Theory of surface effects in binary alloys. I. Ordering alloys

A theory of the (110) surface concentration and short- and long-range orders for an $\mathrm{AB}$ body-centered-cubic alloy is presented. It is based on a model consisting of pairwise interactions between nearest-neighbor atoms only. The entropy is calculated in the pair approximation following Kikuchi's method. It is found that depending on the values of the interaction parameters (a) the surface concentration decreases monotonically as a function of temperature from 100% of one component at $T=0\mathrm{}$ to a random mixture as $T\to \infty$, or (b) it increases from a perfectly ordered $\mathrm{AB}$ layer of equal concentration of either component to a maximum concentration of one component at the order-disorder transition temperature $T_c$ and then decreases again to the disordered $A_{0.5}{B}_{0.5}$ alloy as $T\to \infty$. Long-range and short-range order parameters as functions of temperature are also discussed.