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

✍ Scribed by Herbert Kroll; Hartmut Schlenz; Michael W. Phillips

• Publisher: Springer-Verlag
• Year: 1994
• Tongue: English
• Weight: 607 KB
• Volume: 21
• Category: Article
• ISSN: 0342-1791
• DOI: 10.1007/bf00203931

✦ Synopsis

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: GL= hQ~+ 89

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 recipro-

The comparison of Landau and classical approaches is extended to convergent ordering models which are shown to be incorporated in expressions for non-convergent ordering.