Unique Truncated Cluster Expansions for Materials Design via Subspace Projection and Fractional Factorial Design

Abstract: For alloy thermodynamics, we obtain unique, physical effective cluster interactions (ECI) from truncated cluster expansions (CE) via subspace-projection from a complete configurational Hilbert space; structures form a (sub)space spanned by a locally complete set of cluster functions. Subspace-projection is extended using Fractional Factorial Design with subspace "augmentation" to remove systematically the ECI linear dependencies due to excluded cluster functions - controlling convergence and bias error, with a dramatic reduction in the number of structural energies needed. No statistical fitting is required. We illustrate the formalism for a simple Hamiltonian and Ag-Au alloys using density-functional theory.