Long-Period Superlattices in Alloys. II

A theory, which has been developed recently by the authors to explain the origin and characteristics of the long-period superlattice CuAu II, is used to explain, in a more general way, similar characteristics of long-period superlattices found in face-centered cubic alloys having compositions around the $A_{3}B$. Although there is a difference in symmetry in the atomic arrangement between the $\mathrm{AB}$- and $A_{3}B$-type alloys, the application of the theory can be made in a straightforward manner. It is found that one- and two-dimensional long-period superlattices can exist in the $A_{3}B$-type alloy systems, but that a three-dimensional one should not occur. In the case of the one-dimensional long-period superlattices, the theory can be reduced to the same form as for the CuAu II ($\mathrm{AB}$ type) case. The theory predicts correctly the period of the superlattice, e.g., those found in the Cu-Pd, Cu-Pt, Au-Cd, Ag-Mg, and Au-Zn systems, the type of antiphase, the direction of the period and the sign of the tetragonal distortion which occurs when the long-period superlattice is formed.