Adiabats of quartz, coesite, olivine, and magnesium oxide to 50 kbar and 1000 K, and the adiabatic gradient in the Earth's mantle

Abstract

The adiabats of olivine, magnesium oxide, and quartz were measured up to 50kbar and 1000 K. An end‐loaded piston‐cylinder apparatus with an in situ pressure gauge and a very fine thermocouple was used to measure (∂T/∂P)s during adiabatic compression. A power law between (∂T/∂P)s and compression yields values of the power n = −∂ ln (∂T/∂P)s/∂ ln ρ that agree with previous results from salts, metals, and fluids. Assuming constant values for n, the adiabtic gradient for an olivine upper mantle and a magnesium oxide lower mantle was calculated. The results agree well with some previous theoretical estimates. The volume dependence of the Grüneisen parameter γ was calculated from the thermodynamic equation ∂ ln γ/∂ ln ρ = ∂B/∂P − n, where B is the isothermal bulk modulus. γ is found to a good approximation to be proportional to volume. Table 6 is available with entire article on microfiche. Order from American Geophysical Union, 2000 Florida Avenue, N.W., Washington, D.C. 20009. Document J82‐002; $1.00. Payment must accompany order.

Thermal expansion, heat capacity, and entropy of MgO at mantle pressures

“…Thus, (7) increases with pressure, opposite to the observed decrease with pressure for 7th (e.g. Boehler 1982). Furthermore, this difference in derivatives has also been found in other minerals, orthoenstatite, diopside, spinel, and forsterite (Chopelas 1988(Chopelas a-c, 1990).…”

“…For calculation of the volume and bulk modulus at various pressures, I used a third order finite strain equation of state (Birch 1978 (Boehler 1982). Table 3 lists the results for MgO at various pressures to 10% compression and 298 K. (Anderson 1987), that is with a slope of 3, recently adopted for the seismic equation of state, is included in the figure and is seen to overestimate e by about 30% at 134 kbar, the pressure at 400 km depth in the mantle.…”

Simple covalent potential models of tetrahedral SiO2: Applications to ?-quartz and coesite at pressure

“…This is expected since 0 is not very sensitive to temperature at room temperature (Kieffer 1979). 7o for quartz is reported by Boehler et al (1979) and Boehler (1982). We adopt the former authors' value since they used a fluid pressure medium rather than the nonhydrostatic solid pressure medium of the latter author.…”

“…is approximated by (Anderson 1968): ? (v)=,/o(v/vJ (8) where ?o is the value of 7 at V0, and the parameter q was varied from 0 to 2, the range appropriate for most crystalline materials (Wallace 1972;Anderson 1974;Boehler 1982). The volume dependence of 0 is then given by (Born and Huang 1954):…”

“…The adopted value, 7o(quartz)=0.675, is consistent with the high temperature (350 K-700 K) average 7(0.68_+0.07) calculated by Watanabe (1982) since ? is nearly independent of temperature (Anderson 1968;Boehler 1982). 7o for coesite was calculated from the following identity:…”