### Abstract

Original language | English |
---|---|

Journal | Acta Materialia |

Volume | 139 |

Pages (from-to) | 254-260 |

Number of pages | 7 |

ISSN | 1359-6454 |

DOIs | |

Publication status | Published - 2017 |

### Keywords

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

### Cite this

*Acta Materialia*,

*139*, 254-260. https://doi.org/10.1016/j.actamat.2017.08.008

}

*Acta Materialia*, vol. 139, pp. 254-260. https://doi.org/10.1016/j.actamat.2017.08.008

**Alloy design as an inverse problem of cluster expansion models.** / Larsen, Peter Mahler; Kalidindi, Arvind R.; Schmidt, Søren; Schuh, Christopher A.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Alloy design as an inverse problem of cluster expansion models

AU - Larsen, Peter Mahler

AU - Kalidindi, Arvind R.

AU - Schmidt, Søren

AU - Schuh, Christopher A.

PY - 2017

Y1 - 2017

N2 - 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.

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.

KW - Alloys

KW - Cluster expansion

KW - Computational thermodynamics

KW - Microstructure design

KW - Phase diagrams

U2 - 10.1016/j.actamat.2017.08.008

DO - 10.1016/j.actamat.2017.08.008

M3 - Journal article

VL - 139

SP - 254

EP - 260

JO - Acta Materialia

JF - Acta Materialia

SN - 1359-6454

ER -