Structure and sharpness of phase transitions and mantle discontinuities

The structure of phase transitions expected from equilibrium thermodynamics is examined. We show that in binary systems, the shape of the coexistence region (phase loop) is controlled primarily by the partition coefficient K. We derive a general and simple one-parameter expression for the pressure dependence of the yield of the high-pressure phase and show that this function can be highly nonlinear: most of the transition occurs in a narrow interval near the boundary of the phase loop. Estimates of the effective width of binary phase transitions are less than half the total width of the coexistence region even for relatively mild partitioning (K < 1/4). We generalize these results to multiphase and multicomponent transitions. We show that the presence of nontransforming phases can affect the width of the transition substantially. We predict that the width of the olivine to wadsleyite transition in the presence of pyroxene and garnet is approximately half that of the binary phase loop at typical transition zone temperatures. The estimated effective width of this transition in the mantle (4-8 km) is marginally consistent with observations of high-frequency (0.5-1.0 Hz) P wave reflections from the 410 km discontinuity. We show that the effective width of the garnet to perovskite transition is sufficiently narrow to reflect S wave energy in the frequency range of ScS reverberations (10-40 mHz) and that this transition can account for the observed properties of the 710 km discontinuity.