Theory of unstable growth. II. Conserved order parameter.

Abstract

The theory of domain growth developed previously to treat a nonconserved-order-parameter (NCOP) system is extended to treat the conserved-order-parameter (COP) case (spinodal decomposition). The theory here, as for the NCOP case, leads to universal scaling behavior for the order-parameter structure factor, which depends only on the spatial dimensionality of the system. The short-distance ordering in the system is found to be identical to that found for the NCOP case indicating that the structure near the interface is independent of the driving dynamics. Porod's law, signifying sharp interfaces, is of exactly the same form as for the NCOP case. There are significant differences between the two cases, however. In the COP case the growth mechanism works through a coupling between the ordering component and a diffusing component. This coupling increases the growth law, L(t), from the rather slow surface-diffusion form, ${\mathit{t}}^{1/4}$, to the classical Lifshitz-Slyzov-Wagner form, ${\mathit{t}}^{1/3}$. In the NCOP case, the ordering component is strongly decoupled from any fluctuating component. While the structure factors for the two cases are the same for small values of the scaled lengths (x=R/L\ensuremath{\ll}1) they differ significantly over the rest of the range of x. In the COP case the theoretical expression for the scaled structure factor F(x) agrees well with the best available simulational results. A striking feature of the theory in the NCOP case was the existence of a nonlinear eigenvalue problem associated with the determination of the scaling function F(x). In the COP case one has two such eigenvalues. The additional eigenvalue can be associated with the coefficient ${\mathit{x}}^{2}$ in the expansion of F(x) in powers of x. The nonzero value of this coefficient renders invalid the symmetry [1-F(x)]=-[1-F(-x)] found in the NCOP case.