Thermodynamic modelling of non-convergent ordering in orthopyroxenes: a comparison of classical and Landau approaches

Abstract

Abstract. The excess Gibbs free energy due to non-convergent ordering is described by a Landau expansion in which configurational and non-configurational entropy contributions are separated:Neglecting higher order terms in Qt, this expansion is formally equivalent to the reciprocal solution model for the distribution of Fe 2+ and Mg over the non-equivalent M1 and M2 sites of orthopyroxenes:The Qt term describes a temperature and compositiondependent thermodynamic field that prevents the crystal from attaining full disorder at a finite temperature. The X term models the dependence of the field on composition. It causes the isotherms in a Roozeboom diagram X~ 2 vs. X~ ~ to be asymmetric. The Q[ term incorporates nearestneighbour interactions. Higher order interactions are accounted for by the Q~ term, which is not routinely foreseen in the reciprocal solution model. The critical temperature ~ is interpreted as a ratio of enthalpy and entropy contributions to the free energy, AG~ of a reciprocal reactionThe comparison of Landau and classical approaches is extended to convergent ordering models which are shown to be incorporated in expressions for non-convergent ordering.

Mineral activity–composition relations and petrological calculations involving cation equipartition in multisite minerals: a logical inconsistency

“…Sack, 1980; Chatillon‐Colinet et al. , 1983; Carpenter & Salje, 1994; Kroll et al. , 1994; Sack & Ghiorso, 1994; Stimpfl et al.…”

Dellagiustaite: A Novel Natural Spinel Containing V2+

“…However, it is not a negligible one, as the value of i depends on equilibration temperature, oxygen fugacity, crystal growth kinetics, covalence effects and stabilization energies at the M-sites ( [2] and references therein). Cation order-disorder phenomena in spinel-group minerals represent a non-convergent ordering transformation [3,4] and knowledge of the equilibrium energetics allows for the estimation of the equilibration temperature, from which geothermometric determinations can be obtained. The inversion parameter is also important because physical properties of spinel, such as magnetism, electrical conductivity, bulk modulus, thermal expansion, and compressibility, are largely affected by the order-disorder cation distribution [5].…”