Phase-field crystal model with a vapor phase

Edwin J. Schwalbach*, James A. Warren, Kuo An Wu, Peter W. Voorhees

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


Phase-field crystal (PFC) models are able to resolve atomic length scale features of materials during temporal evolution over diffusive time scales. Traditional PFC models contain solid and liquid phases, however many important materials processing phenomena involve a vapor phase as well. In this work, we add a vapor phase to an existing PFC model and show realistic interfacial phenomena near the triple point temperature. For example, the PFC model exhibits density oscillations at liquid-vapor interfaces that compare favorably to data available for interfaces in metallic systems from both experiment and molecular-dynamics simulations. We also quantify the anisotropic solid-vapor surface energy for a two-dimensional PFC hexagonal crystal and find well-defined step energies from measurements on the faceted interfaces. Additionally, the strain field beneath a stepped interface is characterized and shown to qualitatively reproduce predictions from continuum models, simulations, and experimental data. Finally, we examine the dynamic case of step-flow growth of a crystal into a supersaturated vapor phase. The ability to model such a wide range of surface and bulk defects makes this PFC model a useful tool to study processing techniques such as chemical vapor deposition or vapor-liquid-solid growth of nanowires.

Original languageEnglish (US)
Article number023306
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number2
StatePublished - Aug 27 2013

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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