First-principles modeling of temperature and concentration dependent solubility in the phase separating Fe$_x$Cu$_{1-x}$ alloy system

TL;DR

This paper introduces a temperature-dependent cluster expansion method that incorporates vibrational free energies, enabling accurate first-principles predictions of alloy solubility, exemplified by Fe-Cu alloy system.

Contribution

The novel approach extends the cluster expansion method by including vibrational free energies, improving the accuracy of temperature-dependent alloy property predictions.

Findings

Including vibrational free energy is crucial for accurate Cu solubility prediction.

The method achieves quantitative agreement with experimental data.

Vibrational effects significantly influence alloy phase stability.

Abstract

We present a novel cluster-expansion (CE) approach for the first-principles modeling of temperature and concentration dependent alloy properties. While the standard CE method includes temperature effects only via the configurational entropy in Monte Carlo simulations, our strategy also covers the first-principles free energies of lattice vibrations. To this end, the effective cluster interactions of the CE have been rendered genuinely temperature dependent, so that they can include the vibrational free energies of the input structures. As a model system we use the phase-separating alloy Fe-Cu with our focus on the Fe-rich side. There, the solubility is derived from Monte Carlo simulations, whose precision had to be increased by averaging multiple CEs. We show that including the vibrational free energy is absolutely vital for the correct first-principles prediction of Cu solubility in the bcc Fe matrix: The solubility tremendously increases and is now in quantitative agreement with experimental findings.