Theory for the Slowing Down of the Relaxation and Spinodal Decomposition of Binary Mixtures

The weak nonexponential relaxation $\propto t^{-a^{\prime }}$ recently found in computer experiments on the phase separation of alloys is explained in terms of a cluster reaction and diffusion process. The nonlinear features of this process can be accounted for by a time-dependent diffusion constant. Estimates for the resulting exponents [$a^{\prime }=\frac{1}{\mathrm{}(3+d)\mathrm{}}$] are consistent with the computer simulations. The experimental observability of this slowing down is discussed.