Multi-site order-disorder kinetics in crystalline solids: A generalized formulation

Lian Kun Sha*, Bruce W. Chappell

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)


    Many crystalline solids have multiple nonequivalent sites among which different atoms show substitutional long-range order-disorder phenomena. The order-disorder kinetics of an atom among any n nonequivalent sites in a crystal can be described by the equation xi = ci1 + Σn j=2 cij(t)eλit where xi is the site occupancy of the atom at site si, n is the number of nonequivalent sites, λj1 = 0) is constant at a given temperature, pressure, and total composition of the crystal, and cij(t) is constant or polynomial in t. Four theorems governing a multi-site order-disorder process have been proved, requiring that λj must be either zero (only λ1 = 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.

    Original languageEnglish
    Pages (from-to)325-336
    Number of pages12
    JournalAmerican Mineralogist
    Issue number3-4
    Publication statusPublished - Mar 1997


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