Spinodal decomposition in an order-disorder phase transition with elastic fields

We study the effect of an elastic field in an order-disorder phase transition described by the dynamics corresponding to a model C system. The elastic field is coupled to both the concentration and the order parameter. By assuming that the elastic field relaxes very fast, we express it in terms of the conserved variable and the order parameter. We concentrate our study on the long-range Eshelby interaction that arises due to the difference of shear moduli in the ordered and disordered phases. This elastic interaction modifies dramatically the spinodal decomposition, by changing the morphology of domains and slowing their growth (which in the absence of an elastic field varies as ${\mathit{t}}^{1/3}$). Changes in morphology are more dramatic when there are competing effects between the wetting regime of model C and the elastic energy. The elastic misfits create an energy barrier of soft phase around the hard phase precipitates. This energy barrier leads the system to very sluggish growth and to an eventual frozen metastable state.