Self-oscillatory instability of the driven phase front propagation induced by liberation of latent heat

We theoretically address crystals exhibiting first-order phase transformations subjected to a steadily propagating temperature gradient. The latter drives a nonisothermal propagation of a phase front. We theoretically demonstrate that for the phase transformations of the displacive type, the phase front always steadily follows the isotherm. In contrast, in the case of the order-disorder or hybrid phase transformations in a crystal containing pinning defects, one finds a velocity of the isotherm, the first critical velocity, at which the steady front motion becomes unstable, and a stick-slip front propagation starts. Upon reaching the second critical velocity, the stick-slip behavior vanishes, and the motion becomes steady again. Our results enable one to determine the activation energy of the leading order-disorder process from the measurements of the driven motion of the phase front. In light of these results, we discuss experimental findings for PbTiO_{3} and NaNbO_{3}.