Physical properties of calcium aluminates from vibrational spectroscopy

Heat capacity (C_V) and entropy (S) as a function of temperature were calculated for phases in the CaO-Al₂O₃ system from vibrational spectra using a quasi-harmonic model. Calculated values of C_V at 298 K for the calcium aluminates may have uncertainties as small as ±1%, based on comparison with published calorimetric data for CaO, Al₂O₃, and CaAl₂O₄. For hibonite (CaAl₁₂O₁₉), we predict C_P as 519.3 J/mol-K and S as 391.7 J/mol-K, at 298 K. For grossite (CaAl₄O₇), calculated values of C_P as 195.9 J/mol-K and of S as 172.0 J/mol-K are slightly smaller than the available calorimetric data at 298 K, consistent with calorimetric data having been obtained from samples containing ∼10 wt% hibonite impurities. Thermal conductivity at 298 K (k₀) is predicted from peak widths of the vibrational modes using the damped harmonic oscillator model of a phonon gas. Calculations of k₀ for CaO and Al₂O₃ differ from the measurements by 17% and 5%, respectively. The discrepancy for lime is larger due to uncertainties in its peak widths. This comparison suggests that our results for the calcium aluminates should be more accurate than conventional measurements of k₀ which are commonly uncertain by ∼25%.     

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

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, C _v, and entropy, S, by using statistical thermodynamics of the lattice vibrations. Using the pressure dependence of C _v and other previously measured thermodynamic parameters, the thermal expansion coefficient, , at room temperature was calculated from = K _S (T/P) _S C _V/TVK _T, which yields a constant value of ( ln / ln V)_T= 6.1(5) for forsterite to 10% compression. This value is in agreement with ( ln / 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.     

Olivine intergranular plasticity at mantle pressures and temperatures

The ductile behavior of olivine-rich rocks is critical to constrain thermal convection in the Earth's upper mantle. Classical olivine flow laws for dislocation or diffusion creep fail to explain the fast post-seismic surface displacements observed by GPS, which requires a much weaker lithosphere than predicted by classical laws. Here we compare the plasticity of olivine aggregates deformed experimentally at mantle pressures and temperatures to that of single crystals and demonstrate that, depending on conditions of stress and temperature, strain accommodated through grain-to-grain interactions – here called intergranular strain – can be orders of magnitude larger than intracrystalline strain, which significantly weakens olivine strength. This result, extrapolated along mantle geotherms, suggests that intergranular plasticity could be dominant in most of the upper mantle. Consequently, the strength of olivine-rich aggregates in the upper mantle may be significantly lower than predicted by flow laws based on intracrystalline plasticity models.     

Stability of the assemblage albite plus forsterite at high temperatures and pressures with petrologic implications

The maximum limits of the assemblage albiteforsterite have been determined experimentally at high pressures and temperatures. At subsolidus temperatures, albite plus forsterite is replaced at high pressures by jadeitic clinopyroxene and enstatitic orthopyroxene. The boundary for this reaction lies within experimental uncertainity of that for jadeite=albite+nepheline. Melting of albite+forsterite at high pressures produces enstatite+liquid, which is different from the low-pressure eutectic behavior. Melting rates are very slow and several hundred hours are required to establish equilibrium near the solidus. The subsolidus boundary for albite plus forsterite lies near that for sanidine plus forsterite, but with a shallower slope which more closely matches that of anorthite plus forsterite. Both albite plus forsterite and anorthite plus forsterite are replaced at high pressures by an assemblage containing clinopyroxene plus orthopyroxene, unlike sanidine plus forsterite, which is replaced by a feldspathoid plus orthopyroxene. The presence of sodium enlarges the depth region over which plagioclase lherzolite can stably exist; it may also stabilize alkali feldspar plus olivine in crustal rocks.     

Modeling the thermodynamic parameters of six endmember garnets at ambient and high pressures from vibrational data

Raman and infrared spectroscopic data at ambient and high pressures were used to compute the lattice contribution to the heat capacities and entropies of six endmember garnets: pyrope, almandine, spessartine, grossular, andradite and uvarovite. Electronic, configurational and magnetic contributions are obtained from comparing available calorimetric data to the computed lattice contributions. For garnets with entropy in excess of the computed lattice contribution, the overwhelming majority is found in the subambient temperature regime. At room temperature, the non-lattice entropy is approximately 11.5 J/mol-K for pyrope, 49 J/mol-K for almandine, and 19 J/mol-K for andradite. The non-lattice entropy for pyrope and some for almandine cannot be accounted for by magnetic or electronic contributions and is likely to be configurational in nature. Estimates of low temperature non-lattice entropies for both spessartine and uvarovite are made in absence of calorimetric measurements and are based on low temperature calorimetry of other minerals containing the Mn²⁺ and Cr³⁺ cations as well as on solid solution garnets containing these cations. The estimate for uvarovite non-lattice entropy is approximately 18 J/mol-K, while for spessartine, approximately 45 J/mol-K. Neither of these cations is expected to provide electronic contributions to the entropy. For both iron-bearing garnets, a small electronic or magnetic entropy contribution continues above ambient temperatures. High pressure data on pyrope, grossular and andradite permit calculation of the thermodynamic parameters at high pressures, which are important for computation of processes in the Earth’s mantle. Thermal expansion coefficients of these materials were found to be 1.6, 1.5, 1.6×10⁻⁵ K⁻¹ at 298 K, respectively, using a Maxwell relation. These closely match the literature values at ambient conditions.     

High-temperature infrared properties of forsterite

Polarized emittance measurements were acquired for synthetic forsterite, the pure magnesium end member of the olivines group, on the whole infrared spectral range and up to the melting point by using CO₂ laser heating. The experimental data, fitted with a semi-quantum dielectric function model, allowed the retrieval of the temperature dependence of the absorption coefficient of forsterite both in the opaque and semi-transparent regions. The analysis of the phonon parameters indicates that the lattice dynamics evolve drastically with increasing temperature. The normal modes involving motions of the magnesium cations located in site 1 are the more impacted, and some of them vanish around 1,200 K. The results confirm that the enhancement of the lattice anharmonicity and the increasing mobility of the magnesium cations are closely linked and are at the origin of the anomalies observed in the evolution of the thermophysical properties. This complete set of spectroscopic data may be a step toward a more precise evaluation of the impact of thermal radiation heat transfer inside systems involving forsterite and quantification of their heat budget.     

Hydrostatic compression of γ-Mg2SiO4 to mantle pressures and 700 K: Thermal equation of state and related thermoelastic properties

P-V-T equations of state for the γ phase of Mg₂SiO₄ have been fitted to unit cell volumes measured under simultaneous high pressure (up 30 GPa) and high temperature (up to 700 K) conditions. The measurements were conducted in an externally heated diamond anvil cell using synchrotron x-ray diffraction. Neon was used as a pressure medium to provide a more hydrostatic pressure environment. The P-V-T data include 300 K-isothermal compression to 30 GPa, 700 K-compression to 25 GPa and some additional data in P-T space in the region 15 to 30 GPa and 300 to 700 K. The isothermal bulk modulus and its pressure derivative, determined from the isothermal compression data, are 182(3) GPa and 4.2(0.3) at T=300 K, and 171(4) GPa and 4.4(0.5) at T=700 K. Fitting all the P-V-T data to a high-temperature Murnaghan equation of state yields: K _TO=182(3.0) GPa, K _TO=4.0(0.3), ?K _T /?T)₀=?2.7(0.5)×10^?2 GPa/K and (?² K _T /?P?T)₀=5.5(5.2)×10^?4/K at the ambient condition.     

Flow behavior and microstructures of hydrous olivine aggregates at upper mantle pressures and temperatures

Deformation experiments on olivine aggregates were performed under hydrous conditions using a deformation-DIA apparatus combined with synchrotron in situ X-ray observations at pressures of 1.5–9.8 GPa, temperatures of 1223–1800 K, and strain rates ranging from 0.8 × 10^?5 to 7.5 × 10^?5 s^?1. The pressure and strain rate dependencies of the plasticity of hydrous olivine may be described by an activation volume of 17 ± 6 cm³ mol^?1 and a stress exponent of 3.2 ± 0.6 at temperatures of 1323–1423 K. A comparison between previous data sets and our results at a normalized temperature and a strain rate showed that the creep strength of hydrous olivine deformed at 1323–1423 K is much weaker than that for the dislocation creep of water-saturated olivine and is similar to that for diffusional creep and dislocation-accommodated grain boundary sliding, while dislocation microstructures showing the [001] slip or the [001](100) slip system were developed. At temperatures of 1633–1800 K, a much stronger pressure effect on creep strength was observed for olivine with an activation volume of 27 ± 7 cm³ mol^?1 assuming a stress exponent of 3.5, water fugacity exponent of 1.2, and activation energy of 520 kJ mol^?1 (i.e., power-law dislocation creep of hydrous olivine). Because of the weak pressure dependence of the rheology of hydrous olivine at lower temperatures, water weakening of olivine could be effective in the deeper and colder part of Earth’s upper mantle.     

Thermal diffusivity of silica glass at pressures up to 9 GPa

The thermal diffusivity of silica glass was measured at pressures up to 9 GPa and temperatures up to 1200 K. The measurements involve adopting the Ångström method to a cylindrical geometry in a uniaxial split-sphere apparatus. This method can be used to determine thermal diffusivity in samples with dominant conductive heat transfer. The thermal diffusivity of silica glass has a negative first pressure derivative but a positive second pressure derivative. Although the elastic moduli have minima near 3 GPa, the thermal diffusivity does not has minimum up to 9 GPa, which cannot be explained by the model of Kittel (1949). The negative pressure derivative of thermal diffusivity is a feature probably unique in silica glass, and its magnitude should decrease with the addition of Na₂O.     

Single-crystal absorption and reflection infrared spectroscopy of forsterite and fayalite

Polarized single-crystal absorption and reflection spectra of fundamental modes in both the mid- and far-infrared are presented for microscopic crystals of forsterite and fayalite. All modes predicted by symmetry were observed for forsterite, but two B_3u modes were not observed for fayalite. Consideration of previously determined frequency shifts for isotopically and chemically substituted olivines, along with symmetry analysis, produced a complete set of band assignments satisfying all constraints for forsterite. A plausible assingment was derived for fayalite by analogy. The frequency shifts from forsterite to fayalite are consistently small for bands assigned to SiO₄ stretching and bending, moderate for rotations, and large for translations of M-site ions, suggesting that in olivine, SiO₄ groups vibrate separately from the lattice. Allocating the bending and external modes among multiple continua in Kieffer's (1979c) model considerably improves prediction of quasiharmonic heat capacityC _v and entropy for forsterite (～1% discrepancy from 200–1000 K). The experimental entropy of fayalite is closely accounted for (1.8 to 0.1%) by summing lattice, electronic (from Burns' (1985) optical band assignment), and constant magnetic contributions above 200 K.S _magnetic determined from the difference of the experimental and model lattice entropies shows inflection points at the two magnetic transition temperatures (23 and 66 K) and indicates that complete spin disorder is not achieved below 680 K.     

Compositions of aqueous fluids in equilibrium with pyroxenes and olivines at mantle pressures and temperatures

Solubility experiments were performed at 30 kbars in the system Mg₂SiO₄-SiO₂-H₂O, and at 20 and 30 kbars on omphacitic pyroxene-water mixtures. They confirm that the solubility of the forsterite component in aqueous fluids remains rather low (up to 5 wt.%), whereas the solubility of the SiO₂ component from solids of appropriate SiO₂-rich compositions in the system Mg₂SiO₄-SiO₂-H₂O increases with temperature up to some 75% at 1,100° C. At this temperature a simplified harzburgite consisting of forsterite and enstatite coexists with a fluid containing about 35% (MgO+SiO₂). Hydrous fluids coexisting with omphacitic clinopyroxenes leach sodium silicate component from the solid leaving less jadeitic pyroxenes behind. Most interestingly, the amount of sodium leached at constant temperature increases with decreasing pressure.Comparison of the results with previous solubility studies in the system K₂O-MgO-Al₂O₃-SiO₂-H₂O indicates that hydrous fluids in the mantle must be alkaline rather than silicanormative. Alkali metasomatism caused by such fluids would lead to potassium enrichment in deeper portions of the upper mantle and to sodium enrichment at shallower levels, where amphiboles become stable. This K/Na fractionation in the upper mantle may explain the generation of K-rich or of Na-rich magmas through partial melting at different depths.     

Quartz diorites derived by partial melting of eclogite or amphibolite at mantle depths

Rare earth elements, Rb, Sr, Ba and K have been determined in tonalite, trondhjemite, dacite, tholeiite and graywacke from the 2700 m.y. old Early Precambrian greenstone-granite terrane of northeastern Minnesota-northwestern Ontario, and also in trondhjemite from the 3550 m.y. old Morton Gneiss, southwestern Minnesota; and the Mesozoic Craggy Peak Pluton, Klamath Mountains, California.The Early Precambrian tholeiites have trace element compositions similar to modern oceanic tholeiites, while the quartz dioritic rocks, regardless of age, have total rare earth contents lower than that of tholeiitic basalts, with near chondritic heavy rare earth contents. Rb, Sr, Ba and K contents of the quartz diorites are about five times that of oceanic tholeiites, with similar alkali and alkaline earth ratios. The Early Precambrian graywacke has a rare earth content intermediate between greenstone and quartz diorite, reflecting its provenance.It is proposed that the analyzed quartz dioritic rocks, whether plutonic tonalite, dacite porphyry, gneissic or plutonic trondhjemite, or trondhjemite dikes had similar modes of origin, and were derived by partial melting of amphibolite or eclogite of basaltic or gabbroic composition at depths greater than thirty kilometers, leaving a residue consisting predominantly of garnet and clinopyroxene.     

Thermal equation of state of synthetic orthoferrosilite at lunar pressures and temperatures

Iron-rich orthopyroxene plays an important role in models of the thermal and magmatic evolution of the Moon, but its density at high pressure and high temperature is not well-constrained. We present in situ measurements of the unit-cell volume of a synthetic polycrystalline end-member orthoferrosilite (FeSiO₃, fs) at simultaneous high pressures (3.4–4.8 GPa) and high temperatures (1,148–1,448 K), to improve constraints on the density of orthopyroxene in the lunar interior. Unit-cell volumes were determined through in situ energy-dispersive synchrotron X-ray diffraction in a multi-anvil press, using MgO as a pressure marker. Our volume data were fitted to a high-temperature Birch–Murnaghan equation of state (EoS). Experimental data are reproduced accurately, with a  $\varDelta P$ Δ P  standard deviation of 0.20 GPa. The resulting thermoelastic parameters of fs are: V ₀ = 875.8 ± 1.4 Å³, K ₀ = 74.4 ± 5.3 GPa, and $\frac{{\text d}K}{{\text d}T} = -0.032 \pm 0.005\,\hbox{GPa K}^{-1}$ d K d T = - 0.032 ± 0.005 GPa K - 1 , assuming ${K}^{\prime}_{0} = 10 $ K 0 ′ = 10 . We also determined the thermal equation of state of a natural Fe-rich orthopyroxene from Hidra (Norway) to assess the effect of magnesium on the EoS of iron-rich orthopyroxene. Comparison between our two data sets and literature studies shows good agreement for room-temperature, room-pressure unit-cell volumes. Preliminary thermodynamic analyses of orthoferrosilite, FeSiO₃, and orthopyroxene solid solutions, (Mg_1?x Fe _x ) SiO₃, using vibrational models show that our volume measurements in pressure–temperature space are consistent with previous heat capacity and one-bar volume–temperature measurements. The isothermal bulk modulus at ambient conditions derived from our measurements is smaller than values presented in the literature. This new simultaneous high-pressure, high-temperature data are specifically useful for calculations of the orthopyroxene density in the Moon.     

Thermodynamic properties and equation of state of fcc aluminum and bcc iron, derived from a lattice vibrational method

We use a lattice vibrational technique to derive thermophysical and thermochemical properties of the pure elements aluminum and iron in pressure–temperature space. This semi-empirical technique is based on either the Mie–Grüneisen–Debye (MGD) approach or an extension of Kieffer’s model to incorporate details of the phonon spectrum. It includes treatment of intrinsic anharmonicity, electronic effects based on the free electron gas model, and magnetic effects based on the Calphad approach. We show that Keane’s equation of state for the static lattice is better suitable to represent thermodynamic data for aluminum from 1 bar to pressures in the multi-megabar region relative to Vinet’s universal and the Birch–Murnaghan equation of state. It appears that the MGD and Mie–Grüneisen–Kieffer approach produce similar results, but that the last one better represents heat capacity below room temperature. For iron we show that the high temperature behavior of thermal expansivity can be explained within the Calphad approach by a pressure-dependent Curie temperature with a slope between –1 and 0 K/GPa.     

In situ Raman spectroscopy on kerogen at high temperatures and high pressures

Kerogen samples were treated at temperatures and pressures up to 25–600°C and ~9 GPa, respectively. In situ micro-Raman spectroscopy was used to measure the systematic changes in the first-order Raman spectral features during the process of temperature or pressure increment. Three Raman bands, D1, D2, and G bands, were examined to characterize the structural and chemical changes of kerogen at high temperatures and pressures. We found that the wavenumbers of D1, D2 and G bands showed a linear variation with both temperature and pressure. Therefore, a correlation between R1 and R2 and the peak temperature in regionally metamorphosed rocks cannot be applied to this work. This result implies that the G band may serve as a temperature or pressure indicator during the promotion of maturation of kerogen. Kerogen possesses reversible properties in contrast with the natural samples recovered from the field suffered from prolonged thermal history during regional metamorphism.     

Thermodynamic properties of MgSiO3 ilmenite from vibrational spectra

Unpolarized infrared (IR) reflectance spectra for MgSiO₃ ilmenite taken from a single-crystal and from a densly packed polycrystalline sample possessed all eight peaks mandated by symmetry between 337 and 850 cm^?1. Polarizations were inferred from intensity differences between the two samples. IR peak positions differ by up to 250 cm^?1 from recent calculations, but on average are within 11%. Heat capacity C _p calculated from these data by using a Kieffer-type model are within the experimental uncertainty of calorimetric measurements from 170 to 700 K. Outside this range, calculated C _p is probably accurate within a few percent, based on recent results for garnets. Calculated entropy is only slightly less accurate, giving S ⁰ (298.15 K) as 54.1 ±0.5 J/ mol-K, which is 10% lower than recent estimates based on phase equilibria. The slope of the phase boundary between ilmenite and perovskite is used to predict S ⁰ (298.15 K) of perovskite as 58.7 ±1.4 J/mol-K, which is 10% lower than previous values.     

Thermal expansion of single-crystal forsterite to 1023 K by Fizeau interferometry

Using a Fizeau interferometry technique, we have measured the coefficients of linear thermal expansion of single-crystal forsterite (Mg₂SiO₄) along three axial directions to 1023 K during heating and cooling cycles. Overall, the present data are consistent in magnitude (within 1 to 2%) with those previously reported but have less scatter. We used the Grüneisen statistical mechanical approach in analzying the data. The least-squares method was applied to evaluate thermal parameters (?, Q ₀, k and a) in two cases. The expansion coefficients in wider temperature ranges were extrapolated by using the parameters of solution 2 (i.e., solution by fixing ? and k). In contrast to earlier findings, our results show that for forsterite the Grüneisen parameter decreases with temperature, implying that it does not behave too differently from fayalite (Fe₂SiO₄) and periclase (MgO).