# Atomistic Relaxation Process in a Ni3Al Ordered Phase Using Path Probability Method with Vacancy Mechanisms

## TL;DR

This paper extends the path probability method to explicitly include vacancy mechanisms in the relaxation process of Ni3Al ordered phases, offering a more accurate atomic migration model in alloy systems.

## Contribution

It introduces a computational approach that incorporates vacancy mechanisms into the PPM using cluster probabilities, enabling detailed relaxation analysis in alloy phases.

## Key findings

- Vacancy concentration significantly affects relaxation dynamics.
- The method successfully models atomic configuration relaxation in Ni3Al.
- Explicit vacancy treatment improves the accuracy of atomic migration simulations.

## Abstract

The path probability method (PPM), which is a natural extension of the cluster variation method (CVM) to a time domain, has been employed in a relaxation process of atomic configurations in alloy systems. Although the vacancy mechanism is the main atomic migration process in an alloy system, most studies of PPM have used the spin flipping mechanism (or the direct exchange mechanism) because of the huge computational burden imposed by the vacancy mechanism. In this paper the computational problem is circumvented by treating various path variables in the PPM as cluster probabilities in the CVM, and the vacancy mechanism is explicitly taken into account in the theoretical framework. The method is employed to explore the relaxation process in a Ni3Al ordered phase within the tetrahedron approximation, and the effect of vacancy concentration is investigated.