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, 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, α, at room temperature was calculated from α = K _S (?T/?P) _S C _V/TVK _T, 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.     

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.     

Carbonation and melting reactions in the system CaO–MgO–SiO2–CO2 at mantle pressures with geophysical and petrological applications

Bowen's petrogenetic grid was based initially on a series of decarbonation reactions in the system CaO-MgO-SiO₂-CO₂ with starting assemblages including calcite, dolomite, magnesite and quartz, and products including enstatite, forsterite, diopside and wollastonite. We review the positions of 14 decarbonation reactions, experimentally determined or estimated, extending the grid to mantle pressures to evaluate the effect of CO₂ on model mantle peridotite composed of forsterite(Fo)+orthopyroxene(Opx)+clinopyroxene(Cpx). Each reaction terminates at an invariant point involving a liquid, CO₂, carbonates, and silicates. The fusion curves for the mantle mineral assemblages in the presence of excess CO₂ also terminate at these invariant points. The points are connected by a series of reactions involving liquidus relationships among the carbonates and mantle silicates, at temperatures lower (1,100–1,300° C) than the silicate-CO₂ melting reactions (1,400–1,600° C). Review of experimental data in the bounding ternary systems together with preliminary data for the system CaO-MgO-SiO₂-CO₂ permits construction of a partly schematic framework for decarbonation and melting reactions at upper mantle pressures. The key to several problems in the peridotite-CO₂ subsystem is the intersection of a subsolidus carbonation reaction with a melting reaction at an invariant point near 24 kb and 1,200°C. There is an intricate series of reactions between 25 kb and 35 kb involving changes in silicate and carbonate phase fields on the CO₂-saturated liquidus surfaces. Conclusions include the following: (1) Peridotite Fo+Opx+Cpx can be carbonated with increasing pressure, or decreasing temperature, to yield Fo+Opx+Cpx+Cd (Cd=calcic dolomite), Fo+Opx+Cd, Fo+Opx+Cm (Cm=calcic magnesite), and finally Qz+Cm. (2) Free CO₂ cannot exist in subsolidus mantle peridotite with normal temperature distributions; it is stored as carbonate, Cd. (3) The CO₂ bubbles in peridotite nodules do not represent free CO₂ in mantle peridotite along normal geotherms. (4) CO₂ is as effective as H₂O in causing incipient melting, our preferred explanation for the low-velocity zone. (5) Fusion of peridotite with CO₂ at depths shallower than 80 km produces basic magmas, becoming more SiO₂-undersaturated with depth. (6) The solubility of CO₂ in mantle magmas is less than about 5 wt% at depths to 80 km, increasing abruptly to about 40 wt% at 80 km and deeper. (7) Deeper than 80 km, the first liquids produced are carbonatitic, changing towards kimberlitic and eventually, at considerably higher temperatures, to basic magmas. (8) Kimberlite and carbonatite magmas rising from the asthenosphere must evolve CO₂ at depths 100-80 km, which contributes to their explosive emplacement. (9) Fractional crystallization of CO₂-bearing SiO₂-undersaturated basic magmas at most pressures can yield residual kimberlite and carbonatite magmas.     

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.     

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.     

Heat capacity,entropy, and phase equilibria of dmitryivanovite

The heat capacity (C _p ) of dmitryivanovite synthesized with a cubic press was measured in the temperature range of 5–664 K using the heat capacity option of a physical properties measurement system and a differential scanning calorimeter. The entropy of dmitryivanovite at standard temperature and pressure (STP) was calculated to be 110.1 ± 1.6 J mol⁻¹ K⁻¹ from the measured C _p data. With the help of new phase equilibrium experiments done at 1.5 GPa, the phase transition boundary between krotite and dmitryivanovite was best represented by the equation: P (GPa) = −2.1825 + 0.0025 T (K). From the temperature intercept of this phase boundary and other available thermodynamic data for krotite and dmitryivanovite, the enthalpy of formation and Gibbs free energy of formation of dmitryivanovite at STP were calculated to be −2326.7 ± 2.1 and −2,208.1 ± 2.1 kJ mol⁻¹, respectively. It is also inferred that dmitryivanovite is the stable CaAl₂O₄ phase at STP and has a wide stability field at high pressures whereas the stability field of krotite is located at high temperatures and relatively low pressures. This conclusion is consistent with natural occurrences (in Ca–Al-rich inclusions) of dmitryivanovite and krotite, where the former is interpreted as the shock metamorphic product of originally present krotite.     

Heat capacity,entropy and phase equilibria of stishovite

The low-temperature heat capacity (C _P) of stishovite (SiO₂) synthesized with a multi-anvil device was measured over the range of 5–303 K using the heat capacity option of a physical properties measurement system (PPMS) and around ambient temperature using a differential scanning calorimeter (DSC). The entropy of stishovite at standard temperature and pressure calculated from DSC-corrected PPMS data is 24.94 J mol⁻¹ K⁻¹, which is considerably smaller (by 2.86 J mol⁻¹ K⁻¹) than that determined from adiabatic calorimetry (Holm et al. in Geochimica et Cosmochimica Acta 31:2289–2307, 1967) and about 4% larger than the recently reported value (Akaogi et al. in Am Mineral 96:1325–1330, 2011). The coesite–stishovite phase transition boundary calculated using the newly determined entropy value of stishovite agrees reasonably well with the previous experimental results by Zhang et al. (Phys Chem Miner 23:1–10, 1996). The calculated phase boundary of kyanite decomposition reaction is most comparable with the experimental study by Irifune et al. (Earth Planet Sci Lett 77:245–256, 1995) at low temperatures around 1,400 K, and the calculated slope in this temperature range is mostly consistent with that determined by in situ X-ray diffraction experiments (Ono et al. in Am Mineral 92:1624–1629, 2007).     

Excess heat capacity and entropy of mixing in the high-structural state (K,Ca)-feldspar binary

Low- and high-temperature heat capacities were measured for a series of synthetic high-structural state (K,Ca)-feldspars (Or–An) using both a relaxation and a differential scanning calorimeter. The data were collected at temperatures between 5 and 800 K on polycrystalline samples that had been synthesised and characterised in a previous study. Below T = 300 K, Or₉₀An₁₀, and Or₈₀An₂₀ showed excess heat capacities of mixing with maximum values of ~3 J mol⁻¹ K⁻¹. The other members of this binary (An > 20 mol%) had lower excess heat capacity values of up to ~1 J mol⁻¹ K⁻¹. Above T = 300 K, some compositions exhibited negative excess heat capacities of mixing (with maximum values of −2 J mol⁻¹ K⁻¹). The vibrational entropy at 298.15 K for Or₉₀An₁₀ and Or₈₀An₂₀ deviated strongly from the behaviour of a mechanical mixture, with excess entropy values of ~3.5 J mol⁻¹ K⁻¹. More An-rich members had only small excess vibrational entropies at T = 298.15 K. The difference in behaviour between members with An > 20 mol% and those with An ≤ 20 mol% is probably a consequence of the structural state of the (K,Ca)-feldspars, i.e., (K,Ca)-feldspars with An ≤ 20 mol% have monoclinic symmetry, whereas those with An > 20 mol% are triclinic. At T = 800 K, the vibrational entropy values were found to scatter around the values expected for a mechanical mixture and, thus, correspond to a quasi-ideal behaviour. The solvus for the (K,Ca)-feldspar binary was calculated based on the entropy data from this study in combination with enthalpy and volume of mixing data from a previous study.     

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.     

Heat capacity, entropy, and magnetic properties of jarosite-group compounds

Jarosite phases are common minerals in acidic, sulfate-rich environments. Here, we report heat capacities (C _p) and standard entropies (S°) for a number of jarosite samples. Most samples are close to the nominal composition AFe₃(SO₄)₂(OH)₆, where A = K, Na, Rb, and NH₄. One of the samples has a significant number of defects on the Fe sites and is called the defect jarosite; others are referred to as A-jarosite. The samples, their compositions, and the entropies at T = 298.15 K are:

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.     

Changes of specific heat capacity and heat capacity during weathering

An approach is presented which must be followed in the study of a deep-weathering profile. The present research pursues the evaluation of changes in specific heat capacity and heat capacity during weathering. For the first step to obtain the values of specific heat capacity and heat capacity in practical use, the mutual relationships among vertical changes in various kinds of rock properties are investigated in a weathering profile of granite. Two derivable formulas for estimating the values of specific heat capacity and volumetric heat capacity in weathered rock have been theoretically derived from the values of some properties. The changes of specific heat capacity and volumetric heat capacity in rock during natural weathering are also evaluated on the basis of the available data of physical properties.     

Phase transition in CaGeO3 perovskite: Evidence from X-ray powder diffraction,thermal expansion and heat capacity

High-temperature x-ray powder diffraction study by the full pattern Rietveld method of orthorhombic CaGeO₃ (Pbnm at ambient condition) perovskite confirms the previously observed phase transition at Tc=520 K. The measured volumetric thermal expansion coefficients are 3.1 x 10^-5 (K^-1) below Tc and 3.5x 10^-5 (K^-1) above Tc. The space group at T>Tc has been tentatively identified as Cmcm. Such a transition involves the disappearance of one of the two octahedral rotations in the (001) plane, and the doubling of the unit cell volume, with c axis unchanged. Although this transition should be of first order from symmetry considerations, the distortion of the Pbnm phase decreases continuously as the temperate approaches Tc and there is no observable volume discontinuity at Tc. The measured heat capacity places an upper limit on the enthalpy of transition of 50 J/mol, which is quite reasonable in terms of the crystallographic nature of this phase transition.A National Science Foundation Science and Technology Center     

The thermodynamics of substances at very high pressures and temperatures and some mineral reactions in the earth's mantle

The thermodynamic properties of 25 substances (elements, compounds, modifications) are calculated on the basis of an extrapolation of their caloric values and compressibilities into the region of pressures up to 2mbar and temperatures up to 4,000K. The extrapolation methods are described. The ratio of molar volumes is used to predict the thermodynamic properties of the high pressure modifications. It is inferred that water vapour and oxides of Mg, Fe, and Si ought to be stable in the entire mantle. In the lower mantle garnet should be more stable than the perovskite-type phase of MgSiO₃ (in presence of Al₂O₃ or Fe₂O₃). ‘Perovskite’ phase plus MgO are more stable here than forsterite, Mg₂SiO₄. Pyrrhotite, FeS, reveals astonishing stability in the entire mantle and in the outer core as well. Carbon dioxide, CO₂, may exist only in the upper mantle, whereas methane, CH₄, remains stable in the entire mantle.     

Thermal expansion coefficients for indialite,emerald, and beryl

Thermal expansion coefficients ?₁ and ?₃ calculated for the hexagonal minerals indialite, emerald and beryl are, in general, small with ?₃ being negative near room temperature. This unusual behavior leads to low volume coefficients of thermal expansion (β=2?₁+?₃) making these materials ideal ceramic bodies for catalyst carriers in air-pollution control. The temperature at which the c-cell edge length of beryl is a minimum is strongly dependent upon the presence of trace amounts of impurity atoms. This effect is ascribed to changes in the Grüneisen parameters.     

Thermal expansion of granitoids

The thermal rock properties are particularly important for natural stones whenever a temperature change may occur, which becomes particularly important when different materials are combined on any architectural structure. The thermal expansion of a rock is dependent on the coefficients of the expansion of the individual rock-forming minerals and the rock fabric. A systematic study on 65 different stones, mostly granitoids and others magmatic rocks, most of them are often used as dimensional building stones, was performed. Temperature and moisture are very important parameters in the natural environment. Therefore, the thermal expansion, and in addition the thermohygric expansion on selected examples, was measured. The data were also discussed considering the effect of the mineralogy and the temperature. A modeling approach was introduced to show how the mineralogy and the related single crystal properties affect the thermal properties and how good a simple calculation can help to characterize the measured thermal expansion of a rock. The directional dependence of the thermal expansion was also discussed and explained based on detailed rock fabric measurements. In this study, the bowing of granitoid samples was tested and compared with bowing phenomena of granitoid facade panels. The slabs were cut in different directions and were studied under different conditions of temperatures and water saturation. It could be clearly documented that the temperature and the moisture have a control on the bowing behavior. The implication of our data is that thermal expansion depends greatly on wetting and drying, i.e., the thermal cracking is characterized by the residual strain observed after cooling to room temperature. The sensitivity to the thermal cracking has a significant control on the application in architectural constructions.     

Experimental determination of rare earth element partitioning between hydrous silicate melt,amphibole and garnet peridotite minerals at upper mantle pressures and temperatures

Partition coefficients of Ce, Sm and Tm involving garnet peridotite minerals, amphibole and hydrous silicate melt have been determined experimentally in the temperature and pressure ranges 950–1075°C and 10–25 kbar.Only several parts per million to several tens of parts per million of rare earth element (REE) can dissolve in the minerals before the crystal-liquid partition coefficients begin to vary as a function of REE content. The concentration ranges of constant partition coefficient increase with increasing temperature and are also positively correlated with the magnitude of the crystal-liquid partition coefficients. The upper concentration limits of constant partition coefficient and the value of the crystal-liquid partition coefficient for REE decrease in the order garnet > clinopyroxene > amphibole > orthopyroxene > olivine.Partition coefficients may vary by at least an order of magnitude as a function of bulk composition of the liquid phase (e.g. changing from basaltic to andesitic). The approximate ranges of the values of the partition coefficients as a function of bulk liquid composition are as follows:

$\text{Ce}\text{Sm}\text{Tm}\text{K}{}^{\mathrm{<mtext>ga-liq</mtext>}}\text{0.01–0.1}\text{0.3–3.4}\text{1–10}\text{K}{}^{\mathrm{<mtext>cpx-liq</mtext>}}\text{0.05–0.4}\text{0.09–0.7}\text{0.04–0.4}\text{K}{}^{\mathrm{<mtext>amph-liq</mtext>}}\text{0.04–0.4}\text{0.08–0.8}\text{0.07–0.7}\text{K}{}^{\mathrm{<mtext>opx-liq</mtext>}}\text{0.04–0.1}\text{0.05–0.1}\text{0.08–0.1}\text{K}{}^{\mathrm{<mtext>ol-liq</mtext>}}\text{0.01–0.02}\text{0.01–0.02}\text{0.01–0.02}$

where the values increase with increasing acidity of the melt.     

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.     

Semi-brittle behavior of wet olivine aggregates: the role of aqueous fluid in faulting at upper mantle pressures

The role of aqueous fluid in fracturing in subducting slabs was investigated through a series of deformation experiments on dunite that was undersaturated (i.e., fluid-free) or saturated with water (i.e., aqueous-fluid bearing) at pressures of 1.0–1.8 GPa and temperatures of 670–1250 K, corresponding to the conditions of the shallower regions of the double seismic zone in slabs. In situ X-ray diffraction, radiography, and acoustic emissions (AEs) monitoring demonstrated that semi-brittle flow associated with AEs was dominant and the creep/failure strength of dunite was insensitive to the dissolved water content in olivine. In contrast, aqueous fluid drastically decreased the creep/failure strength of dunite (up to ~?1 GPa of weakening) over a wide range of temperatures in the semi-brittle regime. Weakening of the dunite by the aqueous fluid resulted in the reduction of the number of AE events (i.e., suppression of microcracking) and shortening of time to failure. The AE hypocenters were located at the margin of the deforming sample while the interior of the faulted sample was aseismic (i.e., aseismic semi-brittle flow) under water-saturated conditions. A faulting (slip rate of ~?10^?3 to 10^?4 s^?1) associated with a large drop of stress (Δσ?~?0.5 to 1 GPa) and/or pressure (ΔP?~?0.5 GPa) was dominant in fluid-free dunite, while a slow faulting (slip rate?<?8?×?10^?5 s^?1) without any stress/pressure drop was common in water-saturated dunite. Aseismic semi-brittle flow may mimic silent ductile flow under water-saturated conditions in subducting slabs.