A RATE-EQUATION FOR ATOMIC ORDERING IN MEAN FIELD-THEORY .2. GENERAL-CONSIDERATIONS

The general question addressed here is: what is the appropriate rate equation when one has mixed kinetics of the order parameter, i.e. of both conserved and non-conserved types? The study is motivated by first considering various examples of atomic ordering processes in which it makes sense to analyze the importance of mixed kinetics. The discussion is based on Glauber and Kawasaki types of stochastic processes in a kinetic Ising model with long range interactions, described very well by the mean field approximation. It is found that in the limiting case in which one is not far from the uniform state (i.e. spatially homogeneous) and thermal equilibrium, the rate equation can be cast into the form assumed sometimes in phenomenological rate theories of mixed kinetics. This identification allows for a analysis of various length scales, time scales and mixing coefficients that occur in mixed kinetic processes. In the far-from-equilibrium situation, however, the derived rate equation has a rather complex structure, not amenable to a simple interpretation. Finally, the possibilities of observing mixed kinetics are indicated by way of examples borrowed from atomic ordering phenomena in certain minerals, and a few general conclusions are drawn.