A kinetic model for three-site intracrystalline ordering-disordering in minerals

A kinetic model for describing the site occupancies of a cation at three nonequivalent sites in minerals has been presented as follows x_i = c_i0 + c_i1e^λ1t + c_i2e^λ2t (i = 1, 2, 3), where x_i is the site occupancy of a given cation at site s_i , and c_i0 (>0), c_i1, c_i2, λ₁, and λ₂ are constants at a given temperature and composition of the mineral. The two lemmas concerning three-site ordering-disordering indicate that λ₁ and λ₂ are either negative or complex-valued, and that they guarantee the convergence of the site occupancies with increasing time. The conditions for extrema have been given in the paper. The greatest difference between two-site and three-site order-disorder processes is that two-site ordering-disordering only occurs as either a monotonously increasing function or a monotonously decreasing function of time at a given initial total composition and temperature, while three-site order-disorder kinetics may have local minima or maxima.