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65fac53d66c138172962dc12 | 19 | We strongly recommend our dataset for future studies because of its detailed description of experimental conditions and procedures, including well defined error estimations; the consideration of a wide range of four independent parameters; the use of precise electrolyte titration techniques for establishing the composition and state of charge of the electrolytes; and the cutting-edge equipment used for the dual measurement of density and viscosity at well controlled temperatures. |
67bb9b36fa469535b9994516 | 0 | Acetylation of the nucleoside cytidine, which gives the N 4 -acetylcytidine (ac4C, Figure ) epitranscriptomic modification, has been observed in RNAs including tRNAs, rRNAs, mRNAs and various regulatory RNAs. It plays a wide range of roles in biological systems. Errors related to the modification have been found to be associated with many human diseases . More recently, acetylation of deoxycytidine, which gives the N 4 -acetyldeoxycytidine (4acC, Figure ) epigenetic modification, has also been discovered in the DNA of Arabidopsis, rice, maize, mouse, and human. It is mainly located around transcription start sites and positively correlates with gene expression levels . Several studies using synthetic oligodeoxynucleotides (ODNs) and oligoribonucleotides (ORNs) have shown that acetylation of cytosine can increase the UV melting temperature of duplex oligonucleotides (ONs) by 1 -8 °C . The knowledge sheds a light on the mechanisms by which ac4C plays roles such as enhancing protein synthesis efficiency in the biological system . This shows the significance of the synthesis of ONs containing sensitive modifications such as ac4C and 4acC as well as numerous others . However, standard ON synthesis methods requires deprotection and cleavage under strongly basic and nucleophilic conditions, under which ac4C, 4acC and other sensitive groups are unstable. Although several reported methods may be used for the purpose, they have various limitations as discussed earlier . For example, some methods can only synthesize ONs that contain thymidine or uridine only and thus do not need nucleobase protection . Some require UV irradiation for cleavage, which can damage ON . Some are limited to the synthesis of short ONs . Therefore, the development of practically useful methods for sensitive ON synthesis without any sequence limitations and with broad sensitive group scope is highly significant. Our research group recently reported sensitive ODN synthesis using the Dmoc function for linking, and the meDmoc group for the protection of exo-amino groups of the nucleobases cytosine, adenine and guanine. With these protecting and linking strategy, ODN deprotection and cleavage were achieved under non-nucleophilic and weakly basic conditions . The method enabled us to synthesize ODN sequences containing various sensitive groups including 4acC. In this paper, we report the synthesis of ODNs containing up to four 4acC modifications (ODNs 1a-d, Table ), as well as those containing the N 2acetyldeoxyguanosine (2acG, Figure , ODN 1e), N 6 -acetyldeoxyadenosine (6acA, Figure , 1f), and N 4methoxycarbonyldeoxycytidine (4mcC, Figure , ODN 1g) modifications. Unlike ac4C and 4acC, the 6acA, 2acG, and 4mcC as well as ac6A, ac2G and mc4C modifications have not been found in the nature. However, a demonstration of their incorporation into ODNs is expected to facilitate projects with aims such as evaluating their potential for antisense, RNAi, CRISPR, and mRNA therapeutic applications. |
67bb9b36fa469535b9994516 | 1 | The ODN syntheses were accomplished using phosphoramidites 2a-i, and the linker 2j (Figure ). Among them, 2a-c are standard meDmoc phosphoramidites, and 2j is a standard Dmoc linker. Monomers 2e, 2g-i are known compounds , and they were synthesized in house. The details for the synthesis of 2g-i are provided in the Supporting Information. Monomers 2d and 2f were purchased from commercial sources. The syntheses were carried out under conditions similar to those using standard phosphoramidite chemistry except that capping was achieved using 2-cyanoethyl N,N,N′,N′-tetraisopropylphosphoramidite and the nucleotide at the 5′-end was incorporated using phosphoramidite 2e. At the end of syntheses, the ODNs can be represented by 3 (Figure ), which contained a Tr group (not shown in 3) introduced by 2e. Deprotection and cleavage were achieved in three steps. In the first step, the 2-cyanoethyl groups were removed by washing the CPG with 10% DBU in ACN, which converted 3 to 4. In the second step, the Dmoc and meDmoc groups were oxidized with NaIO 4 converting 4 to 5. In the third step, the oxidized meDmoc and Dmoc groups were cleaved via β-elimination induced by the weak non-nucleophilic base K 2 CO 3 . This gave the fully deprotected ODN with a 5′-Tr group 6 (5′-Tr not shown). All the three steps were convenient to operate because during the first two steps, the ODNs were still on the solid support. Excess reagents and side products could be removed simply by washing. For the third step, the solid support and the ODNs in the supernatant were easy to separate, and the quantity of K 2 CO 3 was minute, which did not require to be removed before HPLC purification of the ODN. In addition, all the deprotection and cleavage reactions were carried out at room temperature, which ensured stability of sensitive groups on the ODNs. The ODNs were purified by precipitation with nBuOH from water to remove small organic molecules resulted from deprotection. The precipitate was then further purified with RP HPLC, which was made possible with the Tr group at the 5′-end of the ODNs. The typical DMTr group was found unstable in the NaIO 4 oxidation step during ODN deprotection and cleavage. The purified Tr-on ODN was then detritylated with 80% AcOH, and purified again with RP HPLC. The purity of the ODNs was evaluated by HPLC and capillary electrophoresis (CE, Figure ) as well as polyacrylamide gel electrophoresis (supporting information). The identity of the ODNs was confirmed with MALDI MS (Figure ). |
67bb9b36fa469535b9994516 | 2 | Using the Dmoc method, ODNs 1a-g (Table ) were synthesized. Among them, 1a-d contain one to four 4acC modifications, respectively. As shown in Figures , the acetylated ODNs showed a major peak in RP HPLC profiles. Unfortunately, besides the major ODN peak, the peak for 1a had a shoulder before the major peak, and in the profiles of 1b-d, a smaller peak appeared at ~10 minutes. However, we believe that these were caused by non-ODN materials from the HPLC system because CE analysis of the samples gave single sharp peaks (Figures ). In addition, the samples all gave single sharp peaks in MALDI MS with predicted molecular mass (Figures ), and gel electrophoresis analysis also gave single bands (supporting information). The MS data indicates that the 4acC modification was stable under the Dmoc ODN synthesis, deprotection and cleavage conditions. It is well known that 4acC and ac4C are highly sensitive modifications. It is remarkable that the ODN 1d, which contained four 4acC modifications densely packed in a short sequence, could be synthesized. The ODNs 1e-f contain a 2acG and 6acA modification, respectively. As shown in Figures , a major peak corresponding to the ODNs was observed although the peak of 1e had a shoulder after the major peak. Again, we believe that it was caused by our HPLC system because both samples gave a single sharp peak in CE profiles (Figures ), and MALDI MS gave a single sharp peak with predicted molecular mass (Figure ). In addition, gel electrophoresis analysis gave single bands (supporting information). The 2acG and 6acA modifications have not been found in nature. However, it is possible that they behave similarly as 4acC and ac4C, and may increase ON cellular stability, duplex stability, and mRNA translational efficiency. The success of their incorporation into ODN is expected to facilitate the study of these and other biophysical properties of such ODNs. It is noted that among the ODNs containing the 4acC, 2acG, and 6acA modifications, the ODN containing 2acG is most labile. The success in synthesizing ODN 1e, and purifying and analyzing it indicates that 2acG, like 4acC and 6acA, is stable enough for applications such as antisense, RNAi, CRISPR, and mRNA therapeutic development. |
67bb9b36fa469535b9994516 | 3 | Besides incorporation of acetylated nucleosides into ODNs, the ODN 1g, which contains the 4mcC modification was also synthesized. As shown by its HPLC (Figure ) and CE (Figure ) profiles, as well as MALDI MS (Figure ) and gel electrophoresis analysis (supporting information), this modification is also stable under the Dmoc DNA synthesis, deprotection and cleavage conditions. This finding is predictable because the electron density of the carbonyl carbon of 4mcC should be higher than that of 4acC. Like 2acG and 6acA, 4mcC has not been found in nature, and probably does not exist in nature. However, ODNs containing it may be useful for therapeutic development and other applications. To further confirm that the acetyl and methoxycarbonyl groups in ODNs 1a-g did not fall off from the ODNs during ODN synthesis, deprotection, cleavage, purification and analysis, the ODNs 1a-b and 1e-g were further analyzed with MALDI MS using the ODN 1h, which has the same sequence as 1a-g but does not have any modifications, as an internal standard. As shown in Figure , the mass differences of ODNs 1a-b and 1e-g, which contain one or more modifications, from the internal standard 1h, which are 42.0, 84.8, 41.1, 41.4, and 58.5, respectively, matches the predicted values 42.0, 84.0, 42.0, 42.0, and 58.0. This unambiguously confirms that the Dmoc ODN synthesis method is suitable for the synthesis of sensitive ODNs containing the modifications 4acC, 2acG, 6acA, and 4mcC. |
67bb9b36fa469535b9994516 | 4 | In summary, using the Dmoc ODN synthesis method, we were able to synthesize sensitive ODNs containing the 6acA, 2acG, and 4mcC, as well as multiple 4acC modifications without any sequence limitations. The 4acC modification is highly sensitive, and therefore the ability of the Dmoc method to incorporate four of it into one ODN sequence is remarkable. The 6acA, 2acG and 4mcC modifications have not been found in nature. However, they may behave similarly as 4acC and ac4C in terms of benefits to DNA and RNA duplex stability, and may found applications such as antisense, RNAi, CRISPR, and mRNA therapeutics. We expect that the demonstration of their incorporation into ODNs in the present work will facilitate projects aimed at studying their biophysical properties and potentials for therapeutic applications. |
67bb9b36fa469535b9994516 | 5 | ODN synthesis, deprotection, cleavage, purification and characterization: All ODNs were synthesized on an MerMade 6 synthesizer on the Dmoc support 2j (26 µmol/g loading, 20 mg, 0.52 µmol) using phosphoramidite chemistry. Deblocking: DCA (3%, DCM), 90 sec × 2. Coupling: Phosphoramidite (2a-d, 2f-i, and 2e for incorporating dC, dA, dG, T, 4acC, 6acA, 2acG, 4mcC, and the T at 5′-end of ODN, respectively; 0.1 M, ACN), 4,5-dicyanoimidazole (DCI, 0.25 M, ACN), 90 sec × 3. Capping: 2-Cyanoethyl N,N,N′,N′-tetraisopropylphosphoramidite (0.1 M, ACN), DCI (0.25 M, ACN), 60 sec × 3. Oxidation: I 2 (0.02 M, THF/pyridine/H 2 O, 70:20:10, v/v/v), 40 sec × 3. At the end of the synthesis, the 5'-trityl group was kept. The CPG (3, Figure ) was divided into 5 equal portions (~0.104 µmol ODN each). One portion was subject to deprotection and cleavage. Removing 2-cyanoethyl groups: The suspension of CPG (3, ~0.104 µmol ODN) in the solution of DBU in ACN (1:9, v/v, 1 mL) in a 1.5 mL centrifuge tube was gently shaken at rt for 5 min. The supernatant was removed. The process was repeated two more times. The CPG was washed with ACN (1 mL × 5). This converted 3 to 4. Oxidizing meDmoc and Dmoc: The suspension of 4 in the solution of NaIO 4 (0.4 M, 1 mL), which has a pH of 4, in a 1.5 mL centrifuge tube was gently shaken at rt for 1.5 h. The supernatant was removed. The process was repeated two times. The CPG was washed with water (1 mL × 5). This converted 4 to 5. Removing oxidized meDmoc groups: The suspension of 5 in the solution of K 2 CO 3 (0.05%, 1 mL), which has a pH of 8, in a 1.5 mL centrifuge tube was gently shaken at rt for 5 h. The supernatant was transferred into a clean 1.5 mL centrifuge tube. The CPG was washed with water (150 μL × 5). The combined supernatant and washes were concentrated to ∼50 μL. To the solution was added nBuOH (450 μL). After mixing by vortex, ODN was precipitated via centrifugation (14.5k rpm, ~14k × g, 15 min). The supernatant was removed leaving deprotected ODN (6) in the tube. RP HPLC purification: ODN (6) was dissolved in H 2 O (100 μL). A portion (35 μL) was purified with RP HPLC (see supporting information for HPLC conditions). The fractions of the Tr-on ODN were combined and concentrated to dryness. To the ODN was added AcOH (80%, 1 mL). The mixture was shaken gently at rt for 3 h. Volatiles were evaporated. The residue was dissolved in water (100 μL), and a portion (50 μL) was purified with RP HPLC. The purified Tr-off ODN was analyzed with RP HPLC. The ODNs were quantified using a reported method [21], and analyzed with MALDI MS. The dissolve-spin desalting method was used for preparing samples for the MS analysis when needed . The purity of the ODNs was further confirmed with capillary gel electrophoresis and PAGE. |
6355620acf6de91a611f0799 | 0 | The development of new alloy materials with desired properties is a time-consuming process that requires exhaustive experimental investigations into elemental compositions and processing conditions. These investigations are traditionally carried out in a trial-and-error manner . The properties of alloys are mainly governed by their composition, phase, and by the manner individual crystalline regions known as "grains" are arranged in the microstructure. Therefore, structural variability in alloys spans multiple scales, from the atomic to the macroscale, giving rise to a myriad of possible alloy systems. Just the elemental composition alone represents a combinatorically complex problem since finding the optimal mixture requires exploring a high dimensional materials space defined by a wide range of chemical compositions and atomic configurations for each of them. Finding new compositions and microstructures for alloys with desired properties is therefore not amenable to traditional random search approaches . This simple fact has led to a situation where modern technologies only utilize a tiny fraction of potentially interesting alloys. |
6355620acf6de91a611f0799 | 1 | Computational modeling and artificial intelligence (AI) have emerged as valuable tools to accelerate this process by simulation and prediction for a wide variety of design factors . Thermal effects on the stability of the different phases, their phase transformations, and equilibrium geometries, among others, are prominent factors hampering the computational design of alloy systems and processes. Nevertheless, progress has been made in recent years, and alloy properties that are nowadays frequently optimized include yield stress, ultimate tensile strength, and oxidation resistance . Due to the complexity of actual alloy processing, the CALPHAD (CALculation of PHAse Diagrams) method , combining experimental data and theoretical results based on thermodynamic Gibbs energy, has been widely utilized to design complicated alloy systems such as solid-solution high entropy alloys. Its Gibbs free energy functions describing an alloy system are indirectly obtained from experiments, with the caveat that probing all possible combinations of alloy elements through experimental measurement is prohibitive. An additional restriction in CALPHAD is that alloy nanoparticle design with a resolution greater than 5 nm is generally not allowed . Recently, mesoscale AI models have been developed to partially alleviate these limitations . |
6355620acf6de91a611f0799 | 2 | On the microscale, atomistic thermodynamic modeling can provide energy information and often is utilized to gain information missing in CALPHAD . The influence of atomic disorder on thermodynamic and mechanical properties has already been explored computationally for various families of crystalline materials including solid solution alloys. Given N lattice sites and p possible pure element types at each site, the dimensionality of the material space characterizing solid solution alloys scales like p N , which explodes for increasing values of N and/or p. A thorough and time-efficient exploration of such a highdimensional space requires fast (but still accurate) evaluations of the target property for every possible atomic arrangement. While state-of-the-art ab initio simulations, e.g. based on density functional theory (DFT), can yield highly accurate energetics and mechanical properties, their computational requirements still prohibit a thorough sampling of vast ranges of chemical composition and atomic configurations, even considering the computational power of massively parallel leadership supercomputers. Also, atomistic modeling of metal alloys is challenging because for non-stoichiometric compositions they are likely to form a disordered solid solution, and one needs to properly account for configurational entropy. Large-scale computational databases such as the Materials Project , the Open Quantum Materials Database (OQMD) , and the AFLOWlib database do not cover structures for sufficiently broad ranges of stoichiometry to cover relevant atomic configurations occuring in solid solution alloys. |
6355620acf6de91a611f0799 | 3 | Lattice-based models (e.g., cluster expansion ) where the atomic positions are fixed are able to accurately account for the configurational entropy. These models can be combined with Monte Carlo (MC) simulations to perform thermodynamic averages to search for optimal structures. However, the contribution of configurational entropy in the total entropy at the high temperature is sometimes small (≈15% in a previous study ), and vibrational contributions are not generally handled in lattice models . Offlattice models, e.g., interatomic potentials, utilize the details of atomic coordinates for the quantities. MC and molecular dynamics (MD) techniques with the interatomic potentials, e.g., modified embedded atom method (MEAM), are utilized to sample reliable atomic configurations and identify phase stability . |
6355620acf6de91a611f0799 | 4 | Data-driven modeling techniques allow for inexpensive and accurate predictions of material properties and thereby enable rapid screenings of large material search spaces to select potential material candidates with desirable properties . In particular, deep learning (DL) models have the potential to accurately represent complex relations between input features and target quantities, but require large volumes of training data to attain high accuracy. Graph convolutional neural networks (GCNNs) are a particular type of DL models, well suited to process data represented as graph samples. Currently, GCNN models are used as surrogates in material science to predict material properties from atomic information by directly mapping the atomic structure input to graphs, with atoms as graph nodes and chemical bonds, or nearest-neighbor interactions, as edges . |
6355620acf6de91a611f0799 | 5 | Previous work with GCNN surrogate models in materials science includes crystal graph convolutional neural networks (CGCNN) and material graph network (MEGNet) . The focus of these efforts was on using GCNNs for prediction of material properties across broad classes of stoichiometric, intermetallic, and ordered crystalline materials, sourced from the Materials Project and the Open Quantum Materials Database (OQMD) . This work showed significant flexibility of GCNNs, simultaneously handling many materials across different properties, with good accuracy relative to the original density functional theory (DFT) results. More recent work started investigating the effectiveness of GCNN models for prediction of mixing enthalpy, atomic charge transfer, and atomic magnetic moment for solid solution ferromagnetic alloys, characterized by disordered atomic configurations, with non-relaxed crystal structure and fixed volume from open-source DFT data . Results showed that the GCNN model can accurately estimate material properties as a function of the configurational entropy . |
6355620acf6de91a611f0799 | 6 | In this work, we extend the use of GCNNs to predicting the formation energy and bulk modulus as a prototypical elastic property of solid solution alloys for disordered atomic configurations in different types of optimized crystal structures with fully relaxed volumes that span the possible compositional range of the binary alloy. As an illustration, we train the GCNN model on an open-source dataset for the nickel-niobium (Ni-Nb) alloy that provides formation energy and bulk modulus calculated with the embedded atom model (EAM) empirical potential for several atomic configurations with optimized crystal structures. We investigate the performance of the GCNN with respect to the radius cutoff, which determines the size and thereby the computer time and memory requirements of the surrogate model, as well as two different graph convolutional layers that are implemented in the Pytorch-Geometric open-source library, namely CGConv and PNAConv, and report the mean absolute errors (MAEs) for combinations of cut-off radius and GCNN type. Our numerical results show that the GCNN model is able to learn the dependency of formation energy and the bulk modulus with respect to the crystal structure over the possible compositional range, but the prediction of bulk modulus is affected by greater deviations from ground truth data than energy predictions. |
6355620acf6de91a611f0799 | 7 | GCNNs are DL models for processing graph data. Representing crystal structures in the form of graphs is natural since the atoms can be viewed as nodes and metallic bonds as edges of the graph. Nodes in the graph retain atomic features in crystal structures and edges in the graph retain the connectivity and (optionally) the mutual distance between nodes. Each graph associated with a specific crystallographic structure can have global graph-level properties such as the formation energy and the bulk modulus. |
6355620acf6de91a611f0799 | 8 | Graph convolutional layers are the core of GCNNs and are used to collect information from neighboring nodes using a message-passing framework. The characterization of the neighborhood is performed through a radius cutoff, which is a hyperparameter of the GCNN model. Each node representing an atom in the structure is connected through an edge to all neighboring nodes within a distance shorter than the radius cutoff, whereas interactions with atoms with a distance longer than the radius-cutoff are disregarded. Even though metallic bonds are characterized by a "sea" of delocalized valence electrons, the cohesive bonding strength nevertheless is strongly determined by the immediate interactions with nearby atoms. Thus forcing nodes in the graph to be locally connected to all neighbouring atoms within a sphere determined by the radius cutoff accurately mimics the physics of metallic alloys. |
6355620acf6de91a611f0799 | 9 | Through consecutive steps of message passing, the graph nodes gather information from nodes that are further and further away, which implicitly accounts for many-body interactions. Global pooling layers are connected at the end of a stack of consecutive graph convolutional layers and aim at aggregating the node feature associated with each atom across a graph into a single feature. This is achieved by summing the local interactions of each atom with its neighbors and using the result to estimate global properties. Finally, fully connected (FC) layers take the results of pooling, i.e., the extracted features, and provide the output prediction for global properties. |
6355620acf6de91a611f0799 | 10 | Differing in the policy adopted to aggregate, transfer, and update nodal information through the message passing policy, a variety of GCNNs have been developed, namely crystal GCNNs (CGCNN) , and principal neighborhood aggregation (PNA) . Their corresponding graph convolutional layers are provided by the open-source PyTorch Geometric library , namely CGConv and PNAConv, and can be used by our implementation of GCNN models called HydraGNN . CGConv and PNAConv differ in the policy used to update node features using information coming from adjacent nodes in the graph. CGConv was specifically developed for atomic crystals, and uses the sum operator to aggregate information from adjacent nodes, whose importance is tuned via a learnable scaling factor. PNAConv combines multiple aggregation policies (e.g., mean, maximum, minimum, standard deviation) to enhance the discriminative power of the model in distinguishing different messages when using a graph convolutional layer, thus resulting in a better preservation of graph isomorphism. Similarly to CGConv, PNAConv also relies on learnable scaling operators to assign different importance to different adjacent nodes. |
6355620acf6de91a611f0799 | 11 | In this work we focus on models for a solid solution binary alloy, where two constituent elements are randomly placed on an underlying crystal lattice with pre-defined unit cell size. Nickel-niobium is one example where niobium and other metal elements are mixed in varying compositions to produce special nickel (Ni) steels and nickel-based super alloys. Niobium (Nb) enhances the mechanical properties, creep resistance and weldability of steels and super alloys . We therefore created and used a dataset for Ni-Nb alloys based on the EAM potential and made it available through the OLCF Constellation . The dataset includes both the formation energy as well as the bulk modulus for each alloy composition and structure. Each atomic sample has a disordered phase which is obtained starting from an initial regular crystal structure of type body-centered cubic (BCC), face-centered cubic (FCC), or hexagonal compact packed (HCP). Geometry optimization were performed using the LAMMPS simulation package to ensure that all the alloy samples reached an equilibrium geometry, characterized by negative formation energies relative to isolated atoms. The EAM potential is a reasonable choice for our purposes as it describes well the behaviors of the liquid and solid phases of Ni-Nb alloy . The structural factors and angular distributions of three atoms are well-matched with X-ray and ab initio-based molecular dynamics data. We prepared the three different crystals with different initial lattice parameters (3.52 Å for FCC, 3.32 Å for BCC, and 3.5 Å for HCP). We performed energy minimization in two steps. Firstly, we minimized the structures with an isotropic unit cell to minimize the side effects from our arbitrary lattice parameters for all other compositions. Then, we applied geometry optimization with a triclinic (non-orthogonal) unit cell to fully minimize the stress components to calculate the elastic constants. In this procedure, we chose 10,000 as the maximum number of allowable steps aimed at obtaining fully relaxed atomic geometries. Figure shows examples of relaxed geometries of initially BCC (a), FCC (b), and HCP (c) with different compositions. The input to the GCNN model for each sample includes the three components of the atom position and the atomic number. The predicted values are the formation energy and the bulk modulus. The dataset consists of three sets of crystal structures. The first set contains 46, 086 irregular crystal structures, each of them with 54 atoms, obtained through topology optimization starting from a regular BCC crystal structure. The second set contains 24, 543 irregular crystal structures, each of them with 32 atoms, obtained through topology optimization starting from a regular FCC crystal structure. The third set contains 39, 303 irregular crystal structures, each of them with 48 atoms, obtained through topology optimization starting from a regular HCP crystal structure. The atomic configurations within each set span the possible compositional range. The three sets have been merged into a global dataset, which is extremely heterogeneous in terms of crystal structures, lattice volumes, and atomic configurations. In order to ensure each composition is adequately represented in all portions of the dataset, splitting between the training, validation, and test sets was done separately for each composition. |
6355620acf6de91a611f0799 | 12 | where N elem is the total number of elements in the system, c i is the molar fraction of each element i, E i is the molar energy of each element i, and ∆E form is the formation energy. We predict the formation energy for each sample by subtracting the internal energy from the EAM-computed total energy. The formation energy is more directly related to the atomic configuration, and emphasizes the importance of an effective GCNN model for accurate predictions. The atomic arrangement makes the task of describing the material properties combinatorially complex; this represents the main difference from open source databases that have very broad elemental and mechanical coverage, but only include ordered compounds . We calculated the elastic constants from all relaxed structures through LAMMPS. The elastic constants were evaluated based on an orthotropic symmetry by calculating the components of the stiffness tensor C 11 , C 22 , C 33 , C 12 , C 13 , C 23 , C 44 , C 55 , and C 66 . The deformation strain was set to ± 0.1%. The components for the cubic crystal (C 11 , C 12 , C 44 ) were obtained by averaging the corresponding values. To estimate the upper and lower boundary of the properties for polycrystalline structures, the bulk modulus was calculated according to the Voigt (B v ) and Reuss (B R ) bounds for cubic crystals by the following equations : |
6355620acf6de91a611f0799 | 13 | where S ij are the components of compliance tensor obtained from the inverse matrix of stiffness tensor. Then, the macroscale effective bulk modulus is estimated from the Voigt-Reuss-Hill approach as . The original dataset contained a few crystal configurations with extreme values of the bulk modulus, which would have acted as outliers during the training of the GCNN model and negatively affected its predictive performance. To stabilize the GCNN training, we therefore pre-screened the dataset and removed any atomic configuration with a bulk modulus lower than 125.0 gigapascal (GPa) and higher than 1,000 GPa. |
6355620acf6de91a611f0799 | 14 | The range of values of the formation energy for the given configurations in the pre-screened dataset, expressed in units of electron Volt (eV), is (-389.96, -159.78) and the range of values of the bulk modulus in units of gigapascal (GPa) is (126.08, 237.53). Since different physical quantities have different units and different orders of magnitude, the inputs and outputs for each quantity are normalized between 0 and 1 across all data. |
6355620acf6de91a611f0799 | 15 | In Figure we show the distribution of the formation energy and bulk modulus for atomic configurations by partitioning the data according to its initial regular BCC, FCC, and HCP crystal structures before applying geometry optimization. From the first row, we notice that the possible range of the formation energy is well represented by a large number of atomic configurations for each portion of the dataset based on the initial regular solid phase, although the distribution of atomic arrangements seems skewed towards energy values that are smaller in magnitude. Moreover, the scatter plots on the second row show that the formation energy is strongly correlated with the chemical composition of the alloy. From the third row, we notice that the distribution of values of the bulk modulus has noticeable high peaked modes, indicating the values of the bulk modulus that occur most frequently across the possible set of atomic configurations. From the last row, we conclude that the dataset does not suggest any clear correlation between the value of the bulk modulus and the chemical composition of the alloy. These widespread scatter plots already suggest that predicting the bulk modulus as a function of the atomic arrangement may be a more challenging task than predicting the formation energy. |
6355620acf6de91a611f0799 | 16 | The architecture of the GCNN model has 10 graph convolutional layers with 100 neurons per layer. At first, we selected a radius cutoff of 5 Å to build the local neighborhoods used by the graph convolutional mask. We attach two FC layers at the end of the stack of convolutional layers, with 50 neurons in the first FC layer and 25 neurons in the second FC layer. Using the same GCNN architecture, two separate training procedures are performed, one to learn the formation energy and one to learn the bulk modulus. The GCNN models are trained using the Adam method with a learning rate equal to 0.001, batch sizes of 32, and a maximum number of epochs set to 200. Early stopping is performed to interrupt the training when the validation loss function does not decrease for several consecutive epochs, as this is a symptom indicating that further epochs are very unlikely to reduce the value of the loss function. The training set for each of the NN represents 70% of the total dataset; the remaining portion of the data is equally split between validation and testing. As discussed in Section 3, compositional stratified splitting was performed to ensure that all the compositions were equally represented across training, validation, and testing datasets. The training of each DL model was performed on an NVIDIA V100 GPU. |
6355620acf6de91a611f0799 | 17 | We conducted a series of "ablation studies" (one parameter is changed at a time) to monitor the change in predictive performance of our HydraGNN model with respect to the most important hyperparameters: policy of message passing performed by the graph convolutional layers, bond length as edge feature, and radius cut-off to define the local environment for information gathering. The mean absolute error (MAE) obtained by the HydraGNN models on the test dataset for predictions of both formation energy and bulk modulus are reported in Table . For both formation energy and bulk modulus, the computational time for training was on average 25,700 wall-clock seconds. |
6355620acf6de91a611f0799 | 18 | The message passing policy used to transfer information across nodes in the graph significantly impacts the predictive accuracy of the HydraGNN model. The MAEs provided in Table and the scatterplots included in the Supplementary Material show that PNAConv outperforms CGConv for both formation energy and bulk modulus, because the PNA better preserves graph isomorphism and thus better distinguishes different atomic disordered configurations. |
6355620acf6de91a611f0799 | 19 | The use of the bond length as edge features allows the graph convolutional layers to weigh the information passed across neighboring nodes based on their Euclidean distance. This additional information helps better discriminate between different crystal structures, thus enhancing the predictive power of model for accurate predictions of both formation energy and bulk modulus. This fact is confirmed both by the values of the test MAE reported in Table , as well as the scatterplots provided in the Supplementary Material. |
6355620acf6de91a611f0799 | 20 | The local environment of an atom describes the region of the crystal inside which the interactions of an atom with neighboring atoms are non-negligible. In our HydraGNN model, the size of the local environment can be adjusted through the radius cut-off, which is a tunable hyperparameter. On the one hand, increasing the radius cut-off allows to retain more information about the local structure of the crystal, with potential benefits in the predictive performance of the model. On the other hand, larger values of the radius cut-off we report the performance of the HydraGNN models using CGConv and PNAConv with values of the radius cut-off set to 3.0 Å, 5.0 Å, 6.9 Å, and 8.0 Å. The value 6.9 Å is considered because it corresponds to the value of the radius cut-off used by the EAM model that generated the training data. Although slight changes in the radius cut-off do not necessarily result in immediate changes of the predictive performance of the HydraGNN models, we can clearly see a change in performance comparing the results when the radius cut-off is equal to 3.0 Å and 8.0 Å, respectively. A very short cutoff radius of only 3.0 Å performs very poorly and has even problem predicting formation energies correctly with an MAE of 1.933 eV for the PNAConv architecture, whereas the improvement in extending the cutoff radius from 5.0 Å (MAE of 0.474 eV for PNAConv) to 8.0 Å (0.293 eV for PNAConv) with our computationally most expensive GCNN is less dramatic. The MAEs of the bulk modulus, on the other hand, are not varying smoothly as a function of the cutoff radius. This finding will be further discussed below. |
6355620acf6de91a611f0799 | 21 | Figure shows the scatterplots that compare the predictions of formation energy and bulk modulus using the PNA convolutional layer with the bond length as edge feature and the radius cut-off set to 8.0 Å. A full comprehensive set of scatterplots for CGConv and PNAConv for all the values of the radius cut-off are provided in the Supplementary Material. |
6355620acf6de91a611f0799 | 22 | When we restrict the dataset to contain only data-samples for Nb concentrations below 0.2 and above 0.8, the predictive performance of the HydraGNN model to estimate the bulk modulus improves, attaining a test MAE equal to 1.9219 GPa. The scatterplot of the predictions is shown in Figure . This is indicative of the fact that structural displacements are less commonly occurring in more regularly ordered crystal structures, and therefore outliers are less common in these structures that conform to a more regular Ni or Nb crystal lattice. |
6355620acf6de91a611f0799 | 23 | For alloy design involving atomistic models, the search for metastable and disordered crystal structures during structural sampling is unavoidable. The enormous complexity of alloy structural variability requires the use of computationally inexpensive surrogate models trained on physics-based simulation methods. In this study, we tested the performance of graph-based neural network surrogate models in predicting the energies and bulk moduli for model systems of solid solution alloy systems. Our study shows the capabilities and limitations of state-of-the-art GCNN surrogate models, by training them on data generated with EAM potentials to inform future, more computationally expensive DFT-based surrogate model development. As expected from previous reports , the surrogate-predicted energy shows good agreement with ground truth data for all composition ranges. However, the predictions from the surrogate model for the bulk modulus of the solid solution alloy model systems were less satisfactory and failed to provide a measure of ranking between them when averaged over the entire composition range. The performance is considerably improved when limiting the composition space to binary mixtures systems having one dominant component (Ni concentration lower than 0.2 and higher than 0.8) with an associated MAE of 1.9219 GPa. We attribute the difficulty of prediction bulk modulus for binary alloys with comparable Ni:Nb ratio (Ni concentration between 0.2 and 0.8) to high variations of the bulk modulus in this region, possibly due to the fact that the EAM-optimized crystal structures are often metastable and correspond only to local minima. |
6355620acf6de91a611f0799 | 24 | The traditional methodology to computationally predict elasticity is to apply different strain tensors on optimized atomic structures. However, an applied tensor can allow the system to escape from one local, metastable minimum to another, nearby minimum, which introduces deviations from a systematic exploration of structures in the elasticity calculations. These structural changes that occur during the calculation of a property for a given materials structure are unfortunately difficult to be captured correctly, using only energyminimized structures. Unless a global geometry optimization scheme is employed for each alloy composition, the accuracy of elasticity predictions for a given structure is hard to improve even if more data was included, because it is difficult to tell just from atomic coordinates alone whether a certain structure is metastable or not. |
6355620acf6de91a611f0799 | 25 | We note that there might be a way to resolve this issue, namely by improving feature engineering. For example, a recent work tried to include the attention mechanism in the GCNN for crystal properties predictions . Nevertheless, in that study, the resulting elasticity prediction improvement was not significant. Another approach might be to utilize the surrogate model to accurately predict atomic-scale potential energy surfaces, and to calculate elasticity by applying the strain tensors. Such an approach, similar in spirit to the neural network potentials by Behler and Parrinello , requires accurate predictions of stress from energy and volume under the deformation by the strain tensors. The generation of reference data in this way will likely require more effort and at least partial human supervision, in order to cover all of the configurational space. |
6355620acf6de91a611f0799 | 26 | We have presented a GCNN model to predict the formation energy and the bulk modulus for the Ni-Nb solid solution binary alloy as a function of the atomic crystal lattice structure. The numerical results describe the predictive performance of the GCNN model on an open-source dataset for model systems of a binary Ni-Nb solid solution alloy , which spans a large variety of irregular crystal structures, each obtained as the result of a topology optimization starting from regular BCC, FCC, and HCP supercells. For each of the optimized crystal geometries, the formation energy and the bulk modulus as a prototypical elastic property are provided. Our PyTorch-based architecture that implements GCNN models, called HydraGNN, allows to flexibly switch between different graph convolutional layers implemented in PyTorch-Geometric that perform different message passing policies to aggregate information across adjacent nodes in the graph, and perform a cross-comparison. The PNAConv graph convolutional layer clearly outperforms the CGConv graph convolutional layer in all cases in terms of accuracy. The HydraGNN model using the PNAConv convolutional layer shows robustness in accurately predicting the formation energy over the diverse set of optimized lattice structures, which shows the potential of GCNN models of playing a pivotal role as effective surrogate models in alloy design, since accurately estimating the formation energy is needed to identify the ensemble of stable crystal structures at a given chemical composition. We found that a radius cut-off larger than 5 Å significantly improves the predictive performance of the surrogate model for the prediction of the formation energy. The HydraGNN performance for predicting the bulk modulus seems less dependent on the cutoff radius, as large structural variations and number of local minima in intermediate concentration ranges between 0.2 and 0.8 of element composition dramatically increase. |
6355620acf6de91a611f0799 | 27 | For future work, a partial improvement of the predictions may be obtained by generating a new dataset where the topology optimization is run with more stringent convergence requirements to ensure that the final crystal structure is fully relaxed. In fact, for some of the crystal structures contained in the current dataset, convergence was not fully reached since the bulk modulus is more sensitive to small changes in geometry than the formation energy. Therefore, the fidelity of bulk modulus evaluations is lower than for the formation energy, which in turn limits the attainable accuracy of the HydraGNN model to predicting the former compared to the latter. Additional improvement in the predictions of the bulk modulus may also be obtained by including additional input features, both geometric features describing the overall crystal structure (e.g., angles) as well as chemical features for each atom species (e.g., valence electrons, electronegativity/electropositivity, atomic mass, atom size), fed into the HydraGNN model. |
631d528a49042ad4acd30fcc | 0 | Lead halide perovskite solar cells (PSCs) have demonstrated power conversion efficiencies (PCE) up to 25.7%, matching the state-of-the-art silicon solar cells (26.1%). These threedimensional perovskite materials (ABX3) typically include a large cation A + (for example: CH3NH3 + , HC(NH2)2 + or Cs + ), a smaller cation B 2+ such as Ge 2+ , Pb 2+ , Sn , and halide anions X -(for example: I -, Br -, Cl -). The formation of perovskite crystals typically needs to fulfil the Goldschmidt tolerance factor (GTF) defined by the equation 𝐺𝐺𝐺𝐺𝐺𝐺 = (𝑟𝑟 𝐴𝐴 + 𝑟𝑟 𝑋𝑋 )/�(𝑟𝑟 𝐵𝐵 + 𝑟𝑟 𝑋𝑋 ) , where 𝑟𝑟 𝐴𝐴 , 𝑟𝑟 𝐵𝐵, 𝑟𝑟 𝑋𝑋 are the radii of A, B and X ions. A large number of different perovskite materials can be formed based on different permutations of the ionic precursors. Optimization of these precursor ratios has helped to improve the performance as well as stability of these compounds. The latter has to date still proven more challenging due to their sensitivity towards moisture, oxygen, light, temperature and electrical bias, among other factors. Ruddlesden-Popper perovskites (RPPs) are a related material class that has shown some promise to be more resilient to environmental stress then conventional ABX3 perovskites. In this work, we study RPPs with the general formula R2(MA)n-1BnX3n+1, where the R + stands for a large cation(s) which typically does not satisfy the GTF rule, methylammonium cation (MA + ), B 2+ metal cation, and halide anion (X -). The quasi-2D structure of RPPs is shown schematically in Figure . Due to their large size, the R + cation cannot be incorporated into the 3D perovskite lattice. |
631d528a49042ad4acd30fcc | 1 | Instead, they assemble into layered separated slabs of [BX6] 4-octahedra and intercalated MA + cations with a structure similar to the one found in ABX3 perovskites. The dielectric mismatch of organic and inorganic components creates a favorable environment for the formation of quantum wells and barriers, generating an excellent perovskite for excitonic phenomena. Like their 3D counterparts, RPPs have easily tunable band gaps, can be solution-processed, and exhibit high device PCE of ~17-18 %. Crystals of RPPs confer a stability increase by virtue of the hydrophobic aliphatic layers of its alternating structure limiting water ingress, and like 3D PSCs, their properties can be enhanced with a range of perovskite additives. For example, polyvinylpolypyrrolidone (PVP), which is widely employed in 3D PSCs, exhibits hydrogen bonding between its carbonyl groups and the protic polar species present in the RPP, leading to the creation of a polymer framework around the crystal structure that furthers enhances stability Additionally, the use of different R + in the crystal lattice relaxes the GTF requirement, resulting in potentially hundreds of thousands of undiscovered, yet highly-performing, compositions. While the RPPs PSC stability is impressive, the current manually fabricated spin-coated devices limit research progress and technology transfer because of lack of cross-laboratory standards and reproducibility. The implementation of fully automated and standardized fabrication and measurement techniques would help to significantly improve the comparability of results between different users and different laboratories. Most highly efficient lead halide PSCs were fabricated via a spin-coating process, yet a number of alternative fabrication techniques have already been employed, primarily: doctor blading, spray, ink-jet, meniscus printing or vacuum deposition. These methods require great skill to control and optimize the film crystallization kinetics, precursor rheology and impact on the film quality. This imposes significant financial and time costs on the optimization of fabrication processes required for production of perovskites with a high degree of reproducibility. Another factor that slows down the progress is the use of one-step-at-atime classical systematic experimentation procedure that has a substantial disadvantage of not considering interactions between input parameters. Remarkably, RPP perovskite precursor solutions at molar concentrations (M) below ~0.7 M crystalize into uniform and highly crystalline films when deposited via a simple drop-casting technique. An interesting method was employed in 2021 by Zuo et al., who used a simple drop casting methodology on mildly preheated substrates for perovskite fabrication. The authors demonstrated that by lowering the concentration of the perovskite precursor solution (< 0.5 M), the solution could spread more evenly across the substrate and form self-assembled, vertically oriented and efficient perovskite films. Extraordinarily, such a simple technique creates new opportunities for rapid compositional screening using drop-cast precursor solutions to form high quality perovskite films. It is known that the reproducibility of PSC fabrication is severely hindered by subtle changes in environmental conditions during deposition, which is likely to impact negatively on the optimization of the fabrication process avoiding this can be accomplished by partial or complete removal of manual handling and human error. In this technique, the mechanism of RPP film formation originates from the precursor solution-substrate surface interactions. Unlike for their 3D counterparts, there are fewer RPP studies focused on crystallization or spread mechanisms (e.g., using additives), controlling the spread and wetting process to ultimately optimize the quality of the resulting RPP film. The drop-casted RPP perovskite film quality depends on a number of factors, such as precursor molarity, substrate temperature and roughness, hydrophilicity or hydrophobicity of the perovskite adjacent charge transporting layer and spread of such precursor, and environmental conditions (pressure, humidity, temperature, atmosphere). Given these factors, we focused on the development of an inexpensive, yet highly controllable and rapidly deployable, technique that expands the mechanism of manual perovskite drop-casting to a rapid combinatorial screening. Herein, we describe the automated, machine learning enhanced combinatorial high-throughput (cHTR) screening deposition strategy that allowed for fabrication of multiple new perovskite film compositions via carefully aliquoted, microfluidically prepared precursors. Our bespoke design of experiment (DoE) allows for fabrication of each PSC layer completely free from human intervention. To further accelerate the parameter optimization process, we developed a state-of-the-art machine learning (ML) protocol from the measurement of electrical and physical properties. This model allows for making predictions on the likely PV properties of RPP films based on a given set of fabrication input parameters. ML algorithms were also used to explore amongst parameters to find the best combinations of permutations in order to develop the device with the highest PV properties. To demonstrate our DoE in this work (Figure ) we selected a small sub-set of compositional and fabrication parameters to be varied and only allow a limited number of discrete values which we chose based on our previous knowledge of RPPs. Within this parameter space we then chose a limited number of permutations, fabricated the RP PSCs, and evaluated their photovoltaic performance. These data sets were then analyzed and employed as data to train a machine learning model. The trained model was then used to gain deeper understanding on the influence of specific parameter values on device performance and to predict a parameter set with optimized performance. For each of the components, there is a number of possible candidates which can be mixed in arbitrary ratios, spanning a de-facto infinite compositional parameter space. In a similar way there is a plethora of processing parameters which need to be defined that will ultimately determine the morphology and quality of the resulting perovskite layer and its performance in a photovoltaic device. This bespoke DoE and the ML model allowed for identification of completely new, improved RPP composition that surpassed the performance of the experimentally chosen champion from the initial subset, yielding to an entirely new champion solar cell with a PCE of ~16.3 % for an active area of 0.1 cm 2 . |
631d528a49042ad4acd30fcc | 2 | Our DoE began with the selection of the parameter space. The main focus was oriented on generating new quasi-2D RPPs. The variables considered are shown in Figure . This defines a parameter space with: 10 × 4 × 5 × 5 × 4 × 4 = 16,000 possible permutations. To ensure reproducibility, all the halide salts of 2D and 3D cations were mixed in stoichiometric ratios to obtain the RPP solutions, resulting in films with specified n-numbers, cation, and halide compositions. The drop-casted solutions further contained additives or alternatively were additive-free (denoted as "none"). The temperature of the perovskite annealing step was also varied. This selection permitted for semi-random list of 100 recipes of theoretically highperforming RPPs. See Supplementary Information for further experimental details. AVA is 5-amminovaleric acid, PEA is phentylammonium, GUA is guanidinium, FA is formamidinium, MA is methylammonium, I is iodide, Br is bromide, MASCN is methylammonium thiocyanate, MACl is methylammonium chloride (where LC is low concentration and HC is high concentration), HI is iodic acid, and None stands for equivalent pure solvent used for dissolving the rest of additives. The RPP film post-annealing was also a varied parameter as denoted. |
631d528a49042ad4acd30fcc | 3 | Importantly, we demonstrate a new, easily adaptable cHTR deposition system that allows for the rapid combinatorial screening of quasi-2D RPPs. We tracked all experimental deposition conditions and parameters to serve as an additional productivity measure and reproducibility check (Supporting Information). This high-throughput system employed pre-cut and prepatterned substrate reported by us earlier, along with a microfluidic precursor solution agitating and dosing system. The substrates were thoroughly cleaned and then automatically coated with NiO following the previously reported method (see Supplementary Information for exact fabrication details). By accurately controlling the precursor aliquots via pre-defined strokes of programmable syringe pump (Chemyx 4000), we were able to quickly and accurately fabricate any given perovskite system. In short, the proposed cHTR system allows us to mitigate the impact of human-induced error, thus improving the lab-to-lab and user-to-user reproducibility. This systematic automated DoE is a promising step towards fully unbiased, rapid exploration and population of vast compositional spaces in order to streamline the generation of a large and widely accessible perovskite libraries of unforeseen quality. After the perovskite deposition, a multi-step evaporation process was employed to assure reproducibility and uniformity of the devices. Finally, we fabricated 600 individual solar cells following the proposed recipes, and then proceeded with the data extraction through the automated electrical characterization (see Supporting Information for more details) whilst ensuring that the only possible difference in the results would originate from RPPs films. |
631d528a49042ad4acd30fcc | 4 | Here, we instead used ML techniques to explore the quantitative relationships between the device fabrication parameters and the photovoltaic performance parameters (PCE, VOC, JSC and FF) of the resulting solar cell devices. To the best of our knowledge, this is the first reported study that employs ML optimization combined with automated fabrication process to design PSCs. We used the MLREM (Multiple Linear Regression with Expectation Maximization) algorithm implemented in the CSIRO-BioModeller® package. In general, ML models require descriptors (mathematical entities that encode physical or chemical properties) to find relationships between descriptors and the target property. In our dataset, the majority of data points (RPP PSCs) had the same chemical components, so molecular descriptors were not required. Thus, we used the list of fabrication parameters for devices (Figure ) as descriptors to build the models. In our DoE we used 1-hot binary descriptors (i.e., 1 if feature is present and 0 if absent) for fabrication parameters such as: 3D-cations, halides, additive options, nnumber of option and annealing temperature. |
631d528a49042ad4acd30fcc | 5 | The MLREM algorithm is a very sparse feature selection method that removes less relevant descriptors in a context-dependent way and optimizes the balance between the variance (model complexity) and bias (model simplicity). The Laplacian prior method is used to give zero weight to irrelevant descriptors and automatically remove them from the model. This feature selection algorithm is similar to the LASSO technique, and is based on L1 regression. In a general machine learning modeling procedure, the dataset would be divided into a training set (e.g., 80% of dataset) to generate the model and a test set (e.g., 20% of the dataset) to evaluate the predictive power of the model. In this study, our aim was mainly focused on investigating the contribution of fabrication parameters on PCE, VOC, JSC and FF rather than developing a model for property prediction purposes. Therefore, we derived the models by applying 100% (squared correlation coefficient), and the standard error of estimation (SEE). Table shows the statistics of MLREM models for PCE, VOC, JSC, and FF. These results indicate the significant parameters (descriptors) for each property. Figure shows the contribution as well as the effect of descriptors on each property where the parameters with positive and negative sign increase and decrease the values of property, respectively. The contribution effects indicated how certain modifications can in general increase or decrease PCE, VOC, JSC, and FF. For example, in the 2D cations category, the AVA can increase PCE, VOC, JSC, and FF, while PEA and GUA negatively impact all of them. The mixture of BA:PEA and BA:GUA positively impact all of them. The mixture of BA:AVA, AVA:PEA and AVA:GUA had very small impact on all properties. The mixture of PEA:GUA showed a negative effect on all properties. In summary, within the 2D cations category, GUA exhibited the largest negative effect while the mixture of BA:GUA showed the largest (or second largest) positive effect on PCE, VOC, JSC, and FF, as they have the largest negative and largest positive coefficients respectively. |
631d528a49042ad4acd30fcc | 6 | In the halides category, the machine learning algorithm showed that adding bromine to iodine can decrease PCE while the opposite trend was shown for VOC. Machine learning algorithms also demonstrate that including 0.025 bromine to iodine would increase JSC and FF, while adding more bromine could decrease the aforementioned properties. Also, by comparing the coefficient contribution of iodine with hydrogen iodine, the PV properties will be increased. In summary, the 35%MACI has the largest positive effect on PCE, VOC and JSC while for FF the 5%MASCN has the largest positive contribution. |
631d528a49042ad4acd30fcc | 7 | In terms of n number of options, there is a pattern that shows increasing the number of option from n=9 up to n=30 decreases the PV properties, while from n=30 to n=60 there is a less negative effect in PCE, VOC, JSC and FF. Machine learning algorithm also indicated that the temperature 140 °C is the optimum temperature for all PV properties. |
631d528a49042ad4acd30fcc | 8 | In the final part of our study, we extracted and employed results from ML models to investigate the effect of fabrication parameters on PV properties. By only applying the parameters that can increase the property values shown in Figure , we obtained the champion recipe, which we used to fabricate the final batch of 2DRP PSCs. The final solar cells were tested for their performance (PCE, VOC, JSC and FF). The fabrication details can be found in the Experimental Section, and the performance metrics can be viewed in Figure in Supporting Information. |
631d528a49042ad4acd30fcc | 9 | A comparison between the photovoltaic properties of the new device based on the champion recipe suggested by machine learning (ML champion) with the experimental champion is shown in Figure . For both experimental and ML champion, we measured the PV properties seven times and each time by forward and reverse measurement, and then compared the results. For PCE, JSC and FF, the devices suggested by ML produced a higher PV values. Only for VOC did the ML champion recipe exhibit a slightly lower value than the experimental champion. Notably, the range of VOC values for each measurement is minimal, which means that the VOC values of this device are extremely reproducible. |
631d528a49042ad4acd30fcc | 10 | Here we describe a new DoE with the combination of a bespoke ML protocol and a reproducible perovskite film fabrication technique that allows for rapid, combinatorial studies and screening of potentially hundreds of thousands of compositions. Our experimental cHTR system can be easily adopted and serve as an inexpensive, cross-reference tool for perovskite material fabrication. The automated approach reduces the sample-to-sample variation of manually produced materials, resulting in better precision of resulting films which could be directly fed into a ML protocol with high degree of trust. Notably, we have shown how the combination of automated perovskite film fabrication and ML modelling can rapidly generate unseen RPPs recipe with improved performance. The ML models elucidate the contributions of key fabrication parameters to make device performance characteristics, aiding the process of device improvement. The complete tracking of the key fabrication steps and conditions and automated performance measurements proposed here generated useful data to train ML models that were subsequently used to design improved PV materials. The insights from the ML models significantly shortened the discovery time and increased productivity. Importantly, our study revealed that some complex compositions, parameters, and additives can be synergistically screened which further accelerates progress in the perovskite photovoltaics. In comparison with manual fabrication, our methodology provides large improvements in the reproducibility and reliability of device manufacture. Moreover, our materials are made in similar conditions to manual drop-casting methods and hence can serve as a state-of-the-art comparison setup. The tracking of all parameters and precise precursor mixing allows for multiple tests and improvements, as well as staggered bleaching. ML protocols significantly narrowed the distribution of parameters that had already been lowered by automation and facilitated fabrication of samples. These results pave the way for rapid, large-scale discovery studies where each fabrication step is carefully recorded and the complete protocol can be reproduced reliably without the variability inherent in manual methods. We have shown that such complex dissection of the fabrication process and automation of crucial steps allows for construction of data libraries that serve as cross-research group reference points and as training data for computational models. In summary, automated fabrication combined ML modeling allows the fabrication of optimal, efficient RPP films of high reproducibility that can be incorporated into devices with very good efficiencies and high long term environmental stability that can readily translate to industrialization of PSCs. |
631d528a49042ad4acd30fcc | 11 | The perovskite precursor solution was prepared in a N2-filled glovebox (MBraun, 02< 0.01ppm, H2O<0.01 ppm) by mixing powders to a specified recipe in order to cover 100 different recipes described. As the stock solution anhydrous N,N-dimethylformamide (DMF), dimethyl sulfoxide (DMSO) and γ-Butyrolactone (GBL) were mixed in order to achieve 4:1:1 v/v. Stock solutions containing MASCN and MACl were produced by adding them proportionally in order to achieve specified concentrations in a 1 mL mixture (4: |
631d528a49042ad4acd30fcc | 12 | Perovskite Solar Cell Fabrication: We used the same perovskite fabrication technique for both films and solar devices. Pre-cut and commercially pre-patterned ITO-coated soda lime glass substrates (Latech, 10 Ω cm -2 ) were cleaned in sequence by sonication in: Milli-Q water (10 minutes at 25 °C), 2% Hellmanex® solution (10 minutes at 25 °C), acetone (10 minutes at 40 °C), isopropanol (15 minutes at 40 °C), ethanol (10 minutes at 25 °C). The substrates were subsequently treated with oxygen plasma for 12 minutes. We then fabricated ligand-modified NiO films employing method developed by Michalska and Surmiak et al. Subsequentially, such prepared substrates with NiO films were transported to the glovebox with the system; they were then preheated on hot plate at 100 °C for 30 minutes and the N2 was constantly applied onto the hot-plate area to remove residual H2O. After that the substrates were brought to deposition pre-set temperature on programmable hot-plate stage. The precursor solution was pushed through the ultrasonic piezoelectric microfluidic device (see Supporting Information for more details) by programmable syringe pump (Chemyx 4000); the purity of the composition is ensured by emptying the dead volume from tubes (at least 3 times the tube length of 20 cm) into the purging waste container. Each pre-heated substrate located inside the cavity was blown with N2 gas to remove any residual particles directly prior the deposition. Aliquots of 6 µL of perovskite precursor solution were deposited on the substrate and 10 seconds was allowed for the precursor solution to spread across the surface prior to quenching with an applied N2 gas stream. The hot-plate was subsequently heated up to chosen annealing temperature, with the temperature maintained for 60 minutes, followed by cooling of the films naturally to RT. |
631d528a49042ad4acd30fcc | 13 | Samples to be used for complete device fabrication were transported in a sealed container into the evaporation glovebox. For complete devices, the perovskite edge was mechanically removed, followed by evaporation of fullerenes C60 (20 nm at 0.1 Å s -1 via thermal evaporation), C70 (10 nm at 0.1 Å s -1 via thermal evaporation), and then bathocuproine (3 nm at 0.1 Å s -1 via thermal evaporation). The devices were completed by the evaporation of 65 nm of the gold electrode at 0.5 Å s -1 through the evaporation mask. The devices were stored in a N2 glovebox for 1 day in the dark before characterization. |
631d528a49042ad4acd30fcc | 14 | Performance characterization: The current density (J-V) characteristics of the devices were measured using a fully automated combinatorial high-throughput solar cell measurement system that was reported by us previously. To simulate solar light, an ABET 3000 solar simulator with a xenon arc lamp, fed with 1000 W input power was used. The light intensity was calibrated using a professional reference silicon cell with an IR-cut off filter (KG5, Schott). |
631d528a49042ad4acd30fcc | 15 | The J-V curves were measured using a BioLogic VMP3 potentiostat in 4-wire sense configuration. All measurements (J-V dark, J-V light, stability and maximum power point tracking) were taken automatically without human interaction employing a high-throughput measurement technique developed by Surmiak et al. A 5 minutes break was applied where the devices were cooled down by a laminar flow of N2. The voltage step was set to 10 mV s -1 , starting voltage was in the reverse direction, and no bias conditioning or light soaking was applied. The working area of the devices was set to 0.1 cm 2 . |
631d528a49042ad4acd30fcc | 16 | Three-dimensional (3D) perovskite solar cells (PSC) reached power conversion efficiencies While thermal and moisture degradation can be minimized using encapsulation, additives or moisture-and oxygen-free fabrication environments, further degradation mechanisms have been reported. These include halide segregation, UV-light induced degradation, ionic movements, decomposition of complex inorganic-organic structures and problems induced by electrical stress. For commercialization of PSCs to be realized, research focus should not be limited to maximizing the efficiency on a smaller laboratory scale, but should be expanded to routinely include inexpensive materials that are deposited with industry-compatible production methods. Typically, most electron and hole accepting layers, along with the perovskite layer itself, are deposited by spin coating, which is not suitable for large-scale or high-throughput applications. To overcome this hurdle, a number of deposition techniques have been employed |
631d528a49042ad4acd30fcc | 17 | for PSC fabrication, such as blade coating, spray deposition, roll-to-roll printing, ink-jet printing and vacuum deposition techniques. While these methods provide a pathway towards commercialization, several challenges still remain. In particular, small variations in wettability, thickness, roughness and morphology causes non-uniformities over large areas, with these variations causing shunts, or even pinholes, which can short-circuit the device. where key parameters can be controlled, allowing for highly reproducible results. cHTR |
65bd55c3e9ebbb4db98a19bd | 0 | MXenes belong to the class of two-dimensional (2D) transition metals carbides or carbonitrides with the general formula of M n+1 X n T x (n = 1-4), where M stands for a transition metal, X for carbon and/or nitrogen, and T for surface termination groups (e.g., -OH, -O, and -F). 2D MXene nanosheets are synthesized by the selective removal of metal atoms (e.g., Al) from precursor materials that belong to a large family of layered carbides/nitrides called MAX phases. The wide range of possible compositions and rich surface chemistry distinguishes MXenes from other commonly studied 2D materials such as graphene and transition metal dichalcogenides. In the past few years, experimental studies of the physical and chemical properties of various MXenes have revealed their great promise for a broad spectrum of applications including electrochemical energy storage, flexible and transparent electronics, chemical and biosensing applications, water desalination and purification, electromagnetic shielding, and catalysis. Despite their intriguing performance, rapid degradation limits the practical applications of MXenes. |
65bd55c3e9ebbb4db98a19bd | 1 | Their 2D nanosheets tend to undergo rapid degradation in aqueous media or humid environments, resulting in the formation of their respective metal oxides. Even the most stable and the most studied Ti 3 C 2 T x MXenes show notable degradation after being dispersed in water for a week. While the lifespan of dried freestanding Ti 3 C 2 T x -MXene layers can be extended even for years, films of different compositions can degrade when stored at ambient conditions. Recent studies have identified two major culprits causing the degradation of MXenes: water and oxygen molecules. The reported exponential decay in the rate of oxidation of MXenes exposed to a humid environment suggests the existence of active sites catalyzing the oxidation reaction. While these sites are saturated, the reaction slows down. Several studies hypothesized that edges of MXenes are more prone to oxidative degradation, while others suggested that degradation starts at the basal plane of MXenes and that the presence of defects should be considered a possible source of instability. Since the conflicting opinions on the origin of material degradation can lead to different degradation prevention strategies, revealing the active sites catalyzing the degradation process is pivotal for the effective design and implementation of MXene-based materials. |
65bd55c3e9ebbb4db98a19bd | 2 | Termination groups are exposed to the environment and can be one of the key factors determining the stability of MXenes. Although MXenes are known for rich and tunable surface chemistry, the role of termination groups in degradation processes remains poorly understood. Moreover, the rich surface chemistry of MXenes represents a significant challenge for ab-initio-based simulations due to a large combinatorial space of surface compositions. Therefore, most of the previous simulations were focused mainly on fully O-, OH-, or F-terminated MXene, which cannot be realized experimentally. Several computational studies quantified the role of termination groups in the stability of MXenes by employing ab initio thermodynamic analysis (i.e., by constructing Pourbaix diagrams and calculating defect formation energies ). These studies indicated that O-terminated MXenes are the most stable, while the presence of hydroxyl and fluorine termination groups decreases the stability, promoting the formation of Ti vacancies. More recent studies employing ab initio molecular dynamics (AIMD) simulations revealed spontaneous degradation of O-terminated surface MXenes surfaces (e.g., Ti 3 C 2 O 2 36,37 and V 2 CO 2 ) in contact with an aqueous environment. These works emphasize the need for advanced computational methods to evaluate the stability and understand the atomistic mechanism of MXene degradation. |
65bd55c3e9ebbb4db98a19bd | 3 | In this computational study, we investigated the degradation reactions at the interface between 2√3 x 4 surface cells of Ti 3 C 2 T x (T x = OH, O, Cl, F, and their mixture) and aqueous solution (Figure ), revealing sites that are the most prone for degradation reaction. (see SI for more details) To quantify the kinetic aspects of MXene stability in contact with water, we used AIMD simulations complemented with enhanced free energy sampling. These methods have been successfully used by us and others to study catalytic and degradation reaction mechanisms at solid-water interfaces. To evaluate activation energy associated with Ti atoms oxidation at MXene-water interfaces, we divided the trajectories obtained from the slowgrowth method into simulation windows separated by 0.1 Å and performed Blue-Moon sampling simulations, collecting energy gradients acting on Ti atom during at least 5 ps and further integrating the trajectory to get free energy surface. The distance between Ti and C atoms was chosen as a reaction coordinate, and the simulations were carried out until the gradients acting on Ti reached zero. As shown in Figure , the release of Ti from the subsurface to the MXene surface is followed by the attack of H 2 O molecule, leading to the stabilization of Ti-OH complex above the termination groups. We further calculated the activation energies (E A ) of the described reaction by integrating the energy gradients along the reaction coordinate. The process is possible to occur spontaneously at the O-terminated Ti 3 C 2 surface 36 due to a low E A of 0.28 eV, as shown in Figure . However, the release of the second Ti atom on the same surface was found to be much less favorable, with E A of 1.04 eV (see Figure ). This result is in qualitative agreement with recent simulations conducted for V 2 CO 2 . We attribute this behavior to changes in electrostatic potential associated with the formation of Ti(V)-OH dipole, as explained in more detail below. We further calculated E A for Ti sites at various Ti 3 C 2 T x surfaces, including O-, OH, F-and their mixed terminations (see Table ). Our simulations revealed that E A varies from 0.28 eV for the O-terminated surface to more than 3.9 eV for the OH-terminated surface, depending on the global composition of We first explored local properties associated with specific Ti sites at Ti 3 C 2 T x surfaces. Figure shows the correlation between the E A and d-band center of Ti site, which characterizes d-orbital occupancy and is commonly applied in predicting the reactivity of transition metals. We propose that the d-band implies a stronger bond, leading to higher E A values of reactions involving bond disruption. The positive correlation between activation energies and Ti vibration frequencies (Figure ) was found to be the strongest among the studied local descriptors. The lower frequency corresponds to softer out-of-plane Ti vibrations, leading to a less steep energy surface for Ti release. In this work, we used the vibration frequencies of Ti along the c-direction, which can be calculated by displacing single Ti atom and fixing the rest atoms in the unit cell as implemented in the finite differences approach. This method is very computationally efficient, while the calculated frequencies demonstrate good agreement with a more accurate projection of the phonon band on Ti atoms (Figure ). These findings highlight an important role of dynamic features, such as vibration frequencies and phonon modes, as promising descriptors associated with not only the conductivity of small ions, but also with surface reactivity and stability. |
65bd55c3e9ebbb4db98a19bd | 4 | We further explored correlations between E A and global properties of Ti 3 C 2 T x surfaces, such as an average distance between Ti and water molecules and work function. We initially hypothesized that a short distance between outer Ti atoms and the first water layer (i.e., "wettability" of Ti 3 C 2 T x surface) could promote a water attack reaction. We calculated the first peak position d Ti-H2O of the radial distribution function (RDF) between water molecules and the outer Ti layer (Figure ), which indicates the average distance between Ti and O atoms belonging to the first layer of water. However, our simulations revealed a relatively weak correlation between d Ti-H2O and E A (Figure ), suggesting that the proximity of water to Ti is not a determining factor of reaction rate. On the other hand, AIMD simulations revealed a strong negative correlation (R 2 = 0.822) between E A and work function of Ti 3 C 2 T x surfaces (Figure ). This property describes the position of the Fermi level in relation to a vacuum level and is associated with the electrostatic potential of the surfaces. Several previous studies correlated work functions to the catalytic activity of metallic surfaces. However, the effect of work function on surface stability has not been explored. In this work, we discovered that the stability of Ti 3 C 2 T x surfaces is linked to their work function: Ti 3 C 2 T x surfaces with lower work functions generally demonstrate higher stability (Figure ). As discussed earlier, we also observed that the subsequent oxidation and release of Ti atoms raised the E A for future reactions, hindering the degradation. We now attribute this behavior to the alteration in work function (6.26 eV vs 6.07 eV after the release of Ti) due to the formation of a Ti-OH dipole on the surface of Ti 3 C 2 O 2 . |
65bd55c3e9ebbb4db98a19bd | 5 | After establishing the structure-stability relationships, we utilized the selected above descriptive properties to predict the stability of Ti 3 C 2 T x with various compositions of termination groups and to identify sites catalyzing the degradation reaction. In order to build a predictive model and identify the best combination of descriptors, we employed symbolic regression machine learning algorithms as implemented in SISSO code. The best performing model obtained after dimensionality reduction (see Figure ) relies on two descriptive properties: |
65bd55c3e9ebbb4db98a19bd | 6 | where E A is the predicted activation energy of Ti release, Φ is the work function (eV) and ω stands for the vibrational frequency of Ti along the c direction (THz). Our results suggest that decreasing the work function of Ti 3 C 2 T x surface and avoiding Ti sites that are loosely anchored to the subsurface (as characterized by soft phonon modes) can improve the surface stability. These surface properties can be rapidly calculated for MXene of any selected composition and therefore, can be used for computational screening and the selection of surface chemistries impeding degradation reactions. can be further used to investigate other possible culprits of degradation reaction, including the role of defects and edges, and would shed light on the instability of MXenes beyond Ti 3 C 2 T x. |
65bd55c3e9ebbb4db98a19bd | 7 | To calculate the Ti vacancy formation energy for Ti3C2T2, unit cells with one removed Ti atom were prepared, cells parameters were fixed, and atomic positions were relaxed. The Ti vacancy formation energy was defined as 𝐸 V = 𝐸 defect -𝐸 perfect + 𝜇 Ti , where 𝐸 V stands for the Ti vacancy formation energy, 𝐸 defect is the free energy of system with vacancy, 𝐸 perfect is the free energy of the original MXene. |
65bd55c3e9ebbb4db98a19bd | 8 | The optimized MXene cells with different terminations were used for further molecular dynamics calculations. To achieve a water density of about 1g/cm 3 , the vacuum gap was filled with 50 H2O molecules. The gamma-point-only version of VASP was used for molecular dynamics simulations, cutoff energies were set to 400 eV, convergency threshold was ΔE = 10 -4 |
65bd55c3e9ebbb4db98a19bd | 9 | eV. Van der Waals interactions have den considered with the use of DFT-D3 Grimme's scheme. To simulate the rare event of water dissociation we employed constrained molecular dynamics algorithm with the Blue Moon approach for free energy gradients extraction . The distance between C layer and Ti atom was used as the reaction coordinate. All AIMD simulations were performed in the Nose-Hoover NVT ensemble with the temperature of 300 K. To estimate the activation energy of water dissociation reaction of water molecule reaction free-energy curves were integrated by trapezoidal method with dissociation distance upper limit. Activation energies of Ti release (EA) for Ti3C2Tx with different terminations are provided in Table . |
65bd55c3e9ebbb4db98a19bd | 10 | Correlations between all calculated descriptors are illustrated in Figure . Vibrational Frequency. To assess the vibrational behavior of titanium atoms in MXenes, we utilized two distinct computational strategies. The first involved a finite difference approach , employing the Phonopy software , which enables the calculation of force constants through finite ionic displacements. The average phonon center for Ti atoms with different coordination for surface with O:F:OH = 5:2:1 was calculated as a projection of the MXene's phonon band structure along c-direction with the use of Phonopy software. Despite its accuracy, these phonon band center calculations are notably resource intensive. To expedite our analysis, we alternatively adopted a more time-efficient approach, where all atoms in the simulation cell except for Ti were fixed. The Ti atom was then permitted to oscillate along the c-axis with defined displacements (±0.01 Å and ±0.02 Å). Comparisons between these methods revealed a strong correlation in their resultant vibrational frequency data, as depicted in Figure . This agreement validates our decision to adopt the faster 'frozen surface' approach for subsequent calculations. iCOHP. Integrated crystal orbital Hamiltonian populations, projected on C-Ti vector, were calculated as implemented in the LOBSTER code using pbeVaspFit2015 basis set . Input files for LOBSTER were generated using VASP. |
65b25b5be9ebbb4db9f4e1a6 | 0 | Optoelectronic energy conversion is very likely to be a key technology for a sustainable energy future. This broad field encompasses photovoltaics (PV, sunlight-to-electricity conversion), photoelectrochemistry (PEC, sunlight-to-fuel conversion through electronic processes), and light emitting diodes (LEDs, electricity-to-light conversion). All these technologies are based on similar fundamental processes: Light absorption and emission, electron-hole separation and recombination, and their transport to/from electrode materials. Although technology-specific requirements exist, PV, PEC, and LEDs exhibit a common thread. They all require a semiconductor material combining a high light absorption coefficient α, long photocarrier lifetimes τ, and high photocarrier mobilities μ. For simplicity, we will refer to such ideal materials as "high-quality semiconductors" throughout this paper. Current materials research efforts in this field are especially targeted at the discovery and development of semiconductors with relatively wide band gaps, often above 1.5 eV. The main reason is the lagging performance of wide band gap sub-cells in cost-effective multi-junction PV and PEC technologies, as well as the location of the low-photon-energy edge of the visible region in LEDs (around 1.6 eV). |
65b25b5be9ebbb4db9f4e1a6 | 1 | The development of new inorganic semiconductors has often been driven by charge-neutral elemental substitutions in already-known semiconductors. Even though these substitutions could be applied on either the cation sites or on the anion sites, history has given a strong preference to the cations, generally leading to the development of multi-cation semiconductors. A well-known example is the substitution starting from CdS to CuInS 2 and further to Cu 2 ZnSnS 4 . The PV field is full of multi-cation materials, such as the inorganic halide perovskite CsPbI 3 and various other ternary absorbers such as ZnSnN 2 and AgBiS 2 . Well-established semiconductors such as InAs x P 1-x and CuIn 1-x Ga x S y Se 2-y are often synthesized with more than one anion. However, these materials are not genuine multi-anion compounds but rather anion solid solutions, in which both anions occupy the same crystallographic sites with different fractional occupancies. In these cases of anion solid solutions, the properties of, say, InAs x P 1-x can be predicted with reasonable accuracy from those of the InAs and InP binaries using Vegard's law. Solid solutions are useful for finetuning the properties of their constituent binaries, such as lattice parameters and band gaps. However, unique or unexpected properties are rare. This behavior is in stark contrast with the genuine multi-cation semiconductors mentioned in the previous paragraph. These are unique compounds where each cation occupies a specific crystallographic site. Hence the properties of CsPbI 3 are unique, instead of simply being a weighted average of the properties of CsI and PbI 2. With the additional degree of freedom given by the extra cation, CsPbI 3 turns out to be an excellent PV absorber, even though CsI and PbI 2 are not. |
65b25b5be9ebbb4db9f4e1a6 | 2 | In contrast to the multi-cation case, experimental investigations of genuine multi-anion materials for optoelectronic energy conversion are much more sparse. There has been some experimental work on certain oxynitrides (e.g., LaTiO 2 N, TaON ), oxysulfides (e.g., Y 2 Ti 2 O 5 S 2 , oxyhalides (e.g., BiOI ) and sulfoiodides (e.g., SbSI ). However, very few multi-anion materials have been explored and their PV efficiencies are generally below 5%. In this Perspective, we will discuss the prospects of multianion and polyanionic phosphosulfides (PSs) as potential high-quality semiconductors. We will see that PSs are still nearly unexplored in the context of optoelectronic energy conversion. Nevertheless, most of the known PS materials feature band gaps in the visible, crystal structures with threedimensional bonding networks, and a remarkable degree of chemical diversity that is not easily matched by other inorganic material families. The fundamental reason for their chemical versatility is the wide range of oxidation states that phosphorus can take in the simultaneous presence of a more electropositive element (a metal) and a more electronegative one (sulfur). The implications for the discovery of optoelectronic semiconductors are intriguing. In fact, it is already possible to identify PSs with direct band gaps in the visible and low carrier effective massespotential indicators of high α and high μwhen phosphorus is both in its maximum (+5) and minimum (-3) oxidation state. We will conclude this Perspective by proposing an approach for the high-throughput synthesis of known and hypothetical PS compounds in thin-film form. |
65b25b5be9ebbb4db9f4e1a6 | 3 | The generic case of an inorganic material containing phosphorus, sulfur and at least one metal in any stoichiometry and structure will be referred to as phosphosulfide (PS) in this paper. Judging from the number of compounds present in the Materials Project (MP) database , PSs have received less attention than oxygen-containing multi-anion materials. Nonetheless, they are among the non-oxide multi-anion families with the most entries (Fig. ). The "synthesised" bar refers to materials that have also been synthesised in bulk form according to the ICSD database. The known PS materials can crystallize in a wide variety of structures, in which the overall structural dimensionality (i.e., the dimensionality of the network of chemical bonds in the material) can be 3D, 2D, 1D, or 0D. In this paper, we will always refer to the structural dimensionalityrather than the thicknesswhen labeling PS materials as 3D, 2D, 1D, or 0D. PS compounds generally do not react with moisture or oxygen, except for at the surface. An exception is PSs with high alkali metal content, which are often reported to be hygroscopic. Various PSs are also reported to be stable in electrolyte solutions under a wide range of pH values. Thus, PSs are not intrinsically air-sensitive materials. |
65b25b5be9ebbb4db9f4e1a6 | 4 | Phosphosulfides with P/S < 1. A closer look at the known PSs indicates that they mainly consist of ternary and quaternary compositions, and that the preferred (molar) stoichiometric P/S ratios are 1, 1/3, 2/7 and 1/4, (Fig ). PSs exhibiting the 1/3, 2/7 and 1/4 ratios are usually called thiophosphates, due to their similarity to their oxide-based counterparts (phosphates). Rather than being true multi-anion materials, thiophosphates are polyanionic compounds in which P and S form a well-defined structural unit (the polyanion) with P in the center. The metal cations only bond to the S atoms of the polyanions, and therefore P is in a positive oxidation state, as it tends to donate electrons to S within the polyanion (Fig. ) (visualized with VESTA ). This is a completely opposite behavior with respect to the well-known III-phosphide semiconductor (In,Ga)P, and also to other emerging phosphide semiconductors such as ZnGeP 2 and CuP 2. In these single-anion semiconductors, P is always in a negative oxidation state (usually -3, unless P-P bonds are present). Instead, thiophosphates have more similarities with polyanionic semiconductors based on other elements, such as the well-studied PEC material BiVO 4 . The most common polyanions in thiophosphates are [PS 4 ] 3- in materials with P/S = 1/4 such as Cu 3 PS 4 ; [P 2 S 6 ] 2-, and [P 2 S 6 ] 4-in materials with P/S = 1/3 such as KPS 3 and NiPS 3 ; and [P 2 S 7 ] -4 in materials with P/S = 2/7 such Ag 4 P 2 S 7 . |
65b25b5be9ebbb4db9f4e1a6 | 5 | These polyanions are shown in Fig. . In all these cases except for [P 2 S 6 ] 4-, each phosphorus atom is tetrahedrally coordinated to four sulfur atoms. The polyanions simply differ by the number of shared S atoms between pairs of tetrahedra (no sharing in [PS 4 ] 3-, corner-sharing in [P 2 S 6 ] 2-, and edgesharing in [P 2 S 7 ] -4 ). The [P 2 S 6 ] 4-polyanion can still loosely be visualized as two linked tetrahedra, but with a P-P bond rather than S atoms as the link. In all these thiophosphates, P is in the +5 or +4 oxidation state (Fig. ). |
65b25b5be9ebbb4db9f4e1a6 | 6 | Phosphosulfides with P/S = 1. The non-thiophosphate compounds with P/S = 1 in the MP database are an intermediate case between the two extremes of "textbook" P-S polyanions and separate P and S anions that are independent of each other. A common anionic motif is a simple P-S bond among materials containing two anions among O, P, N, S, and an arbitrary number of metals. The "synthesised" bar refers to materials that have also been synthesised in bulk form according to the ICSD database . b) Number of unique, thermodynamically stable PSs available in the MP database, grouped by number of elements and coloured by anion stoichiometry. Throughout this paper, "stable" means that the energy above the calculated stability hull (Ehull) is lower or equal to 0.2 eV. c) Summary of general features found in PSs grouped by the anion stoichiometry including the formula of the most common polyanions, the known oxidation states of phosphorus in these polyanions, their structure represented as a ball and stick model visualized with VESTA and the bonds found in the materials with the respective anion ratio. (as in FePS), or two P-S bonds linked by P-P bonds (as in PdPS). Unlike the case of thiophosphates, here P participates in bonding with the metal cations, so it typically appears in intermediate oxidation states (-1 or -2). Among the known compounds with P/S = 1, there are also cases where P-S bonds are completely absent and only metal-S and metal-P bonds exist as in conventional multi-anion materials like oxynitrides or oxyhalides. In these cases (such as YPS and TaPS) the P oxidation state can be between -3 and -1, depending on whether P only bonds to metal atoms or also to other P atoms. |
65b25b5be9ebbb4db9f4e1a6 | 7 | Phosphosulfides with P/S > 1. To the best of our knowledge, PSs with a P/S ratio above 1 have never been synthesized and are rarely present in computational materials databases. The only such material available on MP seems to be Zr 2 P 3 S. Nevertheless, a 2019 computational screening study by Amsler et al. based on density functional theory (DFT) included four PSs with P/S = 2 in their pool of candidates (Mg 4 P 2 S, Ca 4 P 2 S, Sr 4 P 2 S, and Ba 4 P 2 S). Unexpectedly, the authors found all these compounds except for Mg 4 P 2 S to be thermodynamically stable in a previously unknown crystal structure derived from the Ba 3 As 2 structure. The implications of this recent discovery on optoelectronic energy conversion applications will be discussed later. At this stage, we simply note that the results by Amsler et al. suggest that a large portion of the PS material space (i.e., compounds with P/S > 1) may still be awaiting discovery. |
65b25b5be9ebbb4db9f4e1a6 | 8 | Several PS materials have demonstrated high technological value and/or unique properties not found in other groups of materials. For example, Li 10 GeP 2 S 12 demonstrated record ionic conductivity in 2011 and Li-based thiophosphates are among the most promising solid electrolytes for solid-state batteries; in 2020, CuInP 2 S 6 was found to be a ferroelectric material with exotic features; and in 2020, unique excitonic effects were found in atomically-thin, antiferromagnetic NiPS 3 . In general, thiophosphates with 3D structural dimensionality have predominantly been investigated as solid electrolytes for Li and Na batteries and as non-linear optical materials. Thiophosphates with 2D structural dimensionality (often referred to as "van der Waals" materials) have mainly been studied in the fields of Li and Na battery electrodes , ferroelectrics , magnetic materials , and catalysts for the oxidation of S 2- , the reduction of CO 2 , the HER and the OER . |
65b25b5be9ebbb4db9f4e1a6 | 9 | Conversely, only few papers report on optoelectronic characterization of PS semiconductors. Even when such characterization is presented, the samples are generally synthesized in bulk form (crystal or powder) or as nanoparticles. This has so far prevented the fabrication of solid-state devices, such as solar cells and LEDs. PSs in thinfilm form, which would be particularly advantageous for optoelectronic applications, are almost absent from the literature. In the following section, we will review the few studies involving PS in the context of optoelectronic energy conversion. |
65b25b5be9ebbb4db9f4e1a6 | 10 | The only computational study investigating an appreciable range of PS semiconductors for optoelectronic applications is the DFT screening study by Han and Ebert. The authors considered 18 ternary thiophosphates with a MPS 3 (M = Na, K, Rb, Cs, Cu, Ag), MPS 4 (M = B, Al, Ga, In, Sb, Bi) and M 3 PS 4 (M = Li, Na, K, Rb, Cu, Ag) composition. All these compounds are based on the tetrahedral [PS 4 ] 3-or [P 2 S 6 ] 2- polyanions but have different crystal structures. Band gaps between 1.7 and 4.1 eV were determined with the state-of-theart HSE06 functional. Many of the investigated materials had sufficiently low carrier effective masses to be considered for optoelectronic applications where electronic transport matters. Na 3 PS 4 revealed high p-type dopability, a band gap above 3 eV and a low hole effective mass, making it a potential p-type transparent conductor. Ag 3 PS 4 was identified as the most promising PV absorber in the study, due to a direct band gap in the visible and lack of deep defects with a low formation energy. Since the band alignment of Ag 3 PS 4 with the water redox potentials was found to be favorable, Ag 3 PS 4 was also suggested as a potential PEC water splitting absorber. Both Na 3 PS 4 and Ag 3 PS 4 are 3D PSs. |
65b25b5be9ebbb4db9f4e1a6 | 11 | Some of the thiophosphates screened by Han and Ebert have been experimentally investigated. Tiwari et al. studied the optoelectronic properties of BiPS 4 powders for solar energy conversion. BiPS 4 , a 3D PS, was found to have a direct band gap of 1.72 eV, n-type conductivity, moderate electron effective masses, and an encouraging carrier lifetime around 1 ns. Shaddad et al. utilized a BiPS 4 /BiVO 4 heterojunction to increase the photocurrent of a bare BiVO 4 photoanode for PEC water splitting. The Cu 3 PS 4-x Se x solid-solution series (3D) was synthesized in powder form by , and investigated as a potential PV absorber. With increasing sulfur content, the band gap increased from 1.35 eV (Cu 3 PSe 4 ) to 2.38 eV (Cu 3 PS 4 ). This band gap range covers the requirements of many optoelectronic energy conversion technologies. Spectrally narrow photoluminescence close to the band gap energy and a PEC response were subsequently measured for pure-sulfide Cu 3 PS 4 nanoparticles, which were also employed as a hole transport layer in perovskite solar cells. The optoelectronic properties of the 2D PS GaPS 4 were computationally investigated by two groups. Liu et al. predicted a reduction of the band gap and improved band alignment for unassisted PEC water splitting upon introduction of single transition metal atoms into GaPS 4 . Shen et al. performed defect calculations in GaPS 4 to derive favorable growth conditions for n-and p-type doping. Furthermore, they found that a higher optical band gap in GaPS 4 compared to the fundamental calculated band gap is due to dipole-forbidden transitions. This feature was independently found in Ag 3 PS 4 , despite the substantially different structures in the two compounds. Pd 3 (PS 4 ) 2, another 2D PS material with [PS 4 ] 3-anions, was experimentally studied by Roy et al., who reported a PEC response from exfoliated nanosheets of this material. A few 2D thiophosphates with [P 2 S 6 ] 4-anions have also been optoelectronically characterized to a limited extent. In 1979, Brec et al. characterized MPS 3 crystals and powders (M= Mn, Fe, Ni, Zn, Cd, In 0.66 ) and reported their band gaps (1.5-3.5 eV), electrical resistivity (10 2 -10 4 Ωcm) and α (exceeding 10 4 cm -1 just above the fundamental band gap). These materials were also computationally examined by Zhang et al. for PEC applications. The authors calculated their band alignment and optical absorption coefficient, and concluded that FePS sheets in PEC cells, and observed an increased photocurrent when oxygen was incorporated on the CuInP 2 S 6 surface. We could only find a single, very recent study on the optoelectronic properties of a [P 2 S 7 ] 4-thiophosphate (Feng et al. ). Using first-principles calculations, the authors concluded that two different phases of Ag 4 P 2 S 7 possess high α in the visible and suitable band edge positions for PEC water splitting. Moving to non-thiophosphate PSs with P/S = 1, Roy et al. demonstrated working photodetectors based on exfoliated PdPS sheets. Houari and Benissad suggested CoPS as a PV absorber based on first-principle calculations. As mentioned in Section 2.1, it appears that no materials with P/S > 1 have been synthesized in any form. However, the available on the MP database, to account for their systematic underestimation. The corrected values are obtained by polynomial regression between the PBE band gaps and the more accurate band gaps calculated at the HSE06 level on a sample of 62 PSs available in the SNUMAT database . |
65b25b5be9ebbb4db9f4e1a6 | 12 | recent computational screening study by Amsler et al. suggests that some of these hypothetical P-rich compounds may have very promising properties for optoelectronic applications. The authors investigated ternary compounds with a X 4 Y 2 Z stoichiometry, where X =Mg, Ca, Sr, Ba; Y =P, As, Sb, Bi; and Z=S, Se, Te. The study included machinelearning prediction of stable stoichiometries, global structure prediction, and detailed DFT calculations of the hypothetical materials that resulted from the first two steps. Three out of four phosphosulfides (Ca 4 P 2 S, Sr 4 P 2 S, and Ba 4 P 2 S) were found to be on the convex stability hull in their lowest-energy structure. Thus, these materials are likely to be synthesizable. All three materials exhibited a direct band gap at the Γ point and high band edge dispersion (i.e., low effective masses). The former is often correlated with a high α, the latter with high μ. Their band gaps were found to decrease when moving down the group. At the PBE level, Ca 4 P 2 S had a band gap of 1.8 eV and Ba 4 P 2 S had a band gap of 1.3 eV. At the HSE level (known to yield more accurate band gaps), the corresponding band gaps were roughly 2.7 eV and 2.0 eV, respectively. These combined features indicate that these newly discovered PSs could be highly interesting for visible light emission, multijunction solar cells, and PEC water splitting applications. Their potential air sensitivity should, however, be investigated. |
65b25b5be9ebbb4db9f4e1a6 | 13 | We have seen that some PSs have been studied for their optoelectronic properties, but only very few materials have been reported in more than a single publication. In addition, work has almost only focused on thiophosphates. Does the PS material family warrant a broader, rational search for new semiconductors? If so, where should we search? To help answer these questions, we examine selected properties of all the ternary PSs present on MP and predicted to be thermodynamically stable by DFT. The examined properties are band gap (Fig. ), structural dimensionality (Fig. ), and effective masses (Fig. ). When specific materials are discussed, reference is made to their Materials Project ID. |
65b25b5be9ebbb4db9f4e1a6 | 14 | The band gaps (calculated at the PBE level and corrected to the HSE level ) of the lowest-energy ternary PS for each metal cation and the most common P/S ratios are displayed in Figure . See Supplementary Information for details on the correction and the data used from the SNUMAT database . PSs span the whole range from metals to widegap insulators, but most of them are predicted to be semiconductors, often with band gaps in the visible. This is a promising trend for applications within optoelectronic energy conversion. Ternary PSs from s-block metals generally feature the widest band gaps followed by the ternaries incorporating p-block and Group 12 metals, while the PSs including d-block or f-block metals feature the lowest band gaps. For most metal cations, a P/S ratio of 1/1 generally yields the narrowest band gaps and a P/S ratio of 1/4 the widest band gaps. |
65b25b5be9ebbb4db9f4e1a6 | 15 | Although thiophosphates with 2D structural dimensionality have received particular attention, data mining from the MP database reveals that most of the known PSs actually have 3D dimensionality (Fig. ). For quaternary and quinary PSs, the share of 3D-structured materials is even higher than what is found in ternary systems (Fig. ). Interestingly, most of the 2D-structured materials appear in the P/S = 1/3 category (Fig. ) in combination with the [P 2 S 6 ] 4-polyanion (Fig. ). The predominance of 3D structures is encouraging for optoelectronic energy conversion application, because 3D structural dimensionality is usually a necessary (though not sufficient ) condition for good photocarrier transport in all directions. Specifically, 3D structures with high spatial-and energy overlap between the orbitals constituting their band edges usually result in high band dispersion and low effective masses of electrons and holes in all directions. Since μ is inversely related to the effective mass, low effective masses are usually correlated with high carrier mobilities. Indeed, all the inorganic PV absorbers with demonstrated efficiencies above 15% have 3D structural dimensionality. |
65b25b5be9ebbb4db9f4e1a6 | 16 | Along with the structural dimensionality, it is useful to extract quantitative values of the effective masses of the ternary PS semiconductors for which a band structure calculation is available on MP. The direction-averaged effective masses of holes and electrons (extrapolated using the BoltzTrap2 package ) in these PSs are displayed in Fig. . We find that a few compounds have low effective masses in both the valence and conduction band. Some examples are the previously identified Ag 3 PS 4 (mp-12459), Cu 3 PS 4 (mp-3934) and Na 3 PS 4 (mp-28782), the newly identified Zr(PS 3 ) 2 (mp-8203) , as well as various narrow-gap compounds with d-and f-block metals. |
65b25b5be9ebbb4db9f4e1a6 | 17 | However, at least one of the effective masses is greater than the rest mass of the electron m 0 in most of the known ternary PSs (Fig. ). Therefore, the predominance of 3D structures in PSs is generally not sufficient to ensure high μ in this class of compounds. We also note that holes in PSs are generally heavier than electrons, as often seen in semiconductors. Since low effective masses are not fundamentally prohibited by low dimensionality in PSs, we argue that one of the key areas of research in PS semiconductors for optoelectronic energy conversion should be to identify design rules for obtaining low effective masses. |
65b25b5be9ebbb4db9f4e1a6 | 18 | The analysis in the previous section indicates that it might be necessary to move beyond the already-known ternary PSs to find more than a handful of candidates for high-quality semiconductors. Assuming that PSs with band gaps in the visible are plentiful (Fig. ), the key questions are where to Only materials with an electronic band structure calculation available on MP are considered. Thus, the materials shown here for each metal cation and P/S ratio do not always correspond to the ones shown in Fig. . In the case of two materials with equal stoichiometry and Ehull, preference is given to the one with the smaller sum over the effective masses of both carriers. The effective masses are extrapolated from the MP band structures using the BoltzTraP2 package at room temperature and under low doping density. The position in the periodic table indicates the third constituent element of each PS. |
65b25b5be9ebbb4db9f4e1a6 | 19 | find new materials (i) with low effective masses, required to achieve high μ, and (ii) with low defect densities and/or capture cross sections, required to achieve high τ. While we do not have exact answers to these questions at this stage, we will argue in the next three sections that there is significant scope for the discovery of new PSs with such desirable properties. The three main strategies we will outline are: Increasing the number of elements from ternary to quaternary compounds (Sec. 4.1), exploring P-rich compositions with P/S ≥ 1 (Sec. 4.2), and exploiting the chemical versatility of phosphorus (Sec. 4.3). |
65b25b5be9ebbb4db9f4e1a6 | 20 | Unlike most elements, phosphorus can take a wide range of oxidation states from -3 to +5 in solid-state materials. PSs are an ideal material family to see these extreme oxidation states in action. We have already seen that compounds with P/S ≤ 1/3 prefer high positive oxidation states for phosphorus (+5, +4), whereas negative oxidation states (-1,-2,-3) are favored in compounds with P/S ≥ 1. Since phosphorus can easily form bonds with other P atoms in the solid state, all other intermediate oxidation states are in principle possible. The availability of such a wide range of oxidation states indicates that there should be many combinations of elemental compositions that satisfy the requirement of charge neutrality. This translates into a large number of hypothetical PS materials that are chemically plausible and not intrinsically metallic. |
65b25b5be9ebbb4db9f4e1a6 | 21 | To verify this hypothesis, we estimate the number of hypothetical charge-neutral PS compositions with the SMACT package . For ternary PSs, the result is 1,737 distinct compositions assuming M a P b S c formulas including metals up to Bi and stoichiometric coefficients a,b,c between 0 and 10. For comparison, the number of charge-neutral ternary oxysulfides (M a O b S c ) is only 228 using the same rules. For quaternary PSs, the number of distinct charge-neutral composition is 202,829, assuming M1 a M2 b P c S d formulas with stoichiometric coefficients up to 10. Again, the number of oxysulfides is significantly lower . |
65b25b5be9ebbb4db9f4e1a6 | 22 | Although the charge neutrality filter does not guarantee thermodynamic stability, these numbers give an idea of the enormous size of the quaternary PS chemical space, even when compared to other quaternary spaces that do not contain elements with the same versatility as phosphorus. Besides the advantage in size, what are the prospects of finding high quality semiconductors among quaternary PSs? An encouraging trend is that the number of already-known stable quaternary PSs exceeds the number of corresponding ternaries (Figure ). Hence, quaternary PSs should not have intrinsic problems with thermodynamic stability. Other promising features of the existing quaternary compounds are a higher fraction of materials with 3D structural dimensionality with respect to ternaries (Figure ), and a higher fraction of materials with a P/S = 1/4 ratio (Figure ), which typically have lower effective masses (Figure ) than the P/S = 1/3 case. |
65b25b5be9ebbb4db9f4e1a6 | 23 | Another question one may ask is: Can quaternary systems contain semiconductors with improved properties with respect to the ternaries? As an instructive example, let us consider the case of KAg 2 PS 4 (mp-12532). In terms of composition, this compound only differs from Ag 3 PS 4 (mp-12459) by the replacement of one Ag atom per formula unit by a K atom. Although the structures of the two materials are different, they are 3D in both cases. The band gap is predicted to increase from Ag 3 PS 4 to KAg 2 PS 4 (1.0 to 1.2 eV at the PBE level, 1.8 to 2.1 eV with HSE correction). Even though effective masses often tend to increase with increasing band gaps, the direction-averaged hole effective mass of KAg 2 PS 4 actually decreases by 0.48 m 0 , while the electron effective mass remains approximately constant. The resulting effective masses in KAg 2 PS 4 (0.25 m 0 for electrons, 0.78 m 0 for holes) are typical of high-quality optoelectronic semiconductors. This interesting trend might be explained in very qualitative terms by the inductive effect, in which the presence of an electropositive cation (here, K + ) increases the covalency of the remaining bonds (here, Ag-S), and therefore the dispersion of the bands. |
65b25b5be9ebbb4db9f4e1a6 | 24 | Although the band gap of KAg 2 PS 4 is indirect (thus α might be low), this example demonstrates that the properties of quaternary PSs can be superior to the weighted average of the properties of their ternary constituents. Thus, we expect that optimal combinations of properties (high α, μ, and τ) should be accessible in quaternary PSs with an appropriate combination of elements. |
65b25b5be9ebbb4db9f4e1a6 | 25 | We have seen that the majority of the known PSs are polyanionic thiophosphates with low P/S ratios (1/3 and below). Although a combination of visible band gaps and low effective masses can be found in some cases (Fig. and Fig. ), many thiophosphates exhibit relatively flat bands and high effective masses. Disperse bands and low effective masses seem to be more common in PSs with higher phosphorus content and with separate P and S anions, rather than polyanions. For example, a significant fraction of the known compounds with P/S = 1 have low effective masses (Fig. ). While this is a promising trend, three questions remain open for this class of PSs. 1) Are low effective masses common simply because compounds with P/S = 1 tend to have narrow band gaps? 2) Are compounds with P/S = 1 only thermodynamically stable when the metal belongs to either the d-block or the f-block? 3) Are there really so few quaternary compounds with P/S = 1 as Fig. seems to suggest? |
65b25b5be9ebbb4db9f4e1a6 | 26 | Moving to even P-richer compositions, all the currently known PSs with P/S = 2 (Ca 4 P 2 S, Sr 4 P 2 S, and Ba 4 P 2 S) have a favorable combination of direct band gaps in the visible and low effective masses. The only compound we could find with P/S = 3 is Zr 2 P 3 S (mp-1215423). This PS is only slightly metastable (18 meV above the convex hull) and is predicted to be a semimetal at the PBE level. Due to the systematic band gap underestimation of the PBE functional, Zr 2 P 3 S might as well be a semiconductor. It is also plausible that other ternary and quaternary compounds with P/S = 3 may exist. |
65b25b5be9ebbb4db9f4e1a6 | 27 | In Fig. , we show some of the structural motifs seen in PS compounds with P/S ≥ 1 and independent P and S anions. They contrast with the polyanionic motifs shown in Fig. for materials with lower P/S ratios. In some of the materials shown in Fig. (Y 2 PS, Ca 4 P 2 S) the coordination environments of P and S are nearly identical, which may promote disorder in the anion sublattice under certain experimental conditions. This can be a beneficial feature, because control over the order parameter in a semiconductor can be exploited to fine-tune its properties. Other materials shown in Fig. (YPS and Zr 2 P 3 S) have rather different coordination environments for P and S, so less prominent disorder effects are expected. Substantial P-S disorder also seems unlikely in thiophosphates because S and P are in significantly different chemical environments with very different oxidation states and ionic radii. |
65b25b5be9ebbb4db9f4e1a6 | 28 | Our analysis so far has focused on where to find PSs with low effective masses and direct band gaps in the visible. These features are correlated with high μ and high α in an appropriate photon energy range. However, we have not touched upon the third desirable feature mentioned in the Introduction, i.e., a high carrier lifetime τ. Compared to the case of α and μ, it is much more difficult to find simple properties available in materials databases that can be correlated to τ. The carrier lifetime is inversely related to the product of the concentration and capture cross section of crystal defects that are active as Shockley-Read-Hall recombination centers. In addition, the closer a defect state is to mid-gap, the higher the Shockley-Read-Hall recombination rate will tend to be at constant τ. For most compound semiconductors, the dominant defects are not extrinsic impurities, but rather native defects that are thermodynamically favored. Developing general design rules for semiconductors with high τ and low recombination rates ("defect-tolerant") has proved elusive. Nevertheless, there is some consensus that the nature of the electronic states at the band edges plays an important role. Relevant factors include the constituent orbitals, their hybridization, and whether they form bonding or antibonding states. |
65b25b5be9ebbb4db9f4e1a6 | 29 | In this sense, the chemical versatility of PSs gives a design handle that is not available in most other material classes. To see how, we recall our conclusion (Sec. 3.3, Sec. 4.1, Sec. 4.2) that some semiconductors with high α and high μ are likely to be found among PSs with different P/S ratios and oxidation states. This implies that the phosphorus states can be "moved around" between the valence and the conduction band by changing the material, while still keeping a high α and high μ. (mp-1216056), Ca4P2S and Zr2P3S (mp-1215423) are represented as a ball and stick model and visualized with VESTA Phosphorus is always displayed in purple, sulfur in yellow and the respective metal in the third colour. This figure is intended to complement Fig. |
65b25b5be9ebbb4db9f4e1a6 | 30 | An exemplary case is the comparison of Ag 3 PS 4 and Ba 4 P 2 S (Fig. ). From a chemical standpoint, these two materials are completely different. Ag 3 PS 4 is a 3D thiophosphate featuring the common [PS 4 ] -3 tetrahedral polyanion, no metal-phosphorus bonds, and P in the +5 oxidation state. P states give an appreciable contribution to the conduction band minimum (CBM), which is predominantly of Ag(s) character. The valence band maximum (VBM) consists of hybridized Ag(d)-S(p) orbitals and contains no meaningful contributions from P states. Ba 4 P 2 S is a 3D PS with independent P 3-and S 2-anions and no other bonds than metal-P and metal-S bonds. Opposite to the case of Ag 3 PS 4 , the VBM of Ba 4 P 2 S is dominated by P(p) states as in III-V semiconductors. On the other hand, the CBM in Ba 4 P 2 S is mainly composed of Ba(d) states without substantial contributions from P orbitals. Although sulfur states give important contribution to both band edges in Ag 3 PS 4 , they are virtually absent in Ba 4 P 2 S. |
65b25b5be9ebbb4db9f4e1a6 | 31 | Despite all these differences, we recognize similar desirable features in the band structures (visualized with the GPAW code ) of Ag 3 PS 4 and Ba 4 P 2 S (Fig. ). Band gaps are direct and lie in the visible (after applying the HSE correction), and both the CBM and the VBM have high band dispersion. Thus, both materials have significant potential for high α and high μ. Since the chemical origin of the band edges is completely different in the two materials, tuning the P/S ratio (or equivalently, the oxidation state of P) is a design knob unique to PSs. As the character of the band edges can be tuned as a demonstration of the unique chemical versatility of PSs. The crystal structure, electronic band structure, and orbital-resolved electronic density of states (DOS) are shown for Ag3PS4 (top row) and Ba4P2S (bottom row). Most of this information is already available elsewhere. For the sake of consistency, we have recalculated the band structures and DOS at the PBE level using the GPAW code. Even though the character of the band edges is entirely different in the two materials (see DOS), the resulting band structures have similar features (direct band gaps, disperse bands). The same color code is used for atoms and for electronic states. Silver is displayed in grey, sulfur in yellow, phosphorus in purple and barium in green. |
65b25b5be9ebbb4db9f4e1a6 | 32 | We have argued that the space of unexplored PSs is vast, with considerable potential for finding high-quality semiconductors. Computational screening methods based on high-throughput DFT are a useful tool to search for materials with the desired properties in large chemical spaces. However, some of the key properties that are linked to high PV performance (most notably τ) are prohibitively expensive to calculate for more than a handful of materials. Additionally, many physical effects that are likely to affect the experimental τ (defect clusters, entropic effects, grain boundaries etc.) have to be neglected to make the problem computationally treatable. Finally, it is challenging to predict the properties of hypothetical materials with unknown crystal structures, because both composition and structure are required in first-principles calculations as input. Many hypothetical PSs with P/S > 1 and many hypothetical quaternary PSs have unknown crystal structures. Thus, we argue that high-throughput experiments are necessary to rapidly explore the synthesizability and properties of known and unknown PS semiconductors. |
65b25b5be9ebbb4db9f4e1a6 | 33 | Let us consider the synthesis methods reported for PSs so far. Are any of them appropriate for high-throughput studies of optoelectronic materials? Most authors have employed classic high-temperature solid-state reactions and chemical vapor transport of bulk PS powders and crystals. These approaches are low-throughput, as the timeframe for a synthesis run is often in the range of weeks, due to the slow solid-state diffusion process in bulk materials. |
65b25b5be9ebbb4db9f4e1a6 | 34 | Many known PS crystals with 2D dimensionality have been exfoliated to produce one-or few-atom-thin 2D PSs. However, neither the crystal growth nor the exfoliation process are high-throughput, and this method cannot be used for materials with 3D dimensionality. Very recently, Zhou et al. reported a versatile chemical vapor deposition (CVD) method enabling the growth of 8 atomically-thin ternary thiophosphates, as well as 5 quaternary thiophosphate solid solutions. The precursors for sulfur and phosphorus were the elemental solids. Metal chloride powders were used as metal precursors. The vapor composition was simply the evaporated precursors in an Ar/H 2 carrier gas. While this method was designed for atomically thin 2D materials, it may be possible to extend it to grow thicker films of any dimensionality. Some high-throughput capabilities might be engineered in a CVD setup by exploiting temperature gradients at the substrate and in the precursors. |
65b25b5be9ebbb4db9f4e1a6 | 35 | Several papers have reported synthesis of PSs of various dimensionalities as nanoparticles or other nanostructured forms. Although nanoparticle synthesis is amenable to high-throughput combinatorial experiments, material properties may be affected by size effects. Further, measurements of various electrical and optical properties require aggregation of nanoparticles into larger units (typically thin films). In these cases, problems with insufficient nanoparticle coalescence and film compactness can affect the results. |
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