Nonlinear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene

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Authors

HUTER Claas FRIÁK Martin WEIKAMP Marc NEUGEBAUER Joerg GOLDENFELD Nigel SVENDSEN Bob SPATSCHEK Robert

Year of publication 2016
Type Article in Periodical
Magazine / Source Physical Review B
MU Faculty or unit

Central European Institute of Technology

Citation
Web http://journals.aps.org/prb/abstract/10.1103/PhysRevB.93.214105
Doi http://dx.doi.org/10.1103/PhysRevB.93.214105
Field Theoretical physics
Keywords DENSITY-FUNCTIONAL THEORY
Description We investigate nonlinear elastic deformations in the phase field crystal model and derived amplitude equation formulations. Two sources of nonlinearity are found, one of them is based on geometric nonlinearity expressed through a finite strain tensor. This strain tensor is based on the inverse right Cauchy-Green deformation tensor and correctly describes the strain dependence of the stiffness for anisotropic and isotropic behavior. In isotropic one-and two-dimensional situations, the elastic energy can be expressed equivalently through the left deformation tensor. The predicted isotropic low-temperature nonlinear elastic effects are directly related to the Birch-Murnaghan equation of state with bulk modulus derivative K' = 4 for bcc. A two-dimensional generalization suggests K'(2D) = 5. These predictions are in agreement with ab initio results for large strain bulk deformations of various bcc elements and graphene. Physical nonlinearity arises if the strain dependence of the density wave amplitudes is taken into account and leads to elastic weakening. For anisotropic deformation, the magnitudes of the amplitudes depend on their relative orientation to the applied strain.
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