Configurational thermodynamics of aluminous pyroxenes: A generalized pair approximation

Abstract

A pair approximation is used to estimate the effects of short-range order on the thermodynamic properties of aluminous clinopyroxenes on the joins diopside (CaMg-Si₂O₆)-jadeite (NaAlSi₂O₆) and diopside-CaTs (CaAl₂SiO₆). The generalized pair approximation is the simplest model for concentrated solutions which includes short-range order. Short-range order is expected to be especially significant in coupled solid solutions, such as aluminous pyroxenes, since atoms of different valence substitute for each other.

The calculations show that the random model, in which the configurational entropy is calculated as if atoms on each crystallographic site mix randomly, is appropriate as a first approximation. The excess entropy relative to the random model behaves regularly, is always negative, and becomes more negative as temperature decreases or the ordering energies increase. The excess entropy relative to the random model can be modeled reasonably well with a simple power series, or Margules-type, formulation. In contrast, the excess entropy relative to a molecular model, in which the ideal activity is assumed to be equal to some mole fraction, is irregular, can be positive or negative, and even changes in sign with variations in temperature and composition.

The configurational enthalpy is positive at high temperatures, and becomes negative with decreasing temperature or increasing ordering energy. The mixing enthalpy can have non-configurational contributions, in addition to the effective short-range configurational contributions considered explicitly.

The pair approximation predicts an ordering transition from C2/c to P2₁/n for CaTs and diopside-CaTs solutions at moderate to low temperatures, respectively. A field where C2/c orders to C2 is also found. A higher order approximation, different relative ordering energies, or quantitative consideration of strain contributions is required to account for the C2/c to P2/n transition in omphacites.

There is no justification for molecular models, in which the configurational entropy is calculated as if endmember “molecules” were mixing in the crystal, in either concentrated or dilute solutions. Molecular models do not represent limiting ordered states for coupled solid solutions.