3(111) grain boundary of body-centered cubic Ti-Mo and Ti-V alloys: First-principles and model calculations

The energetics and atomic structures of 3[11̄0](111) grain boundary (GB) of body-centered cubic (bcc) Ti-Mo and Ti-V alloys are investigated using density-functional-theory calculations and virtual crystal approximation. The electron density in bcc structure and the atomic displacements and excess energy of the GB are correlated to bcc-ω phase stability. Model calculations based on pairwise interplanar interactions successfully reproduce the chemical part of GB energy. The chemical GB energy can be expressed as a sum of excess pairwise interactions between bcc (111) layers, which are obtained from Gaussian elimination of the total energies of a number of periodic structures. The energy associated with the relaxation near the GB is solved by numerical minimization using the derivatives of the excess interactions. Anharmonic interlayer interactions are necessary for obtaining accurate relaxation energy and excess GB volume from model calculations. The effect of GB on vibrational spectrum is also investigated. Segregation energies of B and Y to a substitutional site on the GB plane are calculated. Preliminary results suggest that Y tends to segregate, while B tends to antisegregate.