Authors: Jörg Rottler1, Michael Greenwood2, Nikolas Provatas3
1)\tDept. of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
2)\tCANMET Materials Technology Laboratory, Hamilton, ON, Canada
3)\tDepartment of Physics & Centre for the Physics of Materials, McGill University, Montreal QC H38 2T8, Canada
Materials phenomena at interfaces such as solidification, solid-solid phase transformations and thin film growth involve complex structural changes that couple atomic scale elastic and plastic effects with diffusional processes. Conventional molecular dynamics is unable to address these problems on experimentally relevant timescales. Highly coarse-grained order parameter (phase field) theories based on Ginzburg-Landau effective Hamiltonians are in widespread use, but are devoid of any atomic level features. Free energy functionals that are minimized by periodic ground states instead (phase field crystals) reflect the discrete structure of matter, and elastic interactions between local deviations from the ground state in the form of defects are naturally incorporated without being constrained to the phononic timescales of MD. Despite their simplicity, these functionals have been shown to capture a wide range of phenomena on a semiquantitative (i.e. scaling) level, including dislocation dynamics, grain boundary energetics, grain coarsening and crystal plasticity. Here we present a new formulation of this approach that permits the selection of ground states with different symmetries (sc, bcc, fcc, etc) [1], determine the phase diagram as well as elastic properties of these "materials" [2]. We also extend the methodology to binary alloys [3] and quasicrystals [4]. The versatility of the technique is illustrated with three examples: nucleation of structurally different daughter phases after a temperature quench [1], lamellae growth in eutectic alloys [3] and monolayer pseudomorphic growth on quasicrystalline surfaces [4].
[1] M. Greenwood, N. Provatas, J. Rottler, Phys. Rev. Lett. 105, 045702 (2010)
[2] M. Greenwood, J. Rottler and N. Provatas Phys. Rev. E 83, 031601 (2011)
[3] M. Greenwood, N. Ofori-Opoku, J. Rottler, and N. Provatas, Phys. Rev. B 84, 064104 (2011)
[4] J. Rottler, M. Greenwood, and B. Ziebarth , J. Phys.: Condens. Matter 24, 135002 (2012)