Anisotropy of Interfaces in an Ordered HCP Binary Alloy

A multiple-order-parameter mean-field theory of ordering on a binary hexagonal- close-packed (HCP) crystal structure is developed, and adapted to provide a continuum formulation that incorporates the underlying symmetries of the HCP crystal in both the bulk and gradient energy terms of the free energy. The work is an extension of the previous treatment by Braun et al. Phil. Trans. Roy. Soc. Lond. A 355:1787 (1997)] of order–disorder transitions on a face-centered-cubic crystal (FCC) lattice. The theory is used to compute the orientation dependence of the structure and energy of interphase and antiphase boundaries in ordering to the Cd₃Mg and CdMg structures, which are the HCP analogs of Cu₃Au and CuAu structures in FCC. As in the corresponding FCC case, the multiple order parameters do not form a vector. Anisotropy is a natural consequence of the underlying crystal symmetries and the multiple-order-parameter continuum formation presented here. The isotropy transverse to the sixfold axis expected for a scalar order parameter is not found.