  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\leq d=D/J<0$ and $-3\leq k=K/J\leq 0$ . The phase diagrams on the ($
kT_{C}/J$, $d$) and the ($kT_{C}/J$, $k$) 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 $AB_{3}(f)$) which have the different stoichiometric Cu-Au
type structures.
