ON THE UNSTABLE PROPAGATION OF A PHASE-TRANSITION IN A SOLID

To explore a possible mechanism of deep earthquakes, this paper analyz es the unstable propagation of a stress-induced phase transition which is initiated in a homogeneous stress field. This Stephen problem is f ormulated as an initial-value problem for the phase boundary, and the driving force of the boundary is computed by using the solution of the boundary-value problem for a partially transformed material. The prop agation of the phase transition under uniform pressure is numerically simulated. It is shown that (1) under lower pressure, the transition i s terminated at a certain size, but it can propagate unstably when an initially transformed region is sufficiently large; and (2) when the p ressure attains a critical value, the propagation becomes unstable, an d goes in a particular direction depending on the initial shape. These results confirm the possibility of the unstable propagation of phase transition, and provide a theoretical basis for the hypothesis that th e phase transition of a mantle material can trigger a deep earthquake.