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arXiv · 1209.6176

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

Teck L. Tan·Duane D. Johnson
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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.

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Teck L. Tan, Duane D. Johnson. 2012-09-27. Unique Truncated Cluster Expansions for Materials Design via Subspace Projection and Fractional Factorial Design. https://arxiv.org/abs/1209.6176

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