PHASE-FIELD MODEL FOR ACTIVATED REACTION FRONTS

We propose a phase-field model to describe reaction front propagation in activated transitions obeying Arrhenius kinetics. The model is appl icable, for example, to the explosive crystallization of amorphous fil ms. Two coupled fields interact during the reaction, a temperature fie ld T(x,t) and a field C(x,t) describing the amorphous/crystal transiti on, which are continuous functions of space x and time t. Unlike previ ous work, our model incorporates a nonzero front width E in a natural way, corresponding to that region in space where T and C undergo rapid variation. In the limit of epsilon-->0, our model reduces to the shar p interface approach of others. Treating the background temperature of the reacting sample as a control parameter, periodic solutions in C a nd T can be found which go through a series of period doubling bifurca tions. We find that the substrate temperature marking the onset of per iod doubling bifurcations decreases with increasing concentration diff usion. Furthermore, it is shown that period doubling bifurcations of C -T solutions of period greater than 2 are generated by dynamics isomor phic to those of the one-dimensional logistic map, for all values of c oncentration diffusion studied.