A. Chopelas

Thermal expansivity in the lower mantle

The pressure dependence of the thermal expansion coefficient, α, previously reported as (∂lnα/∂lnV)T = 5.5 ± 0.5 by Chopelas and Boehler [1989] is refined, using systematics in the volume dependence of (∂T/∂P)s measured for a large number of materials at high pressures and high temperatures. Since (∂ln (∂T/∂P)s/∂(V/V0))T is found to be constant and material independent over a very large compression range, (∂lnα/∂lnV)T is proportional to the compression, V/V0. We find α decreases by a factor of 5 for MgO throughout the mantle, reaching a value of 1.0 · 10−5 K−1 at its bottom. Densities of perovskite (PV) and magnesiowustite (MW) are calculated for lower mantle conditions using our new α(P, T), a room temperature finite strain equation, and recent data on the Mg-Fe partitioning in the PV-MW system. Both minerals have nearly identical densities to those of PREM throughout the entire lower mantle, which allows variable PV:MW ratios. A lower mantle made entirely of PV with a molar ratio of Mg:Fe of 88:12 would be about 0.11 g/cm3 or 2.5% denser than this mixture, but this density would just be within the uncertainty in PREM. A change in chemistry at 660 km depth to a PV mantle requires a thermal boundary which would improve the match in the densities between PV and PREM. These density agreements therefore preclude evaluation of a mineralogical model for the lower mantle using density comparisons. Recent measurements on melting of Fe, FeO, and FeS, however, suggest temperatures at the core-mantle boundary below 3500 K, which tends to favor a geotherm without a large thermal boundary at 660 km depth.

Vibrational spectroscopy of end-member silicate garnets

Infrared reflectance (IR) and Raman spectra were collected on small (ca. 500 micron) single crystals of 5 natural garnets with nearly end-member compositions: pyrope (98% Mg3Al2Si3O12), almandine (83% Fe3Al2Si3O12), spessartine (98% Mn3Al2Si3O12), grossular (97% Ca3Al2Si3O12), and andradite (99% Ca3Fe2Si3O12). Frequencies and symmetry assignments were determined for all 17 IR modes and all 25 Raman modes. By using factor group analysis and by correlating the bands by their intensities, bands were assigned to either one of the SiO4 internal motions, as a rotation, or to a type of translation. The assignments are supported by (1) the distinct trends of frequencies with cell size and cation masses for each of the different types of motion, (2) the similarity of garnet energies for each of the different types of motion to those of olivine with the same cation, and (3) the closeness of the T1u IR frequencies to the T2g Raman frequencies. Mode mixing appears to be weak. Correlations between frequencies and structural parameters suggests a direct dependence of force constants on lattice parameter. This relationship arises from bond lengths in the garnet structure being constrained by the size and compressibility of adjacent polyhedra through edge-sharing. Comparison of our endmember data with previous powder IR studies of intermediate garnets indicates that dodecahedral (X) and octahedral (Y) sites alone exhibit two-mode behavior for those solid solutions involving two ions with considerably different masses. However, for solid solutions involving cations of much different ionic radii, two-mode behavior is found for the translations of SiO4 groups. This is the first report of two-mode behavior that is unrelated to mass, and instead is due to significantly different force constants in the pyralspites compared to the ugrandites.Anomalies in mixing volumes are linked to two-mode behavior of the SiO4 translations, which leads to the suggestion that the mixing volume behavior is caused by the resistance of the Si-O bond to expansion and compression, as well as to changes in the dodecahedral site. Crystal-field effects may also play an important role within the ugrandite series. Deviation of molar volume dependence on composition from a linear to a asymmetric, non-linear (sometimes sigmoidal) dependence can be linked to solid solutions that possess slightly non-equivalent cation sites.

Thermal properties of forsterite at mantle pressures derived from vibrational spectroscopy

The pressure dependence of the Raman spectrum of forsterite was measured over its entire frequency range to over 200 kbar. The shifts of the Raman modes were used to calculate the pressure dependence of the heat capacity, Cv, and entropy, S, by using statistical thermodynamics of the lattice vibrations. Using the pressure dependence of Cv and other previously measured thermodynamic parameters, the thermal expansion coefficient, α, at room temperature was calculated from α = KS(∂T/∂P)SCV/TVKT, which yields a constant value of (∂ ln α/∂ ln V)T= 6.1(5) for forsterite to 10% compression. This value is in agreement with (∂ ln α/∂ ln V)T for a large variety of materials.At 91 kbar, the compression mechanism of the forsterite lattice abruptly changes causing a strong decrease of the pressure derivative of 6 Raman modes accompanied by large reductions in the intensities of all of the modes. This observation is in agreement with single crystal x-ray diffraction studies to 150 kbar and is interpreted as a second order phase transition.

Thermodynamics and behavior of ?-Mg2SiO4 at high pressure: Implications for Mg2SiO4 phase equilibrium

Raman spectra of γ-Mg2SiO4 taken to 200 kbar were used to calculate entropy and heat capacity at various P-T conditions. These new thermodynamic data on γ-MgSiO4, similar data on MgSiO3 perovskite (pv), previous data on β-MgSiO4 and MgO (mw), and previous volumetric data of all phases were used to calculate the phase boundaries in the Mg2SiO4 phase diagram. Our resulting slope for the β→γ transition (50±4 bar K-1) is in excellent agreement with recent multi-anvil studies. The slopes for the β→pv+MgO and γ→pv+MgO are-7±3 and -25±4 bar K-1, respectively, and are consistent with our CO2 laser heated diamond anvil studies. These slopes result in a β-γ-MgO+pv triple point at approximately 229 kbar and 2260 K for the iron free system.

Vibrational spectroscopy of aluminate spinels at 1 atm and of MgAl2O4 to over 200 kbar

Single-crystal Raman and infrared reflectivity data including high pressure results to over 200 kbar on a natural, probably fully ordered MgAl2O4 spinel reveal that many of the reported frequencies from spectra of synthetic spinels are affected by disorder at the cation sites. The spectra are interpreted in terms of factor group analysis and show that the high energy modes are due to the octahedral internal modes, in contrast to the behavior of silicate spinels, but in agreement with previous data based on isotopic and chemical cation substitutions and with new Raman data on gahnite (∼ ZnAl2O4) and new IR reflectivity data on both gahnite and hercynite (∼Fe0.58Mg0.42Al2O4). Therefore, aluminate spinels are inappropriate as elastic or thermodynamic analogs for silicate spinels.Fluorescence sideband spectra yield complementary information on the vibrational modes and provide valuable information on the acoustic modes at high pressure. The transverse acoustic modes are nearly pressure independent, which is similar to the behavior of the shear modes previously measured by ultrasonic techniques. The pressure derivative of all acoustic modes become negative above 110 kbar, indicating a lattice instability, in agreement with previous predictions. This lattice instability lies at approximately the same pressure as the disproportionation of spinel to MgO and Al2O3 reported in high temperature, high pressure work.

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

The effect of pressure on the heat capacity, Cv, and entropy, S, of MgO was determined using vibrational spectroscopy to over 200 kbar by the measurement of several vibronic bands in the fluorescence of Cr3+ doped into the MgO lattice. The results for Cv and S demonstrate that the high pressure thermodynamic properties of MgO can be accurately estimated using a Debye model even at room temperature.Using the pressure dependence of Cv and previously measured thermodynamic quantities, the thermal expansion coefficient, α, at room temperature was then calculated from α = Ks(∂T/∂P)sCv/TVKT, which yields a constant value of (∂ ln α/∂ ln V)T = 6.5 (5) for MgO to 10% compression, in agreement with lattice dynamical calculations. These results imply that α for MgO at the bottom of the lower mantle decreases by an order of magnitude.

Estimates of mantle relevant Clapeyron slopes in the MgSiO3 system from high-pressure spectroscopic data

Abstract The phase diagram for MgSiO3 was estimated using the entropy, enthalpy, thermal expansivity, and volumes of all the phases. Entropy at the various P-T conditions in the phase diagram was estimated using statistical thermodynamics and spectroscopic data at ambient and high pressures for each of the phases. Nearly complete 1 atm polarized Raman spectra of end-member MgSiO3 orthoenstatite and new high-pressure Raman data on orthoenstatite (Pbca) to 24.5 GPa and majorite to 33.6 GPa are presented. Both of these minerals exhibit profound changes in their spectra as pressure is increased and the pressure dependence of the Raman modes changes substantially at 5 GPa for orthoenstatite and 26 GPa for majorite. These, like MgSiO3 perovskite, appear to change symmetry even at room temperature. The slopes for the following transitions are reported: clinoenstatite (C2/c) to majorite, 212 bar/K; majorite to ilmenite, 46 bar/K; ilmenite to perovskite, 246 bar/K, majorite to perovskite, 26 bar/K. A volume change of 0.6 cm3/mol for the orthopyroxene to highpressure clinopyroxene transition was estimated using the previously measured phase boundary and the present entropy data. Clapeyron slopes are overestimated by 20 to 100% if the pressure dependence of ΔS across the transitions at various P-T conditions is not included in the thermodynamic calculations.

Geophysical inferences of thermal‐chemical structures in the lower mantle

Lateral variations of the temperature field in the lower mantle have been reconstructed using new results in mineral physics and seismic tomographic data. We show that, with the application of high-pressure experimental values of thermal expansivity and of sound velocities, the slow seismic anomalies in the lower mantle under the Pacific and Africa can be converted into realistically looking plume structures with large dimensions of 0(10³ km). The outer fringes of the plumes have an excess temperature of around 400 K. In the core of the plumes are found tongue-like structures with extremely high thermal anomalies. These values can exceed 1200 K and are too high to be explained on the basis of thermal anomalies alone. We suggest that these major plumes in the deep mantle may be driven by both thermal and chemical buoyancies or that enhanced conductive heat-transfer may be important there.

Sound velocities of MgO to very high compression

Abstract A new, experimentally simple method for obtaining sound velocities accurately from spectroscopic data taken at high pressures in the diamond anvil cell is presented. The transverse and longitudinal acoustic modes in MgO measured to over 200 kbar in the sideband fluorescence of Cr 3− in MgO directly yield the shear and compressional sound velocities with a resolution high enough to derive the geophysically important parameters: (∂ ln ϱ/∂ln v s ) T = 0.88(8) + 2.4(7) × ln(ϱ/ϱ 0 ) and (ln ϱ/∂ ln v p ) T = 0.73(5) + 2.4(4) × ln(ϱ/ϱ 0 ). These values and their high pressure trends are nearly equal to the seismically derived values for the lower mantle. These increases in ∂ln ϱ/∂ ln v and the strong decrease in the thermal expansion coefficient with pressure suggest lower mantle lateral temperature variations derived from seismic velocity anomalies of 400–600 K. The pressure derivatives for the elastic moduli are obtained as follows: (d K S /d P ) T = 4.08 ± 0.09, ( d 2 K S /d P 2 ) T = −0.0054 ± 0.0016 kbar −1 , (d G /d P ) T = 2.58 ± 0.08, (d 2 G /d P 2 ) T = −0.0034 #x000B1; 0.0010 kbar −1 , in excellent agreement with previous ultrasonic results to 32 kbar.

A thermodynamic theory of the Grüneisen ratio at extreme conditions: MgO as an example

The Grüneisen ratio, γ, is defined as γy=αKTV/Cv. The volume dependence of γ(V) is solved for a wide range in temperature. The volume dependence of αKT is solved from the identity (∂ ln(αKT)/∂ ln V)T ≡ δT-K′. α is the thermal expansivity; KT is the bulk modulus; CV is specific heat; and δTand K′ are dimensionless thermoelastic constants. The approach is to find values of δT and K′, each as functions of T and V. We also solve for q=(∂ ln γ/∂ ln V) where q=δT-K′+ 1-(∂ ln CV/∂ ln V)T. Calculations are taken down to a compression of 0.6, thus covering all possible values pertaining to the earths mantle, q=∂ ln γ/∂ ln V; δT=∂ ln α/∂ ln V; and K′= (∂KT/∂P)T. New experimental information related to the volume dependence of δT, q, K′ and CV was used. For MgO, as the compression, η=V/V0, drops from 1.0 to 0.7 at 2000 K, the results show that q drops from 1.2 to about 0.8; δT drops from 5.0 to 3.2; δT becomes slightly less than K′; ∂ ln CV/∂ In V→0; and γ drops from 1.5 to about 1. These observations are all in accord with recent laboratory data, seismic observations, and theoretical results.