Many crystalline solids have multiple nonequivalent sites among which different atoms show substitutional long-range order-disorder phenomena. Four theorems governing a multi-site order-disorder process have been proved, requiring that lambda j must be either zero (only lambda 1 = 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 number per formula unit is chosen as the unit of all site-occupancy variables, or site multiplicities are explicitly incorporated into the model. When the mole fraction is directly used as the unit, the model becomes unconstrained, but it is a valid treatment that is as equally applicable to the multi-site order-disorder kinetics as the constrained model.

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