The order-disorder transformation at supercooled melt/crystal transition region of binary melts (I) the master equation

Binary melts crystallizing with almost perfectly ordered structures if exposed to conditions close to thermodynamic equilibrium exhibit an increasing tendency to form metastable crystals with increasing disorder when these alloys crystallize on the growth conditions of supercooling. Based on the model of a two-phase transition zone separating a growing crystal from its non-solid surrounding a kinetic master equation is formulated describing the kinetics of competitive atomic exchange processes within the transition region. The theory considers the case of simple cubic structure with equal particle numbers of two components that form a NaCl-type lattice at the state of perfect order. In a subsequent paper solutions of the master equation obtained for steady-state conditions are discussed.