the recent development 
 of colloidal cspbx3 ( x = cl , 
 br , and i ) perovskite nanocrystals ( ncs ) has resulted in a burst of 
 scientific interest , owing to their outstanding optical properties . due to their high photoluminescence quantum yields ( plqys up to 
 90% ) without any additional surface passivation and tunable optical 
 properties throughout the entire visible spectrum , cspbx3 ncs are promising new materials for various optoelectronic applications , 
 such as low threshold one- and two - photon pumped gain 
 materials for lasing and highly efficient leds . moreover , recently , colloidal cspbi3 ncs were 
 used in solution processed photovoltaic cells with device efficiencies 
 exceeding 10% . currently , synthetic 
 protocols for colloidal cspbx3 ncs 
 with a variety of shapes are available , such as cubes , nanowires , and nanoplatelets . besides all - inorganic cspbx3 perovskite ncs , colloidal organic  inorganic perovskite 
 ncs have also been recently prepared . furthermore , 
 the composition of colloidal halide perovskite ncs can easily be postsynthetically 
 tailored through topotactic halide - exchange reactions with preservation 
 of the size and shape of the parent ncs ( despite a small lattice expansion 
 or contraction , depending on the size of the guest halide ) . this is in striking contrast to what has been commonly observed 
 for anion exchange reactions in colloidal ii vi semiconductor 
 ncs , which typically result in severe size and shape transformations , 
 often leading to hollow ncs . topotactic cation 
 exchange reactions are commonplace in colloidal 
 semiconductor ii  vi and iii  v ncs , allowing access to 
 a variety of compositions and shapes that are not attainable through 
 direct synthesis protocols . in contrast , postsynthetic cation exchange in colloidal cspbx3 perovskite ncs remains elusive and has only been addressed 
 in two recent works , which reported conflicting observations . while akkerman et al . report the observation of ch3nh3 ( ma ) for cs exchange 
 in cspbbr3 ncs as an undesired complication in anion exchange 
 protocols using ma  x salts , nedelcu 
 et al . state that attempts to exchange either cs or pb for other cations ( rb , ag , cu , ba , sn , ge , or bi ) in cspbbr3 ncs were invariably unsuccessful 
 and lead only to the decomposition of the parent ncs . the resistance of cspbbr3 ncs to cation exchange 
 was rationalized by nedelcu et al . as a consequence of the fact that 
 the perovskite crystal structure is stabilized primarily by the rigid 
 cationic sublattice . the introduction 
 of impurity ions in colloidal ii vi and 
 iii  v semiconductor ncs provides another synthetic tool to 
 control the optoelectronic properties and to bestow the parent ncs 
 with novel functionalities , such as magnetism due to unpaired electrons 
 in the dopant or increased effective 
 stokes shift due to exciton recombination on the impurity ions . furthermore , impurity doping of perovskite thin films has been shown 
 to improve their performance in solar cells . recently , mn doping in colloidal cspbcl3 perovskite ncs has 
 been achieved by a direct synthesis method , in which pbcl2 and mncl2 precursors were mixed in the desired ratio , 
 leading to ncs with the characteristic mn emission . however , postsynthetic control over the perovskite 
 composition by introducing different impurity ions has yet to be achieved . in this work , we present a novel method to perform postsynthetic 
 cation exchange reactions in cspbbr3 ncs , through which 
 pb cations are partially replaced by divalent cations 
 ( m = sn , cd , and zn ) , yielding 
 doped cspb1xmxbr3 ncs . the pb for m cation 
 exchange results in a blue - shift of the absorption and emission spectra , 
 while preserving the high plqys ( > 50% ) and narrow pl line width 
 ( 80 
 mev ) of the parent ncs . we attribute the blue - shift in the optical 
 spectra to the contraction of the perovskite cubic unit cell , which 
 results in shorter pb br bonds and hence a stronger ligand 
 field within the pb - halide octahedra . a blue - shift of the 
 pl maximum is also observed upon anion exchange reactions from iodide 
 to chloride . however , blue - emitting cspbcl3 ncs obtained by anion exchange methods or direct synthesis 
 protocols have low plqys ( < 15% ) and broad pl line widths ( > 120 
 mev ) , in contrast to the blue - emitting ncs synthesized 
 with our approach ( plqy > 50% , pl line width 80 mev ) . our 
 work opens up many new possibilities to engineer the properties of 
 halide perovskite ncs , which are demonstrated to be the only known 
 system where topotactic cation and anion exchange can be sequentially 
 combined , resulting in compositionally diverse colloidal cspb1xmxbr3 perovskite ncs ( m = sn , zn , and 
 cd ; x  0.1 ) with size and shape 
 preservation and high pl quantum yields . colloidal cspbbr3 ncs 
 ( pl maximum at 512 nm ) were reacted inside a nitrogen - purged glovebox 
 at room temperature with metal bromide salts ( snbr2 , cdbr2 , znbr2 ) and oleylamine dissolved in toluene , leading 
 to a blue - shift of the absorption and pl spectra ( figure 1 ) . the use of metal bromide 
 salts as precursors for the guest cation ensures that solely the cation 
 can be exchanged , since both the parent ncs and the precursor contain 
 the same halide . the spectral position of the pl band blue - shifted 
 over a wide range , depending on the divalent metal cation used and 
 the precursor concentration ( figure 1a  c ) . interestingly , although the blue - shift 
 of the absorption and pl spectra is observed in all cases , i.e. , for 
 all divalent cations and precursor concentrations , it is more pronounced 
 for specific concentrations and cations . for example , the blue - shift 
 is small , i.e. , 30 mev , for both low and high concentrations of snbr2 ( 0.25 mm snbr2 , pl maximum at 506 nm ; 1.7 mm snbr2 , pl maximum at 504 nm ; figure 1d ) , but is much larger ( 170 mev ) for a snbr2 concentration of 0.5 mm , resulting in efficient pl in the blue region 
 of the visible spectrum ( pl maximum at 479 nm , plqy 62% ; figure s1a ) . by varying the concentration of 
 snbr2 in toluene while keeping all other reaction parameters 
 constant , the position of the pl maximum can be tuned between 479 
 and 512 nm . the increase in the snbr2 concentration also 
 results in the appearance of a weak and broad absorption feature at 
 580 nm . the possible nature of this transition and of the 
 observed spectral blue - shift will be discussed later in this paper . photographs of colloidal 
 suspensions under uv illumination of ( a ) perovskite ncs after reaction 
 of cspbbr3 ncs with different concentrations of snbr2 ( 0.5 , 1.25 , and 1.7 mm ) , ( b ) parent cspbbr3 ncs 
 ( right vial ) and product ncs after reaction of cspbbr3 ncs 
 with different concentrations of cdbr2 ( 0.5 and 1.0 mm ) , 
 and ( c ) parent cspbbr3 ncs ( right vial ) and product ncs 
 after reaction of cspbbr3 ncs with different concentrations 
 of znbr2 ( 0.5 and 1.0 mm ) . photoluminescence ( full lines ) 
 and absorption ( dashed lines ) spectra of ( d ) parent cspbbr3 ncs ( green lines ) and product ncs obtained after reaction with different 
 concentrations of snbr2 ( red and brown lines ) and ( e ) parent 
 cspbbr3 ncs ( green lines ) and product ncs obtained after 
 reaction with different concentrations of cdbr2 ( orange 
 lines ) and znbr2 ( blue lines ) . in all cases , a blue - shift 
 of both the absorption and the photoluminescence spectra is observed 
 after reacting cspbbr3 ncs with divalent cation bromides , 
 while the well - defined absorption features and the narrow pl fwhm 
 ( 80 mev ) are preserved . reaction of the cspbbr3 ncs with other divalent 
 ions , 
 i.e. , cd and zn , leads to more pronounced 
 blue - shifts than reaction with snbr2 , resulting in efficient 
 pl between 452 and 512 nm for cspbbr3 ncs reacted with 
 cdbr2 and between 462 and 512 nm for cspbbr3 ncs reacted with znbr2 ( figure 1e ) . the key spectral features of the parent 
 cspbbr3 ncs , such as the sharp optical absorption edge , 
 well - defined absorption peaks , and the narrow pl line width ( fwhm 
  80 mev ) , are maintained after reaction with metal bromide 
 salts . high plqys over 60% are observed after reaction with divalent 
 cations for all samples ( see figure s1a ) . we note that the pl peak shifts further over time ( 100200 
 mev over 4 weeks ) , due to the presence of metal bromide precursor 
 in the stored colloidal dispersions , since the samples could not be 
 purified due to difficulties with precipitation of the ncs . however , 
 the ncs do not deteriorate and do maintain their size , shape , high 
 plqys , and colloidal stability in toluene over the course of ( at least ) 
 several months . furthermore , we find that the absorption increases 
 with 2% over the first 90 min of reaction ( see figure s1b ) . the increase in absorption on longer time scales 
 is hard to quantify , since the absorption spectrum also shifts to 
 higher energies . it has also been observed in other reports that colloidal 
 perovskite ncs require very high centrifugation speeds to be destabilized 
 from colloidal suspension and precipitated . in the present case , such high centrifugation speeds also lead to 
 precipitation of the unreacted metal - bromide precursor , while using 
 stronger antisolvents , e.g. , methanol , deteriorates the ncs . a recent 
 study by luther and co - workers reported a novel purification procedure 
 for perovskite ncs , involving methyl acetate as antisolvent , which 
 does not lead to degradation of the ncs , although it still requires 
 high centrifugation speeds . we also used 
 this purification method , but we were able to recover only a very 
 small amount of ncs from the reaction mixtures ( see experimental methods below for details ) . the pl lifetimes 
 of the parent cspbbr3 ncs and the product 
 perovskite ncs after reaction with metal bromide salts were measured , 
 displaying multiexponential decay for all samples , both before and 
 after the cation exchange reactions ( figure s2 ) . therefore , the average lifetime ( avg ) was calculated , which reveals that avg is 
 of the same order of magnitude ( 10 ns ) in all cases . furthermore , 
 we note that the higher the pl energy , the shorter avg , as expected based on fermi s golden rule . for the cspbbr3 ncs reacted with snbr2 , the average exciton lifetime ( avg ) decreases 
 from 16.8 ns for the parent cspbbr3 ncs to 6.8 ns for the 
 product ncs obtained upon reaction with 1.7 mm snbr2 . a 
 decrease in avg is also observed for the product 
 ncs obtained upon reaction with cdbr2 and znbr2 , to 6.4 and 7.2 ns , respectively . transmission electron 
 microscopy ( tem ) measurements reveal that 
 the shape and size of the ncs are preserved after reaction with metal  bromide 
 salts ( figures 2 , s3 , and s4 ) , since cubes of 9 nm are 
 observed in all cases . electron diffraction ( ed ) analysis shows that 
 the atomic reflections are shifted to larger scattering vectors after 
 the reaction with divalent ions . this indicates that the atomic cspbbr3 lattice contracts due to the incorporation of the smaller 
 sn / cd / zn guest cations ( figure 2d , h ) . the 1d powder 
 ed ( ped ) patterns ( figure 2d , h ) were obtained by azimuthally integrating the 2d ed patterns , 
 displayed as insets in the tem images ( figure 2a  c , e g ) . as displayed in figure 2 , the lattice contraction after reaction with cd and zn this is expected based 
 on the ionic radii of the divalent cations , in case pb ( r(pb ) = 119 pm , coordination number 
 ( cn ) = 6 ) is replaced by the guest divalent cation ( r(cd ) = 95 pm , r(zn ) = 
 74 pm , r(sn ) = 118 pm , cn = 6 in all 
 cases ) . quantification of the { 100 } d - spacing is displayed in figure 2d , h . the diffraction patterns were calibrated 
 with both tlcl and au reference samples ( see supplementary method 1 and figures s5 and s6 for details ) . size and shape preservation 
 and lattice contraction of cspbbr3 nanocrystals ( ncs ) after 
 reaction with mbr2 ( reaction 
 time : 16 h ) . ( a ) parent cspbbr3 ncs 
 and ( b , c ) product ncs obtained after reaction of cspbbr3 ncs with different concentrations of snbr2 precursor 
 ( 0.5 and 1.7 mm , respectively ) . the insets in panels a  c display 
 the 2d electron diffraction ( ed ) patterns , which result in ( d ) 1d 
 powder ed ( ped ) patterns after azimuthal integration ( concentration 
 of snbr2 : 0.25 , 0.50 , 1.0 , 1.25 , and 1.7 mm , from top to 
 bottom , respectively ) . the colors of panels a  c correspond 
 to the colors of the 1d ped patterns in panel d. tem images of ( e ) 
 parent cspbbr3 ncs and ( f ) product ncs obtained after reaction 
 of cspbbr3 ncs with znbr2 and ( g ) with cdbr2 . g display the 2d ed patterns , 
 which result in ( h ) 1d ped patterns after azimuthal integration . the 
 colors of panels e  g correspond to the colors of the 1d ped 
 patterns in panel h. a large lattice contraction is observed upon 
 reaction of cspbbr3 ncs with cd and zn ( h ) , whereas a minor lattice contraction is observed upon 
 reaction with sn ( d ) . quantification of the { 100 } d - spacing is given in panels d and h. enlarged versions 
 of the tem images displayed in panels a g , as 
 well as the tem images and ed patterns of the other samples , can be 
 found in figures s3 and s4 . the lattice contraction of cspbbr3 ncs 
 after reaction 
 with mbr2 salts is also observed in the high - angle annular 
 dark - field scanning transmission electron microscopy ( haadf - stem ) 
 images ( figure 3 ) . 
 here , statistical parameter estimation theory is used to extract structure 
 parameters from the images . one of the structure 
 parameters corresponds to the atomic column positions , which have 
 been used to estimate the absolute distance between neighboring pb / halide 
 columns in order to quantify the lattice parameter ( figure 3 ) . by fitting a normal distribution 
 to these distance estimates the lattice parameter of the parent cspbbr3 ncs was calibrated 
 to the value reported in the literature for the cubic perovskite structure 
 of cspbbr3 . a lattice contraction from |a| = 5.849  0.003  to |a| = 5.839  
 0.005  is observed upon reaction of cspbbr3 ncs with 
 0.5 mm snbr2 . the obtained cspbbr3 unit vector 
 corresponds well to recent x - ray diffraction experiments for the cubic 
 perovskite crystal structure , but it does not exclude the presence 
 of a small portion of orthorhombic distortions of the octahedra in 
 the atomic lattice . similar analysis 
 on cspbbr3 ncs reacted with 0.5 mm cdbr2 and 
 1.0 mm znbr2 shows a lattice contraction from |a| = 5.849  0.003  to |a| = 
 5.819  0.008  ( cd ) and |a| = 5.808  0.014  ( zn ) , respectively . we 
 do not observe clustered areas with larger / smaller lattice vectors 
 in the images showing the deviations from the mean lattice vector 
 ( figure 3 , middle row , 
 red : larger than mean distances , blue : smaller than mean distances ) . 
 from this , we deduce that the incorporated guest cations are homogeneously 
 distributed throughout the ncs . thickness profiles obtained from the 
 total scattered intensities of the atomic columns confirm this observation 
 ( figure s7 ) . quantitative high - angle 
 annular dark - field stem measurements reveal 
 a lattice contraction of ( a ) parent cspbbr3 ncs ( |a| = 5.849  0.003  ) upon reaction with ( b ) 0.5 
 mm snbr2 ( |a| = 5.839  0.005  ) , 
 ( c ) 0.5 mm cdbr2 ( |a| = 5.819  0.008 
  ) , and ( d ) 1.0 mm znbr2 ( |a| = 5.808 
  0.014  ) ( reaction time : 16 h ) . in the haadf - stem images , the mixed pb / halide ( bright contrast ) , cs ( intermediate contrast ) , 
 and halide ( low contrast ) atomic columns can be easily assigned ( top 
 panels ) . after detecting the positions of the pb / halide columns from 
 the haadf - stem images , we calculate the interatomic distances , i.e. , 
 the lattice spacing ( middle panels ) . red bars indicate a larger distance 
 than the mean |a| , and blue bars indicate a smaller 
 distance than the mean |a| . the histogram of distances 
 together with the estimated normal distribution reveal a contraction 
 of the cubic perovskite cspbbr3 atomic lattice upon reaction 
 with snbr2 , cdbr2 , and znbr2 ncs 
 ( bottom panels ) . as can be seen , the lattice 
 contraction for cd- and zn - dopants 
 ( 0.5 and 0.7% , respectively ) is larger than that for the sn - doped 
 ncs ( 0.2% ) , which is in full agreement with the electron diffraction 
 data presented in figure 2 . the statistical student s t test 
 with unequal variances has been used to verify that the found differences 
 are significant . here , the distribution 
 of the measured lattice parameters of the parent cspbbr3 ncs have been compared to a distribution of the measurements on 
 the doped cspb1xmxbr3 ncs at a significance level of 10% , 
 indicating that the distributions have different means . on the basis 
 of these results , we conclude that guest divalent cations are indeed 
 present in the perovskite ncs and are distributed homogeneously across 
 the perovskite lattice . the results presented 
 above suggest 
 that pb cations in cspbbr3 ncs are replaced 
 by other divalent cations , i.e. , sn / cd / zn , resulting in a lattice contraction due to the smaller ionic 
 radius of the incorporated cations . to verify the incorporation and 
 the distribution of the guest cations , energy dispersive x - ray spectroscopy 
 ( eds ) chemical mapping was performed . we note that the eds measurements 
 were performed on areas containing a large amount of ncs , in order 
 to obtain a statistically relevant result . the eds measurements show 
 that cd ( figure 4a  e ) 
 and zn ( figure 4f  j ) 
 are incorporated in the cspbbr3 ncs in low concentrations . moreover , no indication for surface preference or phase segregation 
 is observed , which leads us to conclude that the distribution of the 
 guest cations within the cspb1xmxbr3 ncs is homogeneous , 
 consistent with the observations presented above . quantification of 
 the eds measurements reveals a cd / pb ratio of 0.16 for product cspb1xcdxbr3 ncs obtained after 16 h of reaction with 0.5 mm cdbr2 ( figures s8s10 ) and a 
 zn / pb ratio of 0.05 for product cspb1xznxbr3 ncs obtained 
 after 16 h of reaction with 1.0 mm znbr2 ( figure s11 ) . cspbbr3 ncs reacted with 0.5 mm snbr2 for 16 h were also analyzed with bulk eds measurements , which 
 reveal a sn / pb ratio of 0.1 ( figure s12 ) . we also performed an eds quantification of product cspb1xcdxbr3 perovskite 
 ncs and of portions of the tem grid surrounding clusters of ncs , i.e. , 
 the background . this analysis clearly shows a cd peak at 3.1 kev for 
 the area containing ncs , whereas cd - peaks are below the noise level 
 in the background ( see figure s13 ) . the 
 eds analysis thus clearly demonstrates that divalent guest cations 
 are successfully incorporated in cspbbr3 ncs upon reaction 
 with mbr2 salts . it should be noted that the elemental 
 concentrations are upper limit estimates , since the samples were not 
 washed prior to the eds measurements ( see experimental 
 methods for details ) . a few selected samples were thoroughly 
 purified by precipitating with methyl acetate , which yielded only 
 very small amounts of ncs ( see experimental methods for details ) . the purified ncs showed reduced carbon contamination 
 upon prolonged exposure to the e - beam ( see figure s14 ) . furthermore , the sn / pb ratio for purified ncs ( 0.085 , 
 see figure s15 ) was similar to the sn / pb 
 ratio for the unpurified samples ( 0.1 , see figure s12 ) . this leads us to conclude that the above presented cation / pb 
 ratios are valid upper limit estimates for the incorporated divalent 
 cations . a possible mechanism for the postsynthetic incorporation 
 of divalent cations into cspbbr3 ncs will be discussed 
 below . ( a ) haadf - stem image of cspb1xcdxbr3 ncs and the corresponding 
 maps of ( b ) cs , ( c ) pb , ( d ) br , and ( e ) cd , demonstrating the presence 
 of cd in the perovskite ncs . the inset in panel a shows a photograph 
 of a colloidal suspension of the ncs under uv illumination . ( f ) haadf - stem 
 image of cspb1xznxbr3 ncs 
 and the corresponding maps of ( g ) cs , ( h ) pb , ( i ) br , and ( j ) zn , 
 indicating the presence of zn in the perovskite ncs . the inset in 
 panel f shows a photograph of a colloidal suspension of the ncs under 
 uv illumination . the bright spots observed in the haadf - stem images 
 are metallic pb nanoparticles , formed upon prolonged exposure to the 
 electron beam ( see figure s16 ) . it must be noted that we observe bright spots on 
 the cspbbr3 ncs upon exposure to the electron beam ( see figure 4 ) . high - resolution 
 haadf - stem 
 analysis shows that these spots correspond to metallic pb nanoparticles 
 ( figure s16 ) . this implies that part of 
 the pb ions are reduced to metallic pb upon imaging the 
 ncs with an electron beam . furthermore , the measured atomic ratios 
 indicate that the parent cspbbr3 ncs are halide - deficient 
 ( cs / pb / br = 1:1:2 ; ratio of cation charge / anion charge = 1.5 , figure s8 ) and that the halide deficiency is 
 preserved after reaction with mbr2 salts ( ratio cation 
 charge / anion charge = 1.5 , figures s9s12 ) . cation / anion ratios significantly larger than unity are commonly 
 observed for ncs of ii vi , e.g. , cdse , and of iv  vi , 
 e.g. , pbse , semiconductors synthesized in the presence of x - type ligands , 
 e.g. , oleate , and have been rationalized by considering that the stoichiometric 
 nc is coated by a layer of m  x units . a similar explanation may apply in the present case , since the cspbbr3 ncs were synthesized from cs - oleate and pb - oleate . nevertheless , 
 halide deficiency is commonly observed in bulk perovskites , due to 
 the very low activation energies for the creation of anion vacancies 
 in these materials , and is likely also present in perovskite ncs . density 
 functional theory calculations show that anion vacancies do not result 
 in midgap trap states in halide perovskites , since their energy levels 
 lie within the conduction band . therefore , 
 despite the presence of halide vacancies , the exciting optoelectronic 
 properties of the parent cspbbr3 ncs , such as high plqy 
 and sharp excitonic features , are preserved in the product cspb1xmxbr3 ncs . the results presented above clearly show that divalent 
 guest cations 
 ( sn , cd , and zn ) can be incorporated 
 into cspbbr3 ncs by postsynthetic cation exchange reactions . 
 considering that aliovalent exchange of cs ( radius : 1.88 
  ) for m would strongly destabilize the perovskite 
 structure , since it would result in smaller m cations 
 in sites with coordination number 12 and would require charge compensation , 
 we will assume below that only isovalent exchange of pb for m has taken place , leading to partial substitutional 
 replacement of pbbr6 octahedra by mbr6 octahedra 
 ( figure 5 ) . pb cations are partially replaced by 
 other divalent cations ( sn , cd , and zn ) by postsynthetic cation exchange reactions , resulting in 
 divalent - cation - doped cspb1xmxbr3 ncs ( the mbr6 octahedra are schematically depicted 
 by the blue metal  halide octahedra ) . incorporation of smaller 
 divalent cations results in contraction of the atomic lattice , which 
 induces a blue - shift of the optical transitions ( absorption and pl ) . v , and i  vi semiconductors and have been shown to consist of several inherently linked elementary 
 kinetic steps , which must proceed in a concerted way . the first step 
 is the extraction of the native cation from the parent ncs , which 
 may occur by a direct place exchange reaction , i.e. , extraction of 
 the native cation and incorporation of the guest cation in a direct 
 reaction mediated by a ligand in solution , e.g. , zn for 
 cd exchange in znse , mediated by oleate ligands , or by an independent chemical pathway that is 
 only kinetically coupled to the incorporation of the guest cation , 
 e.g. , cation exchange in cu2xs ncs in the presence of excess phosphines . the rates of extraction of the native cation 
 and incorporation of the guest cation must be balanced ; otherwise , 
 the accumulation of cation vacancies eventually leads to the collapse 
 of the nc . there are several factors involved 
 in the cation extraction process , such as breaking of the cation anion 
 bonds within the nc and formation of cation  ligand bonds , while 
 the incorporation of the guest cation requires breaking the cation the thermodynamic driving force for the cation exchange is determined 
 by the energy balance of the overall reaction . it should also be noted 
 that the cation exchange process is essentially a surface reaction , 
 which in the absence of cation diffusion in the nc would stop as soon 
 as all surface cations had been exchanged by the guest cations . therefore , the cation exchange rates are often 
 limited by the diffusion rates of the outgoing and incoming cations . cation diffusion in semiconductor 
 ncs is often attributed to vacancy - mediated migration , and its rate is therefore limited by the activation energies for 
 vacancy formation . cation exchange reactions have not yet been 
 studied in detail in 
 perovskite ncs , but topotactic anion exchange has been shown to be 
 very efficient and fast in cspbx3 ( x= cl , br , and i ) halide 
 perovskite ncs , due to the low activation energy 
 for the formation and diffusion of halide vacancies in these materials . in contrast , cation diffusion in perovskites is a very slow process , 
 owing to the high activation energies for the formation of cation 
 vacancies and the lack of interstitial sites for interstitial diffusion . a recent study on bulk ch3nh3pbi3 has concluded that vacancy - assisted iodide diffusion in this perovskite 
 material has an activation energy of only 0.58 ev , leading to fast 
 diffusion even at room temperature ( diffusion coefficient : 10 cm.s ) , while cation 
 diffusion has much higher activation energies ( 0.84 and 2.31 ev for 
 ch3nh3 and pb , respectively ) . as a result , ch3nh3 diffusion is 4 orders of magnitude slower than iodide diffusion , 
 and the pb sublattice is essentially immobile . this implies that cation exchange processes 
 involving pb in cspbx3 perovskites would be 
 limited by very slow diffusion fluxes for both the outgoing pb and the incoming m guest cations . our results 
 show that this is indeed the case , since the pb for m exchange reaction is very slow and only occurs partially , 
 despite the large excess of m cations with respect to 
 the parent cspbbr3 ncs ( from 8  10 to 
 3  10 , see experimental methods ) . the number of pb cations in a 9 nm cspbbr3 nc is 3600 ( unit cell volume : 0.2 nm , nc volume : 
 729 nm ) . this means that even in the low precursor concentration 
 regime there is a 2-fold excess of guest m cations with 
 respect to pb implying that full exchange would be possible 
 if a sufficiently strong driving force would be present . as it will 
 be discussed below , the fact that the cation exchange does not reach 
 completion despite the large m / pb ratios used shows that the driving 
 force is small and that the reaction may in fact be self - limited . the use of metal bromide precursors has multiple benefits in our 
 cation exchange protocol , leading to successful partial exchange of 
 pb for m cations in cspbbr3 ncs , 
 which results in doped cspb1xmxbr3 ncs . the presence of br in 
 the guest cation precursor allows us to take advantage of the ease 
 of formation of halide vacancies in cspbx3 ncs and to explore 
 the fact that cspbx3 ncs quickly establish an equilibrium 
 with solvated halides in the solution phase , especially in the presence 
 of amines , allowing fast cross - exchange between ncs with different 
 halides . given that mbr2 does not dissociate 
 in toluene , it binds to the surface br vacancies as a molecular unit , 
 thereby incorporating mbr2 in the nc . this releases energy 
 due to the formation of bonds between the incoming br and the nc but 
 does not consume energy because the m the energy released can then be used to break the bonds 
 between a pbbr2 unit and the nc . because the bonds formed 
 and broken are similar , the energy balance is close to zero ; therefore , 
 the surface pb cations can be quickly exchanged into 
 guest m cations , despite the low temperatures , i.e. , 
 room temperature , used in our cation exchange protocol . to allow the 
 cation exchange process to continue , two diffusion fluxes have to 
 be established : inward diffusion of guest m cations and 
 outward diffusion of pb cations . as discussed above , 
 these fluxes will be slow , since they have high activation energies , 
 and will be primarily driven by the increase in entropy that results 
 from the formation of cspb1xmxbr3 solid solutions . however , 
 the exchange of pb by smaller m cations 
 leads to a progressive contraction of the lattice , which leads to 
 strain within the nc . this increasing strain field counteracts the 
 entropic gain , eventually becoming sufficiently strong to halt the 
 cation exchange process . this could be a reason for a self - limited 
 cation exchange , as we have observed here for several isovalent ions . a schematic representation of the cation exchange mechanism proposed 
 above is given in figure s17 . the 
 fact that the lattice contraction ( and therefore the extent 
 of pb for m exchange ) does not directly 
 scale with the concentration of mbr2 precursors but instead 
 reaches a maximum at intermediate concentrations can be rationalized 
 by considering that the cation exchange is actually driven by the 
 concentration of halide vacancies in template cspbbr3 ncs 
 as discussed above . the formation of halide vacancies is promoted 
 by the olam molecules present in solution , which nevertheless can form olam , the increase 
 in the concentration of mbr2 in the reaction medium will 
 eventually decrease the cation exchange rates by outcompeting the 
 ncs for the limited supply of olam , thereby decreasing the formation 
 rate of halide vacancies . we have also performed a series of 
 experiments at fixed snbr2/nc concentration and total volume 
 but different olam concentrations 
 ( figures s18 and s19 ) . we find that the 
 position of the pl peak after the reaction depends on the amount of 
 olam present in solution , but the exact trend depends on the reaction 
 time : for short reaction times ( 48 h , figure s18 ) , the blue - shift is larger 
 for lower olam concentrations , while for longer reaction times ( 84 
 h , figure s19 ) , the opposite trend is observed . these observations are consistent 
 with the mechanism proposed above and can be rationalized by considering 
 that the cation exchange is driven by the formation of anion vacancies 
 in the ncs , but it is rate - limited by inward diffusion of the guest 
 cations , i.e. , surface sites have to be made available to allow the 
 process to proceed . therefore , increasing the concentration of surface 
 halide vacancies does not directly increase the extent of the cation 
 exchange at shorter reaction times because the cation diffusion rates 
 remain constant . under these conditions , olam will extract from the 
 nc surface not only br but also snbr2 . therefore , higher 
 olam concentrations decrease the relative extent of the cation exchange 
 in the short reaction time regime by shifting the equilibrium toward 
 solvated snbr2 . the inward diffusion of snbr2 competes with its removal from the surface by olam and , albeit slowly , 
 gradually moves sn away from the surface , thereby incorporating 
 it into the nc lattice . as a result , after sufficiently long reaction 
 times , e.g. , 84 h ( figure s19 ) , the concentration of guest cations incorporated 
 in the ncs will reflect the equilibrium concentration of halide vacancies 
 and will thus be larger for higher olam concentrations . it should 
 be noted that higher olam concentrations induce shape distortions 
 and structural changes after long reaction times ( figure s19 ) , indicating that large excesses of olam lead to 
 partial deterioration of the ncs upon prolonged reaction times , probably 
 due to an imbalance between the rate of formation of halide vacancies 
 and the cation exchange rates . we have also observed that the pl intensity 
 of the product cspb1xsnxbr3 ncs is higher for reactions carried 
 out under higher olam concentrations ( see figure s18 ) , which can be attributed to a better surface passivation , 
 by either olam molecules or oleylammonium bromide formed in situ . interestingly , the pl energy of doped 
 cspb1xmxbr3 perovskite 
 ncs scales linearly with that of the lattice vector ( figure 6 ) independently of the type 
 of cation that has been incorporated . this is most evident for the 
 sn - doped ncs , for which more data points are available ( figure 6a ) , but it is also clear when 
 the other two cations are taken into account ( figure 6b ) . photoluminescence ( pl ) energy and lattice vector 
 correlation in 
 cspb1xmxbr3 perovskite ncs . ( a ) pl energy as a function 
 of the lattice vector in doped cspb1xsnxbr3 ncs obtained 
 by postsynthetic pb for sn cation exchange 
 in parent cspbbr3 ncs . ( b ) pl energy as a function of the 
 lattice vector in doped cspb1xmxbr3 ( m= sn , cd , and zn ) 
 ncs obtained by postsynthetic pb for m cation 
 exchange in parent cspbbr3 ncs . the different colors of 
 the symbols in panels a and b correspond to the colors used to identify 
 the different samples in figures 1 and 2 the band gaps of abx3 perovskites are known to 
 increase 
 with the increase of the electronegativity of both b and x atoms and 
 with the decrease of the unit cell volume . it is thus quite remarkable that the trends for the three cations 
 are very similar despite their different radii , electronic configurations , 
 and properties ( pb [ 5d6s6p ] : r = 119 pm , electronegativity  
 = 1.6 ; sn [ 4d5s5p ] : r = 118 pm ,  = 1.7 ; cd [ 4d5s ] : r = 95 pm ,  = 1.5 ; 
 zn [ 3d4s ] : r = 74 pm ,  = 1.7 ; polarizability and lewis hardness decrease 
 from pb to zn ) . this implies that the observed 
 blue - shift of the optical transitions is primarily due to the lattice 
 contraction , and that the mbr6 guest octahedra are electronically 
 decoupled from the pbbr6 framework . this is particularly 
 clear for the sn - doped ncs , since it is reported in literature that 
 the band gap of cssnbr3 and cspb1xsnxbr3 are red - shifted 
 with respect to that of cspbbr3 . this shows that the band - edge absorption and the pl transition of 
 the cspb1xsnxbr3 ncs prepared in this work are solely determined 
 by the pbbr6 octahedra , despite the presence of snbr6 groups in the nc . the additional feature observed at lower 
 energies ( 540600 nm ) in the absorption spectra of the cspb1xsnxbr3 ncs ( figure 1d ) can thus be ascribed to these electronically isolated snbr6 octahedra . the pl transition of abx3 halide 
 perovskites has also 
 been reported to blue - shift upon proceeding along the i , br , and cl 
 series , as clearly illustrated by the pl tunability achieved by synthetic 
 and postsynthetic compositional control in both bulk and nanocrystalline 
 abx3 . although this is accompanied by a contraction 
 of the unit cell , the pl shift does not depend linearly on the lattice 
 contraction , since the widening of the band gap is largely due to 
 the increase in electronegativity along the halide series , which effectively 
 increases the ionic character of the b  x bond . in fact , our work provides 
 the first clear observation of a linear 
 relationship between lattice vector and pl energy in perovskites . a recent work reported a blue - shift of the pl peak of bulk cssnbr3 upon warming ( lattice expansion ) , in striking contrast with our results . similar observations , i.e. , 
 pl blue - shift with increasing temperature , have also been reported 
 for cspbbr3 ncs and bulk cssni3 . however , it should be noted 
 that this behavior ( linear increase of the band gap with increasing 
 temperature ) is anomalous , since most semiconductors show the opposite 
 temperature - dependence , i.e. , linear increase of the band gap with 
 decreasing temperature . this anomalous temperature dependence is also observed 
 for copper halides ( cubr and cucl ) , lead chalcogenides , and black 
 phosphorus and has been attributed to a dominance of the lattice thermal 
 expansion contribution over the electron , the widening of the band gap upon 
 lattice expansion is ascribed to simultaneous narrowing and stabilization 
 of both the valence and conduction bands , as a result of the antibonding 
 character of their maximum and minimum , respectively . pl shifts have also been recently reported for mapbx3 bulk films and single crystals subjected to high pressures . interestingly , small red - shifts ( 50 mev ) were observed in 
 the low - pressure regime ( below 0.351 gpa ) , while strongly 
 nonlinear blue - shifts ( up to 200 mev ) were observed in the high - pressure 
 regime ( above 12.5 gpa ) and were ascribed to amorphization 
 of the mapbx3 lattice . this explanation 
 is however inadequate for the pl blue - shifts reported in our work , 
 since we do not observe any signs of loss of crystallinity , disorder , 
 or phase transitions in the doped cspb1xmxbr3 ncs obtained by 
 postsynthetic pb for m cation exchange , 
 despite very clear lattice contractions . it should be pointed out 
 that also from this perspective the behavior of bulk abx3 halide perovskites seems to be anomalous , since the pl of most common 
 semiconductors , e.g. , gan and cdte , blue - shifts linearly with increasing 
 pressure . the behavior observed for the cspb1xmxbr3 ncs prepared in 
 the present work by postsynthetic pb for m cation exchange in 9 nm cspbbr3 ncs is thus in line with 
 the normal pressure dependence of the band gap energies of bulk semiconductors , 
 but it is opposite to what is observed for bulk abx3 halide 
 perovskites . the contribution of quantum confinement 
 effects to the blue - shift observed in the optical spectra of the cspbbr3 ncs after the cation exchange reaction is however negligible , 
 since the ncs under study here are larger than the estimated exciton 
 bohr diameter for cspbbr3 ( viz . , 7 nm ) and are therefore in the weak confinement regime . 
 although the reduction in the nc size should result in an increase 
 in quantum confinement , the effect would be too small to account for 
 the magnitude of the spectral shifts observed after the cation exchange 
 reactions ( up to 300 mev , which would require a size reduction from 
 9 to 5 nm , according to the theoretical size dependence of 
 the band gap reported in ref ( 1 ) ) . furthermore , protesescu et al . have shown that blue - emitting 
 cspbbr3 ncs are in the sub 4 nm size regime , whereas the cspb1xmxbr3 ncs obtained in 
 this work have a diameter of 9 nm and yet display efficient pl in 
 the blue region of the electromagnetic spectrum . we thus propose 
 that the remarkable behavior observed here for 
 doped cspb1xmxbr3 ncs indicates that they can accommodate larger 
 isotropic compressive strains than bulk abx3 halide perovskites , 
 and as a result , all pbbr6 octahedra within a nc contract 
 without significant ( additional ) distortion so that the compressive 
 strain is homogeneously distributed throughout the nc ( as indicated 
 by figure 3 above ) . distortion and tilting of the bx6 octahedra is known to 
 induce band gap reduction . these distortions 
 are however always accompanied by lattice constant changes that act 
 in the opposite direction , thereby decreasing the extent of the red - shift . recent x - ray diffraction analysis of cspbbr3 ncs suggests that orthorhombic distortions are an important 
 feature of these materials . although 
 the linear relationship observed in the present work between the degree 
 of lattice contraction and the blue - shift of the pl of cspb1xmxbr3 ncs 
 ( figure 6 ) does not 
 rule out the possibility of orthorhombic distortions in the ncs , it 
 implies that their contribution does not significantly change with 
 the nature of m or the extent of the replacement and therefore that 
 the lattice contraction is the dominant effect . this widens the band gap because the conduction band minimum ( cbm ) 
 is composed of the antibonding combinations between pb(6p ) and br(4p ) 
 orbitals and therefore should shift to 
 higher energies with stronger interactions . although the valence band 
 maximum is also antibonding , we expect 
 it to shift less than the cbm because it emerges from the relatively 
 weaker interaction between the br(4p ) orbitals and the 
 pb(6s ) orbitals , which are stabilized by lone pair and 
 relativistic effects . in contrast , the 
 pb(6p)br(4p ) interaction is largely responsible for the chemical 
 bonding in apbx3 perovskites as it leads to charge transfer 
 from the pb(6p ) to the x(np ) orbitals . we present a postsynthetic cation exchange 
 method , which allows 
 us to partially exchange pb ions in cspbbr3 ncs for several other divalent cations ( sn , cd , and zn ) . this isovalent cation exchange results 
 in a blue - shift of the pl bands , without loss of the high plqys ( > 60% ) , 
 narrow emission bandwidth , and sharp excitonic absorption transitions . the blue - shift is attributed to contraction of the perovskite lattice 
 due to the incorporation of smaller divalent guest cations ( sn / cd / zn ) , resulting in shorter pb we show that the blue - shifted pl energy scales linearly with the lattice 
 vector of the doped cspb1xmxbr3 ncs , in striking contrast 
 to what has been reported for bulk perovskite materials . this is the 
 first example of postsynthetic cation exchange in cspbbr3 perovskite ncs , demonstrating that halide perovskite ncs are the 
 only known system in which the complete composition can be postsynthetically 
 tailored with size and shape preservation by sequentially combining 
 topotactic anion and cation exchanges . this opens up a library of 
 possible compositions attainable for colloidal cspbx3 ncs , 
 which might possess unprecedented and unparalleled optoelectronic 
 properties and may prove beneficial for a number of applications . cesium 
 carbonate ( cs2co3 , 99.9% ) , 1-octadecene ( ode , 
 90% ) , oleic acid ( oa , 90% ) , lead bromide 
 ( pbbr2 , 99.999% ) , oleylamine ( olam , 70% ) , tin(ii ) bromide 
 ( snbr2 ) , cadmium bromide tetrahydrate ( cdbr24h2o , 98% ) , zinc bromide ( znbr2 , 99.999% ) , 
 anhydrous toluene ( 99.8% ) , anhydrous hexane ( 95% ) , and anhydrous methyl 
 acetate ( 99.5% ) were obtained from sigma - aldrich . olam and oa were 
 degassed at 120 c for 1 h prior to use . the cspbbr3 ncs were prepared according to the method 
 described by protesescu 
 et al . first , cs - oleate precursor stock 
 solution was prepared by loading 0.814 g of cs2co3 , 2.5 ml of oa , and 40 ml of ode into a 100 ml round - bottomed flask . the mixture was dried under vacuum for approximately 1 h at 120 c 
 and then heated under n2 to 150 c until all cs2co3 had reacted with oa . ode ( 5 ml ) and pbbr2 ( 0.069 g ) were loaded into a separate 25 ml flask and dried 
 under vacuum for 1 h at 120 c . olam ( 0.5 ml ) and oa ( 0.5 ml ) 
 were injected at 120 c under n2 atmosphere . after 
 pbbr2 had dissolved , the temperature was raised to 180 
 c and a 0.4 ml portion of the cs - oleate stock solution was quickly 
 injected . we note that the cs - oleate stock solution had to be preheated 
 to 100 c before injection . after 510 s , the 
 reaction mixture was cooled by an ice - water bath in order to quench 
 the reaction . the cspbbr3 ncs were purified following the method described 
 by de roo et al . the crude synthesis solution was centrifuged 
 for 3 min 
 at 10  000 rpm , and the colored supernatant was discarded . then , 
 300 l of hexane was added , and the ncs were dispersed using 
 a vortex mixer . subsequently , the suspension was again centrifuged 
 for 3 min at 10  000 rpm , after which the precipitate , containing 
 larger ncs and agglomerates , was discarded . another 300 l of 
 hexane was added to the supernatant , resulting in a colloidal dispersion 
 of cspbbr3 ncs . a second purification procedure , 
 based on recent work by luther and co - workers , was also used for a few selected samples of colloidal perovskite 
 ncs after pb for sn cation exchange ( see 
 below ) . the additional purification of the colloidal cspb1xsnxbr3 perovskite 
 ncs was performed by adding 1 ml of methyl acetate to the crude nc 
 solution , followed by centrifugation at 13  000 rpm for 1 h. 
 the amount of precipitate was extremely small . after removing the 
 supernatant , the precipitate was redispersed in 300 l of hexane . 
 subsequently , 300 l of methyl acetate was added , and the ncs 
 were again centrifuged at 13  000 rpm . the supernatant was discarded , 
 and the even smaller amount of precipitate was redispersed in 50 l 
 of hexane before being dropcast on a copper tem grid for further analysis . cation exchange precursor stock solutions 
 were prepared by dissolving 1 mmol of metalbromide salt ( mbr2 , with m = sn , zn , and cd ) 
 in 10 ml of toluene ( 0.1 m mbr2 ) , in the presence of 100 
 l of olam . in a typical cation exchange experiment , 1.5 ml 
 of diluted ncs in toluene ( concentration : 0.01 m , using 
 an extinction coefficient of 37.9 cm m at 335 nm , for cubes of roughly 9 nm ) and 0.5 ml of cation precursor ( different concentrations , 
 ranging between 0.125 and 1.67 mm , [ m]/[nc ] ratio varied 
 between 8000 and 300  000 ) were mixed and stirred 
 at room temperature for 16 h. in the majority of the cases , 
 the ncs were not purified after the cation exchange reactions , due 
 to difficulties with precipitation of the ncs . the second purification 
 procedure described above , in which methyl acetate is used as antisolvent , 
 was applied to a few selected samples after reaction with snbr2 but yielded only very small amounts of ncs , only enough to 
 get submonolayer coverage on a tem grid . the influence of the 
 amount of olam was investigated by replacing a volume of toluene ( 5 , 
 10 , or 30 l ) by olam , while keeping all other variables unchanged , 
 i.e. , total volume , concentration of ncs and snbr2 , as 
 well as the snbr2/ncs ratio . the products of the reaction 
 were analyzed after 48 and 84 h. tem measurements were performed using a tecnai20f 
 ( fei ) microscope equipped with a field - emission gun and a gatan 694 
 ccd camera . eds measurements 
 were performed on fei talos f200x and an aberration corrected  cubed fei titan 60300 electron microscope equipped with a chemistem 
 system operated at 200 and 300 kv , respectively . acquisition time for eds measurements was 300 s. samples for 
 tem imaging were prepared by dripping a diluted nanocrystal solution 
 in toluene on a carbon - coated polymer film copper grid ( 300 mesh ) . 
 the solvent ( toluene ) was allowed to evaporate prior to imaging . high - resolution high - angle annular dark 
 field scanning transmission electron microscopy ( haadf - stem ) measurements 
 were performed using an aberration corrected cubed fei titan 60300 
 electron microscope operated at 300 kv . ped patterns were obtained 
 by azimuthally integrating the 2d ed patterns ( with the freely available 
 software package crystbox ) acquired on 
 a tecnai-12 transmission electron microscope using a selected - area 
 aperture . 2d ed patterns were acquired on areas containing a large 
 number of nanocrystals to make the 1d ped patterns statistically valid 
 ( see supplementary method 1 and figures s5 and s6 for details ) . samples for 
 optical measurements 
 were prepared by diluting the colloidal dispersion of ncs with anhydrous 
 toluene under nitrogen and storing them in sealed quartz cuvettes . absorption spectra were measured on a double - beam perkinelmer lambda 
 16 uv / vis spectrometer . pl spectra were recorded on an edinburgh instruments 
 fls920 spectrofluorimeter equipped with a 450 w xenon lamp as excitation 
 source and double grating monochromators . pl decay curves were obtained 
 by time - correlated single - photon counting on a hamamatsu h742202 
 photomultiplier tube with low dark count rate ( < 10 cts / s ) . a pulsed 
 diode laser ( epl-445 edinburgh instruments , 375 nm , 55 ps pulse width , 
 0.2 mhz repetition rate ) was used as the excitation source . the plqys of the perovskite 
 ncs were determined with respect to the fluorophore lumogen red 350 
 ( plqy = 95% ) . samples for plqy measurements 
 were prepared by diluting the colloidal dispersion of ncs with anhydrous 
 toluene under nitrogen in sealed quartz cuvettes , keeping the optical 
 density of both the lumogen red and the perovskite ncs below 0.1 at 
 442 nm in order to minimize reabsorption . the plqys 
 were calculated using the following equation : in which t is the transmission 
 at 442 nm of the sample , tref is the transmission 
 at 442 nm of lumogen red ,  is the integrated pl photon flux 
 of the sample , ref is the integrated pl photon flux 
 of lumogen red , and qyref is the qy of lumogen red ( 95% ) 
 ( see supplementary method 2 and figure s20 for more details ) .
colloidal 
 cspbx3 ( x = br , cl , and i ) perovskite nanocrystals 
 ( ncs ) have emerged as promising phosphors and solar cell materials 
 due to their remarkable optoelectronic properties . 
 these properties 
 can be tailored by not only controlling the size and shape of the 
 ncs but also postsynthetic composition tuning through topotactic anion 
 exchange . 
 in contrast , property control by cation exchange is still 
 underdeveloped for colloidal cspbx3 ncs . here , we present 
 a method that allows partial cation exchange in colloidal cspbbr3 ncs , whereby pb2 + is exchanged for several isovalent 
 cations , resulting in doped cspb1xmxbr3 ncs ( m= sn2 + , cd2 + , and zn2 + ; 0 < x  0.1 ) , with preservation of the original nc shape . the size 
 of the parent ncs is also preserved in the product ncs , apart from 
 a small ( few % ) contraction of the unit cells upon incorporation of 
 the guest cations . 
 the partial pb2 + for m2 + exchange 
 leads to a blue - shift of the optical spectra , while maintaining the 
 high photoluminescence quantum yields ( > 50% ) , sharp absorption 
 features , 
 and narrow emission of the parent cspbbr3 ncs . 
 the blue - shift 
 in the optical spectra is attributed to the lattice contraction that 
 accompanies the pb2 + for m2 + cation exchange 
 and is observed to scale linearly with the lattice contraction . 
 this 
 work opens up new possibilities to engineer the properties of halide 
 perovskite ncs , which to date are demonstrated to be the only known 
 system where cation and anion exchange reactions can be sequentially 
 combined while preserving the original nc shape , resulting in compositionally 
 diverse perovskite ncs .