The vibrational entropy spectra of grain boundary segregation in polycrystals

The vibrational contributions to the energetics of grain boundary segregation are calculated for binary Ni polycrystals with solutes of Pd, Pt, Ag, Au and Cu. The computational challenge of the problem is to assess each different grain boundary site and produce full spectra of both site energies and entropies, which is addressed through a multiscale approach in which a full harmonic calculation is completed only in the vicinity of the solute atom, and a buffer region based on a local harmonic calculation effects connectivity to the bulk polycrystal. The resulting segregation free energy spectra illustrate the artificial nature of segregation temperature dependencies when the vibrational entropy is not considered, and highlight the importance of including the vibrational entropy spectrum for rigorous calculations. For a 5% solute loading level, for example, the magnitude of the artificial temperature dependence calculated ranges from 31 to 43% of the total effective segregation entropy for the various systems explored. Finally, a strong linear correlation between site segregation energy (which is not much affected by vibrational effects within the harmonic approximation) and vibrational entropy is observed in polycrystals, in agreement with prior works of coincident site lattice boundaries; this correlation promises significant simplification of segregation calculations in polycrystals generally.