Alloy design as an inverse problem of cluster expansion models

Peter Mahler Larsen, Arvind R. Kalidindi, Søren Schmidt, Christopher A. Schuh

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Abstract

Central to a lattice model of an alloy system is the description of the energy of a given atomic configuration, which can be conveniently developed through a cluster expansion. Given a specific cluster expansion, the ground state of the lattice model at 0 K can be solved by finding the configuration of solutes that minimizes the energy of the system. In this paper, we develop a method for solving the inverse lattice problem, where, given a broad class of potential, we find the ground states for all possible values of the effective cluster interaction energies. To do so, we formulate the inverse problem in terms of energetically distinct configurations, using a constraint satisfaction model to identify constructible configurations, and show that a convex hull can be used to identify ground states. To demonstrate the approach, we solve for all ground states for a binary alloy in a 2D hexagonal lattice both with and without an interface, based on pairwise interactions.
Original languageEnglish
JournalActa Materialia
Volume139
Pages (from-to)254-260
Number of pages7
ISSN1359-6454
DOIs
Publication statusPublished - 2017

Keywords

  • Alloys
  • Cluster expansion
  • Computational thermodynamics
  • Microstructure design
  • Phase diagrams

Cite this

Larsen, Peter Mahler ; Kalidindi, Arvind R. ; Schmidt, Søren ; Schuh, Christopher A. / Alloy design as an inverse problem of cluster expansion models. In: Acta Materialia. 2017 ; Vol. 139. pp. 254-260.
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Alloy design as an inverse problem of cluster expansion models. / Larsen, Peter Mahler; Kalidindi, Arvind R.; Schmidt, Søren; Schuh, Christopher A.

In: Acta Materialia, Vol. 139, 2017, p. 254-260.

Research output: Contribution to journalJournal articleResearchpeer-review

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AU - Schmidt, Søren

AU - Schuh, Christopher A.

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AB - Central to a lattice model of an alloy system is the description of the energy of a given atomic configuration, which can be conveniently developed through a cluster expansion. Given a specific cluster expansion, the ground state of the lattice model at 0 K can be solved by finding the configuration of solutes that minimizes the energy of the system. In this paper, we develop a method for solving the inverse lattice problem, where, given a broad class of potential, we find the ground states for all possible values of the effective cluster interaction energies. To do so, we formulate the inverse problem in terms of energetically distinct configurations, using a constraint satisfaction model to identify constructible configurations, and show that a convex hull can be used to identify ground states. To demonstrate the approach, we solve for all ground states for a binary alloy in a 2D hexagonal lattice both with and without an interface, based on pairwise interactions.

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