Modelling microstructural evolution in binary alloys
In this thesis morphologies, coarsening mechanisms and kinetics are examined in a systematic way, when phase separation and subsequent microstructural coarsening is modelled using deterministic mean field and stochastic Monte Carlo methods. For the mean field approach a microscopic diffusion equation due to Khachaturyan is employed, and a variation of it with an environment dependent mobility. Monte Carlo simulations are carried out with vacancy and Kawasaki dynamics, and a residence time algorithm is applied in the vacancy case. In mean field models microstructural evolution results from a direct minimization of a free energy functional, and the mechanism of atomic diffusion does not appear explicitly. In Monte Carlo models, changes in site occupancies are effected by direct exchanges of neighbouring atoms (Kawasaki dynamics), or through vacancy motion. In this thesis the correspondence between mean field and Monte Carlo models in describing phase transformations in binary alloys is examined. Several examples of cases in which these differences between deterministic and stochastic models affect the phase transformation are given, and the underlying differences are analyzed. It is also investigated how the choice of diffusion mechanism in the Monte Carlo model affects the microstructural evolution. Most Monte Carlo studies have been carried out with Kawasaki dynamics, although in real metals such direct exchanges are very unlikely to occur. It will be shown how the vacancy diffusion mechanism produces a variety of coarsening mechanisms over a range of temperatures, which the Kawasaki dynamics fails to capture. Consequently, kinetics and resulting morphologies, especially at low temperatures, are affected. Finally, the question of physicality of time scales in mean field and Monte Carlo models is addressed. Often a linear dependence between Monte Carlo time and real physical time is assumed, although there is no rigorous justifcation for this. In mean field models, time is defined through the atomic mobility. By examining the effect of a realistic diffusion mechanism in systems undergoing phase transformation, a critical discussion of time scales in microscopic mean field models and a Monte Carlo model with Kawasaki dynamics is presented.