Multiplicity of grain boundary structures and related energy variations

Abstract

Ideal minimum-energy grain boundary (GB) structures are usually the only ones considered when characterizing GBs. This limited perspective provides an incomplete view of the possible structural variability of GBs. In the present study, phase field crystal (PFC) simulations are employed in a systematic search of GB states based on γ-surface sampling, demonstrating PFC to be a capable tool for this purpose. It is also shown that a set of microscopic degrees of freedom (DOF) must be considered in addition to the GB’s five macroscopic DOF when identifying variants in GB structure. This set of microscopic DOF comprises three components of relative crystal translation, plus one DOF describing the atomic density in the GB region. GB energy is taken as an example of a key property which is shown to exhibit a considerable spread due to variations in these microscopic DOF, at constant macroscopic DOF. The findings underline the need to consider a spectrum of GB energies for each macroscopic GB configuration, rather than a single value corresponding to an idealized minimum-energy structure. As part of the study, some computationally efficient strategies for setting up the PFC simulation model are also proposed.