Size-Dependent Fault-Driven Relaxation and Faceting in Zincblende CdSe Colloidal Quantum Dots

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1 Supporting Information Size-Dependent Fault-Driven Relaxation and Faceting in Zincblende CdSe Colloidal Quantum Dots Daniele Moscheni, Federica Bertolotti, Laura Piveteau, Loredana Protesescu, Dmitry N. Dirin, Maksym V. Kovalenko, Antonio Cervellino, Jan Skov Pedersen, Norberto Masciocchi * and Antonietta Guagliardi * *To whom correspondence should be addressed: antonella.guagliardi@ic.cnr.it Supplementary Figures Figures S1-S9 Supplementary Tables Tables S1-S3 1

2 Supplementary Figures a b Figure S1. a) HRTEM image of the 3.8 nm CdSe sample, suggesting the slightly anisotropic shape of NCs. The determination of faceting is not so straightforward in very small NCs, due to blurry contours of the particles in 2D projections. 1 b) Double planar defects (highlighted by the red dashed lines) localized in the central portion of a very small ZB NC. The green line is a guide for eye along atoms displaced by the two faults. Figure S2. Absorption spectra of CdSe qdots of nominal sizes 3.0 nm, 3.8 nm and 5.8 nm. 2

3 Figure S3. a) DSE simulations showing the hexagonal features appearing in the X-ray pattern upon introducing extended hh h transitions (WZ intergrowths) within the ZB sequence of a CdSe nanocrystal of 3.0 nm; the inset shows the nanocrystal exhibiting 4h (red) planes within the regular k sequence (green layers); b) DSE best fits to the synchrotron data of CdSe 3.0 nm, obtained by using the localized model at different γ values (and fixed β=0.6 and δ=0.5) leading to the rare formation of 3h, 4h, 5h configurations. γ > 0.7 has undetectable effects on the DSE fit (highly diluted intergrowths), whereas lower γ values (increasing the density of intergrowths, blue and red traces) introduce a manifest hexagonal character worsening the fit and increasing the GoF value. 3

4 Figure S4. a) GoF surface of DSE simulations obtained by spanning the b,d parameters of the localized model (to be compared to the random model in Figure 3), and by fixing all the remaining model parameters. The shallow minimum is found at b = 0.35 and d = 0.50, for the 4.8 nm QDs. (b-d) DSE simulations of representative cases picked up from the 3D map and exhibiting different degrees of matching to the WAXTS data (black dots). The best fit (green curve) in c) corresponds to the minimum in the GoF surface. a b Figure S5. Log-log plots of (solvent-subtracted) SAXS data (black dots, λ=1.34å) collected on CdSe QDs of increasing sizes and best fits using analytical form factors (solid lines) are shown for (a) spherical and (b) prismatic NCs. Experimental uncertainties from counting statistics are given as error bars: the signal at high Q is still much higher than the background scattering from the solvent, so that background subtraction (and uncertainties in the subtraction) do not have any influence when comparing the quality of the fits. The fits using the cuboidal model is much better than for spheres. Average sizes and relative size dispersions for models in a) and b) are reported in Table S2. 4

5 a b c d Figure S6. a, b, c): Log-log plots of (solvent-subtracted) SAXS data (black dots, λ=1.34å) collected on the 5.8 nm or 3.0 nm CdSe QDs, and DSE models (continuous lines). a) Comparison of prismatic NCs exposing {100} facets only (red trace) and (equally dispersed) NCs exposing both {100} and {111} facets (green trace); the latter model, exhibiting a size-dependent growth of {111} facets, as described in the main text, better matches the experimental data; b) alternative models of NCs faceting, with growth of {110} or {111} facets based on constant Area {111}/Area {100} and Area {110}/Area {100} ratios within the NCs population; these models are less effective than those in a); c) comparison of DSE simulations of prismatic {100}-facets NCs (red trace) and (equally dispersed) NCs exposing both {100} and {111} facets for different d thresholds ( x + y + z < d) used for {111}-faceting in the 3.0 nm sample (d = 3.5 nm, green trace; d = 3.8 nm, magenta trace): the best match is provided by prismatic {100}-facets NCs; d) high-q-porod WAXTS data (black dots, λ=0.56 Å) of 5.8 nm CdSe QDs and best DSE fits obtained without subtracting the solvent (labelled as blank): green and red simulations refer to the same models in a), confirming the best {100}+{111} faceting. 5

6 Figure S7. Relaxation dz of the Cd-Se axial bond distance along the [111] ZB axis (blue squares, left y- axis) and stacking fault percentage SF% (red squares, right y-axis) vs the diameter D of CdSe QDs (diameter of the sphere of equivalent volume to the square-cuboids, see Figure 5 of the main text); dz and SF% refer both to the localized model; SF% numerical values are also reported in Table 2 of the main text. Both dz and SF% decrease upon increasing the NCs sizes, thus suggesting a major role of fault deformation in determining the Cd-Se relaxation a 0 a 0 ± σ (V cell ) 1/3 (Å) a qdots = a 0 (1 Ω/D) D (nm) Figure S8. Size dependence of the equivalent cubic lattice parameter (V cell 1/3 ) on the NCs diameter (D). V cell 1/3 is obtained from the WZ-like distorted unit cell in which a and c lattice parameters are independently refined to account for the anisotropic strain observed. The red squares are the experimentally-derived points, the black curve is obtained by fitting them with the inverse size dependence law shown in the figure, 2,3 where a qdots = V 1/3 cell, a 0 the cubic lattice parameter for D and Ω = 4Bγ * 3 a refined parameter depending on the surface tension γ and the bulk modulus B. Using this fitting law, we obtained a 0 = 6.066(3) Å and Ω=-0.019(2) nm, from which γ= ev/nm 2 (assuming B=53 GPa), 4 indicating a negative surface tension at the nanocrystals surface, likely induced by the oleate capping ligands, as previously reported on oleate-capped PbS qdots. 3 6

7 Figure S9. Synchrotron WAXTS data (black dots, λ= å) of colloidal CdSe QDs (3.8 nm top, 4.8 nm bottom) in toluene (blue trace) and DSE best fits obtained using the localized SF model (brown and yellow traces). Insets: 2D maps of the bivariate lognormal size distribution function in the D ab and L c coordinates; D ab is the diameter of the circle of equivalent area of the square base of the NCs, L c the length of the side parallel to the cubic c-axis. 7

8 Supplementary Tables Table S1. Results on the size and morphology of CdSe QDs provided by the WATS-DSE analysis for the random (RND) and localized (LOC) faulting models presented in the main text. Average sizes and size distributions (σ) are given as: D eq, (diameter of the sphere of equivalent volume to the square-cuboids), L a and L c (sides of the square-cuboids); the aspect ratio AR is computed as <L c>/ <L a>. All the averages are numberbased and derived from a bivariate lognormal distribution function. The correlation angle between the two growing directions is fixed to zero. 3.0 nm 3.8 nm 4.8 nm 5.8 nm <D eq> (nm) σ/<d eq> σa/<la> σc/<lc> <La> (nm) <Lc> (nm) AR RND LOC RND LOC RND LOC RND LOC Table S2. Results on the size and morphology of CdSe QDs provided by the SAXS analysis using the analytical form factor (FF) and the DSE modeling (DSE). Average sizes and size distributions (σ x) refer to the two growth directions (<L a>=<l b> and <L c>), for the prismatic model, and to the NCs diameter for the spherical model (D SPH); the surface smearing factor (σ SURF) refers to the FF model only. All the averages are number-based and derived from a bi- or mono-variate lognormal distribution function. 3.0 nm 3.8 nm 4.8 nm 5.8 nm < La>=<Lb> (nm) σa/< La> <Lc> (nm) σc/< Lc> σsurf (nm) <D>SPH (nm) sd/<d>sph FF = σa/< La> / DSE / / / FF = σa/< La> / DSE / / / FF = σa/< La> DSE / / / FF = σa/< La> DSE / / / 8

9 Table S3. Debye Waller factors (B, Å 2 ) and site occupancy factors (s.o.f.) derived by the WAXTS-DSE analysis using the localized SF model. s.o.f. B Seshell Cdcore Seshell Secore Cdshell Cdcore 3.0 nm / nm nm nm References (1) Liu, J.; Olds, D.; Peng, R.; Yu, L.; Foo, G. S.; Qian, S.; Keum, J.; Guiton, B. S.; Wu, Z.; Page, K. Quantitative Analysis of the Morphology of {101} and {001} Faceted Anatase TiO 2 Nanocrystals and Its Implication on Photocatalytic Activity. Chem. Mater. 2017, 29, (2) Cervellino, A.; Frison, R.; Cernuto, G.; Guagliardi, A.; Masciocchi, N. Lattice Parameters and Site Occupancy Factors of Magnetite Maghemite Core Shell Nanoparticles. A Critical Study. J. Appl. Cryst. 2014, 47, (3) Bertolotti, F.; Dirin, D. N.; Ibanez, M.; Krumeich, F.; Cervellino, A.; Frison, R.; Voznyy, O.; Sargent, E. H.; Kovalenko, M. V.; Guagliardi, A.; Masciocchi, N. Crystal Symmetry Breaking and Vacancies in Colloidal Lead Chalcogenide Quantum Dots. Nat. Mater. 2016, 15, (4) Alivisatos, A. P.; Harris, T. D.; Brus, L. E.; Jayaraman, A. Resonance Raman Scattering and Optical Absorption Studies of CdSe Microclusters at High Pressure. J. Phys. Chem. 1988, 89,