Calculations of isothermal elastic constants in the phase-field crystal model

Abstract

The phase-field crystal (PFC) method is an emerging coarse-grained atomistic model that can be used to predict material properties. In this work, we describe procedures for calculating isothermal elastic constants using the PFC method. We find that the conventional procedure used in the PFC method for calculating the elastic constants are inconsistent with those defined from a theory of thermoelasticity of stressed materials. Therefore, we present an alternative procedure for calculating the elastic constants that are consistent with the definitions from the thermoelasticity theory, and show that the two procedures result in different predictions. Furthermore, we employ a thermodynamic formulation of stressed solids to quantify the differences between the elastic constants obtained from the two procedures in terms of thermodynamic quantities such as the pressure evaluated at the undeformed state.

Phase-field crystal model for a diamond-cubic structure

“…We believe the addition of atoms into the system as σ increases is the cause for a decreasing solid-liquid interfacial energy, which is in disagreement with the trend measured experimentally [25,26] and calculated using atomistic simulations [27][28][29] for closed systems. In order to directly compare the dependence of γ p (σ, α 0 , α 0 ) on σ from the PFC model to the dependence of γ p (σ, α 0 , α 0 ) on melting temperature from experiments and atomistic simulations, it is required to keep the number of particles constant as σ is varied, which is similar to what has been implemented for calculating elastic constants [30].…”

Quantifying a two-mode phase-field crystal model for BCC metals at melting point

“…The above-mentioned PFC model is also called one-mode PFC, because it damps the dynamics of the system except near the first density wave length. Examples of different applications of PFC models include simulating solidification [6], elastic deformation [7], spinodal decomposition [8], grain-boundary premelting [9], dislocation dynamics [10], Kirkendall effect [11], structural phase transformation [12,13], and stacking faults [14]. PFC models can be also used in quantitative modeling of materials if its model parameters are determined for the material of interest at a given temperature; e.g.…”

A modified two-mode phase-field crystal model applied to face-centered cubic and body-centered cubic orderings

“…Therefore, it can represent (by only minimizing the free energy) principal RLVs with closed triangle forms, which are hexagonal and BCC structures in two-dimensional (2D) and three-dimensional (3D) spaces, respectively [9]. The one-mode PFC model is already applied to study different phenomena in materials science, including solidification [10], elastic deformation [11], spinoidal decomposition [12], grain boundary premelting [13], dislocation dynamics [14], and Kirkendall effect [15]. Furthermore, it was shown that the one-mode PFC model can be used to quantitatively simulate the two-phase solid-liquid coexistence of Fe [16][17][18] by determining its model parameters from molecular dynamics (MD) simulations.…”