<i>Ab initio</i> prediction of Ge solubility limits in Al-rich alloy

Abstract We present ab initio calculations based on density functional theory to predict the temperature-dependent solubility of Ge in fcc Al. The solubility is modeled as the equilibrium concentration of substitutional Ge defects using periodically repeated supercells. Our results show that solubility is primarily determined by the heat of formation (Δ H form ) at 0 K, with phonon vibrations and thermal expansion playing a secondary role. Including thermal expansion via the quasiharmonic approximation increases predicted solubility. The Perdew, Burke, and Ernzerhof parameterization of the generalized gradient approximation provides results in good agreement with experimental data, given a sufficiently dense k -point mesh. The overall accuracy of the model is within a few molar percent, making it a useful but approximate tool for studying solubility trends.