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Anisotropy of Interfaces in an Ordered HCP Binary Alloy



John W. Cahn, S C. Han, Geoffrey B. McFadden


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 (1997), p. 1787] 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. Ansisotropy is a natural consequence of the underlying crystal symmetries and the multiple-order-parameter continuum formation presented here. The isotropy transverse to the six-fold axis expected for scalar and vector order parameters is not found.
NIST Interagency/Internal Report (NISTIR) - 6217
Report Number


anisotropy, antiphase boundaries, Cahn-Allen equation, diffuse interface, interphase boundaries, mean field theory


Cahn, J. , Han, S. and McFadden, G. (1998), Anisotropy of Interfaces in an Ordered HCP Binary Alloy, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD (Accessed June 18, 2024)


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Created August 31, 1998, Updated October 12, 2021