A unified cluster expansion method applied to the configurational thermodynamics of cubic TiAlN

TL;DR

This paper develops a unified cluster expansion approach to study the thermodynamics of cubic TiAlN alloys, combining methods to accurately model configurational energies and predict phase stability.

Contribution

It introduces a novel combined cluster expansion method incorporating concentration and volume dependence, enhancing the modeling of alloy thermodynamics.

Findings

Metastable c-TiAlN undergoes coherent spinodal decomposition at high temperatures.

The phase diagram shows larger stability range for spinodal decomposition than previously thought.

The approach aligns well with mean-field results, validating its accuracy.

Abstract

We study the thermodynamics of cubic Ti1-xAlxN using a unified cluster expansion approach for the alloy problem. The purely configurational part of the alloy Hamiltonian is expanded in terms of concentration and volume dependent effective cluster interactions. By separate expansions of the chemical fixed-lattice, and local lattice relaxation terms of the ordering energies, we demonstrate how the screened generalized perturbation method can be fruitfully combined with a concentration dependent Connolly-Williams cluster expansion method. Utilising the obtained Hamiltonian in Monte Carlo simulations we access the free energy of Ti1-xAlxN alloys and construct the isostructural phase diagram. The results show surprising similarities with the previously obtained mean-field results: The metastable c-TiAlN is subject to coherent spinodal decomposition over a larger part of the concentration range, e.g. from x >= 0.33 at 2000 K.