The interfacial tension of a sharp antiphase domain boundary

Abstract

An analytic solution is obtained for the interfacial tension of a sharp antiphase boundary in an ordered binary crystal whose atoms interact in pairs. The general solution is valid for an arbitrarily long-range interatomic interaction, and for any orientation of the antiphase boundary in any superstructure. The result can be expressed in terms of the Fourier transform of the interaction energy V(k), or may be written as a series in the potentials W _i that govern the interaction between solutes in the ith-nearest-neighbour positions. In the latter case the coefficients of the successive terms in the series are integrals of simple trigonometric expressions. The results are used to treat {111} and {100} antiphase boundaries in the L1 ₂ (Cu₃Au-type) structure and {100} boundaries in the L1₀ (CuAuI-type) structure. Equations are given for interactions up to the eighth-nearest neighbours. The tension of the {111} antiphase boundary in the Al₃Li (Ll ₂) phase is computed in a second-neighbour interaction model in which the interatomic potentials are chosen to give a best fit to the phase diagram. The result, 72 erg cm⁻², is in reasonable agreement with the most recent determinations by other techniques.