Probability distribution function for a solid with vacancies

TL;DR

This paper derives a probability distribution function considering microstate degeneracy, enabling the description of solid melting as a first-order phase transition without using the order parameter concept.

Contribution

It introduces a novel probability distribution model for solids with vacancies that describes melting without relying on the order parameter.

Findings

Successfully models melting as a first-order phase transition.

Provides a new framework for understanding phase changes in solids.

Eliminates the need for the order parameter in phase transition description.

Abstract

Expression for probability distribution is got taking into account a presence and removal of degeneracy on the microstates. Its application allows to describe the process of melting of solids, as saltatory phase transition of the first kind without bringing in of concept of the order parameter.