Thermodynamics of nonconvergent cation ordering in minerals: II. Spinels and the orthopyroxene solid solution Available to Purchase

Using published experimental data for Q as a function of temperature, T, and for the excess enthalpy as a function of Q, values for the Landau coefficients have been determined. For NiAl₂O₄, these are h = −69400, a = 444, T_c = 686 K, and c = 7680000; for MgAl₂O₄, h = 8580, a = 19.7, T_c = 395 K, and c = 16400; and for En₅₀Fs₅₀, h = 7750, a = 22.5, T_c = 195 K, and c = 12100, with h and c expressed in units of J/mol, and a in J/mol·K.

The observed a coefficients differ from the values that would be expected if the entropy changes were exclusively configurational and due to long-range ordering. In the case of NiAl₂O₄, the large additional excess entropy is consistent with the suggestion that some other process accompanies Ni-Al ordering. For MgAl₂O₄, a reduced excess entropy would be consistent with some short-range ordering. For En₅₀Fs₅₀, an apparently additional entropy could be accounted for by nonconfigurational contributions, though the uncertainty propagated from calorimetric data is large. Nonlinear compositional dependence for the a and c coefficients allows the effects of Mg-Fe²⁺ ordering on the mixing properties of the enstatite-ferrosilite solid solution to be assessed quantitatively, though a fully analytical description has not been derived.

The Landau expansions are compared with more widely used models of nonconvergent ordering. The principal differences are in the simplification of the excess entropy description (S ∝ Q²) and in the extension of the description of excess enthalpy to three terms, one linear in Q, the second quadratic in Q and one higher order term. In principle, both configurational and nonconfigurational entropy contributions can be accounted for.