Domain Growth and Dynamical Scaling during the Late Stages of Phase Separation.

The dynamics of a first order phase transition are studied for a two dimensional system with a continuous, conserved order parameter (model B). Using numerical simulations, domain growth and scaling are investigated by monitoring several measures of the morphology. Different quenches of the system are performed to examine the role of thermal fluctuations and of asymmetry between the phases. For symmetric quenches, convoluted domains are formed, whose characteristic length grows as R(t)~ t ^{1/3} during the late stages. It is only in this time regime that scaling of the correlation function is established. The scaling function and the asymptotic growth law are found to be independent of the strength of thermal fluctuations, although the latter affect the approach to the asymptotic regime. The influence of domain morphology on the growth process is examined for asymmetric quenches. Near the classical spinodal, circular domains coarsen through an evaporation-condensation mechanism. Self -similar growth of the system is observed. For nearly symnmetric quenches, initially convoluted domains are created, which evolve to circular clusters as a function of time. The late stages of phase separation are also examined analytically for the case of no thermal fluctuations in the final state. The problem is characterized by two intrinsic lengthscales in the field theory: the interfacial width and the average domain size. The approach adopted in this thesis extracts the time dependence of the domains by focussing on the dynamics of the interfaces separating coexisting phases. For percolating interfaces, a general dispersion relation is calculated for small amplitude fluctuations in the interfacial position. In addition, by considering the self-interactions of a single, convoluted interface, a scaling form is derived for the curvature correlation function which gives a growth exponent of 1/3 and is consistent with self-similar growth. The analytic work is discussed in the context of the symmetric quench of the model.