This chapter reviews the development, calibration, and some applications of quadrilateral solution models based on pairwise interactions in the generalized point approximation. Solution models that incorporate explicit pairwise cation-cation interactions successfully treat phase equilibria in these ternary systems where traditional ternary solution models (e.g., the regular solution model discussed by many, including Andersen and Lindsley, 1981) based on mixing of chemical rather than structural units cannot predict cation ordering or noncoplanarity of quadrilateral end member free energies. Phase separation in quadrilateral solutions such as pyroxenes and olivines can be described as a result of nonideal mixing within one of the sites available for cation substitution.
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