Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: An overview

Heike Emmerich, Hartmut Löwen, Raphael Wittkowski, Thomas Gruhn, Gyula I. Tóth, György Tegze, László Gránásy

Research output: Contribution to journalReview article

193 Citations (Scopus)


Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC method operates on atomic length and diffusive time scales, and thus constitutes a computationally efficient alternative to molecular simulation methods. Its intense development in materials science started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial studies, dynamical density functional theory and thermodynamic concepts have been linked to the PFC approach to serve as further theoretical fundamentals for the latter. In this review, we summarize these methodological development steps as well as the most important applications of the PFC method with a special focus on the interaction of development steps taken in hard and soft matter physics, respectively. Doing so, we hope to present today's state of the art in PFC modelling as well as the potential, which might still arise from this method in physics and materials science in the nearby future.

Original languageEnglish
Pages (from-to)665-743
Number of pages79
JournalAdvances in Physics
Issue number6
Publication statusPublished - Dec 1 2012


  • colloidal crystal growth and growth anisotropy
  • condensed matter dynamics of liquid crystals
  • nucleation and pattern formation
  • phase-field-crystal models
  • simulations in materials science
  • static and dynamical density functional theory

ASJC Scopus subject areas

  • Condensed Matter Physics

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