Cu$_3$Pd, Mg$_3$In, Co$_3$Pt, etc. exhibit long range order with a $L1_2$–structure below some specific ordering temperature $T_0$. In the $L1_2$–structure four equivalent phases exist, where one of the four simple cubic sublattices building the fcc–lattice are preferentially occupied by the minority atoms. In studying kinetic processes of phase ordering, the following general considerations must be taken into account:

1.  The transition is of first order. Hence, for small enough supercoolings the disordered phase remains metastable. Relaxation at short times after a temperature quench is governed by the formation of ordered nuclei, which grow into the disordered matrix. On the other hand, the concept of spinodal ordering has been advanced [@AllenCsp] to characterize the phase ordering processes under large supercoolings.

2.  The degeneracy of the ordered phase implies a four–component order parameter, $\Psi = (\psi_0,\psi_1,\psi_2,\psi_3)$. Here, $\psi_{\alpha}$ with $\alpha = 1,2,3$, are non–conserved structural order parameter components coupled to a conserved density, $\psi_0$, which describes the concentration of the two atomic species.

3.  The antiphase domain structure is anisotropic as a result of the existence of two types of antiphase domain walls: low–energy (type–I) and high–energy (type–II) walls.

Under these conditions a rich spectrum of kinetic processes is to be expected. 