## Abstract

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 x_{i} = c_{i1} + Σ^{n}
_{j=2} c_{ij}(t)e^{λit} where x_{i} is the site occupancy of the atom at site s_{i}, n is the number of nonequivalent sites, λ_{j} (λ_{1} = 0) is constant at a given temperature, pressure, and total composition of the crystal, and c_{ij}(t) is constant or polynomial in t. Four theorems governing a multi-site order-disorder process have been proved, requiring that λ_{j} must be either zero (only λ_{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.

Original language | English |
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Pages (from-to) | 325-336 |

Number of pages | 12 |

Journal | American Mineralogist |

Volume | 82 |

Issue number | 3-4 |

Publication status | Published - Mar 1997 |