Anharmonicity changes the solid solubility of an alloy at high temperatures

TL;DR

This paper introduces a first-principles method to accurately determine vibrational free energy in alloys, revealing that anharmonic effects significantly influence the high-temperature phase stability of TiAlN alloys.

Contribution

The study presents a novel computational approach to incorporate anharmonicity in phase diagram calculations for substitutional alloys.

Findings

Anharmonic effects lower the maximum miscibility temperature from 6560 K to 2860 K.

Calculated phase diagram matches local chemical composition measurements.

Temperature dependence of mixing enthalpy is crucial for accurate phase stability predictions.

Abstract

We have developed a method to accurately and efficiently determine the vibrational free energy as a function of temperature and volume for substitutional alloys from first principles. Taking Ti$_{1-x}$Al$_x$N alloy as a model system, we calculate the isostructural phase diagram by finding the global minimum of the free energy, corresponding to the true equilibrium state of the system. We demonstrate that the anharmonic contribution and temperature dependence of the mixing enthalpy have a decisive impact on the calculated phase diagram of a Ti$_{1-x}$Al$_x$N alloy, lowering the maximum temperature for the miscibility gap from 6560 K to 2860 K. Our local chemical composition measurements on thermally aged Ti$_{0.5}$Al$_{0.5}$N alloys agree with the calculated phase diagram.