Kinetics of ordering

Abstract

The kinetics of certain complex ordering processes during structural phase transitions in alloys necessitates a fresh look at the validity of the widely used phenomenological equations of the time-dependent Ginzburg-Landau and Cahn-Hilliard types. We start with a longish introduction so as to motivate the need for studying mixed kinetics in which both Glauber and Kawasaki processes occur, as well as segregation of an AB mixture in the presence of anisotropic fields, e.g., gravity. We argue then that the most systematic method of tackling these problems is via the master equation approach to kinetic Ising models. Using such an approach we derive order parameter rate equations for both mixed kinetics and segregation under gravity. Our results show that only under certain limiting conditions do these equations reduce to the usual phenomenological forms. The consequences of complex ordering processes are also discussed.