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

TL;DR

This study uses an improved cellular automaton simulation to explore Cu-Au type orderings in the staggered quadrupolar region of the face-centered cubic Blume-Emery-Griffiths model, revealing multiple ordered phases with distinct structures.

Contribution

It introduces an enhanced CA algorithm for simulating the fcc BEG model and maps out detailed phase diagrams showing various Cu-Au type orderings in the staggered quadrupolar region.

Findings

Identification of five distinct Cu-Au type ordered phases.

Phase diagrams showing stability regions of different orderings.

Confirmation of complex ordering behavior in the staggered quadrupolar region.

Abstract

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.