On the effect of elastic anisotropy and polarizability on solute segregation at low-angle grain boundaries

Abstract

Solute segregation towards grain boundaries is investigated by modeling solute atoms as elastic dipoles interacting with the strain fields of symmetric tilt low-angle grain boundaries (LAGBs). Elastic dipoles are determined using molecular statics (MS) considering both the permanent second-rank tensor and the fourth-rank polarizability tensor, which is needed to capture the elastic dipole dependence on external strain. For cubic lattices, the latter tensors are related to size and modulus effects, respectively. The strain fields of LAGBs are evaluated either through MS or by considering arrays of edge dislocations within the framework of linear isotropic elasticity or heterogeneous anisotropic elasticity using the Stroh formalism. The interaction energies arising from the coupling between elastic dipoles and LAGB strain fields are compared to segregation energies computed on a site-by-site basis using MS. These comparisons are made for three LAGBs and two cubic systems (Cu and Ag) with solute atoms in substitution (Ag and Ni, respectively). The results underscore the critical role of anisotropic elasticity in accurately modeling solute segregation. Notably, variations in behavior between grain boundaries having a same tilt angle are only captured when anisotropic elasticity is considered. Furthermore, despite the inherent limitations in addressing non-linear effects at defect cores, the elastic dipole approximation proves to be an effective method for approximating segregation energy spectra in LAGBs obtained through atomistic simulations. Lastly, the estimation of overall solute concentration at grain boundaries highlights the prominent influence of the modulus effect.