Article

Phase diagram and commensurate-incommensurate transitions in the phase field crystal model with an external pinning potential.

Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 TKK, Finland.
Physical Review E (Impact Factor: 2.31). 09/2006; 74(2 Pt 1):021104. DOI: 10.1103/PhysRevE.74.021104
Source: PubMed

ABSTRACT We study the phase diagram and the commensurate-incommensurate transitions in a phase field model of a two-dimensional crystal lattice in the presence of an external pinning potential. The model allows for both elastic and plastic deformations and provides a continuum description of lattice systems, such as for adsorbed atomic layers or two-dimensional vortex lattices. Analytically, a mode expansion analysis is used to determine the ground states and the commensurate-incommensurate transitions in the model as a function of the strength of the pinning potential and the lattice mismatch parameter. Numerical minimization of the corresponding free energy shows reasonable agreement with the analytical predictions and provides details on the topological defects in the transition region. We find that for small mismatch the transition is of first order, and it remains so for the largest values of mismatch studied here. Our results are consistent with results of simulations for atomistic models of adsorbed overlayers.

0 Bookmarks
 · 
103 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We study the nonlinear driven response and sliding friction behavior of the phase-field-crystal (PFC) model with pinning including both thermal fluctuations and inertial effects. The model provides a continuous description of adsorbed layers on a substrate under the action of an external driving force at finite temperatures, allowing for both elastic and plastic deformations. We derive general stochastic dynamical equations for the particle and momentum densities including both thermal fluctuations and inertial effects. The resulting coupled equations for the PFC model are studied numerically. At sufficiently low temperatures, we find that the velocity response of an initially pinned commensurate layer shows hysteresis with dynamical melting and freezing transitions for increasing and decreasing applied forces at different critical values. The main features of the nonlinear response in the PFC model are similar to the results obtained previously with molecular dynamics simulations of particle models for adsorbed layers.
    Physical Review E 01/2010; 81(1 Pt 1):011121. · 2.31 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this contribution our focus is on the phase-field crystal method, which can be viewed as the youngest methodology in the field of interface computation based on recent work by Elder et al. (Phys. Rev. Lett. 88, 245701 (2002)). It bridges the gap between the molecular simulation approaches and the phase-field approach by operating on diffusive time scales yet atomic length scales. Here we review the fundaments of the phase-field crystal method as well as different models established so far with the aim to capture the main features of the wide range of phase diagrams found in materials science more and more comprehensively.
    European Physical Journal Plus 126(10). · 1.30 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We determine the phase diagram of the phase field crystal model in three dimensions by using numerical free energy minimization methods. Previously published results, based on single mode approximations, have indicated that in addition to the uniform (liquid) phase, there would be regions of stability of body-centered cubic, hexagonal and stripe phases. We find that in addition to these, there are also regions of stability of face-centered cubic and hexagonal close packed structures in this model.
    Journal of Physics Condensed Matter 05/2010; 22(20):205402. · 2.22 Impact Factor

Full-text (2 Sources)

View
21 Downloads
Available from
Jun 3, 2014