Theory of defect superlattices in crystals with application to void/vacancy and nitrogen interstitial lattices in tantalum and vanadium

Abstract

An elastic interaction theory is proposed for the formation of a regular array of substitutional or interstitial defects-the defect superlattice-in a crystal. A Green function method is described for the calculation of the formation energy of a defect superlattice. The theory predicts the formation of a void/vacancy lattice in tantalum and vanadium with the ratio of the void lattice constant to the void radius as eight for both the metals and a lattice of nitrogen interstitials at octahedral sites in tantalum and vanadium with the equilibrium concentration of nitrogen per host atom at 1/64 in tantalum and 1/16 in vanadium. Agreement with the experimental observations where available, namely, the void lattice in tantalum and the nitrogen lattice in vanadium, is good.