Thermodynamics of order-disorder in minerals; I, Symmetric formalism applied to minerals of fixed composition

Abstract

Thermodynamics of order-disorder in minerals may be approached by treating the mineral as a solid solution between an independent set of end-members with which the range of possible states of ordering of the phase can be represented. Thus, a mineral of fixed composition (a one-component phase), requiring s independent order parameters to represent the state of order in the mineral, involves an independent set of s + 1 end-members. This approach is applied by means of symmetric formalism, with the entropy part of the Gibbs energy taken to be the ideal configurational entropy of mixing using a mixing-onsites formulation, and the enthalpy part taken to be that of a regular solution between the s + I end-members. Symmetric formalism is shown to be formally identical to the generalized Bragg-Williams or point approximation, and its treatment of convergent and nonconvergent cation ordering is compared with that of the Landau theory. Its flexibility in describing a wide range of order-disorder behavior is illustrated with applications to sillimanite, spinel, albite, and potassium feldspar, the latter two involving order-parameter coupling.