Abstract
The phase-field crystal (PFC) method is a promising computational model with atomistic resolution and diffusive time scale. In this work, the Fourier-spectral-method (FSM) scheme was developed for evaluating the PFC free energy of a system subjected homogeneous deformation. This scheme addresses the complication where, in numerical implementation of FSM using discrete Fourier transform (DFT), the discretized data may no longer lie along the directions of the Cartesian basis due to deformation. In this scheme, the real-space coordinate transformation is employed so that the (continuous) Fourier transform is performed on the function of the undeformed coordinates. This transformation allows straightforward DFT implementation because the sampling at the undeformed configuration is unaffected by the deformation. This scheme is also shown to be applicable to both the original PFC model and a “CDFT”-type PFC model containing a two-body correlation function.
Highlights
The phase-field crystal (PFC) model [1] is a promising model for simulating atomistic phenomena on diffusive time scale
This scheme utilizes real-space coordinate transformation so that the Fourier transform is performed on the function of the undeformed coordinates and the effect of the deformation instead manifests in the transformation of the Fourier wave vector
The Fourier spectral method (FSM) scheme for evaluating the PFC free energy of a system subjected to homogeneous deformation was developed
Summary
The phase-field crystal (PFC) model [1] is a promising model for simulating atomistic phenomena on diffusive time scale. Since the order-parameter profiles in the PFC model are typically smooth, periodic, and contained in a geometrically simple computational domain, the Fourier spectral method (FSM) provides an efficient and accurate algorithm for evaluating the PFC free energy and solving the dynamic equations. I presented the FSM scheme for calculating the PFC free energy of a system subjected to homogeneous deformation This scheme utilizes real-space coordinate transformation so that the (continuous) Fourier transform is performed on the function of the undeformed coordinates and the effect of the deformation instead manifests in the transformation of the Fourier wave vector.
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