Fractal nanoparticles of phase-separating solid solutions: morphology-dependent phase equilibria in tungsten heavy pseudo-alloys

Abstract

In this paper, we simulate thermodynamically the morphology-dependent phase equilibria in core-shell nanoparticles of a phase-separating solid solution using the example of W-Cr heavy alloy. The morphology of a nanoparticle is described in the framework of the fractal geometry methods. It is shown that there are two possible heterogeneous states in a nanoparticle while the compositions of phases in both states differ from each other. The dependences of mutual solubilities of components on the temperature are obtained while the behavior of these dependences significantly differs depending on the particular state and the morphology of nanoparticle under consideration. In nanoparticles of a very complicated morphology, the phase separation itself gets suppressed and the nanoparticle remains in the homogeneous state at the temperatures significantly below the macroscopic value of the upper critical dissolution temperature. The demonstrated regularities are explained based on three mechanisms of reducing the free energy of the system and the “competition” between them. In the final section, a method for calculating the equlibrium size distributions and average characteristics of nanoparticle ensembles is described along with a technique of measuring nanoparticle fractal dimensions based on the microscopy data.