Thermodynamics of alloys incorporating both the configurational and the vibrational degrees of freedom: the vibrational cluster expansion method

Characterizing thermal conductivity for alloy thermoelectric systems has been considered a challenging task due to the many degrees of freedom in the atomic configurational space needed to approximate truly random alloys. Virtual crystal approximation (VCA) and empirical potentials have been widely applied in lattice dynamics (LD) and molecular dynamics (MD), respectively, to address this problem. However, inaccurate description of strain disorder and strong system dependence limit the applicability of aforementioned methods. We address this problem by constructing a unified model, vibrational cluster expansion (VCE), which explicitly takes both vibrational and configurational degrees of freedom into account by forming coupled vibration-configuration clusters. To deal with the vast number of variables in the model, we apply compressed sensing technique to robustly recover important force constants using training data acquired from density functional theory (DFT) calculations. We demonstrate that our method can efficiently reproduce DFT forces in alloys. An accurate and system-independent force field can then be used in MD calculation to accurately predict lattice thermal conductivity of PbTe-Se, which VCA overestimates and few existing empirical potentials can model properly.