  Electronic structure calculations at macroscopic scales are employed to
investigate the crucial role of a defect-core in the energetics of vacancies in
aluminum. We find that vacancy core-energy is significantly influenced by the
state of deformation at the vacancy-core, especially volumetric strains.
Insights from the core electronic structure and computed displacement fields
show that this dependence on volumetric strains is closely related to the
changing nature of the core-structure under volumetric deformations. These
results are in sharp contrast to mechanics descriptions based on elastic
interactions that often consider defect core-energies as an inconsequential
constant. Calculations suggest that the variation in core-energies with
changing macroscopic deformations is quantitatively more significant than the
corresponding variation in relaxation energies associated with elastic fields.
Upon studying the influence of various macroscopic deformations, which include
volumetric, uniaxial, biaxial and shear deformations, on the formation energies
of vacancies, we show that volumetric deformations play a dominant role in
governing the energetics of these defects. Further, by plotting formation
energies of vacancies and di-vacancies against the volumetric strain
corresponding to any macroscopic deformation, we find that all variations in
the formation energies collapse on to a universal curve. This suggests a
universal role of volumetric strains in the energetics of vacancies.
Implications of these results in the context of dynamic failure in metals due
to spalling are analyzed.
