Microscopic, first-principles model of strain-induced interaction in concentrated size-mismatched alloys

TL;DR

This paper develops a first-principles, configuration-dependent strain interaction model for concentrated size-mismatched alloys, capturing complex many-body effects and accurately predicting ordering temperatures and phonon spectra.

Contribution

It generalizes the harmonic Kanzaki-Krivoglaz-Khachaturyan model to concentrated alloys with size mismatch, incorporating configuration dependence via cluster expansions based on first-principles forces.

Findings

Model captures strong many-body long-range interactions.

Phonon spectra agree with experimental data.

Accurate prediction of ordering temperatures for most alloys.

Abstract

The harmonic Kanzaki-Krivoglaz-Khachaturyan model of strain-induced interaction is generalized to concentrated size-mismatched alloys and adapted to first-principles calculations. The configuration dependence of both Kanzaki forces and force constants is represented by real-space cluster expansions that can be constructed based on the calculated forces. The model is implemented for the fcc lattice and applied to Cu$_{1-x}$Au$_x$ and Fe$_{1-x}$Pt$_x$ alloys for concentrations $x=0.25$, 0.5, and 0.75. The asymmetry between the $3d$ and $5d$ elements leads to large quadratic terms in the occupation-number expansion of the Kanzaki forces and thereby to strongly non-pairwise long-range interaction. The main advantage of the full configuration-dependent lattice deformation model is its ability to capture this singular many-body interaction. The roles of ordering striction and anharmonicity in Cu-Au and Fe-Pt alloys are assessed. Although the harmonic force constants defined with respect to the unrelaxed lattice are unsuitable for the calculation of the vibrational entropies, the phonon spectra for ordered and disordered alloys are found to be in good agreement with experimental data. The model is further adapted to concentration wave analysis and Monte Carlo simulations by means of an auxiliary multi-parametric real-space cluster expansion, which is used to find the ordering temperatures. Good agreement with experiment is found for all systems except CuAu$_3$ (due to the known failure of the generalized gradient approximation) and FePt$_3$, where the discrepancy is likely due to the neglect of magnetic disorder.