Thermal expansion,Debye temperature and Grüneisen parameter of synthetic (Fe,Mg)SiO3 orthopyroxenes

Thermal expansion properties of synthetic orthopyroxenes (Fe_0.20Mg_0.80)SiO₃, (Fe_0.40Mg_0.60)SiO₃, (Fe_0.50Mg_0.50)SiO₃, (Fe_0.75Mg_0.25)SiO₃ and (Fe_0.83Mg_0.17)SiO₃ were systematically studied by means of single-crystal x-ray diffraction in the temperature range from 296 to 1300 K. The measurements of unit cell dimensions as a function of temperature reveal that the a and c dimensions and the unit cell volume V increase nonlinearly with a positive curvature with rising temperature, whereas the b dimension behaves differently, depending on the total Fe content. For Mg-rich orthopyroxenes (Fe/(Fe+Mg)<30%), the b dimension expands similarly as the a and c dimensions, but it exhibits a nonlinear increase with a negative curvature for orthopyroxenes with Fe/(Fe+Mg)>30%. Together with the high temperature neutron diffraction data on enstatite (MgSiO₃) (McMullan, Haga and Ghose, unpublished) and x-ray diffraction data on ferrosilite (FeSiO₃) (Sueno et al. 1976), the measured unit cell dimensions were analyzed in terms of the Grüneisen theory of thermal expansion. The linear thermal expansion coefficients α _a and α _c both increase as temperature is elevated, with α _c increasing faster, while α _b changes gradually from increasing for Mg-rich orthopyroxenes to decreasing for Fe-rich orthopyroxenes. The relative magnitudes of linear thermal expansion coefficients are always in the order α _b >α _c >α _a between 300 and 500 K, but at higher temperatures, the order changes to α _c >α _b >α _a for Mg-rich orthopyroxenes and α _c >α _a >α _b for Fe-rich ones. The linear thermal expansion behavior is interpreted on the basis of the structural mechanical model of Weidner and Vaughan (1982). The anomalous behavior of α _b is mainly attributed to the changes in the Fe₂₊ population at the M2 site and the relative stiffness of the M2(Fe₂₊)-O bonds compared to the M2(Mg₂₊)-O bonds. The volume thermal expansion coefficients are nonlinear functions of temperature and lie between 23 and 49×10^?6/K. The previously reported results of mean volume thermal expansion coefficients appear to represent the α _V values characteristic of higher temperatures compared to our results. The thermal Debye temperatures are composition-dependent, decreasing linearly from 812 (MgSiO₃) to 561 K (FeSiO₃), and are systematically higher than the corresponding acoustic Debye temperatures. The Grüneisen parameters range from 0.85 to 0.89 and do not seem to vary with composition. The linear compressibilities derived from thermal expansion and elastic moduli data agree very well. The pressure derivatives of the isothermal bulk modulus (dK₀/dP) are also composition-dependent and decrease from 11.2 (MgSiO₃) to 8.77 (FeSiO₃). Such large values indicate possible anomalous elastic behavior of orthopyroxenes at high pressures in the Earth's upper mantle.     

Thermal expansion and crystal structure of FeSi between 4 and 1173 K determined by time-of-flight neutron powder diffraction

The thermal expansion and crystal structure of FeSi has been determined by neutron powder diffraction between 4 and 1173?K. No evidence was seen of any structural or magnetic transitions at low temperatures. The average volumetric thermal expansion coefficient above room temperature was found to be 4.85(5)?×?10^?5?K^?1. The cell volume was fitted over the complete temperature range using Grüneisen approximations to the zero pressure equation of state, with the internal energy calculated via a Debye model; a Grüneisen second-order approximation gave the following parameters: θ_D=445(11)?K, V ₀=89.596(8)?ų, K ₀′=4.4(4) and γ′=2.33(3), where θ_D is the Debye temperature, V ₀ is V at T=0?K, K ₀′ is the first derivative with respect to pressure of the incompressibility and γ′ is a Grüneisen parameter. The thermodynamic Grüneisen parameter, γ_th, has been calculated from experimental data in the range 4–400?K. The crystal structure was found to be almost invariant with temperature. The thermal vibrations of the Fe atoms are almost isotropic at all temperatures; those of the Si atoms become more anisotropic as the temperature increases.     

The crystal structure and thermal expansion tensor of MgSO<Subscript>4</Subscript>–11D<Subscript>2</Subscript>O(meridianiite) determined by neutron powder diffraction

We have collected high-resolution neutron powder diffraction patterns from MgSO₄·11D₂O over the temperature range 4.2–250 K. The crystal is triclinic, space-group \( \text{P} \bar{1} \) (Z = 2) with a = 6.72746(6) Å, b = 6.78141(6) Å, c = 17.31803(13) Å, α = 88.2062(6)°, β = 89.4473(8)°, γ = 62.6075(5)°, and V = 701.140(6) ų at 4.2 K, and a = 6.75081(3) Å, b = 6.81463(3) Å, c = 17.29241(6) Å, α = 88.1183(3)°, β = 89.4808(3)°, γ = 62.6891(3)°, and V = 706.450(3) ų at 250 K. Structures were refined to wRp = 3.99 and 2.84% at 4.2 and 250 K, respectively. The temperature dependence of the lattice parameters over the intervening range have been fitted with a modified Einstein oscillator model which was used to obtain the coefficients of the thermal expansion tensor. The volume thermal expansion, α_V, is considerably smaller than ice Ih at all temperatures, and smaller even than MgSO₄·7D₂O (although ?α_V/?T is very similar for both sulfates); MgSO₄·11D₂O exhibits negative α_V below 55 K (compared to 70 K in D₂O ice Ih and 20 K in MgSO₄·7D₂O) The relationship between the magnitude and orientation of the principal axes of the expansion tensor and the main structural elements are discussed.     

The thermal expansion of anhydrite to 1000° C

The thermal expansion of anhydrite, CaSO₄, has been measured from 22° to 1,000° C by X-ray diffraction, using the Guinier-Lenné heating powder camera. The heating patterns were calibrated with Guinier-Hägg patterns at 25° C, using quartz as internal standard. Heating experiments were run on natural anhydrite (Bancroft, Ontario), which at room temperature has lattice constants in close agreement with those of synthetic material. The orthorhombic unit cell at 22° C (space group Amma) has a=7.003 (1) Å, b=6.996 (2) Å and c=6.242 (1) Å, V=305.9 (2) ų. At room temperature, the thermal expansion coefficients α and β (α in °C^?1×10⁴, β in °C^?2×10⁸) are for a, 0.10, ?0.69; for b, 0.08, 0.19; for c, 0.18, 1.60; for V, 0.37, 1.14. Second-order coefficients provide an excellent fit over the whole range to 1,000° C.     

Thermal expansion of hydrated six-coordinate silicon in thaumasite,Ca<Subscript>3</Subscript>Si(OH)<Subscript>6</Subscript>(CO<Subscript>3</Subscript>)(SO<Subscript>4</Subscript>)·12H<Subscript>2</Subscript>O

Thaumasite, Ca₃Si(OH)₆(CO₃)(SO₄)12H₂O, occurs as a low-temperature secondary alteration phase in mafic igneous and metamorphic rocks, and is recognized as a product and indicator of sulfate attack in Portland cement. It is also the only mineral known to contain silicon in six-coordination with hydroxyl (OH)^? that is stable at ambient P–T conditions. Thermal expansion of the various components of this unusual structure has been determined from single-crystal X-ray structure refinements of natural thaumasite at 130 and 298 K. No phase transitions were observed over this temperature range. Cell parameters at room temperature are: a= 11.0538(6) Å, c=10.4111(8) Å and V=1101.67(10) ų, and were measured at intervals of about 50 K between 130 and 298 K, resulting in mean axial and volumetric coefficients of thermal expansion (×10^?5K^?1); α _a =1.7(1), α _c =2.1(2), and α _V =5.6(2). Although the unit cell and ^VIIICaO₈ polyhedra show significant positive thermal expansion over this temperature range, the silicate octahedron, sulfate tetrahedron, and carbonate group show zero or negative thermal expansion, with α _V (^VISiO₆) = ?0.6 ± 1.1, α _V (^IVSO₄)=?5.8 ± 1.4, and α _R (C–O)= 0.0 ± 1.8 (×10^?5 K^?1). Most of the thermal expansion is accommodated by lengthening of the R(O...O) hydrogen bond distances by on average 5σ, although the hydrogen bonds involving hydroxyl sites on ^VISi expand twice as much as those on molecular water, causing the [Ca₃Si(OH)₆(H₂O)₁₂]⁴⁺ columns to expand in diameter more than they move apart over this temperature range. The average Si–OH bond length of the six-coordinated Si atom 〈R(^VISi–OH)〉 in thaumasite is 1.783(1) Å, being about 0.02 Å (?20σ) shorter than ^VISi–OH in the dense hydrous magnesium silicate, phase D, MgSi₂H₂O₆.     

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.     

Anharmonicity and high-temperature heat capacity of crystals: the examples of Ca2GeO4, Mg2GeO4 and CaMgGeO4 olivines

Drop-calorimetry determinations of the isobaric heat capacity (C_P) of Mg₂GeO₄, Ca₂GeO₄ and CaMgGeO₄ have been made up to 1700 K. The thermal expansion coefficient (α) of these olivine germanates has been determined from high-temperature X-ray measurements up to 1500 K. From these measurements and available compressibility data, one calculates that the isochoric heat capacity (C_V) exceeds the harmonic limit of Dulong and Petit above 1000–1200 K. Such an intrinsic anharmonic behaviour can be accounted for by introducing anharmonic parameters a_i=(? ln v _i/?T)_V in vibrational modelling of C_V. These parameters are calculated from pressure and temperature shifts of the vibrational frequencies as measured by Raman spectroscopy up to 10 GPa at room temperature and up to 1300 K at 1 bar. A comparison of the Raman spectra of the three germanates with those of natural olivines justifies once again the use of germanates as silicate analogues. Extensive Ca,Mg disordering likely takes place in CaMgGeO₄, beginning at about 1100 K and leading to unusually high increases of the heat capacity and thermal expansion coefficient.     

Behavior of 10-Å phase at low temperatures

The thermal evolution of 10-Å phase Mg₃Si₄O₁₀(OH)₂·H₂O, a phyllosilicate which may have an important role in the storage/release of water in subducting slabs, was studied by X-ray single-crystal diffraction in the temperature range 116–293 K. The lattice parameters were measured at several intervals both on cooling and heating. The structural model was refined with intensity data collected at 116 K and compared to the model refined at room temperature. As expected for a layer silicate on cooling in this temperature range, the a and b lattice parameters undergo a small linear decrease, α _a  = 1.7(4) 10^?6 K^?1 and α _b  = 1.9(4) 10^?6 K^?1, where α is the linear thermal expansion coefficient. The greater variation is along the c axis and can be modeled with the second order polynomial c _T  = c ₂₉₃(1 + 6.7(4)10^?5 K^?1ΔT + 9.5(2.5)10^?8 K^?2(ΔT)²) where ΔT = T ? 293 K; the monoclinic angle β slightly increased. The cell volume thermal expansion can be modeled with the polynomial V _T  = V ₂₉₃ (1 + 8.0 10^?5 K^?1 ΔT + 1.4 10^?7 K^?2 (ΔT)²) where ΔT = T ? 293 is in K and V in ų. These variations were similar to those expected for a pressure increase, indicating that T and P effects are approximately inverse. The least-squares refinement with intensity data measured at 116 K shows that the volume of the SiO₄ tetrahedra does not change significantly, whereas the volume of the Mg octahedra slightly decreases. To adjust for the increased misfit between the tetrahedral and octahedral sheets, the tetrahedral rotation angle α changes from 0.58° to 1.38°, increasing the ditrigonalization of the silicate sheet. This deformation has implications on the H-bonds between the water molecule and the basal oxygen atoms. Furthermore, the highly anisotropic thermal ellipsoid of the H₂O oxygen indicates positional disorder, similar to the disorder observed at room temperature. The low-temperature results support the hypothesis that the disorder is static. It can be modeled with a splitting of the interlayer oxygen site with a statistical distribution of the H₂O molecules into two positions, 0.6 Å apart. The resulting shortest O_bas–O_W distances are 2.97 Å, with a significant shortening with respect to the value at room temperature. The low-temperature behavior of the H-bond system is consistent with that hypothesized at high pressure on the basis of the Raman spectra evolution with P.     

Effect of high-low quartz transition on compressional and shear wave velocities in rocks under high pressure

The compressional and shear wave velocities in quarzite, granite, and granulite are determined at a fixed confining pressure of 2 kb as a function of temperature up to 720° C. The high-low quartz transition of the constituent quartz minerals is associated with a pronounced decrease in velocity of the compressional waves when approaching the transition and with a significant velocity increase after the transition. In contrast, the effect of the α-β transition on shear wave velocities is small. The drop of V _P is explained by the elastic softening of structure of the constituent quartz minerals near the α-β transition and the opening of grain-boundary cracks, caused by the very high volumetric thermal expansion of the quartz relative to the other component minerals. The velocity increase in the β-field may be attributed to an elastic hardening of the quartz structure. Poisson ratios computed from the velocity data are anomalous for a solid: they become negative within the transition regime. The transition temperature, as indicated by the minimum velocities, is higher in the polycristalline rocks than is expected on grounds of single crystal behavior, and the discrepancy is more marked in granite than in quartzite. The shift of the transition temperature to higher values is explained by internal stresses that arise from the anisotropy of the thermal expansion and compressibility of individual grains and the differences in thermal expansion and compressibility between different component minerals. The role of the α-β quartz transition as a possible cause of low-velocity layers is discussed.     

The thermal expansion and crystal structure of mirabilite (Na<Subscript>2</Subscript>SO<Subscript>4</Subscript>·10D<Subscript>2</Subscript>O) from 4.2 to 300 K,determined by time-of-flight neutron powder diffraction

We have collected high resolution neutron powder diffraction patterns from Na₂SO₄·10D₂O over the temperature range 4.2–300 K following rapid quenching in liquid nitrogen, and over a series of slow warming and cooling cycles. The crystal is monoclinic, space-group P2₁/c (Z = 4) with a = 11.44214(4) Å, b = 10.34276(4) Å, c = 12.75486(6) Å, β = 107.847(1)°, and V = 1436.794(8) Å³ at 4.2 K (slowly cooled), and a = 11.51472(6) Å, b = 10.36495(6) Å, c = 12.84651(7) Å, β = 107.7543(1)°, V = 1460.20(1) Å³ at 300 K. Structures were refined to R _P (Rietveld powder residual, \( R_{P} = {{\sum {\left| {I_{\text{obs}} - I_{\text{calc}} } \right|} } \mathord{\left/ {\vphantom {{\sum {\left| {I_{\text{obs}} - I_{\text{calc}} } \right|} } {\sum {I_{\text{obs}} } }}} \right. \kern-\nulldelimiterspace} {\sum {I_{\text{obs}} } }} \)) better than 2.5% at 4.2 K (quenched and slow cooled), 150 and 300 K. The sulfate disorder observed previously by Levy and Lisensky (Acta Cryst B34:3502–3510, 1978) was not present in our specimen, but we did observe changes with temperature in deuteron occupancies of the orientationally disordered water molecules coordinated to Na. The temperature dependence of the unit-cell volume from 4.2 to 300 K is well represented by a simple polynomial of the form V = ? 4.143(1) × 10^?7 T ³ + 0.00047(2) T² ? 0.027(2) T + 1437.0(1) Å³ (R ² = 99.98%). The coefficient of volume thermal expansion, α _V , is positive above 40 K, and displays a similar magnitude and temperature dependence to α _V in deuterated epsomite and meridianiite. The relationship between the magnitude and orientation of the principal axes of the thermal expansion tensor and the main structural elements are discussed; freezing in of deuteron disorder in the quenched specimen affects the thermal expansion, manifested most obviously as a change in the behaviour of the unit-cell parameter β.     

Phase transition of potassium sulfate,K2SO4 (III); thermodynamical and phenomenological study

The orthorhombic-hexagonal phase transition of K₂SO₄ has been investigated by measurements of the temperature dependencies of the specific heat, expansion, and X-ray intensity of superstructure reflections, correlated with the structural point of view. The values of the net enthalpy and entropy changes are ΔH=4.28 KJ/mol and ΔS=4.98 J/mol·K at the phase transition temperature (587°C), respectively. The thermal expansion along the c axis shows strong anisotropic character above about 300°C and exhibits a very large discontinuous increase at 587°C, whereas those along the a and b axes increase linearly and exhibit small discontinuous decreases at 587°C. The X-ray intensity of superstructure reflections in the low-temperature form gradually decrease with increasing temperature, and come to extinction at 587°C, exhibiting a discontinuity. The observed entropy change and pressure dependence of the phase transition temperature were explained successfully by the use of results of the structural analysis and measured physical properties. The temperature dependencies of the spontaneous strain, X-ray intensity of superstructure reflection, and birefringence were consistently described by introducing a transition parameter on the basis of an instability at the M point in the Brillouin zone of the hexagonal phase.     

High-temperature thermodynamic properties of alkali feldspars

Recent hydrofluoric acid solution calorimetric data are used to derive standard enthalpies and Gibbs free energies of formation of low-albite, high-albite, NaAlSi₃O₈ glass, microcline, sanidine, and KAlSi₃O₈ glass. The data are presented as high-temperature functions from 298.15 to 1400° K.     

The active region Orion KL in polarized emission in the Orion

The fine structure of the active region in the Orion KL gas-dust complex has been measured in polarized H₂O maser emission (epoch December 12, 1998) with an angular resolution of 0.15 mas, or 0.07 AU, and a velocity resolution of 0.05 km/s. The maser emission is concentrated in a line with ΔV = 0.45 km/s, V _LSR = 7.65 km/s, and a flux density of F = 2.1 MJy. The structure consists of a compact source (ejector), highly collimated bipolar outflow, and a toroidal component. The brightness temperature of the ejector is T _b = 2 × 10¹⁶ K, and its degree of linear polarization reaches m ≈ 20%. The variation of the polarization angle across the profile is dX/dV = ?23°/(km/s), which considerably exceeds the Faraday rotation in the HII region foreground to the molecular cloud. The observed “rotation” is explained as an effect of different orientations for the polarization of the ejected outflows. The brightness temperature of the bipolar outflow is T _b ≈ 10¹⁴ K, while that of individual components is T _b ≈ 10¹⁵ K. The degree of polarization in the components exceeds that of the ejector and reaches m ≈ 50%. The position angle of the polarization is X ≈ 45° relative to the outflow. The torus, which is observed edge-on, has a diameter of 0.38 AU and a thickness of 0.08 AU. The brightness temperature of the tangential directions in the torus is T _b ≈ 5 × 10¹⁵ K, and the rotational velocity is V _rot ≈ 0.02 km/s. The degree of polarization is m ≈ 40%, and its position angle relative to the azimuthal plane is X ≈ 43°. The relative deviations of the polarization plane in the bipolar outflow and torus relative to the pumping direction are nearly the same and are determined by Faraday rotation within the HII region.     

Density variations of Cr-rich garnets in the upper mantle inferred from the elasticity of uvarovite garnet

The thermoelastic parameters of Ca₃Cr₂Si₃O₁₂ uvarovite garnet were examined in situ at high pressure up to 13 GPa and high temperature up to 1100 K by synchrotron radiation energy-dispersive X-ray diffraction within a 6-6-type multi-anvil press apparatus. A least-square fitting of room T data to a third-order Birch–Murnaghan (BM3) EoS yielded K₀ = 164.2 ± 0.7 GPa, V₀ = 1735.9 ± 0.3 ų (K’₀ fixed to 4.0). P–V–T data were fitted simultaneously by a modified HT-BM3 EoS, which gave the isothermal bulk modulus K₀ = 163.6 ± 2.6 GPa, K’₀ = 4.1 ± 0.5, its temperature derivative (?K_0,T/?T)_P = –0.014 ± 0.002 GPa K^?1, and the thermal expansion coefficients a₀ = 2.32 ± 0.13 ×10^?5 K^?1 and b₀ = 2.13 ± 2.18 ×10^?9 K^?2 (K’₀ fixed to 4.0). Our results showed that the Cr³⁺ enrichment in natural systems likely increases the density of ugrandite garnets, resulting in a substantial increase of mantle garnet densities in regions where Cr-rich spinel releases chromium through a metasomatic reaction.     

Raman spectra and X-ray diffraction of tuite at various temperatures

High-temperature Raman spectra and thermal expansion of tuite, γ-Ca₃(PO₄)₂, have been investigated. The effect of temperature on the Raman spectra of synthetic tuite was studied in the range from 80 to 973 K at atmospheric pressure. The Raman frequencies of all observed bands for tuite continuously decrease with increasing temperature. The quantitative analysis of temperature dependence of Raman bands indicates that the changes in Raman frequencies for stretching modes (ν₃ and ν₁) are faster than those for bending modes (ν₄ and ν₂) of PO₄ in the present temperature range, which may be attributed to the structural evolution of PO₄ tetrahedron in tuite at high temperature. The thermal expansion of tuite was examined by means of in situ X-ray diffraction measurements in the temperature range from 298 to 923 K. Unit cell parameters and volume were analyzed, and the thermal expansion coefficients were obtained as 3.67 (3), 1.18 (1), and 1.32 (3) × 10^?5 K^?1 for V, a, and c, respectively. Thermal expansion of tuite shows an axial anisotropy with a larger expansion coefficient along the c-axis. The isothermal and isobaric mode Grüneisen parameters and intrinsic anharmonicity of tuite have been calculated by using present high-temperature Raman spectra and thermal expansion coefficient combined with previous results of the isothermal bulk modulus and high-pressure Raman spectra.     

Stability and P–V–T equation of state of KAlSi3O8-hollandite determined by in situ X-ray observations and implications for dynamics of subducted continental crust material

In situ X-ray diffraction measurements of KAlSi₃O₈-hollandite (K-hollandite) were performed at pressures of 15–27 GPa and temperatures of 300–1,800 K using a Kawai-type apparatus. Unit-cell volumes obtained at various pressure and temperature conditions in a series of measurements were fitted to the high-temperature Birch-Murnaghan equation of state and a complete set of thermoelastic parameters was obtained with an assumed K′_300,0=4. The determined parameters are V _300,0=237.6(2) Å³, K _300,0=183(3) GPa, (?K _T,0/?T) _P =?0.033(2) GPa K^?1, a ₀=3.32(5)×10^?5 K^?1, and b ₀=1.09(1)×10^?8 K^?2, where a ₀ and b ₀ are coefficients describing the zero-pressure thermal expansion: α _T,0 = a ₀ + b ₀ T. We observed broadening and splitting of diffraction peaks of K-hollandite at pressures of 20–23 GPa and temperatures of 300–1,000 K. We attribute this to the phase transitions from hollandite to hollandite II that is an unquenchable high-pressure phase recently found. We determined the phase boundary to be P (GPa)=16.6 + 0.007 T (K). Using the equation of state parameters of K-hollandite determined in the present study, we calculated a density profile of a hypothetical continental crust (HCC), which consists only of K-hollandite, majorite garnet, and stishovite with 1:1:1 ratio in volume. Density of HCC is higher than the surrounding mantle by about 0.2 g cm^?3 in the mantle transition zone while this relation is reversed below 660-km depth and HCC becomes less dense than the surrounding mantle by about 0.15 g cm^?3 in the uppermost lower mantle. Thus the 660-km seismic discontinuity can be a barrier to prevent the transportation of subducted continental crust materials to the lower mantle and the subducted continental crust may reside at the bottom of the mantle transition zone.     

Thermal expansion of fayalite,Fe2SiO4

Thermal expansion of single-crystal fayalite has been measured by a dilatometric method at temperatures between 25 °C and 850 °C. The results show the presence of anomalous expansion in the b axis, which is correlated to the anomalous variation of elastic moduli with temperature. Grüneisen's parameter is 1.10 and the thermal Debye temperature is 565 K, which is close to the acoustic Debye temperature of 511 K.     

Partitioning of strontium between calcite,dolomite and liquids: An experimental study under higher temperature diagenetic conditions,and a model for the prediction of mineral pairs for geothermometry

The partitioning of Sr between calcite, dolomite and liquids is essentially independent of temperature between 150° and 350° C. The partition coefficients corrected for number of cation sites are b _calc=0.096 and b _dol= 0.048 for 1 mol cations/6 mol H₂O liquid. Upon dilution the partition coefficients increase, but their ratio stays constant at about 2∶1. This ratio is due to the fact that calcite has twice as many Ca-sites for Sr-substitution as dolomite. The 2∶1 relationship is also observed in natural calcite and dolomite which have undergone diagenesis. The temperature independence of partitioning is caused by the relatively small thermal expansion of calcite and dolomite. Thermal expansion between 25° and 400° C was found to follow the equations V _calc=7.0·10⁻⁴ T(°C)+36.95 and V _dol=6.9·10⁻⁴ T(°C)+32.24, V: cm³/mol. Therefore calcite and dolomite cannot serve as a temperature indicator. To have an ideal geothermometer a mineral pair with high and low thermal expansion is required. Literature date demonstrate that wurtzite, sphalerite, and galena are such minerals.     

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

The Grüneisen ratio, γ, is defined as γy=αK _TV/C_v. The volume dependence of γ(V) is solved for a wide range in temperature. The volume dependence of αK _T is solved from the identity (? ln(αK _T)/? ln V)T ≡ δ _T-K′. α is the thermal expansivity; K _T is the bulk modulus; C _V is specific heat; and δ _Tand K′ are dimensionless thermoelastic constants. The approach is to find values of δ _T and K′, each as functions of T and V. We also solve for q=(? ln γ/? ln V) where q=δ _T -K′+ 1-(? ln C _V/? ln V)T. Calculations are taken down to a compression of 0.6, thus covering all possible values pertaining to the earth's mantle, q=? ln γ/? ln V; δ _T=? ln α/? ln V; and K′= (?K _T/?P)T. New experimental information related to the volume dependence of δ _T, q, K′ and C _V was used. For MgO, as the compression, η=V/V ₀, drops from 1.0 to 0.7 at 2000 K, the results show that q drops from 1.2 to about 0.8; δ _T drops from 5.0 to 3.2; δ _T becomes slightly less than K′; ? ln C _V/? 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.