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

C. V. Achim, M. Karttunen, K. R. Elder, E. Granato, T. Ala-Nissila, and S. C. Ying

Phys. Rev. E 74, 021104 – Published 4 August 2006

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.

Received 6 April 2006

DOI:https://doi.org/10.1103/PhysRevE.74.021104

Authors & Affiliations

C. V. Achim

Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 TKK, Finland

M. Karttunen

Department of Applied Mathematics, The University of Western Ontario, London, Ontario, Canada

K. R. Elder

Department of Physics, Oakland University, Rochester, Michigan 48309-4487, USA

E. Granato

Laboratório Associado de Sensores e Materiais, Instituto Nacional de Pesquisas Espaciais, São José dos Campos, São Paulo, Brazil

T. Ala-Nissila

Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 TKK Helsinki, Finland and Department of Physics, Brown University, Providence, Rhode Island 02912-1843, USA

S. C. Ying

Department of Physics, Brown University, Providence, Rhode Island 02912-1843, USA

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Vol. 74, Iss. 2 — August 2006

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