Phase Transitions in Minerals: From Equilibrium Properties Towards Kinetic Behaviour Progress Report

Abstract

Landau theory is derived from a simple atomistic model. The Gibbs free energy can be written in the displacive limit as where Ts = 1/2Θs is the saturation temperature due to quantum fluctuations. The coefficients A, B,… and degeneracies of the order parameter are determined by the conventional symmetry constraints. For T > Θs, G is the classic Landau potential. Solutions for non-displacive systems and coupled order parameters are discussed. – The theory is applied to some model-minerals such as quartz, Na-feldspar, and calcite as typical examples. It is argued that the structural complexity of minerals is often related to several thermodynamic degrees of freedom. The transition leads to coupling phenomena, which are reviewed in some detail. – Non-equilibrium features in crystals which are “nearly” in thermodynamic equilibrium are domain walls. It is shows that domain walls react very sensitively to small changes in the thermodynamic state of the material. New structural configurations are generated in the wall which do not exist in the bulk. – 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 parameters) as a driving force. This theory draws, thus, a connection between the equilibrium Landau-type theories and kinetic rate theories.