Two-site multi-cation ordering-disordering in minerals: An alternative kinetic model

Mueller's model has been widely applied to modeling kinetic experimental data on the ordering-disordering of cations between two nonequivalent sites. This model is valid only for pure or nearly pure binary systems. For ordering-disordering involving three or more cations (multiple cation or multi-cation) between two sites, Mueller's methodology, which is based on a two-cation exchange reaction, yields no explicit general solution. On the basis of a single-cation exchange reaction, we present an alternative kinetic model for multi-cation ordering-disordering in minerals with two nonequivalent sites. This model is not only suitable for binary systems but is also valid for multi-cation ordering-disordering at two nonequivalent sites. In addition, two kinetic coefficients for each individual cation can be easily obtained using nonlinear parameterization. A comparison of reported experimental data with theoretical calculations has shown that our model can fit both binary and multi-cation ordering-disordering very well and can also explain and predict many kinetic features observed in experiments.