Application of Landau theory for the analysis of phase transitions in minerals

Abstract

Landau-type theories reproduce experimental observations of phase transitions in minerals with sufficient accuracy to be useful for many applications. The displacive limit can be described by two temperatures, namely the transition temperature, T c, and the saturation temperature, θ s, with the Gibbs free energy written as G = 1 2 Aθ s [ coth( θ s T ) − coth( θ s T c )]Q 2 + 1 4 BQ 4 + … . Saturation of the order parameter Q occurs near T s ≈ 1 2 θ s . Pseudo-spin systems (e.g., those exhibiting cation ordering) can be approximated in a similar (nonanalytical) theory, if the order parameter couples with the strain field. The effect of defects, lattice imperfections, etc., is discussed with emphasis on their influence on phase diagrams (i.e., the plateau effect). Coupling between two order parameters is common in minerals and leads to modifications of the transition behaviour. It is shown that kinetic processes with continuous order parameters can be analysed using a general rate equation which contains δG δQ ( G is often a Landau potential, Q is the order parameter) as a driving force. This extended theory, thus, draws a connection between the equilibrium Landau-type theories and kinetic rate theories. Theoretical and experimental results are reviewed.