Phase-field model for activated reaction fronts

@article{citeulike:2317666, abstract = {We propose a phase-field model to describe reaction front propagation in activated transitions obeying Arrhenius kinetics. The model is applicable; for example; to the explosive crystallization of amorphous films. Two coupled fields interact during the reaction; a temperature field T ( x ; t ) and a field C ( x ; t ) describing the amorphous/crystal transition; which are continuous functions of space x and time t . Unlike previous work; our model incorporates a nonzero front width ε in a natural way; corresponding to that region in space where T and C undergo rapid variation. In the limit of ε→0; our model reduces to the sharp interface approach of others. Treating the background temperature of the reacting sample as a control parameter; periodic solutions in C and T can be found which go through a series of period doubling bifurcations. We find that the substrate temperature marking the onset of period doubling bifurcations decreases with increasing concentration diffusion. Furthermore; it is shown that period doubling bifurcations of C - T solutions of period greater than 2 are generated by dynamics isomorphic to those of the one-dimensional logistic map; for all values of concentration diffusion studied. {\copyright} 1996 The American Physical Society.}, author = {Provatas, Nikolas and Grant, Martin and Elder, K. R. }, citeulike-article-id = {2317666}, doi = {http://dx.doi.org/10.1103/PhysRevB.53.6263}, journal = {Physical Review B}, keywords = {phase-field}, month = {March}, number = {10}, pages = {6263+}, posted-at = {2008-02-01 03:48:12}, priority = {2}, publisher = {American Physical Society}, title = {Phase-field model for activated reaction fronts}, url = {http://dx.doi.org/10.1103/PhysRevB.53.6263}, volume = {53}, year = {1996} }

TY - JOUR ID - citeulike:2317666 L3 - citeulike-article-id:2317666 TI - Phase-field model for activated reaction fronts JF - Physical Review B VL - 53 IS - 10 SP - 6263 PB - American Physical Society N2 - We propose a phase-field model to describe reaction front propagation in activated transitions obeying Arrhenius kinetics. The model is applicable; for example; to the explosive crystallization of amorphous films. Two coupled fields interact during the reaction; a temperature field T ( x ; t ) and a field C ( x ; t ) describing the amorphous/crystal transition; which are continuous functions of space x and time t . Unlike previous work; our model incorporates a nonzero front width ε in a natural way; corresponding to that region in space where T and C undergo rapid variation. In the limit of ε→0; our model reduces to the sharp interface approach of others. Treating the background temperature of the reacting sample as a control parameter; periodic solutions in C and T can be found which go through a series of period doubling bifurcations. We find that the substrate temperature marking the onset of period doubling bifurcations decreases with increasing concentration diffusion. Furthermore; it is shown that period doubling bifurcations of C - T solutions of period greater than 2 are generated by dynamics isomorphic to those of the one-dimensional logistic map; for all values of concentration diffusion studied. © 1996 The American Physical Society. KW - phase-field AU - Provatas, Nikolas AU - Grant, Martin AU - Elder, KR PY - 1996/03/01/ UR - http://dx.doi.org/10.1103/PhysRevB.53.6263 ER -