Disordering energy versus disorder in minerals: A phenomenological relation and application to orthopyroxene

Many minerals, such as pyroxenes and amphiboles, show nonconvergent disordering and, therefore, cannot be treated in terms of the classic Bragg and Williams theory. A simple phenomenological model has been developed that is applicable to nonconvergent disordering and reduces to the well-known Bragg and Williams relation for the energy change of disordering from the state of complete order for the special case of linear convergent disordering and 'simple mixture' behavior for the whole crystal. The model has been applied to calculate the energetic parameters of disordering in orthopyroxene from site occupancy and calorimetric data, and compared with the measured or independently derived values of these parameters.