Role of Phase Transitions in a Dynamic Mantle

The interaction of solid‐solid phase transitions with convection in the Earth's mantle involves, for univariant systems: (1) effects of latent heat and advection of ambient temperature on the position of the phase boundary and on its associated body force, and (2) the coupling of latent heat with the ordinary thermal expansivity of the material. For divariant systems, an effective thermal expansion coefficient and a modified adiabatic temperature gradient may be defined for the phase transition zone. Linear stability theory for a fluid layer with a univariant phase change is reviewed and applied to the endothermic spinel‐oxide transformation. The theory of the stability of a fluid layer with a divariant phase transformation is developed and critical Rayleigh numbers are given for a model of the olivine‐spinel transition. Of special interest is the case where the Earth's temperature gradient exceeds the adiabatic temperature gradient outside the phase transition zone but is smaller than the increased adiabatic temperature gradient in the two‐phase olivine‐spinel region. The thermal structure of the descending lithosphere is calculated, including the effects of frictional heating on the slip zone and of the olivine‐spinel and spinel‐oxide transitions; temperature contrasts of 700 °K can exist between the slab and adjacent mantle at 800 km depth. The net body force on the descending slab due to thermal contraction and the major mineralogical phase changes is downward. The olivine‐spinel transition may be responsible for the tensional focal mechanisms of intermediate depth earthquakes while the spinel‐oxide transformation may be related to the compressional focal mechanisms of deep earthquakes.