A Novel Cluster Expansion Approach for Finite and Infinite Systems of Arbitrary Shapes

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) which must be learned. The number of ECI increases when the symmetries of the system are reduced. 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 Letter, a new cluster expansion approach is introduced called the ghost lattice method (GLM). It is transferable, unique, and can readily be implemented in existing cluster expansion software. The GLM can cluster expand any geometry such as nanowires, surfaces, spheres, etc., no matter its shape complexity.