Application of the Method of Lattice Statics to Vacancies inαIron

Abstract

The author has calculated the strain-field displacements produced by a single vacancy in $\ensuremath{\alpha}$ iron and has also calculated the strain-field interaction energies associated with pairs of such defects. These calculations were carried out using the method of lattice statics, which is based on the Fourier transformation of the direct-space force equations within a large supercell of the lattice. The author has also calculated the asymptotic displacements about a vacancy in $\ensuremath{\alpha}$ iron and compared these with the corresponding results obtained from the exact method of lattice statics. This comparison shows that elasticity theory cannot be assumed valid closer than the 14th neighbor to the defect along a $〈111〉$ direction in $\ensuremath{\alpha}$ iron. Since the interatomic potential used consists of a set of splines extending out only to next-nearest neighbors, there is a strong implication that the long-range approach to the asymptotic limit is a feature of the open structure of the bcc lattice. Comparison has been made between these displacements and analogous results obtained by a semidiscrete method in which a spherical crystallite containing 530 atoms was treated on a discrete basis. Differences ranging from 5 to 11% are found between the results of the lattice statics calculation and those obtained from the semidiscrete approach. The interaction energy results show that the next-nearest-neighbor divacancy configuration is the most stable, and the nearest-neighbor pair is the next most stable configuration. The only other vacancy pair having a significant binding energy is that in which the vacancies are fourth-nearest neighbors.