SHORT-RANGE AND LONG-RANGE ORDER OF THE BINARY MADELUNG LATTICE

We discuss the influence of point-ion electrostatics on the long- (LRO) and short-range order (SRO) in binary fcc-, bcc-, and simple-cubic-based (sc) alloys. The electrostatic problem is studied by a combination of (a) a model for the distribution of point charges on lattice sites, motivated by recent first-principles calculations, (b) a mapping of the infinite-ranged Coulomb interaction onto a rapidly convergent series of effective interactions, and (c) Monte Carlo simulated annealing of the ensuing Ising-like expansion. This provides a means to identify the lowest energy structures (ground states) at zero temperature and the dominant wave vectors of the SRO at high temperatures, which are stabilized by ionic interactions. (i) We confirm previous results that the three ground states of the fcc Madelung lattice are the D022 (A3B and AB3) and 40 (AB) structures, which can all be described as 210 superlattices. We further find that the ground states of the bcc and sc Madelung lattices are CsCl and NaCl, respectively. (ii) Despite the fact that the structure 40 has the lowest electrostatic energy of any fcc-type compound, this structure is very rare in nature. We find that this rarity could imply that a highly ionic fcc AB compound will transform to the bcc structure CsCl that is electrostatically more stable for the same charge distribution. The exception is when the energy required to promote the elemental solids A+B from fcc to bcc is larger than the gain in electrostatic energy. (iii) Monte Carlo and mean-field calculations both demonstrate that the dominant wave vectors of LRO and SRO coincide for the bcc and sc Madelung lattices. However, for compositions x0.33 and x0.67 on the fcc lattice, mean-field calculations incorrectly predict SRO peaks at the 11/20 points, whereas Monte Carlo calculations show SRO peaks at the 100 points. Thus, in describing fcc electrostatics, the mean-field theory of SRO is seen to qualitatively fail. (iv) Electrostatic point-ion interactions lead to significant SRO correlations. Near the transition temperature, these correlations account for a 60% change in the energy of the random alloy. © 1995 The American Physical Society.