S U M M A R YWe examine the problem of obtaining the thermal structure and bulk chemical composition of the lower mantle from its seismologically determined velocity and density profiles, and the most recent results on the elastic properties of the relevant phases (including, of particular importance, shear moduli). A novel aspect of this paper is the application of an iterative technique solving generalized non-linear inverse problem, which allows us to simultaneously consider a complex chemical system (the MgO-FeO-SiO 2 -Al 2 O 3 -CaO system, which includes all major components in the lower mantle), and to rigorously evaluate the full covariance and resolution matrices. The effects of experimental uncertainties in the shear moduli are carefully accounted for. We show that although the a posteriori uncertainties in the results for lower-mantle compositions are relatively large, the averaged lower-mantle Mg/Si ratio should be lower than 1.3 in order to satisfactorily fit the 1-D seismic profiles. Two distinct families of best-fitting models are determined. The first is based upon a value for the pressure derivative of the perovskite shear modulus that is representative of various existing experimental measurements (µ 0 = 1.8). Under this assumption, it is not possible to match the lower mantle seismic properties with an adiabatic geotherm and uniform chemical composition. Instead, this family of solutions is characterized by a geotherm with large temperature gradients (dT/dz increases from 0.5 to 0.9 K km −1 between 800 and 2700 km and the temperature reaches 3400 K at the depth of 2700 km), and a depth dependent bulk composition with an Mg/Si ratio decreasing from 1.18 ± 0.14 to 1.03 ± 0.16 between 800 and 2700 km. The second family of solutions is obtained when we attempt to fit the lower mantle with a simpler compositional and thermal structure. This can only be done when the pressure derivative of the shear modulus for perovskite is close to the most recent values obtained by Brillouin spectroscopy, that is, with a µ 0 close to 1.6 instead of 1.8. The resulting temperature gradient is 0.25 K km −1 in the upper part of the lower mantle and 0.5 K km −1 below 1700 km depth; the geotherm reaches 2800 K at a depth of 2700 km. Corresponding Mg/Si ratio remains rather constant and close to 1.16 throughout the lower mantle. We show that the temperature gradient is strongly correlated with the pressure derivative µ 0 of the shear modulus of perovskite: lower values of µ 0 imply lower thermal gradients. We also discuss the importance of the Bullen parameter as an additional constraint. In order to refine conclusions on the lower-mantle structure, additional independent observables, such as accurate observations on electrical conductivity and 1-D Q profiles, are necessary.
Fully optimized quantum mechanical calculations indicate that Al2O3 transforms from the corundum structure to the as yet unobserved Rh2O3 (II) structure at about 78 gigapascals, and it further transforms to Pbnm-perovskite structure at 223 gigapascals. The predicted x-ray spectrum of the Rh2O3 (II) structure is similar to that of the corundum structure, suggesting that the Rh2O3 (II) structure could go undetected in high-pressure x-ray measurements. It is therefore possible that the ruby (Cr3+-doped corundum) fluorescence pressure scale is sensitive to the thermal history of the ruby chips in a given experiment.
We describe fundamental thermodynamic relations (Helmholtz free energy as a function of volume and temperature) for solids and liquids, simple physically based expressions which contain all thermodynamic information about a system. The solid fundamental relation consists of Debye and Birch-Murnaghan finite-strain theory combined in the Mie-Grfineisen framework. The liquid fundamental relation is derived by taking the high-temperature limit of the solid expression. We derive the liquid equation of state, which contains only four parameters, from the liquid fundamental relation and show that it successfully describes measurements of liquid alkali metals, water, and liquid diopside over a wide range of pressure and temperature. We find optimal fundamental relation parameters for diopside, enstatite, i!menite, and perovskite and find the solid relation to be in excellent agreement with data, including heat capacities, thermal expansion, and MgSiO3 phase equilibria. We then combine the liquid and solid fundamental relations to calculate the melting curves of diopside, enstatite, and perovskite, which are found to be in excellent agreement with experiment. All predicted melting curves have dT/dP slopes which decrease steadily with pressure, eventually becoming negative because of liquid-crystal density inversion. Our predicted melting temperature of perovskite in the D" region (3750 K) at the base of the mantle is thousands of degrees lower than previous estimates, yet it is consistent with experimental data. The predicted melting curve, although consistent with the lack of widespread melting in the lower mantle, is much lower than recently proposed geotherms in the D" layer at the base of the mantle. By combining our results with seismic observations of the deep mantle, we propose that the D" layer consists of magnesiowfistite and silica in the form of stishovite or its recently discovered high-pressure modification. INTRODUCTION Melting is one of the most important agents of chemical and thermal planetary evolution. The production and subsequent transport of mobile liquids lead to efficient mass and heat transport in planetary interiors. It has loon been thought that all less basic Earth material is ultimately derived, via incongruent melting processes, from ultrabasic material, taken as representative of the Earth's bulk chemistry [Bowen, 1928, chapter 17]. Subsequent geologic and geochemical evidence has confirmed that igneous processes are primarily responsible for the origin and evolution of the acidic continental crust [Fyfe, 1978; Depaolo, 1981] and for the ongoing formation of the basaltic oceanic crust [Hess, 1962]. More recently, the possibility that larger fractions of the silicate Earth have undergone chemical differentiation by igneous processes has been examined in detail [Stolper et al., 198!;Nisbet and Walker, 1982]. Indeed, there seems to be no shortage of energy sources sufficient to melt the entire Earth early in its history, including accretion [Hanks and Anderson, 1969], core formation [Flasar and...
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