Elastic dipole tensor of a defect at a finite temperature: Definition and properties

Abstract

The concept of the elastic dipole tensor of a defect is generalized to enable the treatment of lattice distortions produced by defects at elevated temperatures. Thermodynamic and statistical mechanics treatments show the feasibility of applying the formalism to the evaluation of formation free energies and finite-temperature elastic dipole tensors of $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}$ prismatic self-interstitial atom dislocation loops. The method exhibits good numerical stability even in the high-temperature limit, and relates discrete atomic and continuum representations of displacement and stress and strain fields of defects.