On the quantification of phase-field crystals model for computational simulations of solidification in metals


Phase-field crystals (PFC) is an atomistic model on diffusive time scale with the capability to simulate solidification/melting and the subsequent nano-structural evolution while naturally accounting for elasticity and plasticity. Although PFC was originally introduced as a phenomenological model in materials science (Elder et al., 2002), it was later shown that it can be derived from density functional theory (DFT) by certain approximations (Elder et al., 2007) providing a significant predictive capability for PFC. However, these approximations in PFC, similar to any other higher-scale computational model derived from DFT, have introduced intrinsic challenges for quantifying of PFC for specific materials; i.e. determining PFC model parameters for specific materials. The objective of this article is to present a variety of possible approaches that can be used for quantifying PFC for solidification/melting modeling. Thus, we present a reformulation of PFC model containing two extra parameters and four possible quantification approaches. Then, representative material properties corresponding for each individual approach are calculated and compared with their available experimental/computational counterparts in literature. The representative material properties include elastic constants, liquid and solid densities, liquid structure factor, latent heat, and solid-liquid interface free energy and its anisotropy. We discuss the quantitative capabilities of each quantification approach regarding their prediction of the mentioned representative material properties for Fe as an example material. The discussion provided in this study can be used as a guideline to select the proper quantification approach for researchers who need to use PFC for quantitative modeling.

Publication Title

Computational Materials Science