MULTISITE ORDER-DISORDER KINETICS IN CRYSTALLINE SOLIDS - A GENERALIZED FORMULATION

Many crystalline solids have multiple nonequivalent sites among which different atoms show substitutional long-range order-disorder phenomen a. The order-disorder kinetics of an atom among any n nonequivalent si tes in a crystal can be described by the equation x(i)=c(il)+(j=2)Sigm a(n) c(ij)(t)e(lambda jt) where x, is the site occupancy of the atom a t site s(i), n is the number of nonequivalent sites, lambda(j)(lambda( j)=0) is constant at a given temperature, pressure, and total composit ion of the crystal, and c(ij)(t) is constant or polynomial in t. Four theorems governing a multi-site order-disorder process have been prove d, requiring that lambda(j) must be either zero (only lambda(l)=0), a negative real number, or a complex-valued quantity with the real part being a nonpositive number. The kinetic model becomes constrained and naturally complies with crystal-chemical conditions when the mole numb er per formula unit is chosen as the unit of all site-occupancy variab les, or site multiplicities are explicitly incorporated into the model . When the mole fraction is directly used as the unit, the model becom es unconstrained, but it is a valid treatment that is as equally appli cable to the multi-site order-disorder kinetics as the constrained mod el.