# Application of Cluster Variation and Path Probability Methods to the Tetragonal-Cubic Phase Transition in ZrO2

## TL;DR

This paper extends the cluster variation and path probability methods to study the kinetics and equilibrium states of the displacive tetragonal-cubic phase transition in ZrO2, a novel application of these techniques.

## Contribution

It introduces a new approach by applying CVM and PPM to displacive phase transitions, viewing atomic displacements as configurational variables.

## Key findings

- Kinetics of phase transition in ZrO2 analyzed.
- Equilibrium states of tetragonal and cubic phases characterized.
- Methodology bridges replacive and displacive transition studies.

## Abstract

Cluster variation method (CVM) and path probability method (PPM) have generally been employed to study replacive phase transitions in alloy systems. Recently, displacive phase transitions have been explored within the realm of replacive phase transition in the CVM theoretical framework by viewing displaced atoms as different atomic species, i.e., by converting a freedom of atomic displacement to a configurational freedom. The same methodology is applied to the PPM calculations in this work, and the kinetics of displacive phase transition from tetragonal to cubic phases in ZrO2 are investigated as well as their equilibrium states.