A theory of order-disorder transition during crystallization of binary systems2

A theory is presented describing the order-disorder transition in binary crystals growing on the condition of supersaturation from nonsolid phases. The theory applies to systems that crystallize with an almost perfectly ordered structure if exposed to conditions close to thermodynamic equilibrium. Based on a model that assumes incorporation and detachment of single atoms to occur at the kink sites of mono-atomic steps existing at an otherwise smooth crystal surface a kinetic master equation for the time dependence of configuration probabilities has been formulated. Several simplifying assumptions have been employed. Any solution for the steady-state conditions depends on a roughness parameter λ, the far-order parameter η, the incorporation frequency ω₊ and a parameter q, related to the atomic interaction energies. The solutions are discussed for conditions prevailing near equilibrium with η 1 and within the range of order-disorder transition with η 0. The analysis reveals that for different incorporation frequencies different critical values of the parameter q exist for which a transition from an ordered to a disordered phase is predicted to occur. Each of these critical values of q corresponds to a critical transition temperature T_t.