A KINETIC-MODEL FOR 3-SITE INTRACRYSTALLINE ORDERING-DISORDERING IN MINERALS

A kinetic model for describing the site occupancies of a cation at thr ee nonequivalent sites in minerals has been presented as follows x(i) = c(i0) + c(i1)e(lambda 1t) + c(i2)e(lambda 2t) (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), lambda(1), and lambda(2) are constants at a given tem perature and composition of the mineral. The two lemmas concerning thr ee-site ordering-disordering indicate that lambda(1) and lambda(2) are either negative or complex-valued, and that they guarantee the conver gence 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 ord ering-disordering only occurs as either a monotonously increasing func tion or a monotonously decreasing function of time at a given initial total composition and temperature, while three site order-disorder kin etics may have local minima or maxima.