### Abstract

We propose a model to study, on an atomistic scale, the effects of elastic misfit strains on the growth and coarsening of domains in phase-separating alloys. The model considered is a two-dimensional square crystal lattice with periodic boundary conditions and with anA orB atom near each site. To model the elastic interaction, nearest and next-nearest neighbours are connected by springs with longitudinal and transverse stiffness. In addition, there is a chemical interaction between nearest neighbours, favouring like against unlike pairs. A mean field analysis predict phase separation into coherent phases, below a temperature which (for a typical set of elastic parameters) increases with the strength of the elastic forces. This critical temperature is less than that for separation into incoherent phases. The analysis also predicts how the anisotropy determines the shapes of domains at early times. A Monte Carlo procedure for implementing Kawasaki dynamics to represent diffusion in this model is described. © 1995 Acta Metallurgica Inc.

Original language | English |
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Pages (from-to) | 2921-2930 |

Number of pages | 10 |

Journal | Acta Metallurgica et Materialia |

Volume | 43 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 1995 |

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### Cite this

*Acta Metallurgica et Materialia*,

*43*(8), 2921-2930. https://doi.org/10.1016/0956-7151(95)00005-G

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*Acta Metallurgica et Materialia*, vol. 43, no. 8, pp. 2921-2930. https://doi.org/10.1016/0956-7151(95)00005-G

**Ising model for phase separation in alloys with anisotropic elastic interaction-I. Theory.** / Fratzl, P.; Penrose, O.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Ising model for phase separation in alloys with anisotropic elastic interaction-I. Theory

AU - Fratzl, P.

AU - Penrose, O.

PY - 1995/8

Y1 - 1995/8

N2 - We propose a model to study, on an atomistic scale, the effects of elastic misfit strains on the growth and coarsening of domains in phase-separating alloys. The model considered is a two-dimensional square crystal lattice with periodic boundary conditions and with anA orB atom near each site. To model the elastic interaction, nearest and next-nearest neighbours are connected by springs with longitudinal and transverse stiffness. In addition, there is a chemical interaction between nearest neighbours, favouring like against unlike pairs. A mean field analysis predict phase separation into coherent phases, below a temperature which (for a typical set of elastic parameters) increases with the strength of the elastic forces. This critical temperature is less than that for separation into incoherent phases. The analysis also predicts how the anisotropy determines the shapes of domains at early times. A Monte Carlo procedure for implementing Kawasaki dynamics to represent diffusion in this model is described. © 1995 Acta Metallurgica Inc.

AB - We propose a model to study, on an atomistic scale, the effects of elastic misfit strains on the growth and coarsening of domains in phase-separating alloys. The model considered is a two-dimensional square crystal lattice with periodic boundary conditions and with anA orB atom near each site. To model the elastic interaction, nearest and next-nearest neighbours are connected by springs with longitudinal and transverse stiffness. In addition, there is a chemical interaction between nearest neighbours, favouring like against unlike pairs. A mean field analysis predict phase separation into coherent phases, below a temperature which (for a typical set of elastic parameters) increases with the strength of the elastic forces. This critical temperature is less than that for separation into incoherent phases. The analysis also predicts how the anisotropy determines the shapes of domains at early times. A Monte Carlo procedure for implementing Kawasaki dynamics to represent diffusion in this model is described. © 1995 Acta Metallurgica Inc.

UR - http://www.scopus.com/inward/record.url?scp=0001294695&partnerID=8YFLogxK

U2 - 10.1016/0956-7151(95)00005-G

DO - 10.1016/0956-7151(95)00005-G

M3 - Article

VL - 43

SP - 2921

EP - 2930

JO - Acta Metallurgica et Materialia

JF - Acta Metallurgica et Materialia

SN - 0956-7151

IS - 8

ER -