MgSiO3 ilmenite: Heat capacity,thermal expansivity,and enthalpy of transformation

A new determination, using high temperature drop-solution calorimetry, of the enthalpy of transformation of MgSiO₃ pyroxene to ilmenite gives H ₂₉₈ = 59.03 ±4.26 kJ/mol. The heat capacity of the ilmenite and orthopyroxene phases has been measured by differential scanning calorimetry at 170–700 K; C_p of MgSiO₃ ilmenite is 4–10 percent less than that of MgSiO₃ pyroxene throughout the range studied. The heat capacity differences are consistent with lattice vibrational models proposed by McMillan and Ross (1987) and suggest an entropy change of -18 ± 3 J-K^-1 ·mol^-1, approximately independent of temperature, for the pyroxene-ilmenite transition. The unit cell parameters of MgSiO₃ ilmenite were measured at 298–876 K and yield an average volume thermal expansion coefficient of 2.44 × 10^-5 K^-1. The thermochemical data are used to calculate phase relations involving pyroxene, -Mg₂SiO₄ plus stishovite, Mg₂SiO₄ spinel plus stishovite, and ilmenite in good agreement with the results of high pressure studies.     

A new method to calculate end-member thermodynamic properties of minerals from their constituent polyhedra II: heat capacity, compressibility and thermal expansion

Thermodynamic calculations in petrology are generally performed at pressures and temperatures beyond the standard state conditions. Accurate prediction of mineral equilibria therefore requires knowledge of the heat capacity, thermal expansion and compressibility for the minerals involved. Unfortunately, such data are not always available. In this contribution we present a data set to estimate the heat capacity, thermal expansion and compressibility of mineral end‐members from their constituent polyhedra, based on the premise that the thermodynamic properties of minerals can be described by a linear combination of the fractional properties of their constituents. As such, only the crystallography of the phase of interest needs to be known. This approach is especially powerful for hypothetical mineral end‐members and for minerals, for which the experimental determination of their thermodynamic properties is difficult. The data set consists of the properties for 35 polyhedra in the system K–Na–Ca–Li–Be–Mg–Mn–Fe–Co–Ni–Zn–Al–Ti–Si–H, determined by multiple linear regression analysis on a data set of 111 published end‐member thermodynamic properties. The large number of polyhedra determined allows calculation of a much larger variety of phases than was previously possible, and the choice of constituents together with the large number of thermodynamic input data results in estimates with associated uncertainty of generally <5%. The quality of the data appears to be sufficiently accurate for thermodynamic modelling as demonstrated by modelling the stability of margarite in the CASH system and the position of the talc–staurolite–chloritoid–pyrope absent invariant point in the KMASH system. In both cases, our results overlap within error with published equivalents.     

含层理砂岩热膨胀系数的试验研究

在放射性核废料处置、地热能源开采以及地下油气储存等工程中,热量的传递将会在很大程度上改变岩土材料的力学性质,因此,岩土体及缓冲材料的热力学参数,包括热传导系数、热膨胀系数、比热容对工程设计以及安全性评价有着至关重要的作用。利用自主研制的岩石膨胀系数测试仪对含层理砂岩进行了热膨胀系数试验,研究了岩石轴向和径向热膨胀系数的变化规律,结果表明:对于含水平层理岩样,随着温度的变化,当膨胀均匀后,轴向热膨胀系数约为14×10~(-6)℃~(-1),而径向热膨胀系数约为9×10~(-6)℃~(-1),前者约为后者的1.56倍,表现出明显的各向异性;相比于含水平层理岩样,含竖直或倾斜层理岩样的轴向膨胀系数未见显著差异,但径向热膨胀系数明显增加;相同温度下,径向热膨胀系数从大到小的顺序为:竖直方向、倾斜方向和水平方向;由于岩样中沉积层的存在,砂岩与沉积物质的膨胀性能并不相同,这将导致岩样的轴向和径向热膨胀系数表现出各向异性。该研究成果对于岩体的热-力耦合特性研究具有一定的参考意义。     

Hydrostatic compression of ilmenite phase of ZnSiO3 and MgGeO3

Accurate measurements of cell parameters were performed on the ilmenite phases of ZnSiO₃ and MgGeO₃ using an X-ray diffraction method under hydrostatic conditions. The linear changes in cell parameter are represented by 1?a/a ₀=(1.06±0.04)×10^?4 P(kbar) and 1?c/c ₀=(2.11±0.04)×10^?4 P for ZnSiO₃, and 1?a/a ₀=(1.37±0.03)×10^?4 P and 1?c/c ₀=(2.05±0.04)×10^?4 P for MgGeO₃. A least-squares calculation using the first-order Birch-Murnaghan equation gives K _T =2.16±0.02 Mbar and K _T =1.87±0.02 Mbar for ZnSiO₃ and MgGeO₃, respectively. Elastic systematics assuming K _T V _m =constant give a predicted value K _T =2.14 Mbar for the ilmenite phase of MgSiO₃.     

A thermodynamic analysis of the system LiAlSiO4-NaAlSiO4-Al2O3-SiO2-H2O based on new heat capacity, thermal expansion, and compressibility data for selected phases

Heat capacity, thermal expansion, and compressibility data have been obtained for a number of selected phases of the system NaAlSiO₄-LiAlSiO₄-Al₂O₃-SiO₂-H₂O. All C _p measurements have been executed by DSC in the temperature range 133–823 K. The data for T ≥ 223 K have been fitted to the function C _p (T) = a + cT ⁻² + dT ^−0.5 + fT ⁻³, the fit parameters being The thermal expansion data (up to 525 °C) have been fitted to the function V ⁰(T) = V ⁰(T) [1 + v ₁ (T−T ⁰) + v ₂ (T−T ⁰)²], with T ⁰ = 298.15 K. The room-temperature compressibility data (up to 6 GPa) have been smoothed by the Murnaghan equation of state. The resulting parameters are These data, along with other phase property and reaction reversal data from the literature, have been simultaneously processed by the Bayes method to derive an internally consistent thermodynamic dataset (see Tables 6 and 7) for the NaAlSiO₄-LiAlSiO₄-Al₂O₃-SiO₂-H₂O quinary. Phase diagrams generated from this dataset are compatible with cookeite-, ephesite-, and paragonite-bearing assemblages observed in metabauxites and common metasediments. Phase diagrams obtained from the same database are also in agreement with the cookeite-free, petalite-, spodumene-, eucryptite-, and bikitaite-bearing assemblages known to develop in the subsolidus phase of recrystallization of␣lithium-bearing pegmatites. It is gratifying to note that the cookeite phase relations predicted earlier by Vidal and Goffé (1991) in the context of the system Li₂O-Al₂O₃-SiO₂-H₂O agree with our results in a general way. Received: 19 May 1998 / Accepted: 25 June 1998     

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     

Analytical expressions to determine the isothermal compressibility tensor and the isobaric thermal expansion tensor for monoclinic crystals: application to determine the direction of maximum compressibility in jadeite

Expressions are presented to allow the simple determination of the magnitudes and directions of the principal axes for the isothermal compressibility tensor and the isobaric thermal expansion tensor for monoclinic crystals. The method is applied to re-evaluate the apparently contradictory results that have recently been obtained for the direction of maximum compressibility in jadeite. The term ‘unit strain’ to describe these second rank tensors is discouraged and the use of the representation quadric for visualisation of second rank tensors is recommended.     

On the use of the volumetric thermal expansion coefficient in models of ocean floor topography

The use of the volumetric thermal expansion coefficient, instead of the linear coefficient, in successful models of ocean floor topography implies that the elastic rigidity of the lithosphere relaxes, enabling isostasy to be achieved. However, the presence of a thin elastic lid in the lithosphere, inferred from gravity investigations, implies some rigidity at the top of the lithospheric column and suggests that the volumetric thermal expansion coefficient derived from rheologically uniform models of the topography is about 15% too small.     

The ZnSiO3 clinopyroxene-ilmenite transition: Heat capacity,enthalpy of transition,and phase equilibria

ZnSiO₃ clinopyroxene stable above 3 GPa transforms to ilmenite at 10–12 GPa, which further decomposes into ZnO (rock salt) plus stishovite at 20–30 GPa. The enthalpy of the clinopyroxene-ilmenite transition was measured by high-temperature solution calorimetry, giving ΔH⁰=51.71 ±3.18 kJ/mol at 298 K. The heat capacities of clinopyroxene and ilmenite were measured by differential scanning calorimetry at 343–733 and 343–633 K, respectively. The C _p of ilmenite is 3–5% smaller than that of clinopyroxene. The entropy of transition was calculated using the measured enthalpy and the free energy calculated from the phase equilibrium data. The enthalpy, entropy and volume changes of the pyroxene-ilmenite transition in ZnSiO₃ are similar in magnitude to those in MgSiO₃. The present thermochemical data are used to calculate the phase boundary of the ZnSiO₃ clinopyroxene-ilmenite transition. The calculated boundary,

High-temperature thermal expansion of lime, periclase, corundum and spinel

The high-temperature cell parameters of lime (CaO), periclase (MgO), corundum (Al₂O₃), and spinel (MgAl₂O₄) have been determined from 300 up to 3000 K through X-ray diffraction experiments with synchrotron radiation. The good agreement found with dilatometric results suggests that vacancy-type defects do not make a large contribution to thermal expansion for these oxides, even near the melting point, justifying the use of X-ray diffraction for determining volume properties up to very high temperatures. Thermal expansion coefficients were determined from the measured cell volumes with equations of the form α=α₀ + α₁ T + α₂/T ². Along with available isobaric heat capacity and compressibility data, these derived coefficients clearly show that anharmonic effects contribute little to the isochoric heat capacities (C _v ) of CaO, MgO, and Al₂O₃, which do not depart appreciably from the 3nR Dulong and Petit limit. Received: 31 March 1999 / Revised, accepted: 23 June 1999     

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).     

Heat capacity calculations for Al2O3 corundum and MgSiO3 ilmenite

We have used Kieffer's vibrational model to calculate heat capacities and entropies for Al₂O₃ corundum and MgSiO₃ ilmenite, using available vibrational and elastic data for these phases. The calculated heat capacity for corundum is within 1–2 percent of the experimental values between 100 K and 1,800 K, while that for MgSiO₃ ilmenite is within 1–2 percent of the experimental data between 350 K and 500 K. We have calculated the heat capacity for MgSiO₃ ilmenite from 50 K to 1,800 K, which extends the range of available heat capacity data for this phase. The results of this calculation suggest that there may be differences in the vibrational properties of corundum and MgSiO₃ ilmenite. Finally, we have used the results of our calculation to obtain a transition entropy of near -18.8 J/mol.K for the MgSiO₃ pyroxene-ilmenite reaction.     

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:

The thermal expansion of ScAlO3 — A silicate perovskite analogue

The crystal structure of ScAlO₃ has been refined at temperatures up to 1100° C on the basis of x-ray powder diffraction data. The thermal expansion is adequately described by a Grüneisen-Debye model with the elastic Debye temperature and an effective Grüneisen parameter of 1.6. The volumetric thermal expansion of 3.0% between 10 and 1100° C, corresponding to a mean thermal expansion coefficient of 2.7 × 10⁻⁵ K⁻¹, is entirely attributable to the expansion of the AlO₆ octahedra. The interoctahedral angles, though not fixed by symmetry, do not vary significantly with temperature —indicating that the expansivities of the constituent AlO₆ and distorted ScO₈ polyhedra are well matched. Similar considerations of polyhedral expansivity suggest thermal expansion coefficients of ∼2 × 10⁻⁵K⁻¹ for cubic CaSiO₃ perovskite and a value between 2 × 10⁻⁵ K⁻¹ and 4 × 10⁻⁵ K⁻¹ for MgSiO₃ perovskite. The lower value is consistent with the reconnaissance measurements for Mg_0.9Fe_0.1SiO₃ (Knittle et al. 1986) below 350° C, with low-temperature measurements of single-crystal MgSiO₃ (Ross and Hazen 1989), and with the results of some recent calculations. The markedly greater expansivity ∼4 × 10⁻⁵ K⁻¹ measured at higher temperatures (350–570° C) by Knittle et al. is inconsistent with the simple Grüneisen-Debye quasiharmonic model and may reflect the marginal metastability of the orthorhombic perovskite phase. Under these circumstances, extrapolation of the measured expansivity is hazardous and may result in the under-estimation of lower mantle densities and the drawing of inappropriate inferences concerning the need for chemical stratification of the Earth's mantle.     

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.     

High-temperature study and thermal expansion of phlogopite

 Unit-cell dimensions of a natural phlogopite from Pargas, Finland, have been determined in the temperature interval of 27–1050 °C by X-ray powder diffraction technique. Expansion rates vary discontinuously with temperature with a break at 412 °C. Below this temperature, the linear expansions (α) for a, b and c axis lengths are 3.74 × 10⁻⁵ K⁻¹, 1.09 × 10⁻⁵ K⁻¹, and 1.19 × 10⁻⁵ K⁻¹, respectively, and above that they are 0.86 × 10⁻⁵ K⁻¹, 0.80 × 10⁻⁵ K⁻¹, and 1.93 × 10⁻⁵ K⁻¹. The volume thermal expansion coefficients are 6.26 × 10⁻⁵ K⁻¹ and 3.71 × 10⁻⁵ K⁻¹ for low-temperature and high-temperature intervals, respectively. The observed kink in the rate of thermal expansions with temperature could be due to the different mode of structural changes. Thermogravimetric analysis of the sample indicates the oxidation of iron in the temperature range of 500–600 °C and dehydroxylation as well as decomposition of phlogopite in the temperature range of 900–1200 °C. Received: 8 September 1998 / Accepted: 28 February 2000     

Molar volume and thermal expansion of glaucophane

The molar volume of glaucophane [Na₂Mg₃Al₂Si₈O₂₂(OH)₂] has been determined in this study by correcting synthetic glaucophane-rich amphiboles made in the system Na₂O–MgO–Al₂O₃–SiO₂–H₂O for very small deviations from ideal glaucophane composition using recent volume data on key amphibole components. The derived unit-cell volume for end-member glaucophane is 862.7±1.6 Å³, which gives a molar volume of 259.8±0.5 cm³/mol and a calculated density of 3.016±0.006 g/cm³. This value has been corroborated through an essentially independent method by correcting the volumes of natural sodic amphiboles reported in the literature for non-glaucophane components, particularly including calcium-rich components, to yield a value of 861.2±1.9 Å³. The unit-cell volume derived from the synthetic amphiboles, which is considered here to be more reliable, is somewhat smaller than that reported previously in the literature. A thermal expansion (α_V) at 298 K of 1.88±0.06×10^?5/K was derived from unit-cell volumes measured in the range of 25–500°C for a synthetic glaucophane sample, which is noticeably smaller than previously reported.     

Compression and coordination changes in pyroxenoids: an EXAFS study of MgGeO3 enstatite and CaGeO3 wollastonite

The evolution of the distortion of MgGeO₃ enstatite and CaGeO₃ wollastonite with increasing pressure, has been investigated using X-ray absorption spectroscopy (XAS) in a diamond anvil cell. At room temperature and low pressure (P<7 GPa), the compressibility of the GeO₄ tetrahedron is higher in MgGeO₃ enstatite (K _[GeO4]∼135 GPa) than in CaGeO₃ wollastonite (K _[GeO4]≥ 280 GPa). The compression mechanisms of the two compounds are different: the whole mineral compressibility of Ge-enstatite appears to be very homogeneous, in contrast to that of Ge-wollastonite which exhibits an inhomogeneous tretrahedral compressibility. This result is consistent with the variation of the Debye-Waller factors of the two compounds with increasing pressure. At higher pressures, the coordination of germanium atoms in the two compounds gradually changes from fourfold to sixfold. For CaGeO₃ the coordination change starts at 7 GPa and is complete a 12 GPa, whereas it starts at about 8.5 GPa for MgGeO₃ and is not complete at 31 GPa. The progressive evolution of the measured Ge-O distances as well as the modification in the X-ray absorption near-edge structure indicate two coexisting different sites rather than a progressive site modification. The transformation is found to be partially reversible in CaGeO₃ wollastonite, whereas it is totally reversible in MgGeO₃ enstatite.     

Heat capacity and phase equilibria of hollandite polymorph of KAlSi3O8

The low-temperature heat capacity (C _p ) of KAlSi₃O₈ with a hollandite structure was measured over the range of 5–303 K with a physical properties measurement system. The standard entropy of KAlSi₃O₈ hollandite is 166.2±0.2 J mol⁻¹ K⁻¹, including an 18.7 J mol⁻¹ K⁻¹ contribution from the configurational entropy due to disorder of Al and Si in the octahedral sites. The entropy of K₂Si₄O₉ with a wadeite structure (Si-wadeite) was also estimated to facilitate calculation of phase equilibria in the system K₂O–Al₂O₃–SiO₂. The calculated phase equilibria obtained using Perple_x are in general agreement with experimental studies. Calculated phase relations in the system K₂O–Al₂O₃–SiO₂ confirm a substantial stability field for kyanite–stishovite/coesite–Si-wadeite intervening between KAlSi₃O₈ hollandite and sanidine. The upper stability of kyanite is bounded by the reaction kyanite (Al₂SiO₅) = corundum (Al₂O₃) + stishovite (SiO₂), which is located at 13–14 GPa for 1,100–1,400 K. The entropy and enthalpy of formation for K-cymrite (KAlSi₃O₈·H₂O) were modified to better fit global best-fit compilations of thermodynamic data and experimental studies. Thermodynamic calculations were undertaken on the reaction of K-cymrite to KAlSi₃O₈ hollandite + H₂O, which is located at 8.3–10.0 GPa for the temperature range 800–1,600 K, well inside the stability field of stishovite. The reaction of muscovite to KAlSi₃O₈ hollandite + corundum + H₂O is placed at 10.0–10.6 GPa for the temperature range 900–1,500 K, in reasonable agreement with some but not all experiments on this reaction.