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

TL;DR

This paper introduces a novel method for deriving unique and physically meaningful effective cluster interactions in alloy thermodynamics by combining subspace projection with fractional factorial design, reducing computational effort and eliminating the need for statistical fitting.

Contribution

The paper presents a new approach that ensures unique ECIs from truncated cluster expansions using subspace projection and fractional factorial design, improving convergence and reducing data requirements.

Findings

Successfully applied to a simple Hamiltonian model.

Demonstrated on Ag-Au alloys with density-functional theory.

Achieved reduction in structural energy calculations.

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.