Asymptotic Interaction Energy between Pairs of Point Defects in Cubic Metals

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Abstract
We have calculated the asymptotic interaction energies between pairs of interstitial Cu atoms in Cu and between pairs of vacancies in Al, Na, and K. These calculations were performed using the asymptotic equations of the method of lattice statics. The exact method of lattice statics is based on the Fourier transformation of the direct-space equilibrium equations for a "supercell" of the lattice containing one defect surrounded by a large number of host atoms. The asymptotic interaction energies were compared with the corresponding results obtained from the exact method of lattice statics. This comparison indicates that elasticity theory cannot be used to obtain strain-field interaction energies for defects nearer than at least 26 or 27 neighbors from each other, and is probably not truly valid until much larger interdefect separations are considered. This result places a heavy restriction on the use of elasticity theory in practical defectinteraction calculations.