Phase transitions and short timescale sinusoidal motions

Abstract

While the effects of phase transitions of mantle materials are considered in convection studies, models of geophysical processes that occur on shorter timescales, such as seismic normal modes and Earth tides, often ignore these effects. A common justification is that the latent heat released from the material changing phase could not conduct away from the boundary on timescales shorter than those of convection, and thus the phase transition would not proceed. In this study, we first examine the behavior of a phase boundary to a periodic pressure perturbation by solving the heat equation. If all the latent heat is released at an infinitely thin boundary, we find that the phase transitions do not proceed. However, if the latent heat is released over a region of 1–5 km thickness, which might occur due to the divariant nature of the phase boundaries, then some of the material changes phase regardless of the period of the forcing. We apply these results to predictions of seismic normal mode center frequencies and elastic Love numbers. The perturbations to the normal mode frequencies can be two orders of magnitude greater than the differences between the observed frequencies and those predicted using the Preliminary Reference Earth Model. However, we have not considered kinetics, the energetics of the mechanisms of the phase transitions, in this formulation. This work suggests a greater knowledge of the kinetics near equilibrium phase boundaries is required because the kinetics may be the limiting factor in these short period, small amplitude motions.