we provide kinetic evidence that the metastable , 
 magic - size ( cdse)34 nanocluster is near the critical - nucleus 
 size for cdse and 
 supports the growth of wurtzite cdse nanocrystal platelets 
 at room temperature ( 2025 c ) . typical conditions for 
 the synthesis of cdse nanocrystals are temperatures above 200 c . to our knowledge , the growth of cdse quantum platelets ( qps ) reported 
 here , via the intermediacy of ( cdse)34 nanoclusters , constitutes 
 the lowest temperature at which crystalline cdse has been produced . we ascribe the low - temperature crystal growth to facile nucleation 
 resulting from ( cdse)34 being near to the critical size , 
 such that the nucleation barrier has largely been surmounted in the 
 formation of this magic - size nanocluster . a crystal nucleation 
 and growth process that is driven by a chemical 
 reaction requires a proper ordering of nucleation , growth , and reaction 
 barriers ( activation energies , scheme 1 ) . according 
 to the classic crystal - growth model , nucleation barriers are higher than the 
 activation energies for growth steps , such that conditions resulting 
 in nucleation will also support crystal growth . we argue that the 
 barrier for a monomer - generating chemical reaction must be higher than the nucleation barrier to support nanocrystal 
 growth ( scheme 1 , curve a ) . here , monomers 
 are defined as small ( cdse)n molecules 
 or clusters . if the nucleation barrier exceeds the 
 reaction barrier ( scheme 1 , curve b ) , then 
 monomer is produced by the reaction under conditions that preclude 
 crystal formation , and thus , amorphous aggregates and precipitates 
 are formed instead . ( a ) the reaction barrier is 
 higher than the nucleation barrier , and nanocrystal growth occurs 
 on the black free - energy curve . ( b ) the reaction barrier is lower 
 than the nucleation barrier , precluding nucleation and crystal growth . 
 instead we suspect that the high temperatures typically 
 employed in semiconductor - nanocrystal 
 syntheses reflect high nucleation barriers for assembling the critical - size 
 nucleus , such that high - barrier chemical reactions are also required . 
 however , if a critical - size nucleus could be assembled under milder 
 conditions , then in principle semiconductor - nanocrystal nucleation 
 and growth could be achieved at lower temperatures . we propose that 
 ( cdse)34 is near the critical size , such that its binary 
 combination exceeds the critical size . if so , then the critical - nucleus 
 size for cdse under our conditions is in the range of ( cdse)34(cdse)68 . we previously reported syntheses 
 of cdse quantum belts ( nanoribbons ) 
 in lamellar , n - octylamine - bilayer templates at the 
 comparatively mild temperatures of 7080 c . we determined that the magic - size nanocluster ( cdse)13 was an intermediate in the formation of the quantum belts and later 
 isolated and characterized a series of [ ( cdse)13(primary 
 amine)13 ] adducts . we now report 
 that crystalline , wurtzite , cdse quantum platelets 
 ( qps ; also known as nanoplatelets or quantum disks ) are formed at room temperature by employing di - n - alkylamine cosolvents or by varying the primary - amine 
 solvent . reaction monitoring and mechanistic analyses indicate that 
 ( cdse)34 is the magic - size nanocluster intermediate under 
 these conditions , which converts to cdse qps at room temperature by 
 first - order kinetics with no detectable induction period . alternatively , 
 at 0 c , ( cdse)34 converts to ( cdse)13 , 
 which then requires temperatures above 40 c to form cdse qps . our interpretation of these results is that ( cdse)34 is 
 nearer to the cdse critical - nucleus size . a ligated derivative 
 of ( cdse)34 is obtained as a slushy 
 solid that is stable indefinitely at 0 c . we suggest that this 
 derivative , [ ( cdse)34(n - octylamine)16(di - n - pentylamine)2 ] , may effectively 
 function as cdse crystal nuclei that may be stored in a bottle . its 
 use in templates of varying geometries may afford low - temperature 
 routes to cdse nanocrystals having other controlled morphologies . di - n - octylamine ( + 98% ) , di - n - pentylamine 
 ( 99% ) , di - n - propylamine ( 99% ) , diethylamine ( > 99.5% ) , 
 phenethylamine 
 ( 99% ) , n - dodecylamine ( 99% ) , n - octylamine ( + 99% ) , n - pentylamine ( + 99% ) , n - propylamine ( + 98% ) , cd(oac)22h2o ( > 98% ) , trin - octylphosphine ( top ) ( 97% ) , and 
 oleylamine 
 ( or cis-9-octadecenylamine , technical grade , 70% ) were obtained from 
 sigma - aldrich . toluene 
 was obtained from sigma - aldrich ( chromasolv for hplc , 99.9% ) . transmission electron microscopy ( tem ) sample grids ( cu with holey 
 carbon film ) were obtained from ted pella , inc . all synthetic 
 procedures were conducted under dry n2 , except the final 
 washing steps , which were conducted in the ambient atmosphere . the synthetic products were generally 
 stored as reaction mixtures , after addition of top ( see below ) . in a typical 
 procedure , cd(oac)22h2o ( 65 mg , 0.24 mmol ) was dissolved in di - n - octylamine ( 5.7 g , 24 mmol ) 
 in a septum - capped schlenk tube and placed in a benchtop sonicating 
 bath ( 10 min ) to achieve dissolution . in a glovebox , selenourea ( 50 
 mg , 0.41 mmol ) was dissolved in n - octylamine ( 1.2 
 g , 9.3 mmol ) in a septum - capped amber vial . the vial was removed from 
 the glovebox and placed in a benchtop sonicating bath ( 10 min ) to 
 achieve dissolution . the selenourea solution was injected into 
 the [ cd(oac)22h2o ] solution at room temperature 
 ( 2025 c ) . the colorless reaction mixture became cloudy 
 within 10 s , viscous and light green within 5 min , cloudy and yellow 
 green within 60 min , and cloudy and light yellow at longer reaction 
 times . after 2 h , the mixture was nearly clear and colorless with 
 a light - yellow precipitate . after 2 days , the yellow precipitate remained 
 in the presence of a light - red supernatant , the color of which was 
 due to a se side product from ( cdse)34 formation . top ( 0.250.50 
 ml ) was injected to scavenge the se side product through the formation 
 of colorless ( n - octyl)3p = se . the 
 light - yellow precipitate of bundled cdse qps was then stored at room 
 temperature in the reaction mixture under n2 for further 
 analyses . the procedure 
 was conducted in the same manner as that for the 1.8 nm thick cdse 
 qps ( see above ) , except for the amount of n - octylamine 
 used ( 2.4 g , 18 mmol ) and the reaction temperature , which was raised 
 to 70 c . the color changes occurred more rapidly , from colorless 
 ( 0 min ) to viscous and yellow ( 10 s ) , cloudy and orange ( 1 min ) , and 
 cloudy and orange - red ( > 120 min ) . after the reaction mixture stood 
 for 2 days at 70 c , the cdse qps were deposited as an orange - red 
 precipitate in the presence of a red supernatant . top ( 0.250.50 
 ml ) was injected to scavenge the se side product from the ( cdse)34 formation responsible for the red coloration of the supernatant , 
 which became colorless . the dispersion of bundled cdse qps was then 
 stored at room temperature in the reaction mixture under n2 for further analyses . in a typical 
 procedure , cd(oac)22h2o ( 65 mg , 0.24 mmol ) was dissolved in phenethylamine ( 5.74 g , 47 mmol ) in a septum - capped 
 schlenk tube and heated in a 70 c oil bath ( 1 h ) to dissolve 
 the cadmium precursor . in a glovebox , selenourea ( 50 mg , 0.41 mmol ) was dissolved in phenethylamine ( 1.2 g , 9.9 mmol ) in a septum - capped 
 amber vial . the vial was removed from the glovebox and placed in a 
 benchtop sonicating bath ( 10 min ) to achieve dissolution of the selenourea . the clear , colorless 
 reaction mixture became clear and light yellow within 1 h , viscous 
 and white ( 6090 min ) , and then cloudy and white - yellow ( > 90 
 min ) . after 2 h , the solution became nearly clear and colorless upon 
 formation of a white - yellow precipitate . after 2 days , cdse qps were 
 deposited as a white - yellow precipitate in the presence of a light - red 
 supernatant . top ( 0.250.50 ml ) was injected to scavenge the 
 se side product from ( cdse)34 formation responsible for 
 the red coloration of the supernatant , which became colorless . the 
 white - yellow precipitate of bundled cdse qps was then stored at room 
 temperature in the reaction mixture under n2 for further 
 analyses . in a typical procedure , cd(oac)22h2o 
 ( 65 mg , 0.24 mmol ) was dissolved in di - n - pentylamine 
 ( 5.74 g , 36 mmol ) in a septum - capped schlenk tube and then was stored 
 in an ice bath ( 0 c ) placed inside a refrigerator . in a glovebox , 
 selenourea ( 50 mg , 0.41 mmol ) was added to n - octylamine 
 ( 1.2 g , 9.3 mmol ) in a septum - capped amber vial . the vial was removed 
 from the glovebox and placed in a benchtop sonicating bath ( 10 min ) 
 to achieve dissolution of the selenourea . the clear , colorless reaction mixture became viscous 
 and light yellow within 6 h , cloudy and yellow within 8 h , and cloudy 
 and green - yellow at longer times ( 0 after 18 h at 0 c , 
 ( cdse)34 was formed as a green - yellow precipitate mixed 
 with colorless supernatant . the greenish - yellow precipitate 
 was separated using a benchtop 
 centrifuge ( 700 g , 30 s ) at room temperature , and 
 the colorless supernatant was discarded . this purification 
 process was repeated , for a total of two such cycles , yielding [ ( cdse)34(n - octylamine)16(di - n - pentylamine)2 ] as a slushy , greenish - yellow solid after 
 drying in vacuo for 12 h ( 0.061 g , 95.7% ) . visible ( toluene ) 
 max , nm : 360 , 390 , 418 ( figure 9a ) . ms m / z ( relative area , 
 assignment ) : 6508.2572 ( 100% , ( cdse)34 ) , 6319.5733 ( 42.6% , 
 ( cdse)33 ) , 3651.5768 ( 17.0% , ( cdse)19 ) , 2502.4747 
 ( 52.4% , ( cdse)13 ) ( figure 11 ) . calcd for [ ( cdse)34(n - octylamine)16(di - n - pentylamine)2 ] : c , 20.00 ; 
 h , 3.94 ; n , 2.84 . found , c , 19.94 ; h , 3.95 ; n , 2.93 . all values are 
 given as percentages . [ ( cdse)34(n - octylamine)16(di - n - pentylamine)2 ] was generally used 
 immediately for analyses or further reactions . the compound was stable 
 at room temperature for at least 24 h under n2 and for 
 longer than one month at 0 c under n2 . other 
 di - n - alkylamine derivatives of ( cdse)34 were prepared under the same general conditions , except 
 for the reaction cosolvents employed . di - n - propylamine 
 or diethylamine were used to replace di - n - pentylamine 
 for the cd(oac)22h2o solution , while n - octylamine was used for the selenourea solution . the reaction mixture was then removed from the ice bath and 
 stored at room temperature ( 2025 c ) for an additional 
 12 h. the reaction mixture was periodically monitored by uv  visible 
 spectroscopy to determine the extent of the conversion , which was 
 found to be complete after 12 h. cdse qps were deposited as a light - yellow 
 precipitate in the presence of a light - red supernatant . ( 0.51.0 
 ml ) was injected into the reaction mixture to scavenge the red selenium 
 side product from ( cdse)34 formation , resulting in a colorless 
 supernatant . the conversion of ( cdse)34 to cdse qps was 
 accelerated by adding additional di - n - pentylamine 
 to the reaction mixture at room temperature after the formation of 
 ( cdse)34 . a ( cdse)34 sample was prepared as described 
 above . an aliquot ( 26 mg ) taken from the reaction mixture was diluted 
 into a di - n - pentylamine ( 2.5 g ) and n - octylamine ( 0.07 g ) mixture in a quartz cuvette at room temperature 
 ( 2025 c ) . visible spectra were collected in 
 the wavelength range of 400500 nm at 1 h intervals . during 
 data collection , the 418 nm absorption of ( cdse)34 and the 423 and 448 
 nm absorptions of cdse qps were extracted from the spectra by nonlinear 
 least - squares fitting using origin software ( http://originlab.com/ ) . the initial ( t = 0 h ) spectrum was fit by a single 
 lorentzian function , yielding the center position of the 418 nm absorption . the final ( t = 12 h ) was fit with three lorentzian 
 functions , the first centered at 418 nm , and a background - scattering 
 function ( a/ , where a was an adjustable parameter ) , yielding the center positions of the 
 423 and 448 nm qp absorptions . all of the intermediate spectra were 
 fit with three lorentzian and the one background - scattering functions , 
 with the lorentzians initially centered at 418 , 423 , and 448 nm . the peak areas determined from the nonlinear least - squares fits 
 were used for the kinetic analyses . all three absorptions gave first - order 
 plots of absorption peak area vs time over three half - lives . the error 
 in the slope of the plots was determined by conducting three kinetic 
 trials and observing the range in the integrated peak areas in the 
 final ( t = 12 h ) spectra . the range of slopes that 
 accommodated these final values was assigned as the error in the slopes . the kinetic parameters kobs and t1/2 were extracted from the slopes , and their 
 errors determined by propagation in the normal manner . these values 
 are reported in the results section . the preparation of ( cdse)34 was conducted as described 
 above . the reaction temperature equilibrated near 0 c in the 
 refrigerator , even after the ice in the bath melted . when di - n - pentylamine was used as the cosolvent , the complete conversion required 
 longer than 1 month , during which the greenish - yellow precipitate 
 gradually changed to white with formation of a small amount of black 
 precipitate , which was a selenium side product . top ( 0.51.0 
 ml ) was injected into the reaction mixture , whereupon the black solid 
 disappeared , leaving ( cdse)13 as a white precipitate . when 
 diethylamine or di - n - propylamine was used as the 
 cosolvent , the conversion of ( cdse)34 to ( cdse)13 was more rapid and completed in 23 weeks . the conversion 
 was also accelerated by adding additional n - octylamine 
 to the reaction mixture after the formation of ( cdse)34 . we previously reported 
 that reaction of cd(oac)22h2o and selenourea 
 in n - octylamine solvent at room temperature selectively 
 produced magic - size ( cdse)13 nanoclusters entrained within 
 a spontaneously formed , double - lamellar , n - octylamine - bilayer 
 template ( eq 1 , scheme 2 ) . these intratemplate ( cdse)13 nanoclusters were subsequently converted to crystalline , cdse quantum 
 belts ( qbs ) at relatively mild temperatures ( 7080 c , 
 eq 1 ) . the lengths , widths , and thicknesses 
 of the quantum belts were determined by the dimensions within the 
 spontaneously formed , double - lamellar templates ( scheme 2 ) . we sought to purposefully 
 vary these dimensions by varying the nature of the amine solvent , 
 and those efforts led to experiments using di - n - alkylamine 
 cosolvents.1 ( a ) cd(oac)2 and 
 the primary - amine solvent forms a lamellar , amine - bilayer mesophase 
 ( blue and purple ) . ( b ) magic - size ( cdse)34 clusters are 
 initially formed within the template when primary- and secondary- 
 amine co - solvents are employed ( yellow dots , blue and purple ) . ( c ) 
 ( cdse)34 clusters are converted to bundled qps at room 
 temperature in the co - solvent mixtures ( orange and purple ) . ( d ) addition 
 of a long - chain primary amine results in the spontaneous exfoliation 
 of the qps by ligand exchange at room temperature ( orange and green ) . reaction of cd(oac)22h2o and selenourea 
 in an n - octylamine / di - n - octylamine 
 cosolvent mixture at room temperature gave a yellow precipitate , which 
 contrasted with the white ( colorless ) [ ( cdse)13(n - octylamine)13 ] isolated from the eq 1 reaction . the uv  visible spectrum of the yellow 
 precipitate dispersed in toluene ( figure 1 ) 
 closely matched those previously obtained for cdse qbs and could not be assigned to ( cdse)13 or other magic - size nanoclusters . tem images ( figure 2 ) revealed the formation of pseudorectangular cdse qps having 
 mean widths and lengths of 7 and 50 nm , respectively . because the 
 qps have the electronic properties of quantum wells , their spectrum depended only on thickness and was effectively indistinguishable 
 from those previously obtained for 1.8 nm thick qbs . the sharp pl spectrum ( figure 1 ) 
 also matched those of the corresponding cdse qbs . like the qbs , the qps gave high pl quantum efficiencies 
 ( pl qe = 25% ) . we surmised that , in the cosolvent mixture , the reaction 
 proceeded through magic - size nanocluster intermediates ( see below ) 
 to cdse qp nanocrystals at room temperature ( eq 2).2figure 1a uv  visible extinction spectrum in a toluene dispersion 
 ( black curve ) and a photoluminescence spectrum in an oleylamine  toluene 
 solution ( 12% w / w , red curve ) of 1.8 nm thick cdse qps.figure 2tem images of cdse qps synthesized in n - octylamine 
 and various di - n - alkylamine cosolvents . ( a , b ) di - n - octylamine , ( c , d ) di - n - pentylamine , 
 ( e , f ) di - n - propylamine , and ( g , h ) diethylamine . a uv  visible extinction spectrum in a toluene dispersion 
 ( black curve ) and a photoluminescence spectrum in an oleylamine  toluene 
 solution ( 12% w / w , red curve ) of 1.8 nm thick cdse qps . tem images of cdse qps synthesized in n - octylamine 
 and various di - n - alkylamine cosolvents . ( a , b ) di - n - octylamine , ( c , d ) di - n - pentylamine , 
 ( e , f ) di - n - propylamine , and ( g , h ) diethylamine . we next sought to establish the crystallinity of the 
 qps grown 
 by the room - temperature synthesis . an x - ray diffraction ( xrd ) pattern 
 of the as - prepared material ( figure 3 ) matched 
 those previously obtained for wurtzite cdse qbs . like those qbs , the qps exhibited a lattice contraction 
 associated with the surface tension of the thin nanocrystals . the lattice parameters extracted from the xrd 
 data ( a = 4.07  0.02  , c = 6.82  0.03  ) were smaller than the bulk values ( a = 4.30  , c = 7.02  ) by nearly 
 the same amounts as those of the qbs . an 
 xrd pattern of 1.8 nm thick cdse qps . the black sticks are the 
 peak positions for bulk cdse in the wurtzite structure , and the red 
 sticks are the peak positions for bulk cdse in the zinc - blende structure . the indexed reflections for the wurzite qps are shifted to a higher 
 angle than in the bulk pattern because of the lattice contraction 
 ( see the text and ref ( 22 ) ) . figure 4a views a stack of bundled 
 qps parallel to the qp edges ( individual qps are identified by arrows ) . the 0002 lattice spacings appearing as parallel fringes were clearly 
 evident and provided another measure of the lattice parameter c = 6.86  0.04  . a fourier transform of the 
 hrtem image of the face of a qp was consistent with the ( 1120 ) 
 plane of wurtzite ( figure 4b inset ) , as with 
 the previously reported qbs . the lattice 
 parameter a = 4.04  0.08  was extracted 
 from the fringe pattern in the image of the face ( figure 4b ) . white arrows in ( a ) indicate the length dimension 
 of the bundled qps . although amorphous nanoparticles 
 may be crystallized under the 
 electron beam in the tem , we did not observe such a process ; the qps 
 were crystalline from the outset of tem observations . thus , the sharp 
 extinction and pl spectra ( figure 1 ) , the comparatively 
 sharp xrd pattern that clearly indexed to wurtzite ( figure 3 ) , and the high - resolution tem data ( figure 4 ) all indicated that the cdse qps obtained from 
 the room - temperature synthesis were crystalline as formed . the 
 qp synthesis was repeated using other combinations of primary 
 and secondary amines . experiments were conducted using n - octylamine and various di - n - alkylamine cosolvents . as summarized in table 1 , the secondary amine 
 influenced the mean lengths of the qps , without strongly affecting 
 widths or thicknesses . interestingly , the mean qp lengths were inversely 
 proportional to the lengths of the alkyl groups on the di - n - alkylamine cosolvent ( figure 5 ) . we do not understand the origin of this effect . a plot 
 of the qp mean length vs the inverse of the carbon number 
 of the di - n - alkylamine cosolvent alkyl chain . another set of experiments was 
 conducted in which the primary amine 
 was varied and the secondary amine was held constant . in contrast 
 to the above , systematic dependences of the qp sizes or morphologies 
 on the primary amine were not observed . however , the results established , 
 as described below , that the top and bottom qp facets were predominantly 
 passivated by the primary amine . the qps were produced in bundled 
 stacks that were derived from the lamellar , amine - bilayer templates 
 in which they grew ( see scheme 2 and figures 2 and 4a ) . consequently , the inter - qp spacing ( d spacing ) 
 provided a measure of the amine - bilayer thickness . low - angle xrd patterns 
 of qps obtained from various primary - amine and diethylamine cosolvents 
 are given in figure s1 ( supporting information ) . the d spacing was dependent on the primary amine 
 and consistent with the lengths of the alkyl chains . the experiments 
 described above in n - octylamine and di - n - alkylamine cosolvents gave d spacings consistent 
 with n - octylamine , with no influence by the di - n - alkylamine ( figure s2 , supporting 
 information ) . these results required that the primary amine 
 was responsible for lamellar , amine - bilayer template formation , and 
 consequently , the large qp facets inherited primary - amine passivation 
 from the growth template . many combinations of primary and secondary 
 amines were investigated 
 as cosolvents ( see table s1 , supporting information ) . the best results were achieved when the length of the alkyl chain 
 on the primary amine ( ch3(ch2)nnh2 ) was equal to or longer than the length of the 
 alkyl chains on the secondary amine [ ch3(ch2)m]2nh ( n  m ) . when this empirical rule was violated , 
 the uv  visible spectra of the resulting qps were broadened 
 and in some cases contained absorptions for platelets of other discrete 
 thicknesses ( see below ; figure s3 , supporting 
 information ) . each of the syntheses conducted at room 
 temperature and as described 
 above gave qps with a discrete thickness of 1.8 nm . the 2.2 nm thick 
 qps were obtained with an n - octylamine / di - n - octylamine cosolvent mixture when the synthesis was conducted 
 at 70 c . low - resolution tem images of the qps ( figure 6a , b ) showed widths of 1020 nm and a mean 
 length of 50 nm . a discrete qp thickness of 2.2 nm was established 
 by high - resolution tem ( figure 6c ) . as expected , the three characteristic qp absorptions 
 were red - shifted from those of the 1.8 nm thick qps ( figure 7 ) . ( a , 
 b ) tem image and ( c ) hrtem image of the qps viewed from the edge . visible extinction spectra in toluene dispersions of 
 bundled 1.4 nm thick cdse qps ( blue curve ) , 1.8 nm thick cdse qps 
 ( black curve ) , and 2.2 nm thick cdse qps ( red curve ) . 1.4 nm thick qps were obtained in the solvent 2-phenethylamine 
 at 40 c with no secondary - amine cosolvent . low - resolution tem 
 images of the qps ( figure 8a , b ) showed widths 
 of 24 nm and a mean length of 700 nm . we note that these lengths 
 are closer to qbs along the qp  qb length spectrum than the 
 cases discussed above . a discrete qp thickness of 1.4 nm was established 
 by high - resolution tem ( figure 8c ) . in this 
 case , the three characteristic qp absorptions were blue - shifted from 
 those of the 1.8 nm thick qps ( figure 7 ) . thus , 
 we have prepared cdse qps of three discrete thicknesses ( 1.4 , 1.8 , 
 and 2.2 nm ) . by comparison , dubertret and co - tem 
 and hrtem images of bundles of 1.4 nm thick cdse qps ( 1.4 nm 
 thickness ) . our prior study established magic - size cdse nanoclusters 
 to be intermediates in the formation of cdse qbs . however , the eq 1 reaction in primary - amine 
 solvents at room temperature gave ( cdse)13 , whereas the eq 2 reaction 
 in primary - amine / secondary - amine cosolvents at room temperature gave 
 cdse qps . visible spectroscopy to determine if magic - size nanocluster 
 intermediates participated in the reaction . the eq 2 reaction was conducted in an n - octylamine / di - n - octylamine cosolvent mixture at room temperature as described 
 above . an aliquot removed from the reaction mixture after 1 h gave 
 the spectrum in figure s4a , supporting information , which has been previously assigned to the magic - size nanocluster 
 ( cdse)34 . in our prior study , we mistakenly assigned one of these spectroscopic 
 features to ( cdse)66 , but the results reported here ( see 
 below ) demonstrate that the spectrum does indeed correspond to ( cdse)34 . a second aliquot was removed from the reaction mixture 
 after 2 days , which gave the spectrum in figure s4b , supporting information , clearly assignable to cdse qps . thus , 
 spectroscopic monitoring suggested that ( cdse)34 was an 
 intermediate in the formation of the qps ; other magic - size nanoclusters 
 were not observed . we then combined the eq 2 reactants in an n - octylamine / di - n - pentylamine cosolvent 
 mixture at the lower temperature of 0 c , to determine if other 
 nanocluster intermediates would be detected . ( the reaction was conducted 
 in a different cosolvent mixture because n - octylamine / di - n - octylamine mixtures are solid at 0 c . ) the spectrum 
 of an aliquot taken after 12 h at 0 c corresponded exclusively 
 to ( cdse)34 ( figure 9a ) . the spectrum after 14 days corresponded to a mixture 
 of ( cdse)34 and ( cdse)13 ( figure 9b ) . after 1 month , the ( cdse)34 was completely 
 converted to ( cdse)13 ( figure 9c ) . 
 for a similar reaction conducted at 0 c in a n - propylamine / di - n - ethylamine cosolvent mixture , 
 the conversion of ( cdse)34 to ( cdse)13 was complete 
 in about 1 week ( see figure s5 , supporting information ) . the results established that , under these conditions , ( cdse)13 was more thermodynamically stable than ( cdse)34 , a conclusion supported by another observation ( see below ) . spectral evolution 
 upon transformation of ( cdse)34 to 
 ( cdse)13 in an n - octylamine / di - n - pentylamine cosolvent at 0 c . visible 
 extinction spectra of ( a ) ( cdse)34 after 12 h ( black curve ) , 
 ( b ) a mixture of ( cdse)34 and ( cdse)13 after 
 14 days , and ( c ) ( cdse)13 after 1 month . we next sought to determine if the secondary - amine 
 cosolvent was 
 merely an inert diluent of the primary - amine component ( an inert cosolvent ) 
 or was an active participant in the initial , selective formation of 
 ( cdse)34 . consequently , the room - temperature synthesis 
 described above was conducted using the inert cosolvent 1-octadecene 
 in place of the secondary - amine cosolvent . reaction monitoring after 
 5 min revealed the ( unselective ) formation of a mixture of ( cdse)13 and ( cdse)34 , from which the ( cdse)34 was gradually converted to a mixture of ( cdse)13 and 
 cdse qps . the results indicated that ( cdse)34 is a kinetic 
 product , and its conversion to the thermodynamically more stable ( cdse)13 is actively hindered in the presence of a secondary amine . the conversion kinetics of ( cdse)34 to cdse qps were 
 determined by uv  visible spectroscopy . figure s6 , supporting information , shows the spectrum of 
 ( cdse)34 prepared in an n - octylamine / di - n - pentylamine cosolvent mixture at 0 c , as described 
 above , having a prominent absorption feature at 418 nm ( black curve ) . over the course of several hours at room temperature , a sharp absorption 
 feature emerged at 448 nm corresponding to the lowest - energy transition 
 in the spectrum of cdse qps ( red and blue curves ) . a second qp feature 
 grew in at 423 nm , only slightly shifted from the 418 nm absorption 
 of ( cdse)34 . the blue curve in figure s6 , supporting information , corresponds to the fully transformed 
 sample . the kinetics of the appearance of cdse qps and the disappearance 
 of ( cdse)34 were monitored by curve fitting of the 418 , 
 423 , and 448 nm absorptions ( figure s7 , supporting 
 information ) . for kinetic analysis , ( cdse)34 was diluted into a cosolvent 
 mixture having a lower n - octylamine / di - n - pentylamine ratio ( which increased the conversion rate ) . the appearance 
 of cdse qps at room temperature was followed by the integrated area 
 of the qp absorption at 448 nm derived from the curve fitting . as 
 shown in figure 10 , the log of the integrated 
 absorption vs time was linear over three half - lives ( kobs = ( 4.94  0.47 )  10 s ; t1/2 = 233  
 22.2 min ) , establishing a first - order process . the inverse of the 
 integrated absorption vs time was nonlinear , ruling out second - order 
 kinetics ( figure 10 ) . significantly , no induction 
 ( nucleation ) period was observed ; first - order qp growth began immediately 
 upon warming the ( cdse)34 solution to room temperature . kinetic 
 data for the conversion of ( cdse)34 to cdse 
 qps at room temperature . the black squares in the first - order plot 
 ( left axis ) were obtained from the integrated area of the 448 nm qp 
 absorption ( see the text ) . the data are also plotted for second - order kinetics ( red points ) , 
 which are nonlinear . the kinetics were also analyzed by the disappearance of the 
 fitted 
 418 nm ( cdse)34 feature and the appearance of the fitted 
 423 nm cdse qp feature . these data also gave linear first - order plots 
 over three half - lives ( figures s8 and s9 , supporting 
 information ) . the kinetic parameters for the disappearance 
 of ( cdse)34 were determined to be kobs = (4.69  0.81 )  10 s ; t1/2 = 247  
 42.6 min . this rate constant is , within experimental error , the opposite 
 of that for the appearance of cdse qps ( see above ) , establishing that 
 the conversion of ( cdse)34 to cdse qps occurs without the 
 accumulation of an intermediate . the appearance of cdse qps analyzed 
 using the 423 nm feature gave kobs = ( 5.14 
  1.03 )  10 s ; t1/2 = 225  50.5 min , in good agreement 
 with the more - precise 448 nm data . thus , the conversion was demonstrated 
 to be a first - order process , with no induction period . the room - temperature 
 conversion rates of ( cdse)34 were 
 influenced by the alkyl - chain lengths on the primary and secondary 
 amine cosolvents and on the primary / secondary amine ratio . shorter - chain 
 lengths on both the primary and secondary amines increased the rates 
 of room - temperature conversion of ( cdse)34 to cdse qps , 
 presumably by enhancing diffusion . lower primary / secondary amine ratios 
 increased the room - temperature conversion rates of ( cdse)34 to cdse qps , perhaps by the increased lability of secondary - amine 
 ligands on ( cdse)34 . higher primary / secondary amine ratios 
 decreased the room - temperature conversion rates of ( cdse)34 to cdse qps , by facilitating the conversion of ( cdse)34 to ( cdse)13 . the cluster ( cdse)13 seems particularly 
 stabilized by primary - amine ligation . a ligated derivative of ( cdse)34 as a slushy , greenish - yellow 
 solid was obtained from preparations conducted in n - octylamine and di - n - pentylamine cosolvents . the 
 uv  visible spectrum ( figure s10 , supporting 
 information ) matched those of ( cdse)34 in figures 9a and s6 , supporting information . although no features assignable to other magic - size nanoclusters 
 were detected , the presence of ( cdse)13 , ( cdse)19 , or ( cdse)33 in small amounts was not ruled out , because 
 their absorptions appear at shorter wavelengths and may have been 
 obscured by the absorptions of ( cdse)34 . the isolated 
 ( cdse)34 specimen was further characterized by laser - desorption - ionization 
 ( ldi ) mass spectrometry ( see figure 11 ) . the spectrum contained a prominent ion centered 
 at m / z 6508 corresponding to the 
 bare ( cdse)34 nanocluster , indicating ligand desorption 
 had occurred during the experiment . peaks were also present for each 
 fragment nanocluster ( cdse)x , over the 
 range of x = 3313 . the ( cdse)19 ( m / z 3652 ) and ( cdse)33 ( m / z 6320 ) ions were slightly 
 more abundant , and the ( cdse)13 ( m / z 2502 ) ion was significantly more abundant , than those 
 of the other fragment ions . significantly , the figure 11 ldi mass spectrum differed markedly from the one that we 
 previously reported for isolated [ ( cdse)13(n - octylamine)13 ] and was consistent 
 with a simple fragmentation process from the ( cdse)34 parent . however , the data did not confirm that ( cdse)34 had been 
 isolated in a pure form , because of the presence of the fragment ions 
 corresponding to the other magic sizes ( cdse)13 , ( cdse)19 , and ( cdse)33 . the results did establish that 
 the sample was at least highly enriched in ( cdse)34 . an ldi mass 
 spectrum of [ ( cdse)34(n - octylamine)16(di - n - pentylamine)2 ] . the composition of the ligand shell was determined by calibrated 
 mass spectrometry ( see the supporting information ) . analysis of the isolated ( cdse)34 derivative gave an n - octylamine / di - n - pentylamine ligand ratio 
 of 8.1  0.5 . that ratio was used to fit the c , h , and n analyses , 
 providing an excellent fit to the formula [ ( cdse)34(n - octylamine)16(di - n - pentylamine)2 ] . on the basis of that formula , nanoclusters of ( cdse)34 dispersed in a di - n - alkylamine solvent were stable 
 for over one month at room temperature . 
 isolated [ ( cdse)34(n - octylamine)16(di - n - pentylamine)2 ] was stable at room 
 temperature for over one week and stable for longer periods when stored 
 at 0 c . a color change to reddish orange was observed when the 
 greenish yellow [ ( cdse)34(n - octylamine)16(di - n - pentylamine)2 ] was subjected 
 to a vacuum ( 0.1 torr ) for longer than 12 h. however , after redispersion 
 of such samples in toluene , analysis by uv visible spectroscopy 
 showed that the ( cdse)34 nanocluster remained intact , with 
 no evidence for other species . syntheses 
 of flat cdse nanocrystals may be categorized in two general 
 types . in the first type , long - chain cadmium carboxylate precursors 
 and high reaction temperatures ( 170 c ) are employed , 
 yielding qps having zinc - blende structures . the second type , used here , employs simple cadmium 
 salts and amine solvents at comparatively low temperatures ( 25100 
 c ) , producing cdse qps and qbs having wurtzite structures . the spectroscopic properties of the two types of flat cdse nanocrystals 
 are closely related and produce comparable quantum - well absorption 
 and emission spectra . the preparation of cdse 
 qps having three discrete thicknesses , 
 1.4 , 1.8 , and 2.2 nm , is described here . these discrete thicknesses 
 correspond to integer numbers of cdse monolayers . because the wurtzite 
 qps exhibit a [ 1120 ] orientation , the monolayer thickness is a/2 = 0.20 nm , which is half of the basal unit - cell face 
 diagonal . note that both a and c are compressed in the qps relative to the bulk values , so that a/2 here is smaller than the bulk value ( see the results ) . therefore , the three discrete qp thicknesses 
 we have obtained are 7 , 9 , and 11 monolayers . in comparison , dubertret 
 and co - workers have prepared cdse qps 
 having 4 , 5 , 6 , and 7 monolayers , corresponding to discrete thicknesses 
 of 1.2 , 1.5 , 1.8 , and 2.1 nm . because of the zinc - blende structure 
 and   orientation of dubertret s qps , the monolayer thickness 
 is a/2 = 0.30 nm , explaining the apparent discrepancy 
 between the monolayer and actual thicknesses of the two sets of nanocrystals . we also report here the isolation of a ligated form of ( cdse)34 having the empirical formula [ ( cdse)34(n - octylamine)16(di - n - pentylamine)2 ] . our results may be compared to the room - temperature synthesis 
 and isolation of n - octylamine - ligated ( cdse)34 recently described by sardar and co - workers . their nanocluster specimen is a bright yellow 
 solid having a strong , narrow lowest - energy absorption feature at 
 418 nm , where we observed it in [ ( cdse)34(n - octylamine)16(di - n - pentylamine)2 ] ( figure 9a ) . the sardar absorption 
 spectrum also contains the two higher - energy features we also observed 
 for our amine - ligated ( cdse)34 ( figure 9a ) . moreover , sardar and co - workers reported ldi mass spectra 
 in which the ( cdse)34 parent ion was the ( most - intense ) 
 base peak . by recording ldi mass spectra at varying laser powers , 
 they demonstrated that the lower - mass peaks present in the spectra 
 were fragment ions of ( cdse)34 . the evidence strongly supported 
 the isolation of a purified , ligated form of ( cdse)34 , 
 which compares very closely to the [ ( cdse)34(n - octylamine)16(di - n - pentylamine)2 ] isolated in this study . prominent , reasonably narrow 
 absorption features having max values in the range 
 of 410420 nm have been frequently 
 observed in studies of small cdse nanocrystals or nanoclusters . in 
 some cases , these absorptions more recently , such features have been assigned to ( cdse)33 , ( cdse)34 mixtures , or exclusively to ( cdse)34 , as in the present study . cossairt and owen isolated a nanocluster 
 having a cd35se28 stoichiometry ( with additional 
 charge - balancing ligation ) , which also gave a prominent absorption 
 at 418 nm . whether a variety of small 
 cdse nanoclusters has absorption features in this range or whether 
 they equilibrate to the same absorbing species is presently unknown . the ligand - to - cluster stoichiometry of [ ( cdse)34(n - octylamine)16(di - n - pentylamine)2 ] is not readily reconciled with the theoretically proposed 
 structures of the bare ( cdse)34 nanocluster . both cage and core - cage structures 
 have been proposed for ( cdse)34 , the latter of which has 
 a structure ( cdse)6@28 , in which 6 formula units of cdse 
 are in the core of an outer cage structure . if one presumes amine binding to each surface cd atom , the expected 
 ligand / cluster ratio would be 34 or 28 , respectively . that we have 
 measured a ligand / cluster ratio of 18 suggests either that not all 
 surface cd atoms are ligated or that the cluster structure has only 
 18 surface cd atoms . in our previously reported synthesis of 
 ( cdse)13 at 
 room temperature in primary - amine solvents , an initial mixture of 
 ( cdse)13 , ( cdse)19 , ( cdse)33 , and 
 ( cdse)34 , was observed to equilibrate exclusively to ( cdse)13 . the results here show that the 
 same synthesis conducted in a primary - amine / secondary - amine cosolvent 
 mixture initially produces ( cdse)34 as the only detectable 
 nanocluster product , at both room temperature and at 0 c ( scheme 3 ) . at the lower temperature , ( cdse)34 eventually converts to ( cdse)13 , establishing that ( cdse)13 is more thermodynamically stable under these conditions 
 and that ( cdse)34 is a kinetic product ( scheme 3 ) . the secondary - amine cosolvent slows the conversion 
 of ( cdse)34 to ( cdse)13 . the ( cdse)13 generated from ( cdse)34 in this manner requires temperatures 
 above 40 c for conversion to cdse qps , whereas this conversion 
 occurs readily at room temperature from ( cdse)34 ( scheme 3 ) . thus , ( cdse)34 is a more potent nanocrystal 
 precursor than is ( cdse)13 , because we propose ( cdse)34 is much closer to the critical crystal - nucleus size . the nanocluster ( cdse)34 ( yellow - green dot ) is the kinetic product at 0 c , 
 which slowly converts to the thermodynamic product ( cdse)13 ( gray dot ) at 0 c or to crystalline , wurtzite cdse qps ( orange 
 platelets ) at 25 c . temperatures of > 40 c are required 
 to convert the ( cdse)13 generated by the scheme to cdse 
 qps . the room - temperature conversion of ( cdse)34 to cdse 
 qps occurs by first - order kinetics , with no induction period . the first - order nature of the conversion suggests that 
 an activated , partially ligated form of ( cdse)34 is generated 
 by a ligand dissociation in the rate - determining step , which itself 
 either functions as a critical - size nucleus or coalesces with a fully 
 ligated ( cdse)34 nanocluster in a subsequent fast bimolecular 
 collision to exceed the critical - nucleus size . if correct , then the 
 critical - nucleus size ( cdse)x is in the 
 range of x = 3468 . other experimental determinations 
 of the cdse critical - nucleus are in the diameter range of 1.21.6 
 nm . for comparison , ( cdse)34 has 
 a theoretical diameter of 1.45 nm , and 
 thus , the critical - size range we elucidate here is consistent with 
 the prior measurements . the very low temperature ( 25 c ) 
 at which crystalline cdse 
 is produced here is surprising . the early syntheses of cdse colloids 
 conducted at room temperature within the water pools of inverse micelles 
 gave materials of low crystallinity . the crystalline 
 coherence lengths in such colloids were shown to be much smaller than 
 the particle sizes . consequently , most 
 syntheses of cdse nanocrystals are conducted at temperatures well 
 above 200 c . for example , the now - classical cdse quantum - dot synthesis in topo 
 solvent reported by murray , norris , and bawendi employed nanocrystal - growth 
 temperatures of 230260 c . crystalline cdse nanosheets and quantum belts have been grown at the low temperatures of 100 
 c and 4580 c , respectively , using n - octylamine as the solvent and via magic - size nanocluster intermediates . crystalline cdse quantum dots have been obtained under aqueous conditions 
 at 55 c . to our knowledge , the 
 synthesis of cdse quantum platelets reported here , via the intermediacy 
 of ( cdse)34 nanoclusters , constitutes the lowest temperature 
 at which crystalline cdse has been obtained . in the introduction , we argue that the 
 monomer - generating reaction and crystal nucleation must be the two 
 highest - barrier processes participating in semiconductor - nanocrystal 
 growth . therefore , we surmise that the high temperatures typically 
 employed in nanocrystal synthesis reflect either high reaction barriers 
 or high nucleation barriers with the use of conventional precursors 
 and conditions . the very mild conditions for cdse qp growth found 
 here suggest that the nucleation barrier has nearly been surmounted 
 in ( cdse)34 . magic - size nanoclusters should be ideal precursors 
 to support semiconductor - nanocrystal growth and have been observed 
 as reaction intermediates in nanocrystal synthesis since the early observations of henglein 
 and co - workers . the critical sizes 
 and stoichiometries of crystal nuclei are likely 
 precursor and condition dependent . to our knowledge , a stoichiometry 
 for the critical - size crystal nucleus has not been previously determined 
 for cdse but has been reported to be ( zno)254 for 
 zno and ( znse)181109 for znse by gamelin and co - workers . the magic - size nanocluster ( cdse)34 has been shown to 
 be a potent , room - temperature precursor for crystalline cdse qps . the first - order conversion kinetics suggest that the critical nucleus 
 is achieved in a deligated form of ( cdse)34 or in its combination 
 with a second ( cdse)34 , which supports room - temperature 
 crystal growth . the nanocluster is obtained in isolable form as [ ( cdse)34(n - octylamine)16(di - n - pentylamine)2 ] , which functions as critical crystal nuclei 
 that may be stored in a bottle . the results suggest a strategy 
 for making low - temperature nanocrystal 
 synthesis more generally achievable . magic - size nanoclusters like 
 ( cdse)34 of other compositions should be near to the critical 
 size and function as potent nucleating agents . incorporating these 
 into other mesophase - template geometries may provide low - temperature 
 routes to well - passivated nanocrystals having a range of compositions 
 and morphologies .
reaction 
 of cd(oac)22h2o and selenourea 
 in primary - amine / secondary - amine cosolvent mixtures affords crystalline 
 cdse quantum platelets at room temperature . 
 their crystallinity is 
 established by x - ray diffraction analysis ( xrd ) , high - resolution transmission 
 electron microscopy ( tem ) , and their sharp extinction and photoluminescence 
 spectra . 
 reaction monitoring establishes the magic - size nanocluster 
 ( cdse)34 to be a key intermediate in the growth process , 
 which converts to cdse quantum platelets by first - order kinetics with 
 no induction period . 
 the results are interpreted to indicate that 
 the critical crystal - nucleus size for cdse under these conditions 
 is in the range of ( cdse)34 to ( cdse)68 . 
 the 
 nanocluster is obtained in isolated form as [ ( cdse)34(n - octylamine)16(di - n - pentylamine)2 ] , which is proposed to function as crystal nuclei that may 
 be stored in a bottle .