Model of heterogenous nucleation on cubic nanoparticles

Abstract

A mathematical model of heterogeneous nucleation of a solid phase on highly activated wet-ted nanosubstrates of cubic form is proposed. This model is based on the classical thermodynamic approach. In accordance with the classical approach to describing the process of heterogeneous nucleation, it is assumed that critical nuclei have the shape of a spherical segment, and can be located on all six faces of a cubic seed particle. In the framework of the proposed model, we have obtained new expressions for the energy of formation and the rate of nucleation of crystallization centers on cubic nanoseeds which take into account the influence of size and capillary effects. Numerical experiments were carried out for an aluminum melt modified with nanoparticles of titanium nitride (TiN). The results of calculations show that the wettability of the surface of the nanoparticle has the greatest influence on the process of heterogeneous nucleation. An increase in the dispersion of nanosubstrates increases the nucleation rate of the solid phase. Taking into account the size dependence of the surface tension at the nucleus-melt interface significantly affects the nucleation processes only when the ratio of the Tolmen parameter to the critical radius is 2 δ / R 0 > 0.01. This study is of interest for the development of a mathematical model of heterogeneous crystallization describing the processes of structure formation in metals and alloys modified by refractory nanoparticles.