Size and shape effect on the phase transitions in a small system with fractal interphase boundaries

Abstract

Shape effect as a property of small volume systems is considered in an example of a stratifying solid solution. Phase diagrams, which demonstrate phase equilibria dependence on the shape of system’s boundaries, are calculated by the methods of equilibrium chemical thermodynamics. Shape of system is modeled by coefficient kf, which is equal to the ratio between the system’s area and the area of a sphere of the same volume. Core-shell configurations are considered, where system’s external boundary shape is a parameter and can differ and core-phase’s form is spherical. Shell-phases external boundary form affects components’ mutual solubility, upper critical temperature of stratification and core- and shell-phases volume ratio. The area of heterogeneous states’ thermodynamical stability decreases and the area of metastable states’ increases with the growth of kf. This model can also be used when shell-phase’s shape is fractal. In this case, on the one hand, the fractal dimension can be regarded as a thermodynamical function, on the other hand, it can be measured experimentally.