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In materials science the phase field crystal approach has become popular tomodel crystallization processes. Phase field crystal models are in essenceLandau-Ginzburg-type models, which should be derivable from the underlyingmicroscopic description of the system in question. We present a study onclassical density functional theory in three stages of approximation leading toa specific phase field crystal model, and we discuss the limits ofapplicability of the models that result from these approximations. As a testsystem we have chosen the three--dimensional suspension of monodisperse hardspheres. The levels of density functional theory that we discuss arefundamental measure theory, a second-order Taylor expansion thereof, and aminimal phase-field crystal model. We have computed coexistence densities,vacancy concentrations in the crystalline phase, interfacial tensions andinterfacial order parameter profiles, and we compare these quantities tosimulation results. We also suggest a procedure to fit the free parameters ofthe phase field crystal model.

physical review. e, statistical, nonlinear and soft matter physics

Description of hard sphere crystals and crystal-fluid interfaces: a  critical comparison between density functional approaches and a phase field  crystal model