Predicting Low Thermal Conductivity Si-Ge Nanowires with a Novel Cluster Expansion Approach

The cluster expansion enables fast alloy property computations especially useful for predicting alloy thermodynamics. It expands configurational alloy properties in basis functions called clusters with associated expansion coefficients called effective cluster interactions (ECI). The number of ECI depends on the symmetries of the system. Therefore, when applied to non-bulk low-symmetry systems, the cluster expansion faces difficulties. To improve the cluster expansion of low-symmetry structures, the coarse grained meta cluster expansion (MCE) was recently invented. However, it suffers from important practical issues. The cluster grouping in the MCE depends on both the system and the property being studied, in which sense it is not transferable. An MCE grouping is not unique either. Furthermore, it is not readily implemented in existing cluster expansion software built for bulk systems. Therefore, in this work, we develop a new cluster expansion approach called the ghost lattice method (GLM), which is transferable, unique, and readily implemented in existing cluster expansion software. The GLM can cluster expand any geometry such as nanowires, surfaces, spheres, etc., no matter its complexity. We demonstrate that it can successfully predict the thermal conductivity versus configuration of silicon-germanium (Si-Ge) nanowires.