Calculation of volume fraction of phase growing by a diffusion-type law

Abstract

The problem of determining the volume fraction of a phase is considered for the case where the rate of nucleus growth is a decreasing function of its radius. The solution is obtained within the framework of the geometrical-probabilistic method suggested earlier. The procedure of successive approximations is described, which allows one to determine the volume fraction of a phase with the required accuracy. The errors arising in the calculation of the volume fraction of a phase from the Kolmogorov formula are estimated analytically. As an example of numerical estimates, the case of the diffusion growth mechanism is considered. It is shown that in the three-dimensional space, this error lies within 0.01 irrespective of the initial parameters of the problem.