Temperatures Induced by Shock Waves in Minerals: Applications to Geophysics

Abstract

The temperatures of initially transparent minerals of geophysical interest are measured using a six-channel optical pyrometry system operating over the range 450 to 790 nm. The radiative temperatures and emissivity of minerals are measured by recording spectral radiances versus time during the time interval that an intense shock wave is driven through the sample. The shock wave is induced by the impact of a projectile accelerated by a two-stage light-gas gun. Taken together with the pressure-density Hugoniot data, complete pressure-density-temperature equations of state may be constructed over the entire pressure range present within the earth. Shock temperature and shock pressure data for NaCl extending to 1,040 kbar (104 GPa) demonstrate that a transition from the B1 to B2 phase occurs below 300 kbar (with a phase transition energy of ~0.2 MJ/kg) and melting of the B2 phase occurs above 550 kbar. Shock temperatures for the high-pressure phase assemblage of Mg_2SiO_4, believed to be MgO (periclase) and MgSiO_3 (perovskite), are closely matched by theoretical calculations that assume a phase transition energy from olivine to this assemblage of ~1.5 MJ/kg. Shock temperature data for α -quartz and fused quartz shocked into the stishovite regime display dramatic decreases in shock temperatures at ~700 and ~1,050 kbar, which are interpreted as representing shock-induced melting of stishovite. The observed data can be fit theoretically by assuming that stishovite is driven into the super-heated regime ~1,000 K above the melting point and melts suddenly to a temperature of 4,400 K (at 700 kbar) with a latent heat of melting of 3.5 MJ/kg. Assuming that SiO_2 stishovite is a component in a ternary MgO-SiO_2-FeO mantle and taking into account the expected decrease in the solidus of this system relative to the oxides, the minimum melting point obtained implies a maximum lower mantle temperature of 3,500 K. The slight increase in the melting point of stishovite may be used in conjunction with a Weertman-type relation between homologous temperature and creep viscosity to estimate the effect of pressure on viscosity. Such an analysis for SiO_2 suggests an activation volume for the lower mantle of the earth of ~1 to 4 cm^3 /mole for Mg_2SiO_4. This value is a factor of 2 to 4 less than inferred from measurements of the activation volume of an upper mantle mineral such as olivine. This small activation volume implies a maximum increase of viscosity with depth in the lower mantle of a factor of between ~1 to ~10^4 depending on the assumed rheological model, activation energy, and the temperature. Whereas a slight increase with depth of viscosity in the earth's lower mantle as compared with the upper mantle supports theories of convection throughout the mantle, an increase in viscosity by a factor of 10^4 probably precludes single-cell, mantle-wide convection.

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