Local Stress Density Research Articles

First-principles energy and stress fields in defectedmaterials

New methods are presented for microscopically characterizingdefects in materials in terms of local energy and stress fieldscalculated at the first-principles level of theory. Thesefields provide a quantitative measure of the local disturbancecreated by defect-induced electronic and atomic inhomogeneitiesin a solid. The local stress density {σαβ}(r) is computed by explicitly evaluating the strain derivative of a suitably defined energydensity field, ε(r). Althoughε(r) and {σαβ}(r) are defined only up to a gauge transformation, they yield thecorrect total energy and the average macroscopic stress tensor,respectively, when integrated over the entire volume of theunderlying unit cell. In systems with defects, it is shown thatwell-defined averages of ε(r) and{σαβ}(r) can be constructed byrestricting the domain of integration to smaller volumes, whichare integral multiples of the Wigner-Seitz cell for thesupercell containing the defect. These fields can provideimportant insights into the nature of atomic-scale defects. Explicit expressions for ε(r) and{σαβ}(r) are derived within the densityfunctional plane-wave pseudopotential formalism. For the testcases of bulk Al with a vacancy and a Al(001) surface, it isshown that the averaged forms of ε(r) and{σαβ}(r) help characterize the defectsin a physically meaningful manner. Potential applications ofε(r) and {σαβ}(r) tothe characterization of surface relaxations and to multi-scalestudies of materials are suggested.

Defects in Aluminum: A Density Functional Study

ABSTRACTWe describe a new method of examining defects and their interactions with each other at a microscopic level of detail. This involves efficiently calculating local properties at arbitrary spatial points, applicable in periodic supercell calculations. In particular, we have identified two quantities, the local energy density, ε(r) and the local stress density, σαβ(r), which are constrained to yield the total energy and the average macroscopic stress tensor, respectively, when integrated over the entire volume of the supercell. In systems with defects, these microscopic quantities provide important insights about the local nature and environment of defects. For the test case of bulk Al with a point defect, we demonstrate that these concepts result in meaningful local quantities characteristic to the point defect. We propose to use these methods to study the microscopic nature of vacancies at a grain boundary and their interaction with each other.