Application of Landau theory to cation ordering in omphacite II: Kinetic behaviour
Carpenter, Michael A.; Domeneghetti, Maria-Chiara; Tazzoli, Vittorio
published: Mar 8, 1990
manuscript accepted: Sep 4, 1989
manuscript received: Jan 18, 1989
ArtNo. ESP147050201003, Price: 29.00 €
Abstract The kinetics of cation disordering have been followed in single crystals of omphacite which were annealed in evacuated silica tubes at 900, 950 and 1000 °C. The X-ray intensities, Ik, of superlattice reflections were used to monitor changes in the macroscopic order parameter, Q, with annealing time (Ik α Q2). A purely empirical analysis of the kinetic data gives a rate law of the form ln(Q2) α t1/2 and an enthalpy of activation of ~615 ± 65 kJ.mole-1. The data are also approximately described by Q2 α n lnt for a range of t. Time-dependent order parameter theory provides a more rigorous basis for analysing the disordering transition and the data have been compared with a specific solution of the Ginzburg-Landau equation : which gives This equation describes continuous disordering in crystals which remain homogeneous with respect to Q and in which the effective entropy of activation varies with Q2. Numerical solutions give good agreement with observations using ΔH* = 540 kJ.mole-1, Tc = 1138 K, Q0 = 0.83, a = 22.8 J.mole-1.K-1 and c = 25.9 kJ.mole-1, if εs = 20 J.mole-1K-1 and exp(-ΔS*/R)γλ = 9×10-19 secs. The analysis provides an example of how Landau theory for equilibrium behaviour can be coupled with the Ginzburg-Landau equation for kinetics to describe structural phase transitions in minerals under non-equilibrium conditions.