Cu-Au type orderings in the staggered quadrupolar region of the fcc Blume Emery Griffiths model

The spin-1 Ising (BEG) model has been simulated using a cellular automaton (CA) algorithm improved from the Creutz cellular automaton (CCA) for a face-centered cubic (fcc) lattice. The ground state diagram ($k$, $d$) of the fcc BEG model has ferromagnetic ($F$), quadrupolar ($Q$) and staggered quadrupolar ($SQ$) ordering regions. The simulations have been made in the staggered quadrupolar region for the parameter values in the intervals $-24\le d=D\mathrm{/}J<0$ and $-3\le k=K\mathrm{/}J\le 0$ . The phase diagrams on the ($k{T}_C\mathrm{/}J$, $d$) and the ($k{T}_C\mathrm{/}J$, $k$) planes have been obtained through $k=-3$ and $d=-4$ lines, respectively. The staggered quadrupolar ordering region separates into five ordering regions ($A_{3}B(a)$, $A_{3}B(f)$, $AB$ (type-I), $AB$(type-II) and $A{B}_3(f)$) which have the different stoichiometric Cu-Au type structures.