Structure and energetics of vacancies in body centered cubic hafnium under pressure: First-principles study

The structure and energetics of vacancies in hafnium in the body centered cubic (bcc) structure is investigated as function of pressure from 0 to 100 GPa by means of first principles electronic structure calculations in the framework of the density functional theory in the local density approximation using the plane-wave pseudopotential method. The structural relaxation around the vacancy in the cubic symmetry is exceptionally large with a relaxation energy above 2.2 eV at all pressures, i.e. including at pressures where the bcc structure is dynamically stable (P > 45 GPa) and even energetically stable (P > 56 GPa). The oscillatory behavior, typical of bcc metals, displayed by the relaxation pattern is shown to be connected with the displacement field induced by the L 2/3 [111] phonon. The configuration where an atom is placed halfway between two nearest neighbor vacant sites - corresponding usually to the saddle point configuration for migration - has a lower energy than the normal cubic configuration for P<67 GPa. According to our calculations, the vacancy therefore adopts an unexpected split configuration in a finite pressure range where the bcc structure is energetically stable.