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

Abstract

In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic description of the system in question. We present a study on classical density functional theory in three stages of approximation leading to a specific phase field crystal model, and we discuss the limits of applicability of the models that result from these approximations. As a test system we have chosen the three--dimensional suspension of monodisperse hard spheres. The levels of density functional theory that we discuss are fundamental measure theory, a second-order Taylor expansion thereof, and a minimal phase-field crystal model. We have computed coexistence densities, vacancy concentrations in the crystalline phase, interfacial tensions and interfacial order parameter profiles, and we compare these quantities to simulation results. We also suggest a procedure to fit the free parameters of the phase field crystal model.

21 pages

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Cited by in corpus (24)

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• Classical dynamical density functional theory: from fundamentals to applications
• Phase-field modeling of crystal nucleation in undercooled liquids -- A review
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• Heterogeneous nucleation of/on nanoparticles: a density functional study using the phase-field crystal model
• Solid phase properties and crystallization in simple model systems
• Phase diagram of two-dimensional hard rods from fundamental mixed measure density functional theory
• Classical density functional theory, unconstrained crystallization, and polymorphic behavior
• Crystal growth from a supersaturated melt: relaxation of the solid-liquid dynamic stiffness
• Phase-Field Crystal Model with a Vapor Phase
• Free energy of the bcc-liquid interface and the Wulff shape as predicted by the Phase-Field Crystal model
• Dense ionic fluids confined in planar capacitors: in- and out-of-plane structure from classical density functional theory
• The direct correlation function of a crystalline solid
• Liquid crystals of hard rectangles on flat and cylindrical manifolds
• Vacancy diffusion in colloidal crystals as determined by dynamical density-functional theory and the phase-field-crystal model
• Anisotropic pair correlations in binary and multicomponent hard-sphere mixtures in the vicinity of a hard wall: A combined density functional theory and simulation study
• Structure and dynamics of interfaces between two coexisting liquid crystalline phases
• Stable and metastable hard sphere crystals in Fundamental Measure Theory
• Fluid - solid transition in simple systems using density functional theory
• Phase diagrams and crystal-fluid surface tensions in additive and nonadditive two-dimensional hard disk mixtures
• Extension of the primitive model by hydration shells and its impact on the reversible heat production during the buildup of the electric double layer
• Amplitude expansion of the phase-field crystal model for complex crystal structures
• Hard rectangles near curved hard walls: tuning the sign of the Tolman length
• Anisotropy and memory during cage breaking events close to a wall