the wet - chemical synthesis 
 of colloidal nanocrystals ( ncs ) is a 
 well established method providing highly monodisperse quantum dots for applications such as bright and stable fluorophores . among these , vi lead chalcogenides ( pbx , x = s , se , 
 or te ) ncs provide efficient emission over a large spectral range 
 in the infrared . they are promising for applications , e.g. , where 
 pbs ncs act as optical active materials in organic photodiodes for 
 the near - infrared . the applications for 
 pure lead salt ncs are limited , however , because of their instability 
 in the emission quantum yield over time caused by surface oxidation 
 processes . this problem can be overcome by growing a protective shell 
 around the ncs for chemical passivation 
 with the advantage of an additional electronic passivation preventing 
 the transfer of excitonic energy to surface trap states . the core / shell architecture for nanostructures also allows semiconductor  metal 
 hybrid nanoparticles with enhanced functionalities to be realized 
 that are otherwise not accessible . in 
 contrast to other postsynthetic shell growth techniques like epitaxial 
 shell growth on top of the core or galvanic replacement 
 applied to nobel metal ncs , we investigate in this 
 study the core / shell growth driven by cationic exchange . the replacement of pb by cd is achieved by adding an excess of cd 
 oleate to the pbx nc suspension resulting in a well - defined cdx shell 
 around the pbx core as it was shown for pbse , pbte , and pbs . shell 
 ncs show strongly enhanced photoluminescence ( pl ) quantum yield as 
 compared to pure pbs ncs , whereas the passivating hard protective 
 cds shell allows additionally the pbs / cds ncs to be stabilized in 
 water or to be encapsulated in an amorphous 
 glass matrix . the pbs / cds ncs also show 
 a higher efficiency and stability within photodetectors and within solar cells . the maximum quantum yield was found for a thin layer of around 0.7 
 nm and is reduced again for shell thicknesses exceeding 2 nm . this was explained by defect formation caused 
 by the 2% lattice mismatch between the rock salt ( rs ) crystal structure of the core and zinc blende ( zb ) structure of the shell . in this study , we investigate the cationic exchange process 
 for 
 three different initial pbs nc diameters of 4.7 nm ( small ) , 6.3 nm ( medium ) , and 8.7 nm ( large ) , resulting in three different final cds shell thicknesses tshell of 0.9 , 1.5 , and 2 nm after maximum exchange 
 time . the chemical composition profiles of the individual core / shell 
 nc ensembles as a function of reaction time are derived from anomalous 
 small - angle x - ray scattering ( asaxs ) using synchrotron radiation . the crystalline structure of the ncs is retrieved from x - ray diffraction 
 ( xrd ) experiments combined with transmission electron microscopy ( tem ) 
 analysis . we relate this received chemical and structural information 
 to the measured pl intensities of the core / shell ncs to probe if the 
 crystal structure of cds - shell affects the optical properties . pristine 
 pbs nanocrystals ( ncs ) were prepared according to the 
 method proposed by hines and scholes . briefly , in a typical synthesis of 9 nm pbs nanocrystals , pbo ( 0.45 
 g ) , oleic acid ( oa , 10 ml ) , and 1-octadecene ( ode , 10 ml ) were loaded 
 in a three - neck flask and heated up to 110 c under vacuum . during 
 this time , pb oleate is formed , indicated by the discoloration of 
 the reaction mixture . then , the reaction flask was backfilled with 
 ar , and the temperature was increased to 150 c . at 150 c , 
 the injection mixture , containing 0.21 ml of hexamethyldisil - thiane 
 and 10 ml of anhydrous ode , was injected , after which the temperature 
 dropped to about 130 c . the reaction flask was allowed to cool 
 down to 100 c within 3 min . the temperature of 100 c was 
 kept for another 5 min before quenching the reaction by means of a 
 water bath . samples were washed by a 1:1 hexane / ethanol mixture three 
 times and redispersed in hexane . smaller sizes of pbs nanocrystals 
 were prepared by decreasing the amount of oleic acid , while keeping 
 a constant total volume of the solution . the pbs / cds core / shell 
 ncs were synthesized following the method 
 of pietryga et al . a pbs nc solution , 
 containing 90 mg pbs ncs , was dried , and ncs were redispersed in 5 
 ml of anhydrous oa . after the pbs / oa solution was heated to 80 c , 
 20 ml of 0.4 m cd oleate solution in anhydrous diphenylether was added . the reaction temperature was kept constant and after several time 
 step aliquots were taken , which were cooled rapidly to room temperature . these samples were washed and dissolved again in toluene or hexane 
 with a concentration of 12 wt % . alternatively , the cd oleate 
 solution ( 0.4 m , 20 ml ) was added every hour , which provided thicker 
 cds shells at shorter reaction times . this method was applied to the 
 growth of the large core / shell ncs , whereas for the 
 growth of the medium and small ncs 
 only in the beginning of the cationic exchange process was a sufficiently 
 large amount of cd oleatic solution added . the cd solution was prepared 
 as described in ref ( 18 ) . a jeol 2011 fastem transmission electron microscope ( tem ) 
 operated 
 at an acceleration voltage of 200 kv was used to obtain high resolution 
 tem images . the direct electron beam intensity used for the imaging 
 mode the tem images were created and 
 analyzed by a supplementary digital micrograph software package . tem 
 image contrast differences can be created by many types of amplitude 
 and phase contrasts . in this work , the 
 darkfield images were created by using the diffraction contrast method , 
 where either the rock salt bragg peaks or the zinc blende peaks alone were used to create the tem image . the excitation source for the photoluminescence ( pl ) measurements 
 was a spectra physics continuous wave argon - ion laser , model 163a 
 5216 , emitting at a wavelength of 514 nm . the exciting beam was chopped 
 by a chopper wheel and focused on the cuvettes containing the ncs 
 in solution . the photoluminescence ( pl ) was collected by two caf2 lenses and spectrally resolved by an acton research corporation 
 spectra pro 150 monochromator . the monochromatic light was detected 
 by a nitrogen cooled judson j10-m204-r10 m insb photodiode . this signal 
 was amplified with a judson pa-7 preamplifier and a stanford research 
 system sr510 lock - in amplifier , which used the excitation source chopper 
 frequency as a reference . a self - written program running on a personal 
 computer operated the monochromator over the desired spectral range 
 and evaluated the amplified signals at the different wavelengths to 
 obtain the photoluminescence spectra . to quantify the luminescence 
 enhancement , the optical density of all samples was adjusted to have 
 the same value at a wavelength of 500 nm . the contrast variation 
 in anomalous small - angle x - ray scattering 
 ( asaxs ) is due to the energy dependency of the atomic scattering factor f(z , e ) in the vicinity 
 of x - ray absorption edges , where e is the x - ray energy 
 and z the atomic number . it can be shown that the total measured intensity is composed of a nonresonant and 
 a resonant scattering contribution . the nonresonant scattering term 
 depends only on the total electron density within a material and is 
 related to the overall elementary composition and the bulk density , 
 whereas the resonant scattering term depends on e. thus , the total amplitude deviates significantly from the atomic 
 number z by varying the energy around an elemental 
 absorption edge . by tuning the x - ray energy just below the pb - liii - edge at e = 13.035 kev , the contribution 
 of pb as the strongest scatterer with z = 82e to the total scattering amplitude f(z , e ) and hence to the 
 total scattering intensity i(q , e ) can be varied significantly . hence , for asaxs experiments 
 synchrotron x - ray sources have to be used where the x - ray energy can 
 be continuously varied . the asaxs spectra for the large and small sample series have been measured at the 
 7t - mpw - saxs beamline at the bessy ii synchrotron ( hzb berlin , germany ) , 
 whereas the medium sized ncs have been recorded at 
 the beamline id01 at the european synchrotron radiation facility esrf 
 ( grenoble , france ) . in asaxs the scattered intensity is a function 
 of the scattering 
 vector q and the x - ray energy e , with q = 4 sin / and  the x - ray wavelength . 
 for a minimum set of three scattering curves measured at different 
 energies the pb - electron density and the total electron density within 
 the core and the shell can be derived independently . this is achieved 
 by applying a unique spherical core / shell model to fit up to five 
 different scattering curves . all scattering curves have been calibrated 
 into absolute units ( i.e. , macroscopic scattering cross sections in 
 units of cross - section per unit volume cm / cm = cm ) . for all energies the scattering of the 
 solvents toluene and hexane was measured with the same statistical 
 accuracy and was removed from the scattering curves of the sample 
 before applying the fitting procedure . by varying randomly the scattering 
 data within the experimental error band and repeating the fitting 
 procedures up to 20 times , the stability of our results is tested 
 and the errorbars for the density profiles are obtained . the 
 rutherford backscattering spectrometry ( rbs ) method is based 
 on elastic collisions between light , energetic ions ( h , he with a 
 few hundred kev up to 2 mev ) and the atomic nuclei in a stationary 
 sample . scattering 
 kinematics permits the elements present in a thin layer to be identified 
 from the yield of particles backscattered from the sample in a large 
 angle . rbs measurements were performed , employing the van de graaff 
 accelerator an700 ( 30700 kev ) . the monte carlo program simnra was used to evaluate the sample compositions 
 by fitting the peaks corresponding to the individual elements in the 
 measured spectra . x - ray diffraction ( xrd ) experiments in transmission 
 geometry were 
 performed with the nanostar instrument from bruker axs , in the wide - angle 
 x - ray scattering ( waxs ) configuration with a sample to detector distance 
 of 6 cm . this allows diffraction peaks up to a 2 angle of around 
 44 to be recorded with the cu  k x - ray wavelength 
 of 1.5418  . twelve of the 14 individual nc ensembles used for 
 the asaxs experiments were measured sealed in quartz - glass capillaries 
 of 1.5 mm diameter . the 2d detector ( bruker histar ) images showed 
 x - ray diffraction powder rings , and thus for the data analysis line 
 scans were extracted from the 2d images by azimuthal integration . 
 for further analysis of the peak width q the 
 detector resolution of this setup was determined using the peak widths 
 of a diffraction standard ( al2o3-powder ) . from the q - value we derive directly d as a measure 
 for the crystalline diameter using the scherrer formula d = k2/q with a k - value close 
 to one for the ncs without a shell . these 
 values are only 10% to 20% smaller as compared to asaxs , which can 
 be related to an additional peak broadening due to imperfections in 
 the crystal structure . we modified the previously 
 reported method for the synthesis of 
 pbs / cds ncs . in particular , we applied 
 multiple injections of the cadmium precursor , which leads to a faster 
 cds shell growth and consequently to shorter growth times . after heating 
 the pbs nc solution in toluene up to 80 c , cd aliquots were taken after defined time steps as 
 shown in the reaction scheme in figure 1a . the shell formation for the large core / shell ncs 
 was proven by high resolution tem ( hr - tem ) studies . in figure 1b the structure of one single pbs / cds nc is shown 
 after 3 h of exchange time , where the core ( indicated by a red dashed 
 line ) depicts different lattice spacings as compared to the shell 
 region . for the core with about 7 nm diameter we derive the rock salt ( rs ) crystal structure ( fm3 m ) , whereas within the 1 nm 
 shell the lattice plane configuration indicates the zinc blende ( zb ) structure ( f43 m ) . these two crystalline phases are also visible in dark field hrtem 
 images , where either the rs or the zb electron diffraction peaks were used for highlighting the corresponding 
 crystalline phase within hr - tem images ( see figure s1 , supporting information ) . from the aliquot samples pl spectra were recorded and compared to that of the pure pbs ncs 
 ( see figure 1c ) . the peak maximum at around 
 1800 nm is increased by a factor of 4 for the samples after 1 and 
 2 h reaction time , but after 3 h this enhancement in the peak maximum 
 is again slightly decreased . the resolution of our tem analysis , however , 
 did not allow differences to be revealed in the thickness or the composition 
 of the cds shells between 1 and 3 h exchange time . furthermore , tem 
 analysis alone is restricted to a small sample set of ncs ( typically 
 around 100 individual ncs ) deposited on a flat substrate , but the 
 pl spectra are produced by a large ensemble of individual ncs in solution . 
 as complementary methods we have chosen x - ray scattering techniques 
 that allow mean structural parameters of a large ensemble of ncs with 
 subnanometer resolution to be determined . the scattering experiments 
 were directly performed on the nc solutions sealed in glass capillaries 
 of 1.5 mm diameter resulting in nc ensembles of 10 individual particles probed during one single x - ray measurement . therefore , we can probe in detail the influence of the mean structural and compositional core / shell parameters of the ncs on 
 their optical output . this analysis was done for the three samples 
 series ( large , medium , and small ) with initial particle diameters from 9 to 5 nm at 
 various reaction time steps , resulting in 14 different nc ensembles . ( a ) scheme 
 of the synthesis of pbs / cds core / shell nanocrystals 
 driven by cationic cd for pb exchange starting with pure pbs ncs ( red 
 sphere ) in the rock salt crystal phase and resulting in core / shell 
 particle with the same diameter , but surrounded by a cds shell ( blue ) . ( b ) high resolution tem image of a single 9 nm sized core / shell nc 
 after 3 h of exchange time , where the dashed circles indicate the 
 pbs core ( red ) and the cds shell region ( blue ) . ( c ) pl spectra of large sized pbs and pbs / cds ncs with diameters d of around 9 nm , measured after different reaction time steps . small angle x - ray scattering ( saxs ) 
 is a method widely used in the 
 analysis of nanoscale structures . an 
 extension of saxs , asaxs allows element specific contrast 
 variation and hence the possibility to 
 determine the chemical compositions of the core and the shell of a 
 macroscopic ensemble of ncs . the contrast variation in asaxs is due 
 to the energy dependency of the atomic scattering factor f(z , e ) in the vicinity of x - ray 
 absorption edges . from a minimum set of three asaxs patterns measured 
 at different energies we can separate independently the total electron 
 density from the pb - electron density inside the core / shell ncs . this 
 was achieved by applying a step - like spherical core / shell model to 
 fit all scattering curves ( see the section methods and the supporting information for a detailed description 
 of the asaxs method ) . in figure 2a the experimental 
 scattering curves are shown together with the model fits for the large core / shell ncs measured after 1 h of exchange time . all five curves were fitted with the same unique spherical core / shell 
 model with the following fitting parameter : the inner radius rcore , the shell thickness tshell , the pb density , and the total electron density 
 in the core and the shell , as well as the total size distribution 
  of the spherical core / shell ncs (  is assumed to be 
 equal for the core and the shell ) . the accordance between data and 
 fit is generally excellent ; small deviations are only visible at large q - values , where the error band of the scattering data is 
 getting larger due to statistics . to illustrate the energy dependent 
 effect , the position in q of the first minimum in 
 the asaxs curves ( see figure 2a ) is plotted 
 over e in the inset . the resonant shift is in the 
 range of 2% , whereas the reference minimum - position of pb 
 ncs without cds - shell ( dashed red line ) is constant within 0.3% . this 
 shift can be directly related to a difference in the pb electron densities 
 between core and shell . ( a ) experimental asaxs curves ( symbols ) fitted 
 with a unique spherical 
 core / shell model ( lines ) for the large core / shell 
 pbs / cds nc - sample after 1 h of reaction time . the absolute intensity i(q , e ) plotted over the 
 scattering vector q was recorded at five different 
 x - ray energies below the pb - liii - edge . the curves , except 
 the black one , are shifted vertically by a factor of 2 for clarity . inset : the squares show the shift in q of the first 
 minimum in the asaxs curve as a function of e , whereas 
 the red dashed line shows the position of the pure pbs nc as reference . 
 in ( b ) , ( c ) , and ( d ) the resulting density profiles for the large , medium , and small sized pbs / cds samples are depicted . the pb - density ( red line ) is 
 plotted on the left axis and the total electron density ( blue line ) 
 on the right axis as a function of the distance from the particle 
 center . ( e ) scheme of the final shell formation for all three initial 
 particle sizes , i.e. , large , medium , and small , after maximum exchange time . the received structural parameters 
 from figure 2a result in the density profile 
 shown in figure 2b . the red line depicting 
 the pb - density ( left axis ) gives 
 a value of 19.9  0.25 pb - atoms / nm within the core 
 with a diameter of 7.34  0.03 nm ( rcore = 3.67 nm ) . also the total electron density shown on the right 
 axis in figure 2b with 1568  13 e / nm matches the expected 
 value of 1566 e / nm for pbs . no pb can be traced in the 0.69 nm shell , whereas the e - density reaches 86% of that expected 
 for bulk cds in the zb crystal phase . this slight 
 discrepancy can be related to a small deviation of the nc from the 
 spherical shape due to surface roughness or facetting , which is not 
 included in our model . from the composition profile we can conclude , 
 however , on an atomically sharp interface between pbs - core and a pure 
 cds - shell as was already reported for the pbx / cdx core / shell systems . a similarly well - defined 
 but much thicker cds - shell is formed around 
 the medium sized pbs - ncs as shown in figure 2c . this density profile is derived from measurements 
 and fits shown in figure s2a in the supporting 
 information . we start from pure pbs ncs with an initial diameter 
 of around 6 nm applying a similar synthesis procedure as for the large core / shell ncs . here we took more samples at times 
 even below 1 h reaction time and we monitored the shell growth up 
 to 18 h. within a total diameter dtotal of 6.2 nm a 3.4 nm diameter pbs - core is formed surrounded by a 1.5 
 nm thick cds - shell . the pb - density ( red line ) and the total e - density ( blue line ) of the core meet 
 quite closely the expected values for pbs , and the electron density 
 of the shell that for cds , respectively . again a different profile results 
 from the asaxs data of the small pbs ncs ( see figure 
 s2b , supporting 
 information ) with initial 5 nm size as shown in figure 2d . in the core / shell ncs with a dtotal of 4.7 nm only a 0.8  0.05 nm pbs - core remains , 
 whereas a 1.9  0.02 nm thick shell is formed containing 4.5 
  0.25 pb / nm within the cds shell . the e - density of the shell , however , reaches only 65% 
 of the value for pure cds ( blue line in figure 2d ) . the low total shell electron density is a strong indication that no cd1xpbxs alloy is formed , because such a ternary compound 
 should have a significantly larger density value with respect to pure 
 cds and not a lower one . a similar amount of pb is detectable for 
 all small nc samples taken at different time steps 
 during the pb  cd exchange up to 
 29 h reaction time . in our simple core / shell model we can not unambiguously 
 determine where exactly the detected pb is located within the shell 
 to give the observed result . two extreme pb positions within the shell 
 are possible : ( i ) the pb can be located close to the remaining pbs - core , 
 or ( ii ) the pb - atoms can be bound on top of the cds shell surface 
 forming an additional pb - surface shell . the last scenario ( ii ) may 
 be related to the proposed growth mechanism for a cationic shell growth 
 thicker than one monolayer : the pb ions have to diffuse toward the particle surface , where 
 they are subsequently exchanged by the cd ions of the 
 cd oleatic compound within the solution ( see more details in 
 the supporting information and in ref ( 36 ) ) . if this last reaction 
 step is not fully completed , e.g. , due to a too low cd  oleate 
 concentration , a submonolayer ( ml ) of pb - atoms should remain on the 
 surface . the 4.5 pb / nm found within the cds shell would 
 correspond to an 75% ml - coverage of pb on top of the cds shell . thus , an additional second surface shell with a reduced 
 electron density should be detectable with a thickness in the range 
 of two times the ionic radius of pb with 0.133 nm and the -ml thickness of pbs of around 0.34 nm . analyzing 
 the data with an extended model consisting of three density steps , 
 i.e. , a core plus two shells , the fit at a fixed x - ray energy gives 
 indeed a surface shell with 0.38 nm thickness and a reduced electron 
 density of around 800 e / nm . moreover , the derived e - density value of the thick intermediate cds - shell of 1.5 nm thickness 
 matches now to 96% of the cds value ( see figure s3 , supporting information ) . the alternative model ( i ) , 
 where the total pb amount in the small core / shell 
 ncs is concentrated close to the particle 
 center , would require a pbs - core with nearly 3 nm diameter . the simulated 
 data using this large pbs core compared to the experimental saxs data 
 shows , however , that the model ( i ) for the pb - distribution can be 
 ruled out ( see figure s3a , supporting information ) . thus , our detailed saxs analysis suggests that the small core / shell ncs are surrounded by a second surface shell consisting 
 of a sub - ml of pb atoms remaining after a not fully completed cd for 
 pb exchange ( see figure s3d , supporting information ) . to test the reliability of the retrieved 
 pb - density distributions , 
 we calculate from these core / shell profiles the total pb - concentrations 
 within the ncs we compare these values with the pb concentrations 
 that are derived from an independent method , which is not sensitive 
 to the internal pb - distribution . for this purpose , the elementary 
 ratio of pb : cd : s was probed by rutherford backscattering spectroscopy 
 ( rbs ) for all investigated large and small pbs / cds ncs ( summarized in table s1 , 
 see supporting information ) . the amounts 
 of pb derived from both methods , rbs and asaxs , are in very good agreement 
 as can be seen in figure 3d , where the pb - concentration 
 is plotted as a function of the exchange time . the small core / shell ncs contain a large amount of cd and only a small amount 
 of pb in the range of 13 atom % to 18 atom % , which is in good accordance 
 with a profile with a thick cds shell , a small pbs core , and some 
 remaining surface pb atoms . it can bee seen for all three sample series that the total pb amount decreases while the cds - shell 
 increases and remains constant when the maximum shell thickness is 
 reached , corresponding to a decreasing pbs core during the cd for 
 pb exchange . in figure 2e we summarize schematically 
 the final core / shell parameters as obtained from asaxs for all three 
 sample series . a clear trend is visible : the cds shell increases and 
 hence the pbs cores decrease with decreasing initial 
 pbs - nc diameter . the shrinkage of the pbs core is also reflected in 
 a shift of the peak wavelength in the pl spectra to shorter wavelengths ( see figure 1c and figure 
 s5 , supporting information ) . a detailed 
 investigation of the peak shift as a function of the core diameter 
 and of the cds shell thickness is presented in the supporting information and shown in figure s6 . additional important conclusions can be 
 drawn from the time dependence of the core / shell structural parameters , 
 when relating them to the optical performance of the large , medium , and small ncs . in figure 3a the time evolution of the cds - shell thickness tshell is plotted over the square root of the 
 exchange time in minutes to cover the whole range of the investigated 
 time steps , starting from 20 min up to 29 h. the values at growth 
 time zero originate from the pure starting pbs - ncs . the initial diameter 
 and the total core / shell diameter dtotal remains constant within the error bars during the cationic exchange 
 process that means the cds - shell increases with the same rate as the 
 pbs - core shrinks . the large cds - shell of the small 
 ncs ( green symbols ) is already fully formed after 60 min exchange 
 time and remains quite constant up to the maximum growth time of 29 
 h. for the medium sized ncs ( cyan symbols ) we can 
 observe between 40 and 120 min after cd - injection small variations 
 in the tshell - value , whereas after 2 h 
 the final shell thickness of 1.5 nm is reached . for the large ncs ( black symbols ) the cds - shell increases from 0.7 
 nm up to 0.9 nm after 3 h. whether this is already the final shell 
 thickness can not be answered here , since no data above 3 h are available . ( a ) cds - shell 
 thickness tshell vs exchange 
 time for the large ( black ) , medium ( cyan ) , and small ( green ) core / shell 
 ncs . ( b ) the time dependence of the pb amount 
 within the shell is shown , whereas in ( c ) the normalized integrated 
 pl emission of the ncs vs time is depicted . ( d ) the total pb - amount 
 within all ncs derived from the asaxs profiles ( full circles ) together 
 with the rbs values ( open squares ) are shown over the exchange time . ( e ) the integrated pl 
 emission normalized to the values of the pure pbs ncs is plotted over 
 the cds - shell thickness . no significant increase in the total size distribution as 
 reported 
 for pbte / cdte core / shell ncs is found 
 during the whole exchange time . the initial size distributions of 
 12% , 14% , and 15% for the large , medium , and small ncs is found to be constant within 1% . over the whole time series no pb can be traced within the cds - shells 
 of the large and medium sized core / shell 
 ncs ( black and cyan symbols in figure 3b ) , 
 whereas the amount of pb on top of the thick cds shell of the small ncs ( green symbols ) varies between 3.5  0.2 
 and 4.7  0.3 pb - atoms / nm . the pb - amount within the 
 pbs - core is found to be also constant within 0.7 pb / nm around the theoretical value for rock salt pbs 
 of 18.9 pb / nm for all three sample series . in figure 3c we depict the pl emission of 
 all three sample series also as a function of the exchange time and 
 can thus relate the optical performance of the core / chell ncs to their 
 different structural and chemical compositions . the integral pl emission 
 is derived from the total area under the pl emission spectra with 
 peak wavelengths between 1200 and 1900 nm increasing from the small 
 to the large nc samples ( see figure 1c and 
 figure s5 , supporting information ) . the 
 integral intensity values are all normalized to one at the corresponding 
 value of the initial pure pbs ncs . the strongest relative increase 
 in the normalized pl , and hence the relative increase in the quantum 
 yield , is observed for the thin shell growth around the large pbs / cds ncs . the intensity is enhanced by a factor of over 4 with 
 respect to the pure pbs ncs sample . after the strong enhancement after 
 1 h growth time the further increase after 2 h is moderate and constant 
 after 3 h , although the cds - shell increases in the last growth step 
 from 0.7 to 0.9 nm ( black symbols ) . the medium and small core / shell 
 ncs reveal a smaller enhancement of the pl by a factor of 2 , 
 but only after short growth times ( cyan and green symbols ) . for both 
 series in the further reaction time steps a decrease in the pl and hence in the quantum yield can be observed . this decrease 
 can not be directly related to a pronounced change in the chemical 
 composition profile of the core / shell ncs as shown in figure 3a , b , d , where only small variations in the shell 
 thickness are visible . this effect is better visualized in figure 3e , where the integrated pl intensity is plotted 
 as a function of the shell thickness tshell , where initially an increase of the pl - enhancement with growing 
 shell thickness can be observed . after this initial increase , however , 
 the relative pl intensity levels off and even decreases from a maximum 
 pl value with longer exchange times . since there is no evidence for a compositional 
 origin of this unexpected optical behavior , we have additionally investigated 
 the crystal structure of the core / shell ncs by recording powder x - ray 
 diffraction patterns . in figure 4a the diffraction 
 patterns of the large , medium , and small initial pbs ncs are shown together with their fits 
 using gaussian peak shapes on top of a linear background . the vertical 
 dashed lines mark the positions of the bragg peaks for rock 
 salt ( rs ) pbs ( apbs = 5.936  ) and zinc blende ( zb ) cds ( acds = 5.818  ) bulk structures . 
 the peak positions for the pure pbs ncs matches very well the theoretical 
 values indicating that the ncs are fully relaxed . from the fits we 
 derive the peak maximum value , the center position , the full width 
 half - maximum , and the area under the peaks giving the integrated crystal 
 peak intensity iint . ( a ) experimental diffraction 
 pattern of the large , medium , and small initial pbs 
 ncs are shown ( open circles ) together with their fits ( lines ) . the 
 vertical dashed lines mark the positions of the bragg peaks for rock salt ( rs ) pbs and zinc blende ( zb ) cds bulk structures . ( b ) the xrd pattern for 
 pbs / cds core / shell ncs after maximum exchange time . in ( c ) the ratio 
 between the integrated peak intensity of the ( 200 ) and ( 111 ) diffraction 
 peaks is shown over the exchange time , in ( d ) the position in q of the ( 220 ) peak maximum . an interpretation of the core / shell diffraction patterns 
 shown 
 in figure 4b can not be done in a straightforward 
 manner due to the strong overlapping of two broad peaks related to 
 the small lattice constant difference of 2% between pbs and 
 cds . one can observe , however , directly a change in the peak intensity 
 ratio between the ( 111 ) and the ( 200 ) peak , as well as a shift in 
 the peak position toward the cds bulk position . these effects are 
 most pronounced for the medium and small core / shell samples , where the diffracted intensity mainly originates 
 from the thick cds shells ( see figure 4b ) . the intensity ratio change can be interpreted in terms of a change 
 in the crystals structure from rocksalt to zinc blende , because the zb structure of 
 bulk cds depicts a strongly reduced ( 200 ) bragg peak with respect 
 to the rs structure of pbs ( blue and red squares 
 in figure 4a , b ) . the shift of the peak positions , 
 especially that of the ( 220 ) bragg peak , where we are most sensitive 
 to changes in the lattice spacings , can be caused by both a different 
 crystal phase and strain effects . the assumption of a metastable rs phase fraction 
 in the cds shell is motivated by the fact that due to cationic exchange 
 in ncs the chemically new compound can preserve the crystal structure 
 of the starting nc . in our case the cds 
 shell should keep to a certain extent the rs structure 
 of the pbs core . zb phase 
 ratio within the shell as a function of the exchange time and the 
 shell thickness . for this we calculate the individual diffraction 
 patterns for all pure pbs ncs and the pbs / cds ncs by means of the 
 debeye formula using the individual chemical 
 composition data for 12 different sample sets as retrieved from asaxs 
 ( see the supporting information for a detailed 
 description ) . we assume for the pbs core always a pure rs structure , but for the cds - shell either the rs or 
 the zb structure . fitting the simulated diffraction 
 data with the same procedure as the experimental data ( see figures 
 s8s10 , supporting information ) 
 we retrieve for each single chemical composition the theoretical intensity 
 ratio and peak shift for the cds shell being either 100% in the rs ( red dashed lines in figure 4c , d ) 
 or 100% in the zb phase ( blue dashed lines ) . this 
 allows the relative amount of the two crystalline phases within the 
 cds shell to be determined , where a value of one means pure rs - phase and a value of zero a pure zb - phase , 
 respectively . in figure 4c the ( 200)/(100 ) 
 intensity ratio of all samples and hence a measure for the rs the reliability of our model is reflected by the 
 values for the pure rs pbs ncs ( black dashed line ) 
 in the range between 0.95 and 1 . for the large core / shell 
 ncs ( black symbols ) the peak intensity ratio for the two slightly 
 thinner cds shells formed after 1 and 2 h gives values of around 0.70 . after 3 h the signal drops , however , significantly to a lower value 
 corresponding to 20% of a remaining rs phase . a similar behavior , decreasing amount of the rs phase with exchange time , is visible for the medium ( cyan symbols ) and small ( green symbols ) sized 
 core / shell samples , but here already the first formed shells depict 
 a significantly lower amount of cds in the rs phase . 
 the shell of the medium sized ncs with 1.4 nm thickness 
 exhibits 50% of rs phase fraction , whereas the nearly 
 2 nm shell of the small ncs contains only 30% of 
 this metastable phase . furthermore , only the 2 nm thick cds shell 
 reaches the zb phase finally after 29 h of exchange 
 time , whereas the medium sized ncs keep within their 
 shell 30% of the metastable rs crystal phase . the same trend is also reflected in the shift of the ( 220 ) bragg 
 peak depicted in figure 4d . the cds shells 
 of the large ncs show a quite linear shift from the pbs lattice constant 
 to the cds value , whereas the shell lattice constant in the medium 
 sized core / shell ncs finally seems to remain constant in the middle 
 between pbs and cds . both sample series are chemically stable during 
 the growth time as derived from the asaxs profiles , so the peak shift 
 can be related to different crystalline phases within the shell . to 
 conclude from the lattice constant values alone on the amount of crystalline 
 phases within the shell is not unambiguous , due to the fact that the 
 lattice spacing can be altered by strain . this is reflected in the 
 lattice constant values of the small sample series , 
 where after maximum exchange time the lattice constant of the shell 
 is even smaller than that of the bulk cds value . this can be explained by a compressive strain caused 
 by a surface relaxation due to the high surface / volume ratio for the 
 small sized ncs . this can be already seen for the small pure pbs ncs 
 depicting a 0.4% smaller lattice constant with respect to the bulk 
 pbs value . the lattice spacing for the 2 nm thick cds shell after 
 the longest growth time is even 0.9% smaller . this effect was already 
 reported for zns nanocrystals , where 
 the magnitude of the compressive strain for 5 nm 
 nanocrystals is in the same order of magnitude . the different 
 crystal structures , the rs and zb - phase , can be realized by keeping the anionic s position 
 in both lattice types constant , whereas only the positions of the 
 cations differ . the pb - ions in the rs structure have 
 six nearest neighbors and occupy a face - centered - cubic ( fcc ) sublattice 
 displaced by ( 1/2 , 1/2 , 1/2 ) of the cubic lattice constant apbs . the more covalent bound cd ions are fourfold 
 coordinated , which occupy fcc positions that are displaced by ( 1/4 , 
 1/4 , 1,4)acds ( see figure 5a ) . hence , we explain the appearance of the metastable rs structure within the shell by a fast cd for pb exchange 
 process , where the cd cations occupy in the beginning the same lattice 
 positions as the expelled rs core pb - ions . the change 
 from this metastable rs phase to the zb - phase is caused by a subsequent cd - ion transition to their equilibrium 
 positions within the zb lattice , whereas the anionic 
 s - sublattice in both crystal structures is unchanged . such a stable 
 anionic sublattice was recently found for the homogeneous cationic 
 exchange in cdse ncs . a continuous anionic 
 sublattice between the rs and the zb structure is also identified by hr - tem and verified by ab 
 initio simulations for pbte quantum dots embedded in a cdte 
 matrix . ( a ) scheme of the crystals phases of cds 
 occurring during the cationic 
 cd for pb exchange . first the cds - shell mimics nearly fully the core rock salt ( rs ) structure of pbs , and later 
 both the rs ( cyan ) and the equilibrium zinc 
 blende ( zb ) phase ( blue ) of cds can be found 
 within the shell . the indicated distribution of the metastable rs phases within the shell is only a suggestion . ( b ) integrated 
 pl intensity normalized to the cds layer thickness plotted over the zb phase fraction within the shell . the cd structural transition starts to a certain extent directly 
 after the cd for pb exchange ; the full rearrangement of the cd - ions 
 in the zb structure , however , takes up to 30 h at 
 a temperature of 80 c as can be deduced from figure 4c , d . we could not observe any change of the phase 
 fractions with time after cooling the samples to room temperature . the proposed scheme is sketched in figure 5a , where it is also indicated that the highest amount of rs - phase is found for the thinnest cds shell , i.e. , for 
 the largest initial sphere diameter . the influence of the shell thickness 
 on the rs phase fraction is shown by comparing rs phase fraction values at 1 h exchange time . we found 
 values of 70% , 50% , and 30% for the rs phase for 
 the large , medium , and small ncs , respectively ( see figure 4c ) . we expect 
 that these amounts of metastable crystal phases are not homogeneously 
 distributed along all crystallographic directions , but our current 
 xrd data do not allow preferred crystallographic directions to be 
 identified , in which this metastable phase is enriched . an additional 
 indication for the coexistence of the zb and rs phases within one single shell is found in the dark field 
 hrtem images of a large core / shell nc after 3 h of exchange time . 
 in figure s1d , e ( supporting information ) either the rs or the zb electron 
 diffraction peaks are used for highlighting the corresponding crystal 
 phase . the bright rs core phase in figure s1d extends in the shell region , whereas in figure s1e the bright zb phase 
 depicts an inhomogeneous distribution within the shell . this kind of polytypism 
 of crystal phases within one shell was also found for shells grown 
 epitaxial on top of the core . the driving force 
 for the thickness dependence of the amount of 
 the rs phase fraction can be related to the strain 
 energy built up within the cds - shell due to the lattice mismatch of 
 around 2% between pbs and cds . the piled up tensile 
 strain with increasing number of mls of the 
 thicker shells can be fast relaxed by creating stacking faults that can trigger the transition from the rs to 
 the zb crystal structure . the relation between phase 
 fraction and shell strain is summarized in figure s11 ( supporting information ) . these defects in the 
 shell should be reflected in a reduced pl emission due to a partial 
 extension of the exciton wave function into the shell material . indeed , the core / shell ncs with medium and thick 
 shells depict only half of the pl increase with respect 
 to the thin - shell samples . to investigate only the influence of the rs - zb phase fraction on the pl we relate 
 in figure 5b the ratio of the rs to the zb phase to the normalized pl emission values . 
 here , the 
 pl intensity values of the samples are additionally normalized to 
 the individual shell thickness values . two distinct features 
 are visible : a decrease of the pl with decreasing rs phase fraction is visible for all three samples series . additionally , 
 a pronounced jump in the relative pl increase between 
 the large samples with shells below 1 nm and the medium and small ncs with shells above 
 1.3 nm is visible . these thick - shell samples depict more than three 
 times lower relative pl values as the thin - shell samples compared 
 at the same phase fraction value of around 0.5 . the slope of the decrease , 
 however , is constant for all three sample series . this is demonstrated by the two black lines in figure 5b having the same slope as derived from a linear fit to the 
 data of the thin - shell samples only . within the three thin - shell samples 
 the metastable rs phase fraction changes from 70% 
 to 20% while the relative pl is decreased by around 16% . the thick - shell 
 samples start already with 75% decreased relative pl value at 50% rs phase fraction and reach only 10% of the initially relative 
 pl increase . these experimental findings suggest that two different 
 mechanisms 
 are involved to mediate the transition from the metastable rs phase to the equilibrium zb structure 
 of the cds shell . one mechanism for transitions between fourfold and 
 sixfold coordinated crystal structures was reported for ncs that implies a collective sliding of crystal planes accompanied 
 by the creation of stacking folds . this martensitic - like phase transition 
 from a fourfold to a sixfold phase is induced by high external applied 
 pressures . in contrast , in our pbs / cds core / shell ncs the sliding 
 of the cd - sublattice 
 planes from the sixfold rs phase to the fourfold zb structure , i.e. , in the reverse direction , is driven 
 by the tensile stress within the cds shell . during 
 this phase transition an alternative transition - path mechanism can avoid the creation of 
 stacking faults but is based on the uniaxial compression of crystal 
 planes and results in an increase of the surface energy . in theoretical studies by grnwald et al . it was shown that the fourfold to a sixfold phase transition starts 
 via the compression path mechanism nucleating on the crystal surface 
 and is continued by the sliding plane mechanism , but depending on 
 the size and surface structure also a mixture of both is possible . moreover , very recently it was shown by the 
 same group that the transformation mechanisms for metastable phases 
 within core / shell ncs depends strongly on the shell thickness . for shells below 3 mls thickness taking these studies into 
 account we interpret our observations 
 summarized in figure 5b as follows : for the 
 thin - shell samples the transformation between the metastable rs phase and the zb phase , and hence the 
 relaxation of the shell - strain , is realized by the surface nucleation 
 mechanism , which results in an only moderate decrease of the pl due 
 to surface defects . for the thick - shell samples the initial transformation 
 proceeds via the sliding plane mechanism resulting in stacking faults 
 that considerably decrease the pl intensity . due to the stacking fault formation , thin shell layers below 3 mls are created , in which the 
 compression mechanism mediates a further rs to zb phase transition with reduced influence on the pl . the 
 physical origin of this pronounced influence of the shell on the pl 
 intensity is related to the delocalization of charge carriers over 
 the whole core / shell volume . in conclusion , we have demonstrated that , during the cds shell 
 growth around pbs nanocrystals due to a cd for pb cationic exchange , 
 the shell initially maintains the metastable rock salt crystal structure of the core within a chemically pure cds shell . such a metastable phase within a core / shell system , which does not 
 occur in the bulk material under ambient pressure , was quite recently 
 theoretically predicted . for the first 
 time we have determined the quantitative amount of the metastable 
 phase in the shell as a function of the exchange time and the shell 
 thickness . moreover , the core / shell ncs show a pronounced pl enhancement 
 after the cds shell formation with the pl showing a clear dependence 
 on the rs / zb phase fraction : it 
 decreases with decreasing rs phase and increasing zb structure . this revealed correlation is related to the 
 formation of lattice distortions during the phase transitions . the 
 control of this metastable phase within the shell to optimize the 
 core / shell interface will have significant impact on tailoring the 
 optical properties of core / shell ncs also in related material systems .
we reveal the existence of two different 
 crystalline phases , i.e. , 
 the metastable rock salt and the equilibrium zinc blende phase within the cds - shell of pbs / cds core / shell 
 nanocrystals formed by cationic exchange . 
 the chemical composition 
 profile of the core / shell nanocrystals with different dimensions is 
 determined by means of anomalous small - angle x - ray scattering with 
 subnanometer resolution and is compared to x - ray diffraction analysis . 
 we demonstrate that the photoluminescence emission of pbs nanocrystals 
 can be drastically enhanced by the formation of a cds shell . 
 especially , 
 the ratio of the two crystalline phases in the shell significantly 
 influences the photoluminescence enhancement . 
 the highest emission 
 was achieved for chemically pure cds shells below 1 nm thickness with 
 a dominant metastable rock salt phase fraction matching 
 the crystal structure of the pbs core . 
 the metastable phase fraction 
 decreases with increasing shell thickness and increasing exchange 
 times . 
 the photoluminescence intensity depicts a constant decrease 
 with decreasing metastable rock salt phase fraction 
 but shows an abrupt drop for shells above 1.3 nm thickness . 
 we relate 
 this effect to two different transition mechanisms for changing from 
 the metastable rock salt phase to the equilibrium zinc blende phase depending on the shell thickness .