Evaluation of grain boundary energy, structure and stiffness from phase field crystal simulations

Abstract

A two-mode phase field crystal (PFC) model is employed to investigate the equilibrium configurations of a range of grain boundaries in fcc-structured materials. A total of 80 different symmetrical tilt grain boundaries are evaluated by PFC simulations in 3D and the results are shown to agree well with data taken from the literature, both regarding the variation of grain boundary energy and also in terms of the resulting grain boundary structures. This verification complements existing PFC studies which are almost exclusively focused either on grain boundaries found in 2D systems or in bcc lattices in 3D. The present work facilitates application of PFC in the analysis of grain boundary mechanics in an extended range of materials, in particular such mechanics that take place at extended time scales not tractable for molecular dynamics (MD) simulations. In addition to the verification of predicted grain boundary energies and structures, wavelet transforms of the density field are used in the present work to obtain phase fields from which it is possible to identify grain boundary fluctuations that provide the means to evaluate grain boundary stiffness based on the capillarity fluctuation method. It is discussed how PFC provides benefits compared to alternative methods, such as MD simulations, for this type of investigations.