KINETICS OF PHASE TRANSITIONS.
Abstract
In broad terms, the purpose of the current work is to investigate and advance the statistical theory of first-order phase transitions. Specifically, we have studied both the statics and kinetics of order-disorder transformations (ODTs) in a system with a first-order phase transition. The statics of the system were studied by the cluster-variation method (CVM), while the kinetics were studied by the path-probability method (PPM). This was the first application of a systematic, kinetic, statistical theory to a first-order transition, so we have chosen the simplest problem of this type: a binary system with nearest-neighbor pair interactions on a two-dimensional trangular lattice. The static characteristics of this ODT have been investigated in great detail by the CVM. A number of equilibrium states were determined for use as endpoints of the kinetic calculations. The generalized free energy has been calculated for a large number of nonequilibrium states. Perhaps most importantly, the phase boundary between the ordered and disordered phases was calculated at six levels of approximation. This provided new information on the convergence of the CVM as the level of approximation is changed. It also required the development of new programming techniques which were necessary to carry out the derivation and solution of the higher approximations. The pair approximation of the PPM, which has been used extensively in the past, yields especially simple and tractable results. However, the nature of the system required us to make the first attempt to advance the PPM beyond the pair approximation. The three-point approximation of the PPM was developed and formulated for a numerical solution. The course of the ODT was studied for the following types of heat treatments: up-quenching an ordered state to a temperature in the disordered region, quenching a disordered state to a temperature in the ordered region, annealing a nonequilibrium state at its fictive temperature, and cooling a disordered state so that ordering is suppressed as is done in experimental work on glass transitions. The differential equations for the most probable path were used to make a first-order expansion around the equilibrium state. The expansion was then used to determine the relaxation times for the system as functions of temperature. These results include a new effect: one relaxation time shows critical slowing-down above the lower critical temperature and below the upper critical temperature. The differences and similarities between first- and second-order phase transitions are clarified.
Degree
Ph.D.
Subject Area
Materials science
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