Single-Particle X-ray Scattering Reveals a High Local Supersaturation of Precursors as the Origin of CoO Assembly Formation

Abstract

Single-particle small-angle X-ray scattering (SP-SAXS) enables quantitative morphological analysis by recording diffraction snapshots from isolated particles using X-ray free-electron laser (XFEL) pulses. Unlike conventional X-ray techniques, which average over the entire illuminated sample volume, SP-SAXS resolves low-contrast, less abundant, or transient species within heterogeneous particle populations that would otherwise remain hidden. Here, we apply SP-SAXS to investigate the solvothermal formation of CoO nanocrystal assemblies from a Co(acac)$_3$ precursor in benzyl alcohol. The single-particle data reveal amorphous, uniform-density Co(acac)$_2$ spheres as transient intermediates that directly crystallize into cavernous CoO nanocrystal assemblies, which explains why CoO forms as hierarchical aggregates rather than as isolated nanocrystals. These results demonstrate that SP-SAXS provides a powerful framework for disentangling morphological heterogeneity in nanoparticle formation processes.

Figures (12)

• Figure 1: Experimental and analytical workflow of single particle SAXS (SP-SAXS) compared to conventional SAXS. In conventional SAXS, the diffraction pattern comprises scattering contributions of all species within the illuminated sample volume of the X-ray beam from a synchrotron or laboratory source. In SP-SAXS, diffraction patterns from individual particles are averaged into classes, each representing a distinct particle population within the sample. The relative hit ratio of each class, $\mathrm{n}_j$, reflects the concentration of the corresponding particle species $j$. In principle, the sum of all SP-SAXS class diffraction patterns, $\mathrm{I}_j^{\mathrm{SP\text{-}SAXS}}$, reproduces the total diffraction pattern obtained in conventional SAXS, $\mathrm{I}^{\mathrm{SAXS}}$.
• Figure 2: Representative diffraction images (a–c) and corresponding radial integrations (d–f) of selected SP-SAXS classes. The diameter D of the sphere classes is fitted with the a spherical form factor, where the error represents the standard deviation of the Gaussian distribution. The diameter of the assembly classes is estimated by the intensity bump maximum as marked by the red arrow. The relative occupancy of each class at 20, 30, and 40 min reflects the temporal evolution of the populations.
• Figure 3: SP-SAXS analysis of the reaction aliquots at 20, 30, and 40 min. (a-c) Summed radial integrations of the sphere, assembly, and all classes. (d-f) Histogram of the size distribution of the sphere and assembly classes. The solid trace shows a kernel density estimate of the histograms.
• Figure 4: Schematic illustration of the proposed formation pathway of CoO nanocrystal assemblies after the reaction of Co(acac)$_3$ in benzyl alcohol. Initially, Co(acac)$_3$ reduces to Co(acac)$_2$, which subsequently phase-separates to spherical amorphous precipitates. With increasing reaction time, these Co(acac)$_2$ precipitates crystallize into CoO nanocrystal assemblies. The asterisks (*) denote extrapolated reaction states before and after the measured time points of 20, 30, and 40 min.
• Figure S1: Diffraction images of all SP-SAXS classes.