Nonequilibrium Kinetics of the Initial Stage of a Phase Transition

Abstract

The Kolmogorov–Feller and Einstein–Smoluchowski kinetic partial derivative equations with nonlinear coefficients are solved by new stable numerical methods. The theory of stochastic dynamic variables relates the solution of the Ito equation in the Stratanovich sense for trajectories of Wiener random processes to the transition probability density of these processes or the distribution functions of kinetic equations. The classical nucleation (formation of first-order phase transition nuclei) theory describes the nonequilibrium stage of the condensation process by a diffusion random process the phase space nuclei size, when fluctuations influence the nucleus clusterization. The model of formation of vacancy-gas defects (VGD) (pores and blisters) in a crystal lattice, which appear as a result of its irradiation by inert Xe⁺⁺ gas is supplemented by the consideration of the Brownian motion of nonpoint lattice defects, which occurs under action of the superposition of pair long-range model potentials of an indirect elastic interaction of VGDs to each other and to the layer boundaries. The spacial-temporal porosity structures in a sample form for times of 10‒100 μs as a result of the Brownian motion of vacancy-gas defects, which is simulated using stable algorithms. The nonequilibrium kinetic distribution functions of VGDs on sizes and coordinates in layers of irradiated materials have been found as a result of calculations of 10⁶ trajectories; these functions characterize the fluctuation instability of the initial stage of the phase transition and they are used to estimate local stresses and the porosity in a model volume.