New methods were presented for the microscopic characterization of defects in materials in terms of local energy and stress fields calculated from first principles. These fields provided a quantitative measure of the local disturbance created by defect-induced electronic and atomic inhomogeneities in a solid. The local stress density {σαβ}(r) was estimated by explicitly evaluating the strain derivative of a suitably defined energy density field, ε(r). Although ε(r) and {σαβ}(r) were defined only up to a gauge transformation, they yielded the correct total energy and the average macroscopic stress tensor, respectively, when integrated over the entire volume of the underlying unit cell. In systems with defects, it was shown that well-defined averages of ε(r) and {σαβ}(r) could be constructed by restricting the domain of integration to smaller volumes which were integral multiples of the Wigner-Seitz cell for the super-cell containing the defect. These fields could provide important insights into the nature of atomic-scale defects. Explicit expressions for ε(r) and {σαβ}(r) were derived within the density functional plane-wave pseudopotential formalism. For the test case of bulk Al with a vacancy and an Al(001) surface, it was shown that the averaged forms of ε(r) and {σαβ}(r) helped to characterize the defects in a physically meaningful manner.

First-Principles Energy and Stress Fields in Defected Materials. R.Ramprasad: Journal of Physics - Condensed Matter, 2002, 14[22], 5497-516