Kinetics of disorder -> order transformations in highly nonequilibrium materials

Citation

Anthony, Lawrence (1993) Kinetics of disorder -> order transformations in highly nonequilibrium materials. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5e9h-nh03. https://resolver.caltech.edu/CaltechETD:etd-08092005-083533

Abstract

Of late, there has been need for rigorous first-principles theoretical considerations of materials that are far removed from equilibrium. This is especially true as nonequilibrium materials of all shapes (e.g., thin film structures) and sizes (e.g., nanocrystalline composites) gain ever-increasing technological importance. To this end, the main contribution of this dissertation is to the study of the kinetics of disorder -> order transformations in highly nonequilibrium binary alloys, specifically body-centered cubic alloys exhibiting B2, D0_3, and/or B32 order at equilibrium. This study takes several independent approaches. Chapter 2 presents two analytical methods. The first of these, a master equation method, is formulated in the Bragg-Williams or point approximation. The second analytical technique employs the path probability method of Kikuchi in the Bethe or pair approximation. Chapter 3 employs kinetic Monte Carlo simulations instead. Apart from the presentation of individual results using these three different techniques, the thermodynamic and kinetic trends exhibited by these different approaches are compared and discussed. One of the more compelling features exhibited by all three of these diverse approaches is the appearance, during ordering, of certain well-developed transient states, which do not persist at equilibrium, e.g., the transient appearance of B2 order during ordering in an alloy that exhibits equilibrium B32 order. These transient states are discussed within the context of pseudostability. Central to the notion of pseudostability is the concept of a free energy surface or manifold in order parameter space. While it is quite straightforward to obtain a closed-form, analytical (albeit approximate) expression for the configurational entropy and free energy in the master equation method and the path probability method, there is no simple, direct means of obtaining the same in the kinetic Monte Carlo simulations. Chapter 4 seeks to remedy this limitation of the Monte Carlo method and introducs a hybrid Monte Carlo-cluster variation method approach to order-disorder kinetics. This method is used to reexamine some of the results of Chapter 3 in the context of the time evolution of the free energy. Chapter 5 summarizes the results of the preceeding chapters and suggests avenues for further investigation.

Thesis Files