Phase-field-crystal models and mechanical equilibrium

V. Heinonen, C.V. Achim, Ken Elder, S. Buyuddagli, T. Ala-Nissila

Research output: Contribution to journalArticleScientificpeer-review

32 Citations (Scopus)
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Phase-field-crystal (PFC) models constitute a field theoretical approach to solidification, melting, and related phenomena at atomic length and diffusive time scales. One of the advantages of these models is that they naturally contain elastic excitations associated with strain in crystalline bodies. However, instabilities that are diffusively driven towards equilibrium are often orders of magnitude slower than the dynamics of the elastic excitations, and are thus not included in the standard PFC model dynamics. We derive a method to isolate the time evolution of the elastic excitations from the diffusive dynamics in the PFC approach and set up a two-stage process, in which elastic excitations are equilibrated separately. This ensures mechanical equilibrium at all times. We show concrete examples demonstrating the necessity of the separation of the elastic and diffusive time scales. In the small-deformation limit this approach is shown to agree with the theory of linear elasticity.
Original languageEnglish
Article number032411
Pages (from-to)1-11
JournalPhysical Review E
Issue number3
Publication statusPublished - 2014
MoE publication typeA1 Journal article-refereed


  • grain growth
  • mechanical equilibrium
  • phase-field crystal model


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