1/8 are taken for the “face” and “corner” sites, respectively).

As can be seen from Eq. (2), each of the non–conserved components of the order parameter describes a modulation of the $B$–atom concentration along one of the cubic axes. For example, $\psi_1 \ne 0$ means that the system contains alternating $B$–enhanced and $B$–depleted atomic layers along the $x$-axes. As a consequence of such layerwise arrangement of $B$–atoms, the (100) peak shows up in an X–ray diffraction experiment in addition to the (200), (020), (002) and (111) peaks characteristic of the underlying fcc–lattice. Similarly, $\psi_2$ and $\psi_3$–type ordering leads to additional (010) and (001) peaks, respectively.[@Warren] For a distance $\vec{k}$ from these superstructure peaks the scattering intensity is described by the structure factors,

$$S_{\alpha}(\vec{k},t) = \langle{|\Psi_{\alpha}(\vec{k},t)|^2}\rangle,$$

which in a non–equilibrium state depend on time $t$. In Eq. (3), $\Psi_{\alpha}(k_x,k_y,k_z,t)$ denotes the Fourier transform of the order parameter $\psi_{\alpha}(x,y,z,t)$, and $\alpha=1,2,3$. The widths of these intensity profiles are determined by the sizes of antiphase domains.[@Warren] As mentioned in the Introduction, this system displays two types of antiphase boundaries, low–energy type–I boundaries with no change in the arrangement of nearest neighbors, and high–energy type–II boundaries.[@KikuchiC] Since the Hamiltonian, Eq. (1), involves only nearest 