Insights into Nucleation and Growth of Colloidal Quaternary Nanocrystals by Multimodal X-ray Analysis

Copper chalcogenide nanocrystals find applications in photovoltaic inks, bio labels, and thermoelectric materials. We reveal insights in the nucleation and growth during synthesis of anisotropic Cu2ZnSnS4 nanocrystals by simultaneously performing in situ X-ray absorption spectroscopy (XAS) and small-angle X-ray scattering (SAXS). Real-time XAFS reveals that upon thiol injection into the reaction flask, a key copper thiolate intermediate species is formed within fractions of seconds, which decomposes further within a narrow temperature and time window to form copper sulfide nanocrystals. These nanocrystals convert into Cu2ZnSnS4 nanorods by sequentially incorporating Sn and Zn. Real-time SAXS and ex situ TEM of aliquots corroborate these findings. Our work demonstrates how combined in situ X-ray absorption and small-angle X-ray scattering enables the understanding of mechanistic pathways in colloidal nanocrystal formation.

.1. Edge step normalized X-ray absorption near edge structure (XANES) together with reference spectra recorded from the final sate of the same process with just Cu as well as Cu / Sn cation precursors.
Figure. S1.2. Reaction kinetics as extracted from in Situ X-ray absorption spectroscopy at the K-edge of Copper by linear combination analysis using internal reference spectra from the indicated points of the reaction. Here the data from Figure 2d was smoothed applying a Savitzki-Golay filter over 500 points with a polynomial order of 4, as it was done on the raw spectra to extract EXAFS data. It is clearly visible that such a filter does not significantly smear out the kinetics. Highly monodisperse spherical nanocrystals obtained at 200°C are shown in Figure S1. EDX line scan analysis of this sample across the measured line (depicted in Figure S1d) revealed that the nanocrystals were composed of two elements at this stage, specifically Cu and S. At 10°C above this aliquot, a slight morphological change was observed (Figure 5b), with EDX analysis of this sample detecting minor quantities of tin in the nanocrystals as shown in the line scan in Figure S1e. This signals the onset of tin incorporation into the nanocrystals at 210°C. At 220°C, bullet-shaped nanorods were formed in the reaction ( Figure S1c) and EDX line scans across this sample detected equal quantities of both zinc and tin in the nanorods ( Figure S1f). These observations clearly identify the region between 200°C and 220°C as crucial in the formation of CZTS nanorods, with both tin and zinc incorporating into the pre-formed Cu2-xS nuclei, respectively, and within a short timeframe in this narrow temperature range.

Section S3 Details on EXAFS analysis
EXAFS spectra are generated by applying a 4 th order Savitzky-Golay filter on 500 spectra around the respective reference point in time. EXAFS spectra are extracted as described in the article and are analyzed using Athena, Atremis and FEFF from the Demeter software package.      The SAXS patterns after bubbling in the reaction flask ( Figure S3 right) show significant agglomeration resulting in a strong Porod-like background. Ignoring this, the total volume fraction of particles in solution -as obtained by fitting the SAXS patterns-does not follow the expected behavior from the XANES signals LCA fits.
In order to still extract valuable information, the patterns are fitted with altered models before and after this agglomeration occurs, as described in the following.
-All patterns are fitted between 0.09 and 0.22 1/nm -The SASview software package was used to fit the individual patterns Before bubbling of the solution: The point, where 100% of the Cu is in solid Cu2-xS (from XANES) was taken as a reference point to start the fitting. SAXS patterns therefore can be treated in a quantitative way. The volume fraction was calculated based on the total concentration of Cu-precursor salt reacted fully into Cu2-xS particles resulting in 0.00113. The SAXS pattern was fitted with a cylinder + Porod (exp-4) P(Q) model together with the assumption of hard spheres for S(Q). The only free variables were the total scale, the Porod scaling and the radius of the cylinders. The length was fixed to 1nm because of the assumption of platelets (as seen from aliquots). The exact value is arbitrary and does not significantly influence the fit in this region. The only thing, which is influenced is the absolute scaling and the exact value of the radius.
All following patterns until the bubbling in the reaction flask (and agglomeration) begins are fitted with the same model, keeping the scaling constant as determined, while varying only the radius and Porod scale. The volume fraction for each point was fixed to the value obtained from XANES.
Polydispersity is needed in order to describe the SAXS patterns well, see Figure S4. The exact value of the polydispersity influences the resulting value of the radius but was arbitrarily fixed to 1. Therefore, the radius cannot be taken as an absolute measure. For radii smaller than 1nm the length was set to the value of the double radius to come closer to the symmetrical points. Due to the background level, it was not possible to fit for times < 788s.
After bubbling in the solution: all patterns after the agglomeration show a strong prod contribution (from agglomeration) and a much weaker signal of the particles itself. As reference pattern, a pattern from the end of the reaction is taken. Polydispersity was therefore disabled for all fits after the bubbling in the reaction flask. The pattern was fitted with the porod + cylinder model fixing the radius and the scaling to the values from before the bubbling in the reaction flask. The final length was fixed to 30 nm according to a comparison with TEM images. The polysidpersity in lengths was estimated from TEM images to be around 30%, which has no significant effect on the SAXS pattern. The only free variables during the fit were the volume fraction of particles in solution and the porod scale. After evaluating the final pattern, all patterns after the bubbling in the reaction flask were fitted with this model, keeping every value as determined from the final pattern and varying the length and the Porod scale only.
The volume fraction of "free" (not agglomerated) particles was determined to 0,00018 which is about 10% of this before agglomeration.

Further processing:
Because of the specific implementation of the porod + cylinder model in SASview the porod scale is relative and must be corrected /radius^2/length to obtain the porod contribution to the pattern. The porod contribution can be used as a measure of agglomeration.
Further the particle density -the number of particles per volume are calculated based on the volume fraction together with the single particle volume as determined from the fit. After the bubbling in the reaction flask, the absolute volume fraction was corrected by adding the single particle SAXS volume fraction together with a proportionality factor times the porod contribution to estimate the number of particles as it would be without agglomeration. T he proportionality factor was determined taking the final reference pattern as a measure to reach the final number of particles as it can be calculated from the particle dimensions together with the weighted precursor amounts.