Non-exponential rate behaviour

Abstract

Three of the mechanisms which lead to non-exponential rate behaviour in phase transitions are identified and reviewed in some detail. The first mechanism is related to spatial variations of the order parameter susceptibility. It is shown that the volume averaged rate behaviour of the order parameter is simply the Laplace transform of the probability distribution of the susceptibility. Analytical solutions for Gaussian, Maxwellian and power-law probabilities are derived.

The second mechanism is based on the intrinsic non-linearity of the kinetic driving force. A general time dependent Landau-Ginzburg rate equation is reduced to the Extended Fisher-Kolmogorov (EFK) equation. It is shown that oscillatory front propagation occurs for a large range of physically meaningful model parameters. The rate behaviour depends crucially on the local conservation properties of the order parameter.

Non-exponential relaxations and rate behaviour also results from the time evolution of domain patterns. The lateral movement of twin boundaries is usually prevented by strong pinning forces but bending of walls and the formation of needle domains are typical time dependent processes. Dynamical excitations close to domain walls and the kinetics of wall straightening are discussed.

Key Words:

• Kinetic rate behaviour
• Domain pattern formation
• Twin boundaries
• Needle domains
• Glass-phase transitions