*T.. +SR_ALPHA-2*GHSEROO +15... O-2 VA...0) 298..SR+2:O-2. ENTER-PAR G(LA2O3SS..15 +GSRO2SOL.0) 298..... @@ ENTER-PHASE LA2O3_CUBSS..... ENTER-PAR G(LA2O3_CUBSS. ENTER-PAR G(LA2O3SS.. ENTER-PAR G(MN1O2.SR+2:VA....1) 298.SR+2:O-2. 2 2 3 LA+2 LA+3 SR+2.SR+2:VA.LA+3... 182 .0).. ENTER-PAR L(LA2O3SS. +SR_ALPHA+GHSEROO +15... +SRH_ALPH-2*GHSEROO +15.... O-2 VA.0) 298. ENTER-PAR G(LA2O3_CUBSS. @@ ---------------------------------------------------------------------@@ Ternary oxides @@ @@ LA-SR-O..0).034109635*T**2+7...15 -20000.0).81E+01*T...LA+3:VA..LA+3. +LA_BETA.. O-2 VA....LA+3:O-2. +GLA2O3H-3*GHSEROO.0). 2 1 2 MN. ENTER-PAR G(LA2O3_CUBSS.. ENTER-PAR L(LA2O3_CUBSS. +SRX_ALPH+GHSEROO+15..SR+2:O-2.15 -20000.15 +2... ENTER-PAR G(LA2O3_HEXSS...LA+2:O-2. ENTER-PAR G(LA2O3SS... Grundy.0). 2 2 3 LA+3 SR+2.........0).15 +2.0) 298..149E+05-7..LA+3..0)..0). +GLA2O3X. @@ La4SrO7 as BETA phase ENTER-PHASE BETA..LA+3:O-2.LA+3:VA..87691*T. +LA_BETA-3*GHSEROO. O...33333333*RE_BETA +15.. ENTER-PAR G(SRO2.... +SR_ALPHA+416100+GHSEROO -0.1*T..SR+2:VA.. @@ ENTER-PHASE LA2O3_HEXSS.. ENTER-PAR L(LA2O3_CUBSS.1*T.LA+3:O-2.. ENTER-PAR G(BETA.. ENTER-PAR G(LA2O3SS.. ENTER-PAR G(LA2O3_CUBSS.. +GLA2O3D-3*GHSEROO.1*T. MN1O2 ENTER-PHASE MN1O2. Grundy @@ @@ STOICHIOMETRIC PYROLYSITE.MN:O.0).0) 298.LA+3:O-2..LA+3. ENTER-PAR G(BETA..SRO2....SR+2:VA.0). O-2 VA.LA+3:VA.1*T.0) 298..15 +GLAO.. ENTER-PAR L(LA2O3SS.. +GLA2O3H.15 +168700-78.0) 298.0). +SRX_ALPH2*GHSEROO+15..0).. 2 2 3 LA+3 SR+2. 1 SRO2..15 +168700-78.87691*T.277845E-07*T**3-5. ENTER-PAR G(LA2O3_HEXSS. ENTER-PAR G(LA2O3_HEXSS. 6000 N @@ @@ @@ -------------------------------------------------------------------@@ Phases @@ ------------------------------------------------------------------@@ Binary oxides @@ @@ Sr oxides.0) 298...20451E+08*T**(-1)....15 +193600-78.SR+2:VA.87691*T..87691*T.... ENTER-PAR G(LA2O3SS.SR+2:O-2.. ENTER-PAR L(LA2O3_HEXSS.SR+2:VA.1) 298.LA+3:VA..0) 298. Chen @@ ENTER-PHASE LA2O3SS. Risold @@ ENTER-PHASE SRO2.15 +GLA2O3D..15 +GMN1O2.LA+2:VA....0) 298.LA+3.SR+2:O-2. @@ @@ Mn oxides..0).
O-2. MN+3. 3 7 4 15 SR+2... ENTER-PAR G(SR4MN3O10.. +GSROSOL. 3 16 7 44 LA.0). ENTER-PAR G(L2MNO4.. @@ ENTER-PHASE LMN2O5. ENTER-PAR G(LA2CR3... CR.0).. 3 2 3 12 LA+3... 2 1 1 LA+3 SR+2 VA.. ENTER-PAR G(SRMN3O6.SR+2:MN+3:O-2. Grundy @@ ENTER-PHASE L2MNO4.. ENTER-PAR G(SRMN3O6... O-2 VA.0) 298.0) 298.....0)... @@ STOICHIOMETRIC LA7 @@ ENTER-PHASE LA7.....LA+3:MN+3:MN+4:O-2.SR+2:MN+3:O-2:MN+3:VA..... O.. Grundy @@ ENTER-PHASE SR7MN4O15. +GSM3_HEX-2. MN+4. 3 4 3 9 LA+3......0).. @@ @@ SR-MN-O.0). ENTER-PAR G(SRMNO3_HEX....SR+2:MN+4:O-2. MN+4..8*T.SR+2:VA... MN+3... CR. O. @@ @@ LA-MN-O. @@ ENTER-PAR G(LA7...SR+2:O-2.. O-2.15 +GLA2CRO6. ENTER-PAR G(SRMN3O6.....66666667*RE_BETA+15.0) 298..87691*T. ENTER-PAR G(SRO.....0) 298.23859*T.5*GHSEROO +11... O-2.0). +2*GLA2O3D+3*GSROSOL+229800 -136.... ENTER-PAR G(SRO..LA+3:CR+6:O-2....SR+2:MN+3:O-2:MN+3:O-2. +GSM4OZ.0). CR+6. ENTER-PAR G(SRO..LA+3:SR+2:O-2.SR+2:VA.... @@ SrO Solid Solution ENTER-PHASE SRO.15 +GLA7.. @@ ENTER-PAR G(LA16...0) 298.0)... MN+4. Povoden @@ @@ STOICHIOMETRIC LA2CRO6 ENTER-PHASE LA2CRO6.... ENTER-PAR G(SRMN3O6. O-2.....LA+3. @@ ENTER-PHASE SRMNO3_HEX. 183 . 5 1 2 3 1 3 SR+2. 3 1 1 3 SR+2.. @@ @@ STOICHIOMETRIC LA2CR3O12 ENTER-PHASE LA2CR3...0). 3 2 1 6 LA+3.VA:O-2.5*GHSEROO +11.0).. ENTER-PAR G(LA2CRO6. MN+2..LA:CR:O.SR+2:MN+3:O-2:MN+4:VA.23859*T.. 3 2 1 4 LA+3.. +GSM4OZ-3*GHSEROO.LA+3:O-2.0). SR+2. +GSM3_HEX+0.. ENTER-PAR G(SR7MN4O15....8*T.0) 298.15 +GLMN2O5.SR+2:MN+3:VA. 3 4 3 10 SR+2.0).0) 298.... 4 1 1 1 5 LA+3...23859*T...LA+3:MN+2:O-2.15 +GLA16.. +GSM3OZ+0.0) 298..... O-2.. O-2.5*GHSEROO +11. O-2. @@ ENTER-PHASE SR4MN3O10.5*GLA2O3D+113700.. MN+3 MN+4. ENTER-PAR L(BETA.. 3 7 2 16 LA. +GSM4_RP3.. @@ intermediate La-chromates @@ STOICHIOMETRIC LA16 @@ ENTER-PHASE LA16..23859*T....5*GHSEROO +11.15 +GL2MNO4. 0.LA:CR:O.LA+3.15 +GLA2CR3.. MN+3 MN+4. +0.SR+2:MN+3:O-2:MN+4:O-2...LA+3:CR+6:O-2... O-2.SR+2:MN+4:O-2. ENTER-PAR L(BETA.75*T. @@ La4Sr3O9.. Stoichiometric ENTER-PHASE LA4SR3O9.0). +GS7M4. @@ ENTER-PHASE SRMN3O6..Appendix ENTER-PAR G(BETA. O-2.SR+2:O-2.. +SR_ALPHA+416100-2*GHSEROO +0. CR+6.15 -121000-237..15 -121000-237. ENTER-PAR G(LMN2O5. @@ @@ LA-CR-O. ENTER-PAR G(LA4SR3O9. ENTER-PAR G(SRMNO3_HEX. +GSM3OZ-2... O-2 VA....
ENTER-PAR G(MN2O3. ENTER-PAR G(MN2O3..15 +GMN2O3-3*GHSEROO..VA:O-2.15 +3*GSROSOL+GMN2O3+GHSEROO.0).. Grundy..3.MN+3:VA:O-2. ENTER-PAR BMAGN(MN2O3. 2 1 1 MN+2 MN+3 CR+3 VA... ENTER-PAR BMAGN(MN2O3.. @@ @@ ESKOLAITE. ENTER-PHASE MNO_HALIT..0) 298.MN+3:O-2.. ENTER-PAR G(MN2O3.. SR+2.SR+2:CR+4:O-2.15 +GS2CO4. @@ SRCRO4..CR+3:VA:VA. 3 1 2 7 SR+2.0) 298.15 +GS3C2O8. NONSTOICHIOMETRIC CR2O3 SOLID SOLUTION.. MN+3 MN+4. ENTER-PAR G(S2CO4.. 3 1 1 4 SR+2...0) 298.15 +GSC2O4..SR:CR:O.15 +GMN1O1-21883. ENTER-PAR G(MNO_HALIT.MN+2.87691*T... O-2. 3 2 1 4 SR+2...0) 298.67CR2O8 ENTER-PHASE S3C2N.87691*T...0) 298..MN+3:O-2:VA. 4 1 2 2 7 SR+2. @@ SRCR2O7.15 +GSCO4.28 ENTER-PAR TC(MN2O3. ENTER-PAR G(S3C2N.CR+3:O-2:VA.SR+2:MN+4:O-2....CR+3:O-2:VA... Povoden @@ @@ SRCR2O4 ENTER-PHASE SC2O4.MN+2:O-2...0) 298.SR+2:CR+6:O-2.15 +308.... Grundy.MN+3:O-2:VA.1853365*T.0) 298. @@ @@ Mn2O3 (Compatible with C-Y2O3.0) 298.666667 2 8 SR....SR+2:SR+2:MN+4:O-2..0) 298.. ...SR+2:SR+2:MN+3:O-2.15 +309. ENTER-PAR G(SC2O4.0) 298.Appendix ENTER-PAR G(SRMNO3_HEX.. ENTER-PAR G(RP2. ENTER-PAR G(MNO_HALIT.15 +GSC2O7.MN+3:O-2....5213 -22.CR+3:O-2.. ENTER-PAR G(MN2O3.0) 298.15 +GS4O_RP2.. @@ ENTER-PAR G(SC2O7.CR+3:VA:O-2..15 +3. ENTER-PAR G(MN2O3.MN+2...0) 298...5*GCR2O3-7....MN+3:O-2:VA.15 +0..... 3 2 3 1 MN+3 CR+3. Chen...0) 298...87691*T.93845*T +71549.. 3 2.15 +GMN1O1. ENTER-PAR G(MNO_HALIT.0) 298....15 +GCR2O3+3459... @@ SR2CRO4 ENTER-PHASE S2CO4..MN+3:O-2:O-2..21048766E+04..15 +GCR2O3+GHSEROO +100000+15.... Povoden-Karadeniz 184 . O-2 VA. @@ @@ CR-MN-O... O-2. +GSM4_HEX-3*GHSEROO..CR+3:O-2:VA.15 0. CR.0) 298.0) 298...6. ENTER-PAR G(MN2O3.. Povoden-Karadeniz) ENTER-PHASE MN2O3...1) 298... ENTER-PAR G(MNO_HALIT. O-2.0). Grundy modified it in LSM modeling ENTER-PHASE RP2.. CR+3. ENTER-PAR TC(MN2O3...0) 298.. CR+6.0) 298.. Povoden-Karadeniz ENTER-PHASE SCO4.CR+3:O-2:O-2...15 -4.MN+3:VA:VA.... 3 1 2 4 SR+2.. ENTER-PAR G(SCO4.. +GSM4_HEX.... @@ @@ RP2. ENTER-PAR L(MNO_HALIT. O.15 +GMN2O3+GHSEROO +100000+15. ENTER-PAR G(MN2O3. @@ @@ SR-CR-O. ENTER-PAR G(MN2O3.15 +4. ENTER-PAR G(SRMNO3_HEX...15 +GMN2O3-2*GHSEROO +100000+15... Povoden @@ @@ NONSTOICHIOMETRIC MANGANOSITE (MNO) SOLID SOLUTION....0) 298.15 +GMN2O3.MN+3:O-2.0) 298.15 +GCR2O3-3*GHSEROO...SR+2:CR+6:O-2.15 +GCR2O3-2*GHSEROO +100000+15. O-2. ENTER-PAR L(MNO_HALIT.. O-2.0) 298.59..87691*T..15 +0.0) 298. ENTER-PAR G(RP2. CR+6..SR+2:CR+3:O-2. @@ @@ SR2. AMEND-PHASE MN2O3 MAGN.65131533E+04. doubtful phase @@ ENTER-PHASE SC2O7. O-2 VA.0) 298... O-2.0) 298... CR+4. Povoden-K.SR+2:MN+4:VA.
0) 298.MN+3:CR+3:O-2. ideal extensions from lower-order systems @@ @@ high temperature rhombohedral perovskite.28 ENTER-PAR TC(CR2O3.15 +308.MN+3:CR+3:O-2.CR+2:MN+3:O-2.. ENTER-PAR G(TMNCR2O4. ENTER-PAR G(CR2O3. ENTER-PAR TC(CR2O3.. +GMS4O. ENTER-PAR BMAGN(CR2O3. ENTER-PAR G(LS3MN2O7. Grundy...6.0) 298..0) 298.. @@ -----------------------------------------------------------------------@@ Quaternary oxides @@ @@ La-Sr-Mn-O...15 +GS4O_RP2.....15 +GCRO0 +.. ENTER-PAR G(CR2O3..CR+2:VA:O-2.47717*T. @@ ENTER-PAR G(RPEROV.15 +GCR2O3+GHSERCR.CR+3:VA:O-2.CR+2:CR+3:O-2. O-2.15 +309.15 +GCR2O3...15 +GCMN3O4.MN+3:VA:O-2... ENTER-PAR G(CMNCR2O4.15 +3.SR+2:SR+2:MN+3:O-2..MN+3:CR+3:O-2..23859*T.0) 298. ENTER-PAR BMAGN(CR2O3.15 +GTMN3O4...0).0) 298.SR+2:LA+3:MN+3:O-2. LA+3 SR+2..CR+2:VA:O-2. +GMS3O+GL2O-GL3OR2*GHSEROO+22.0) 298... @@ -----------------------------------------------------------------------@@ Quinary phases....0)..MN+2:CR+3:O-2...15 +GCR3O4+GCMN3O4-GSPINEL... MN+3 CR+3. MN+3 CR+3.15 +3.CR+2:CR+3:O-2.15 +GCRO0 -0.. ENTER-PAR G(LS3MN2O7. ENTER-PAR G(RPEROV. ENTER-PAR TC(CR2O3...6... Grundy.0) 298. ENTER-PAR BMAGN(CR2O3.15 +GTSPINEL..0) 298.CR+3:VA:O-2..CR+3:CR+3:O-2. MN+3 MN+4..CR+3:VA:O-2..SR+2:MN+2:O-2. @@ DISTORTED_SPINEL.0) 298.. ENTER-PAR G(LS3MN2O7.. ENTER-PAR G(LS3MN2O7.0) 298.15 +308..6...0) 298. 3 1 1 3 LA+3 SR+2 VA..0) 298... 185 . ENTER-PAR G(RPEROV. ENTER-PAR G(CR2O3.59. O-2.15 +GL3O_RP2+GS4O_RP2 -3*GSROSOL -GMN2O3-GHSEROO-R_RP2. CR+3 VA.SR+2:LA+3:MN+4:O-2. Grundy... ENTER-PAR TC(CR2O3....SR+2:MN+3:O-2.. O-2.0) 298.15 +308. ENTER-PAR TC(CR2O3.15 +0. 3 1 2 4 MN+2 CR+2..2923*T... ENTER-PAR BMAGN(CR2O3.. Povoden-Karadeniz ENTER-PHASE CMNCR2O4......MN+2:MN+3:O-2.0) 298.15 +308.SR+2:SR+2:MN+4:O-2.15 +GL3O_RP2.MN+2:CR+3:O-2.15 +GMN2O3+GSERCR+39503.....MN+3:VA:O-2. ENTER-PAR TC(CR2O3..CR+3:CR+3:O-2.15 +3.. .0) 298. Povoden-Karadeniz ENTER-PHASE TMNCR2O4. 3 1 2 4 MN+2. ENTER-PAR BMAGN(CR2O3.CR+2:VA:O-2. ENTER-PAR BMAGN(CR2O3. ENTER-PAR G(CR2O3...2923*T... 3 2 1 3 MN+3 CR+2 CR+3. AMEND-PHASE CR2O3 MAGN.Appendix ENTER-PHASE CR2O3...MN+2:MN+3:O-2.MN+3:VA:O-2... ENTER-PAR G(CR2O3..0) 298.47717*T.0) 298.59.. @@ @@ CUBIC SPINEL.... ENTER-PAR G(CR2O3.33333333334*GHSERCR -5. +GMS3O+0. +GMS3O+GL2O-GL3OR+GHSEROO +22....... 4 1 2 2 7 SR+2.0) 298... ENTER-PAR G(CMNCR2O4..0) 298.0) 298.SR+2:MN+4:O-2.... MN+2 MN+3 MN+4 CR+3 CR+4 VA.0) 298.0)..666666666667*GHSERCR -5. ENTER-PAR G(RPEROV. ENTER-PAR G(CMNCR2O4...0) 298.15 +309.0) 298. O-2 VA..... ENTER-PAR G(TMNCR2O4......5*GHSEROO+11.15 +GMN2O3+39503. Povoden-Karadeniz ENTER-PHASE RPEROV.0) 298.15 +GCR3O4...0) 298...0) 298.CR+3:CR+3:O-2..15 +0..0) 298...15 +3*GSROSOL+GMN2O3 +GHSEROO..15 +3.0) 298.CR+2:CR+3:O-2..0). ENTER-PAR G(CMNCR2O4..CR+2:CR+3:O-2.SR+2:MN+2:VA.6. Grundy @@ ENTER-PHASE LS3MN2O7..15 +GSPINEL. O-2..
ENTER-PAR G(RPEROV.. ENTER-PAR G(RPEROV.76318*T.. ENTER-PAR G(RPEROV.. +GVVV+3*GHSEROO.VA:MN+2:VA. +GL2O+0..VA:MN+3:O-2.. ENTER-PAR G(RPEROV..0).. @@ Optimized interactions 186 ..SR+2:MN+4:VA..VA:VA:O-2..5*GHSEROO+1... ENTER-PAR G(RPEROV.. ENTER-PAR G(RPEROV.SR+2:MN+3:VA. +GMS3O+2*GL4O-1.5*GV4O -0..0). +2*GL4O+0...LA+3:CR+3:O-2.5*GV4O+0.82596*T.VA:CR+4:VA.41263*T. +GL2O-2.41263*T..Appendix ENTER-PAR G(RPEROV..0). G(RPEROV.....5*GV4O+0..0)..62121*T.5*GHSEROO-1...LA+3:MN+2:O-2...0).1666667*GS4O +0. G(RPEROV..333*GLACR4O -2*GHSEROO+4. ENTER-PAR G(RPEROV... +GS4O. +GVVV.LA+3:CR+3:VA. G(RPEROV. ENTER-PAR G(RPEROV.5*GHSEROO-1.3333*GVVV -1.41263*T.. +GL2O+1..VA:MN+3:VA.35057*T..5*GVVV-2*GL4O -GHSEROO+9.. +GLACRO3+1. ENTER-PAR G(RPEROV... +2*GL4O-1.0)...LA+3:VA:VA.41263*T...0).0).0).23859*T.5*GVVV -2*GLACR4O+1.....0).166667*GVVV -3. +2*GVCR4O+0.5*GHSEROO+11. +GMS3O-GL3OR+2*GL4O -1....LA+3:MN+4:VA...5*GVVV-1. +GMS3O-2..0).0)..5*GVVV-GL3OR -GHSEROO+12. ENTER-PAR G(RPEROV.. +2*GV4O+0..5*GHSEROO+11.5*GVVV -2*GLACR4O-1.5*GV4O+0. ENTER-PAR ENTER-PAR ENTER-PAR ENTER-PAR ENTER-PAR G(RPEROV.0). ENTER-PAR G(RPEROV. ENTER-PAR G(RPEROV. ENTER-PAR G(RPEROV....33333*GL4O +GHSEROO+4..76318*T. +GL3OR-3*GHSEROO.0).... G(RPEROV..SR+2:CR+4:VA.0).1666667*GS4O +0.5*GVVV-2*GL4O +1. ENTER-PAR G(RPEROV..0). ENTER-PAR G(RPEROV.. +GN+0.0). +GLACRO3+1.0).5*GVCR4O+0.5*GHSEROO+11. ENTER-PAR G(RPEROV.0).. ENTER-PAR G(RPEROV... GS4O+GLACRO3-GN-0.LA+3:MN+2:VA..62121*T. G(RPEROV.LA+3:CR+4:VA. +GLACRO3....5*GVVV +2*GHSEROO+12.SR+2:CR+3:VA... ENTER-PAR G(RPEROV.VA:CR+4:O-2...LA+3:VA:O-2. +GS4V... +0...5*GHSEROO+5.5*GVVV-2*GL4O -1...VA:CR+3:VA.41263*T. G(RPEROV.VA:VA:VA...2386*T.1666667*GS4O -0. +GMS4O-3*GHSEROO.VA:MN+4:O-2..35057*T..LA+3:MN+3:VA.VA:CR+3:O-2.0).3333*GVVV-1. +GL3OR+1.5*GHSEROO -1......LA+3:MN+4:O-2....0).0).5*GV4O -0.33333*GVVV -1...SR+2:VA:VA..66667*GL4O+0.5*GVVV +1. G(RPEROV.5*GHSEROO +1...SR+2:CR+3:O-2.. ENTER-PAR G(RPEROV.35056*T..5*GV4O+0..333*GL4O -2*GHSEROO+4.0)..41263*T.0).. +2*GV4O+0.. +2*GVCR4O+0... +GLACRO3-3*GHSEROO.0).0).LA+3:MN+3:O-2.VA:MN+4:VA.SR+2:VA:O-2.0)...LA+3:CR+4:O-2.8333333*GS4V. GS4O-GN-0.. +GL3OR+1..16666667*GS4V. +GN-0..5*GHSEROO+5.16666667*GS4V.SR+2:CR+4:O-2.8333333*GS4O +0...5*GV4O +0.5*GHSEROO -1.. ENTER-PAR G(RPEROV.5*GV4O+0.2386*T.5*GV4O -1.... G(RPEROV.33333*GLACR4O +GHSEROO+4.0)...0).0).66667*GL4O+0.35056*T.5*GVCR4O+0..0). +GL3OR.... ENTER-PAR ENTER-PAR ENTER-PAR ENTER-PAR ENTER-PAR G(RPEROV. +0.166667*GVVV -0..16666667*GS4V+GLACRO3 -3*GHSEROO.33333*GVVV-1.
.MN+2:O-2. @@ @@ Ruddlesden-Popper phase...MN+2:VA....1) 298. ENTER-PAR L(RPEROV...SR+2:MN+4:O-2.LA+3:CR+3.MN+3:O-2.MN+3:O-2.0) 298.15 +GLCR3O_RP1.LA+3:O-2.....15 +2*GSROLIQ.VA:O-2....SR+2:SR+2:CR+4:O-2:O-2.... MN+3 MN+4 CR+3 CR+4...CR+3:O-2....MN+3:O-2.LA+3..15 +GSRLIQ... ideal extension from lower-order systems.0) 298... @@ Interaction parameters from ternaries ENTER-PAR L(ION.CR+2:O-2. ENTER-PAR G(ION.LA+3...15 -3. ENTER-PAR L(ION..0) 298.15 -11316. ENTER-PAR L(RPEROV. @@ -----------------------------------------------------------------------@@ Liquid.SR+2:CR+4..0) 298. ENTER-PAR L(RPEROV..54590000E+04.SR+2:CR+4.CR+2:VA..5*GHSEROO.LA+3:CR+3.6.... ENTER-PAR G(ION.0) 298.0) 298.LA+3:CR+3. -117000.. ENTER-PAR L(ION.MN+2:O-2...0) 298. @@ ENTER-PAR G(RP...SR+2:MN+4:VA. 20.15 1.SR+2:LA+3:MN+3:O-2:O-2.0) 298..15 +121000..SR+2:SR+2:MN+4:O-2:O-2.MN+3:O-2.15 GS2CO4+GLCR3O_RP1 @@ -GREFRP. -136600.. -2..1).1) 298...0) 298.0).MN+2:VA....15 +GCR2O3_L.38590000E+04.LA+3.CR+3:VA.VA. @@ Interaction parameters from binaries ENTER-PAR L(ION.15 +GMN_L.. @@ ENTER-PAR G(RP..15 0.1)..SR+2:O-2. ENTER-PAR G(ION.. 9248....LA+3:CR+3.... -136600...0) 298.. ENTER-PAR L(ION.CR+2:O-2.0) 298.15 +GS4O_RP1..LA+3. @@ ENTER-PAR G(RP...15 +2*GMN_L+GMN2O3_L-3*GMN1O1_L..0)..15 +2*GCR_L+GCR2O3_L-3*GCR1O1_L. ENTER-PAR L(RPEROV...MN+2:O-2. ENTER-PAR G(ION.LA+3:MN+4..15 +GCR_L.. -117000.LA+3:CR+4:O-2:O-2. ENTER-PAR G(ION...CR+3:O-2.SR+2:MN+3:O-2.. ENTER-PAR G(ION. ENTER-PAR L(RPEROV...0) 298.15 -4..0) 298.15 +121000.15 -119062..0) 298.MN+3:VA.MN+4:O-2.. ENTER-PAR G(ION...LA+3..SR+2:MN+2:VA.LA+3.0) 298. @@ next two interaction parameters can be used to fit @@ Cr4+ amount in perovskite ENTER-PAR L(RPEROV..LA+3:CR+3:O-2:O-2.... @@ ENTER-PAR G(RP.15 2*GCR1O1_L. @@ ENTER-PAR L(RP.0) 298. ENTER-PAR L(RPEROV.15 3766.15 -1...SR+2:LA+3:CR+4:O-2:O-2.15 GS2CO4.MN+2:VA..4. @@ ENTER-PAR G(RP.SR+2:VA... ENTER-PAR L(ION..0) 298..SR+2:LA+3:MN+4:O-2:O-2....15 100000.MN+2.....0) 298..LA+3....0) 298..0).LA+3:VA.15 +11368.0) 298..SR+2:SR+2. Povoden-Karadeniz ENTER-PHASE IONIC_LIQUID Y LA+3 SR+2 MN+2 MN+3 CR+2 CR+3.15 +GL3O_RP1+GS4O_RP1 @@ -2*GSROSOL-0... ENTER-PAR L(RPEROV.1) 298.. O-2.SR+2:SR+2:MN+3:O-2:O-2.5*t.0) 298. ENTER-PAR L(RPEROV. ENTER-PAR L(ION.. ENTER-PAR G(ION.LA+3:CR+4.15 -1297.LA+3.MN+3:O-2. @@ ENTER-PAR G(RP. ENTER-PAR L(RPEROV.SR+2:SR+2.15 +GMN2O3_L.0) 298..15 +2*GMN1O1_L. AMEND-PHASE IONIC_LIQUID COMP 2.15 +GLALIQ.29519000E+05.. 187 .VA:O-2... ENTER-PAR G(ION...0) 298. @@ ENTER-PAR L(RP......15 100000.LA+3:MN+4..5*GMN2O3 @@ +0. LA+3 SR+2. ENTER-PAR G(ION. scarce experimental data @@ ENTER-PHASE RP....0) 298.0).15 +GL3O_RP1.15 +GLA2O3LIQ.0) 298...VA. ENTER-PAR L(RPEROV. ENTER-PAR L(RPEROV. @@ ENTER-PAR G(RP... @@ ENTER-PAR G(RP.1).0) 298..... ENTER-PAR G(ION.SR+2:MN+2:O-2..LA+3.....MN+3:O-2.....15 GREFRP...0) 298.0) 298.0) 298..0) 298. 5 1 1 1 3 1 SR+2. @@ O-2.MN+2:O-2. ENTER-PAR G(ION.1) 298...SR+2:LA+3:CR+3:O-2:O-2.15 0.0) 298.15 185.1). preliminary.Appendix ENTER-PAR L(RPEROV. 250000.SR+2:SR+2:CR+3:O-2:O-2.. 250000....0) 298..5*GHSEROO.15 +2*GSROSOL+0.. ENTER-PAR L(RPEROV.5*GMN2O3 @@ -0..VA:MN+4:O-2.. ENTER-PAR L(RPEROV.. O-2 VA.MN+3:O-2.0).VA:O-2. ENTER-PAR L(ION.VA.VA.
LA+3.CR1O1.SR+2.MN+2:VA.CRH2O3.1) 298.0) 298.15 +GCR1O3_G+RTLNP.0) 298.CRH4O4.6587*T.CRH5O5.CRH1O2.. ENTER-PAR L(ION.15 -101850.0) 298.15 -101850. ENTER-PAR L(ION..MN+2:VA. ENTER-PAR L(IONIC..15 +GCRH6O6_G+RTLNP.15 +64573-23*T...0) 298.. ENTER-PAR G(GAS..15 +F10983T+RTLNP.15 +GCRH4O5_G+RTLNP.15 +HGAS+RTLNP.15 -176300.H2O1. ENTER-PAR L(ION.0) 298.. 6000 N ENTER-PAR G(GAS.0) 298..15 +H2GAS+RTLNP...49*T.15 -619869.CR1O3.1) 298.LA+3.15 +GCRH3O3_G+RTLNP.CRH1O3.LA+3.CRH1.0) 298.0) 298....CR+2:O-2. 6000 N ENTER-PAR G(GAS. ENTER-PAR G(GAS.15 +F14021T+RTLNP..15 +GCRH5O5_G+RTLNP.CRH3O4...0) 298. @@-----------------------------------------------------------@@ Cr-GAS..0) 298.LA+3.1) 298...0) 298. ENTER-PAR G(GAS..15 -15009+13.. ENTER-PAR L(ION...15 -179575....O2.. 20000 N ENTER-PAR G(GAS.CRH3O3..15 +60713-5.H1O2.. ENTER-PAR L(ION. ENTER-PAR G(GAS..0) 298..CR+3:O-2. ENTER-PAR L(ION. ENTER-PAR G(GAS..15 +504+0... ENTER-PAR G(GAS...4) 298..H1O1.CR+3:O-2... ENTER-PAR G(GAS..... ENTER-PAR L(IONIC.15 +GCRH3O4_G+RTLNP.15 200000... ENTER-PAR L(ION...CR1O2.LA+3.CR+2:O-2.CR+2:VA. ENTER-PAR L(ION. 6000 N ENTER-PAR G(GAS.CR+2:O-2. ENTER-PAR L(IONIC..0) 298.9479*T..SR+2. ENTER-PAR G(GAS.15 +GCRH2O3_G+RTLNP.15 +GCRH2O4_G+RTLNP.Appendix ENTER-PAR L(ION. 20000 N ENTER-PAR G(GAS.O.MN+2.0) 298.15 +F10963T+RTLNP...15 +GCRH1O2_G+RTLNP...15 +GCRH1O3_G+RTLNP.. ENTER-PAR L(ION.15 +46000.SR+2..CRH2O2....15 +F13349T+RTLNP.CR+2:VA..MN+3:O-2.0) 298.. 1500 N ENTER-PAR G(GAS..LA+3... ENTER-PAR L(ION.0) 298..O3.0) 298. ENTER-PAR G(STEAM.. ENTER-PAR L(IONIC..0) 298. ENTER-PAR L(IONIC.15 +GCR1O1_G+RTLNP. ENTER-PAR L(ION.....0) 298..CR+3:O-2......SR+2.0) 298..15 +F13704T+RTLNP.H2O2.15 +F10666T+RTLNP.CR+3:O-2. ENTER-PAR L(ION.15 +GCR1O3_G+RTLNP. 188 .CRH6O6..1) 298...0) 298..15 +GCR1O2_G+RTLNP.1) 298.MN+2:O-2.0) 298. ENTER-PAR L(IONIC.7.....0) 298.0) 298....MN+2..0) 298..CR+2:VA.15 -188487.. @@ @@ CRO3 reference gas ENTER-PHASE CRGAS. 1 CR1O3. ENTER-PAR G(GAS.MN+3:O-2. 1 O2.H2O1..15 -176300. ENTER-PAR G(GAS. @@ @@ H2O reference gas ENTER-PHASE STEAM..0) 298. 20000 N @@ @@ O2 reference gas ENTER-PHASE O2GAS....0) 298. 6000 N ENTER-PAR G(GAS.CR+2:VA.1) 298.15 -179575.SR+2.. 20000 N ENTER-PAR G(GAS. 6000 N ENTER-PAR G(GAS.15 +F10729T+RTLNP. ENTER-PAR G(CRGAS.0) 298.15 +F10963T+RTLNP.0) 298.SR+2... ENTER-PAR G(GAS.0) 298. ENTER-PAR G(GAS.. Povoden-Karadeniz ENTER-PHASE GAS G 1 CR CR1O1 CR1O2 CR1O3 O O2 O3 H2 H H2O1 H1O1 H1O2 H2O2 CRH1 CRH1O1 CRH1O2 CRH1O3 CRH2O2 CRH2O3 CRH2O4 CRH3O3 CRH3O4 CRH4O4 CRH4O5 CRH5O5 CRH6O6.15 -39016..CRH2O4.CR+3:O-2..15 +GCRH4O4_G+RTLNP..0) 298.CR+2:O-2.CRH1O1..CR1O3..LA+3.MN+3.H2.SR+2..0) 298.H..SR+2..15 -39016.. ENTER-PAR G(GAS...15 +F7586T+RTLNP..0) 298.0) 298..15 +GCRH1O1_G+RTLNP...0) 298.CR+2:VA.15 -619869. ENTER-PAR G(GAS.. 1 H2O1.15 +GCRH2O2_G+RTLNP...0) 298. ENTER-PAR G(GAS.0) 298. SGTE and reassessments by Chen.0) 298.CRH4O5.0) 298.15 -9111.LA+3. 6000 N ENTER-PAR G(GAS..15 -119062.
15 @@ GO PAR @@ SET-OUT-LEVEL... 189 .. N..0) 298..O2.. set-interactive +2*GHSEROO+RTLNP..Appendix ENTER-PAR G(O2GAS..
Nonmetallic Inorganic Materials. Prof. thesis: " Thermodynamic Database of the La-Sr-Mn-Cr-O Oxide System and Applications to Solid Oxide Fuel Cells". D. Georg Hoinkes and Prof. N. 1992-1999 Geoscience Studies. Burkhard. Graz. 1973. Dr. Switzerland. Abart. Karl-Franzens University Graz Master thesis: "Kontaktmetamorphose und Fluid-Gestein-Interaktion in der östlichen Monzoni Kontaktaureole". Oxygen. Erwin Date and place of birth: March 18.Curriculum vitae Curriculum Vitae Personal data Povoden-Karadeniz. 190 . Dr. Miner. Graz 1979-1983 Elementary School.. 2002. Dr. Austria Education 01/2005 – 12/2008 Ph. M. Badertscher. 143. and E. Berliner Ring. ETH Zurich. Pestalozzistrasse 5. Gauckler. carbon and strontium isotope systematics in two profiles across the Glarus thrust: implications for fluid flow. Povoden. Contr. pp. Graz Publications R. Ludwig J. Prof. Petrol. Department of Materials. Rainer Abart 1983-1991 Realistisches Gymnasium. 192-208.
J. 2006. M. T. E. Thermodynamic reassessment of the Cr-O system in the framework of solid oxide fuel cell (SOFC) research. pp. Thermodynamic assessment of the La-Fe-O system.J. Povoden. A. Chen. 2006. 569-78. Phase Equilib.J. 353-62. Gauckler. Res. Presentations Assessment of the Cr-O system in the frame of SOFC research E. J.N. T..Diff. and L. Grundy. 97.J. Ivas. Diff. E. Gauckler. A. Povoden-Karadeniz.N. Thermodynamic assessment of the La-Cr-O system. Petrol.J. Chen. 2009. Povoden. and L. Povoden. M. Grundy. to be submitted.J. 12-27. Grundy. Povoden. Ivas. Grundy. to be submitted. M. E. and L. Povoden. Grundy. 2002.N.. pp.J. M.Curriculum vitae E. Ivas. Mater.N. A. 1. E. Gauckler. Contact metamorphism of siliceous dolomite and impure limestones from the Werfen formation in the eastern Monzoni contact aureole. and L. 2006. Gauckler 191 . Phase Equilib. Thermodynamic assessment of the Mn-Cr-O system for solid oxide fuel cell (SOFC) materials. 33-41. Ivas. 30. and L. and R.N. pp. E. 99-120. Gauckler. Povoden.. Povoden. Int. Calculation of defect chemistry using the CALPHAD approach.J. A. Calphad. J. M. Gauckler. T. Thermodynamic La-Sr-Mn-Cr-O oxide database for solid oxide fuel cell applications. Miner.. T. Chen. A. A. Grundy. Gauckler. 76. 27. Chen. pp.J. Thermodynamic calculations of impacts of chromium on Sr-doped Lanthanum manganite (LSM) cathodes for solid oxide fuel cells (SOFC). E. Diff. and L. pp. Gauckler. Abart. E. Grundy. to be submitted. and L. and L. Povoden. Phase Equilib. Degradation of planar solid oxide fuel cells with (La1-xSrx)1-yMnO3 cathodes and Cr-alloy interconnects. J. (accepted) E. Gauckler. Horacek. and L.J.N. Povoden. A.N.
2005 Thermodynamic assessment of the Cr-Mn-O system for solid oxide fuel cell (SOFC) materials E. Gauckler Poster Presentation CALPHAD XXXVI. and L. September 18th – 22nd. Maastricht. Grundy. Povoden.Curriculum vitae Poster Presentation CALPHAD XXXIV. Vienna. May 6th – 11th. 2005 Thermodynamic Assessment of the Cr-Mn-O System for Solid Oxide Fuel Cell (SOFC) Materials E. Peng. EMPA Dübendorf. 2006 Thermodynamic assessment of the La-Mn-Cr-O system for applications on solid oxide fel cell (SOFC) materials E. 2006 Thermodynamic assessment of the La-Mn-Cr-O system for applications on solid oxide fuel cell (SOFC) materials using the CALPHAD approach E. Grundy. Gauckler Oral Presentation 3rd Fuel Cell Research Symposium. USA. May 06th -11th. Grundy. Boulder.J. and L. students. Povoden.J. and L.J. Gauckler Oral Presentation Thermo 2006. Colorado. A. A.D. Z. and L. 2006 The BiO3/2-SbO3/2-ZnO Phase Diagram at 1115°C in air E. 2007 Thermodynamic assessment of the La-Cr-O and LaO3/2-MnOx-CrO3/2 Systems 192 . USA. Povoden. Gauckler Oral Presentation HTMC XII. March 16th. Povoden. Austria.N. A.J. Povoden Oral Presentation 1st EMPA symposium for Ph. EMPA Dübendorf. Switzerland. Netherlands.N. Switzerland. October 20th. Pennsylvania. Pennsylvania State University.N. August 4th.
Povoden.N.5-CrO1. Povoden.J. Finland. Gauckler Oral Presentation CALPHAD XXXVI. A.5-SrO-MnO1. ETH Zurich. Pennsylvania State University. M. 2007 Thermodynamic modeling for solid oxide fuel cell research .5 and LaO1. Chen. June 27th. Gauckler Oral Presentation CALPHAD XXXVII.5-SrO-FeO1. Grundy.5 databases for solid oxide fuel cells (SOFC) applications E. 2008 Thermodynamic LaO1.J. Povoden Oral Presentation 2nd MRC Graduate Symposium . and L. Lehrstuhl für physikalische Chemie. Pennsylvania. Monatnuniversität Leoben.5-SrO-FeO1. Povoden Oral Presentation Guest Talk. 2007 The thermodynamic LaO1. March 28th. 2008 193 .5 databases for SOFC applications using the CALPHAD approach E. Grundy.The La-Sr-Mn-Cr-O system E. A.5 and LaO1. June 16th – 21st.5-CrO1. and L. USA.5-CrO1. May 6th – 11th.N.Curriculum vitae E.5-SrO-MnO1.5-CrO1. Saariselkä.
. A further reason why we use this description is that for SOFC applications we are primarily interested in the oxide portion of the phase diagram and we have found that the endmember Me(O)3 used to describe oxygen solubility in the metallic phase can inadvertently appear in the oxide portion of the phase diagram. p 2837 the correct model is (La. For these reasons. Phase Equilib. accepted. and in order to keep this assessment compatible with our previous assessments we reassess the oxygen solubility in bcc Fe using the model (Fe)(O. that it is energetically very unfavorable to simultaneously occupy both the octahedral interstitial sites on the cube faces and cube edges as these lie very close to each other.Cr)(O.O)3 is undoubtedly a reasonable model description for the oxygen solubility in bcc.3.3. lines 7-14 and Table 4.Va)1.Va)1.Erratum. p. p.X)3 is to be used…" Thus the model was also corrected in the thermodynamic assessment of the La-Fe-O system.. J. 109. Povoden-Karadeniz et al. Diff. 2007.5: "…in case there is information of the ordering of element X between different vacant positions in bcc described by (Me)1(Va)1(Va)1(Va)1 this is taken into account. In previous papers the authors have proposed the model Me(Va." .5 was given in a preliminary manuscript of the La-FeO system and is repeated here for the sake of clarification: "…as there are three octahedral interstitial sites per metal atom in the bcc unit cell located on the cube faces and cube edges Me(Va. Calphad. 31(1). (Me)1(Va.Va)3 and not (La. otherwise the disordered model for interstitials in bcc.. 112 According to the latest discussion by B.Cr)(O.5 based on the argument. Hallstedt et al. The following argumentation for modeling of the oxygen solubility in bcc using (physically wrong!) Me(O.Va)1.5….O)1.
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