Kinetics Studied by PPM

Division of Materials Science and Engineering, Graduate School of Engineering, Hokkaido University Kita-13 Nishi-8, Kita-ku, Sapporo 060 Japan 

As is well recognized, various macroscopic properties such as mechanical properties are controlled by microstructure, and the stability of a phase which consists of each microstructure is essentially the subject of electronic structure calculation and statistical mechanics of atomic configuration. The main subject focused in this article is configurational thermodynamics and kinetics in the atomic level, but we start with a brief review of the stability of microstructure, which also poses the configurational problem in the different hierarchy of scale. 

Transmission electron microscopic observaiion reveals various morphologies of precipitates depending upon the constituents and composition of an alloy system, history of heat treatments etc. Typical examples are spherical precipitates found in Nl-Cr-Al system and cuboidal precipitates in Fe-Mo system [1]. The first question raised is what determines the shape of a precipitate. 

It should be realized that unlike the study of equilibrium thermodynamics for which a model is often mapped onto Ising system, elementary mechanism of atomic motion plays a deterministic role in the kinetic study. In an actual alloy system, diffusion of an atomic species is mainly driven by vacancy mechanism. The incorporation of the vacancy mechanism into PPM formalism, however, is not readily achieved, since the abundant freedom of microscopic path of atomic movement demands intractable number of variational parameters. The present study is, therefore, limited to a simple spin kinetics, known as Glauber dynamics [14] for which flipping events at fixed lattice points drive the phase transition. Hence, the present study for a spin system is regarded as a precursor to an alloy kinetics. The limitation of the model is critically examined and pointed out in the subsequent sections. 

Since a considerable amount of review articles on both theoretical frameworks and calculated results have been reported[15-25], the main objective of the present study is placed on the comparisons with experimental results. The organization of the present report is as follows In the next section, for the sake of completeness, a brief theoretical description of the PPM is summarized from the previous articles. In the third section, disorder-LIq transition is focused and visualized atomic (spin) configuration is compared with recent high resolution electron micrograph. In the fourth section, ordering relaxation 

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