Elastic constants of stressed and unstressed materials in the phase field crystal model

Abstract

A general procedure to investigate the elastic response and calculate the elastic constants of stressed and unstressed materials through continuum field modeling, particularly the phase field crystal (PFC) models, is presented. It is found that for a complete description of system response to elastic deformation, the variations of all the quantities of lattice wave vectors, their density amplitudes (including the corresponding anisotropic variation and degeneracy breaking), the average atomic density, and system volume should be incorporated. The quantitative and qualitative results of elastic constant calculations highly depend on the physical interpretation of the density field used in the model, and also importantly, on the intrinsic pressure that usually pre-exists in the model system. A formulation based on thermodynamics is constructed to account for the effects caused by constant pre-existing stress during the homogeneous elastic deformation, through the introducing of a generalized Gibbs free energy and an effective finite strain tensor used for determining the elastic constants. The elastic properties of both solid and liquid states can be well produced by this unified approach, as demonstrated by an analysis for the liquid state and numerical evaluations for the bcc solid phase. The numerical calculations of bcc elastic constants and Poisson's ratio through this method generate results that are consistent with experimental conditions, and better match the data of bcc Fe given by molecular dynamics simulations as compared to previous work. The general theory developed here is applicable to the study of different types of stressed or unstressed material systems under elastic deformation.

14 pages, 4 figures. To be published in Phys. Rev. B

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Cited by in corpus (8)

• Deriving phase field crystal theory from dynamical density functional theory: consequences of the approximations
• A coarse-grained phase-field crystal model of plastic motion
• Field Dislocation Mechanics and Phase Field Crystal models
• Stress in ordered systems: Ginzburg-Landau type density field theory
• Thermo-Density Coupling in PFC Type Models for the Study of Rapid Crystallization
• Minimal phase-field crystal modeling of vapor-liquid-solid coexistence and transitions
• Control of phase ordering and elastic properties in phase field crystals through three-point direct correlation
• Gradient elasticity in Swift-Hohenberg and phase-field crystal models