Coagulation and Aggregation Model of Silicon Nanoparticles from Laser Pyrolysis

For spherical silicon nanoparticles produced by laser pyrolysis in a temperature range below the melting point of the bulk phase, the average particle size measured by transmission electron microscopy has been found to be larger than the crystallite size derived from profile fitting of broadened X-ray diffraction peaks. This result, interpreted in terms of aggregation and solidification of particles during the coagulation process, has been explained by a sectional model suitably developed to describe coagulation and aggregation of particles. The model predicts the evolution of the size distribution of both macroscopic polycrystalline particles and of crystallites composing the aggregates. Single crystal particles are supposed to form not only by collisions between liquid particles but also by collisions between a larger solid and a smaller liquid particle coexisting in the system due to capillarity effects which are responsible for the decreasing of the melting point of nanometre-sized particles with respect to the bulk phase. On the other hand, polycrystalline aggregates are supposed to form by collisions between solid particles. The spheroidal shape of particles found in the analysed powders has been explained by observing that the characteristic sintering time was at least one order of magnitude smaller than the characteristic time for coagulation.

The good predictive capabilities of the model for the average particle size of both the macroscopic size distribution and that of crystallites have confirmed that the hypothesis of aggregation is able to quantitatively reproduce the experimental findings.

Acknowledgments

The authors gratefully acknowledge Mr. D. Venditti of Centro Sviluppo Materiali for preparing the TEM specimens of Si nanopowders.