Electrical conductivity of dry and hydrous NaAlSi<Subscript>3</Subscript>O<Subscript>8</Subscript> glasses and liquids at high pressures

We report the first study of electrical conductivities of silicate melts at very high pressures (up to 10 GPa) and temperatures (up to 2,173 K). Impedance spectroscopy was applied to dry and hydrous albite (NaAlSi₃O₈) glasses and liquids (with 0.02–5.7 wt% H₂O) at 473–1,773 K and 0.9–1.8 GPa in a piston-cylinder apparatus, using a coaxial cylindrical setup. Measurements were also taken at 473–2,173 K and 6–10 GPa in two multianvil presses, using simple plate geometry. The electrical conductivity of albite melts is found to increase with temperature and water content but to decrease with pressure. However, at 6 GPa, conductivity increases rapidly with temperature above 1,773 K, so that at temperatures beyond 2,200 K, conductivity may actually increase with pressure. Moreover, the effect of water in enhancing conductivity appears to be more pronounced at 6 GPa than at 1.8 GPa. These observations suggest that smaller fractions of partial melt than previously assumed may be sufficient to explain anomalously high conductivities, such as in the asthenosphere. For dry melt at 1.8 GPa, the activation energy at T > 1,073 K is higher than that at T < 1,073 K, and the inflection point coincides with the rheological glass transition. Upon heating at 6–10 GPa, dry albite glass often shows a conductivity depression starting from ~1,173 K (due to crystallization), followed by rapid conductivity enhancement when temperature approaches the albite liquidus. For hydrous melts at 0.9–1.8 GPa, the activation energies for conductivity at ≥1,373 K are lower than those at <973 K, with a complex transition pattern in between. Electrical conductivity and previously reported Na diffusivity in albite melt are consistent with the Nernst–Einstein relation, suggesting the dominance of Na transport for electrical conduction in albite melts.     

High-<Emphasis Type="Italic">P</Emphasis>, <Emphasis Type="Italic">T</Emphasis> phase relations in the NaAlSi<Subscript>2</Subscript>O<Subscript>6</Subscript> system from first principles computation

Vibrational density of states of the NaAlSi₂O₆ jadeite and NaAlSiO₄ calcium ferrite (CF)-type, and SiO₂ stishovite is calculated as a function of pressure up to 50 GPa using density functional perturbation theory. The calculated frequencies are used to determine the thermal contribution to the Helmholtz free energy within the quasi-harmonic approximation and to derive the equation of state and several thermodynamic properties of interest. A dissociation of jadeite into a mixture of a CF-type phase and stishovite is predicted to occur at 23.4 GPa and 1,800 K with a positive Clapeyron slope of 2.8 MPa/K. Elastic anisotropy for jadeite, the CF-type phase, and stishovite also computed clearly shows that stishovite and the CF-type phase are the most anisotropic and isotropic in these three phases, respectively.     

Thermoelastic properties of chromium oxide Cr<Subscript>2</Subscript>O<Subscript>3</Subscript> (eskolaite) at high pressures and temperatures

A new synchrotron X-ray diffraction study of chromium oxide Cr₂O₃ (eskolaite) with the corundum-type structure has been carried out in a Kawai-type multi-anvil apparatus to pressure of 15 GPa and temperatures of 1873 K. Fitting the Birch–Murnaghan equation of state (EoS) with the present data up to 15 GPa yielded: bulk modulus (K _0,T0), 206 ± 4 GPa; its pressure derivative K′_0,T , 4.4 ± 0.8; (?K _0,T /?T) = ?0.037 ± 0.006 GPa K^?1; a = 2.98 ± 0.14 × 10^?5 K^?1 and b = 0.47 ± 0.28 × 10^?8 K^?2, where α _0,T  = a + bT is the volumetric thermal expansion coefficient. The thermal expansion of Cr₂O₃ was additionally measured at the high-temperature powder diffraction experiment at ambient pressure and α _0,T0 was determined to be 2.95 × 10^?5 K^?1. The results indicate that coefficient of the thermal expansion calculated from the EoS appeared to be high-precision because it is consistent with the data obtained at 1 atm. However, our results contradict α ₀ value suggested by Rigby et al. (Brit Ceram Trans J 45:137–148, 1946) widely used in many physical and geological databases. Fitting the Mie–Grüneisen–Debye EoS with the present ambient and high-pressure data yielded the following parameters: K _0,T0 = 205 ± 3 GPa, K′_0,T  = 4.0, Grüneisen parameter (γ ₀) = 1.42 ± 0.80, q = 1.82 ± 0.56. The thermoelastic parameters indicate that Cr₂O₃ undergoes near isotropic compression at room and high temperatures up to 15 GPa. Cr₂O₃ is shown to be stable in this pressure range and adopts the corundum-type structure. Using obtained thermoelastic parameters, we calculated the reaction boundary of knorringite formation from enstatite and eskolaite. The Clapeyron slope (with \({\text{d}}P/{\text{d}}T = - 0.014\) GPa/K) was found to be consistent with experimental data.     

H<Subscript>2</Subscript>O storage capacity of olivine and low-Ca pyroxene from 10 to 13 GPa: consequences for dehydration melting above the transition zone

The onset of hydrous partial melting in the mantle above the transition zone is dictated by the H₂O storage capacity of peridotite, which is defined as the maximum concentration that the solid assemblage can store at P and T without stabilizing a hydrous fluid or melt. H₂O storage capacities of minerals in simple systems do not adequately constrain the peridotite water storage capacity because simpler systems do not account for enhanced hydrous melt stability and reduced H₂O activity facilitated by the additional components of multiply saturated peridotite. In this study, we determine peridotite-saturated olivine and pyroxene water storage capacities at 10–13 GPa and 1,350–1,450°C by employing layered experiments, in which the bottom ~2/3 of the capsule consists of hydrated KLB-1 oxide analog peridotite and the top ~1/3 of the capsule is a nearly monomineralic layer of hydrated Mg# 89.6 olivine. This method facilitates the growth of ~200-μm olivine crystals, as well as accessory low-Ca pyroxenes up to ~50 μm in diameter. The presence of small amounts of hydrous melt ensures that crystalline phases have maximal H₂O contents possible, while in equilibrium with the full peridotite assemblage (melt + ol + pyx + gt). At 12 GPa, olivine and pyroxene water storage capacities decrease from ~1,000 to 650 ppm, and ~1,400 to 1,100 ppm, respectively, as temperature increases from 1,350 to 1,450°C. Combining our results with those from a companion study at 5–8 GPa (Ardia et al., in prep.) at 1,450°C, the olivine water storage capacity increases linearly with increasing pressure and is defined by the relation C_{\textH2 \textO}^\textolivine ( \textppm ) = 57.6( ±16 ) ×P( \textGPa ) - 169( ±18 ). C_{{{\text{H}}_{2} {\text{O}}}}^{\text{olivine}} \left( {\text{ppm}} \right) = 57.6\left( { \pm 16} \right) \times P\left( {\text{GPa}} \right) - 169\left( { \pm 18} \right). Adjustment of this trend for small increases in temperature along the mantle geotherm, combined with experimental determinations of D_{\textH2 \textO}^{\textpyx/olivine} D_{{{\text{H}}_{2} {\text{O}}}}^{\text{pyx/olivine}} from this study and estimates of D_{\textH2 \textO}^{\textgt/\textolivine} D_{{{\text{H}}_{2} {\text{O}}}}^{{{\text{gt}}/{\text{olivine}}}} , allows for estimation of peridotite H₂O storage capacity, which is 440 ± 200 ppm at 400 km. This suggests that MORB source upper mantle, which contains 50–200 ppm bulk H₂O, is not wet enough to incite a global melt layer above the 410-km discontinuity. However, OIB source mantle and residues of subducted slabs, which contain 300–1,000 ppm bulk H₂O, can exceed the peridotite H₂O storage capacity and incite localized hydrous partial melting in the deep upper mantle. Experimentally determined values of D_{\textH2 \textO}^{\textpyx/\textolivine} D_{{{\text{H}}_{2} {\text{O}}}}^{{{\text{pyx}}/{\text{olivine}}}} at 10–13 GPa have a narrow range of 1.35 ± 0.13, meaning that olivine is probably the most important host of H₂O in the deep upper mantle. The increase in hydration of olivine with depth in the upper mantle may have significant influence on viscosity and other transport properties.     

Viscosity of albite melt at high pressure and high temperature

 The viscosity of albite (NaAlSi₃O₈) melt was measured at high pressure by the in situ falling-sphere method using a high-resolution X-ray CCD camera and a large-volume multianvil apparatus installed at SPring-8. This system enabled us to conduct in situ viscosity measurements more accurately than that using the conventional technique at pressures of up to several gigapascals and viscosity in the order of 10⁰ Pa s. The viscosity of albite melt is 5.8 Pa s at 2.6 GPa and 2.2 Pa s at 5.3 GPa and 1973 K. Experiments at 1873 and 1973 K show that the decrease in viscosity continues to 5.3 GPa. The activation energy for viscosity is estimated to be 316(8) kJ mol⁻¹ at 3.3 GPa. Molecular dynamics simulations suggest that a gradual decrease in viscosity of albite melt at high pressure may be explained by structural changes such as an increase in the coordination number of aluminum in the melt. Received: 6 January 2001 / Accepted: 27 August 2001     

High-pressure Raman studies and heat capacity measurements on the MgSiO<Subscript>3</Subscript> analogue CaIr<Subscript>0.5</Subscript>Pt<Subscript>0.5</Subscript>O<Subscript>3</Subscript>

Raman spectroscopy and heat capacity measurements have been used to study the post-perovskite phase of CaIr_0.5Pt_0.5O₃, recovered from synthesis at a pressure of 15 GPa. Laser heating CaIr_0.5Pt_0.5O₃ to 1,900 K at 60 GPa produces a new perovskite phase which is not recoverable and reverts to the post-perovskite polymorph between 20 and 9 GPa on decompression. This implies that Pt-rich CaIr_1−xPt_xO₃ perovskites including the end member CaPtO₃ cannot easily be recovered to ambient pressure from high P–T synthesis. We estimate an increase in the thermodynamic Grüneisen parameter across the post-perovskite to perovskite transition of 34%, of similar magnitude to those for (Mg,Fe)SiO₃ and MgGeO₃, suggesting that CaIr_0.5Pt_0.5O₃ is a promising analogue for experimental studies of the competition in energetics between perovskite and post-perovskite phases of magnesium silicates in Earth’s lowermost mantle. Low-temperature heat capacity measurements show that CaIrO₃ has a significant Sommerfeld coefficient of 11.7 mJ/mol K² and an entropy change of only 1.1% of Rln2 at the 108 K Curie transition, consistent with the near-itinerant electron magnetism. Heat capacity results for post-perovskite CaIr_0.5Rh_0.5O₃ are also reported.     

First-principles simulation of high-pressure polymorphs in MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript>

We have used density functional theory to investigate the stability of MgAl₂O₄ polymorphs under pressure. Our results can reasonably explain the transition sequence of MgAl₂O₄ polymorphs observed in previous experiments. The spinel phase (stable at ambient conditions) dissociates into periclase and corundum at 14 GPa. With increasing pressure, a phase change from the two oxides to a calcium-ferrite phase occurs, and finally transforms to a calcium-titanate phase at 68 GPa. The calcium-titanate phase is stable up to at least 150 GPa, and we did not observe a stability field for a hexagonal phase or periclase + Rh₂O₃(II)-type Al₂O₃. The bulk moduli of the phases calculated in this study are in good agreement with those measured in high-pressure experiments. Our results differ from those of a previous study using similar methods. We attribute this inconsistency to an incomplete optimization of a cell shape and ionic positions at high pressures in the previous calculations.     

Elasticity and equation of state of Li<Subscript>2</Subscript>B<Subscript>4</Subscript>O<Subscript>7</Subscript>

A single crystal X-ray diffraction study on lithium tetraborate Li₂B₄O₇ (diomignite, space group I4₁ cd) has been performed under pressure up to 8.3 GPa. No phase transitions were found in the pressure range investigated, and hence the pressure evolution of the unit-cell volume of the I4₁ cd structure has been described using a third-order Birch–Murnaghan equation of state (BM-EoS) with the following parameters: V ₀  = 923.21(6) ų, K ₀  = 45.6(6) GPa, and K′ = 7.3(3). A linearized BM-EoS was fitted to the axial compressibilities resulting in the following parameters a ₀  = 9.4747(3) Å, K _0a  = 73.3(9) GPa, K′ _a  = 5.1(3) and c ₀  = 10.2838(4) Å, K _0c  = 24.6(3) GPa, K′ _c  = 7.5(2) for the a and c axes, respectively. The elastic anisotropy of Li₂B₄O₇ is very large with the zero-pressure compressibility ratio β _0c /β _0a  = 3.0(1). The large elastic anisotropy is consistent with the crystal structure: A three-dimensional arrangement of relatively rigid tetraborate groups [B₄O₇]²⁻ forms channels occupied by lithium along the polar c–axis, and hence compression along the c axis requires the shrinkage of the lithium channels, whereas compression in the a direction depends mainly on the contraction of the most rigid [B₄O₇]²⁻ units. Finally, the isothermal bulk modulus obtained in this work is in general agreement with that derived from ultrasonic (Adachi et al. in Proceedings-IEEE Ultrasonic Symposium, 228–232, 1985; Shorrocks et al. in Proceedings-IEEE Ultrasonic Symposium, 337–340, 1981) and Brillouin scattering measurements (Takagi et al. in Ferroelectrics, 137:337–342, 1992).     

Stabilities of NAL and Ca-ferrite-type phases on the join NaAlSiO<Subscript>4</Subscript>-MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> at high pressure

Stabilities of hexagonal new aluminous (NAL) phase and Ca-ferrite-type (CF) phase were investigated on the join NaAlSiO₄-MgAl₂O₄ in a pressure range from 23 to 58 GPa at approximately constant temperature of 1,850 K, on the basis of in situ synchrotron X-ray diffraction measurements in a laser-heated diamond-anvil cell. The results show that NAL is formed as a single phase up to 34 GPa, NAL + CF between 34 and 43 GPa, and only CF at higher pressures in 40%NaAlSiO₄-60%MgAl₂O₄ bulk composition. On the other hand, both NAL and CF coexist below 38 and 36 GPa, and only CF was obtained at higher pressures in 60%NaAlSiO₄-40%MgAl₂O₄ and 20%NaAlSiO₄-80%MgAl₂O₄ composition, respectively. These results indicate that NAL appears only up to 46 GPa at 1,850 K, and CF forms continuous solid solution at higher pressures on the join NaAlSiO₄-MgAl₂O₄. NAL has limited stability in subducted mid-oceanic ridge basalt crust in the Earth’s lower mantle and undergoes a phase transition to CF in deeper levels.     

High-pressure phase behavior of MnTiO<Subscript>3</Subscript>: decomposition of perovskite into MnO and MnTi<Subscript>2</Subscript>O<Subscript>5</Subscript>

The phase relations and compression behavior of MnTiO₃ perovskite were examined using a laser-heated diamond-anvil cell, X-ray diffraction, and analytical transmission electron microscopy. The results show that MnTiO₃ perovskite becomes unstable and decomposes into MnO and orthorhombic MnTi₂O₅ phases at above 38 GPa and high temperature. This is the first example of ABO₃ perovskite decomposing into AO + AB₂O₅ phases at high pressure. The compression behavior of volume, axes, and the tilting angle of TiO₆ octahedron of MnTiO₃ perovskite are consistent with those of other A²⁺B⁴⁺O₃ perovskites, although no such decomposition was observed in other perovskites. FeTiO₃ is also known to decompose into two phases, instead of transforming into the CaIrO₃-type post-perovskite phase and we argue that one of the reasons for the peculiar behavior of titanate is the weak covalency of the Ti–O chemical bonds.     

Thermal equation of state of CaIrO<Subscript>3</Subscript> post-perovskite

The pressure–volume–temperature (P–V–T) relation of CaIrO₃ post-perovskite (ppv) was measured at pressures and temperatures up to 8.6 GPa and 1,273 K, respectively, with energy-dispersive synchrotron X-ray diffraction using a DIA-type, cubic-anvil apparatus (SAM85). Unit-cell dimensions were derived from the Le Bail full profile refinement technique, and the results were fitted using the third-order Birth-Murnaghan equation of state. The derived bulk modulus \( K_{T0} \) at ambient pressure and temperature is 168.3 ± 7.1 GPa with a pressure derivative \( K_{T0}^{\prime } \) = 5.4 ± 0.7. All of the high temperature data, combined with previous experimental data, are fitted using the high-temperature Birch-Murnaghan equation of state, the thermal pressure approach, and the Mie-Grüneisen-Debye formalism. The refined thermoelastic parameters for CaIrO₃ ppv are: temperature derivative of bulk modulus \( (\partial K_{T} /\partial T)_{P} \) = ?0.038 ± 0.011 GPa K^?1, \( \alpha K_{T} \) = 0.0039 ± 0.0001 GPa K^?1, \( \left( {\partial K_{T} /\partial T} \right)_{V} \) = ?0.012 ± 0.002 GPa K^?1, and \( \left( {\partial^{2} P/\partial T^{2} } \right)_{V} \) = 1.9 ± 0.3 × 10^?6 GPa² K^?2. Using the Mie-Grüneisen-Debye formalism, we obtain Grüneisen parameter \( \gamma_{0} \) = 0.92 ± 0.01 and its volume dependence q = 3.4 ± 0.6. The systematic variation of bulk moduli for several oxide post-perovskites can be described approximately by the relationship K _T0  = 5406.0/V(molar) + 5.9 GPa.     

Compressibility of strontium orthophosphate Sr<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript> at high pressure

High pressure in situ synchrotron X-ray diffraction experiment of strontium orthophosphate Sr₃(PO₄)₂ has been carried out to 20.0 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields a volume of V ₀ = 498.0 ± 0.1 Å³, an isothermal bulk modulus of K _T  = 89.5 ± 1.7 GPa, and first pressure derivative of K _T ′ = 6.57 ± 0.34. If K _T ′ is fixed at 4, K _T is obtained as 104.4 ± 1.2 GPa. Analysis of axial compressible modulus shows that the a-axis (K _a  = 79.6 ± 3.2 GPa) is more compressible than the c-axis (K _c  = 116.4 ± 4.3 GPa). Based on the high pressure Raman spectroscopic results, the mode Grüneisen parameters are determined and the average mode Grüneisen parameter of PO₄ vibrations of Sr₃(PO₄)₂ is calculated to be 0.30(2).     

H<Subscript>2</Subscript>O storage capacity of MgSiO<Subscript>3</Subscript> clinoenstatite at 8–13 GPa, 1,100–1,400°C

We present H₂O analyses of MgSiO₃ pyroxene crystals quenched from hydrous conditions in the presence of olivine or wadsleyite at 8–13.4 GPa and 1,100–1,400°C. Raman spectroscopy shows that all pyroxenes have low clinoenstatite structure, which we infer to indicate that the crystals were high clinoenstatite (C2/c) during conditions of synthesis. H₂O analyses were performed by secondary ion mass spectrometry and confirmed by unpolarized Fourier transform infrared spectroscopy on randomly oriented crystals. Measured H₂O concentrations increase with pressure and range from 0.08 wt.% H₂O at 8 GPa and 1,300°C up to 0.67 wt.% at 13.4 GPa and 1,300°C. At fixed pressure, H₂O storage capacity diminishes with increasing temperature and the magnitude of this effect increases with pressure. This trend, which we attribute to diminishing activity of H₂O in coexisting fluids as the proportion of dissolved silicate increases, is opposite to that observed previously at low pressure. We observe clinoenstatite 1.4 GPa below the pressure stability of clinoenstatite under nominally dry conditions. This stabilization of clinoenstatite relative to orthoenstatite under hydrous conditions is likely owing to preferential substitution of H₂O into the high clinoenstatite polymorph. At 8–11 GPa and 1,200–1,400°C, observed H₂O partitioning between olivine and clinoenstatite gives values of D ^ol/CEn between 0.65 and 0.87. At 13 GPa and 1,300°C, partitioning between wadsleyite and clinoenstatite, D ^wd/CEn, gives a value of 2.8 ± 0.4.     

EPR study of coordination of Ag and Pb cations in BaB<Subscript>2</Subscript>O<Subscript>4</Subscript> crystals and barium borate glasses

It is shown the possibility to determine the coordination of paramagnetic ions in disordered solid structures, e.g., in barium borate glasses. For this purpose the electron paramagnetic resonance (EPR) method was used to study α-and β-BaB₂O₄ crystals and glasses of 45·BaO × 55·B₂O₃ and 40·BaO × 60·B₂O₃ (mol%) composition activated by Ag⁺ and Pb²⁺ ions. After the samples were exposed to X-rays at 77 K, different EPR centers were observed in them. In α-and β-BaB₂O₄ crystals and glasses the EPR centers Ag²⁺, Ag⁰, Pb⁺, Pb³⁺, and hole centers of O⁻ type were studied. The EPR parameters of these centers and their arrangement in crystal structure were determined. It is shown that Pb³⁺ ions in β-BaB₂O₄ crystals occupy Ba²⁺ position in an irregular polyhedron from the eight oxygen, whereas in α-BaB₂O₄ crystals they occupy Bа₂ position in a sixfold coordination. Pb⁺ ions in α-BaB₂O₄ crystals occupy Bа₁ position in a ninefold coordination from oxygen. In barium borate glasses, Pb³⁺ ions were studied in coordination polyhedron from six oxygen atoms and in a polyhedron from nine to ten oxygen atoms. It is assumed that the established difference in the structural position of Pb³⁺ ions in glasses is due to their previous incorporation in associative cation–anion complexes (AC) and “free” structure-forming cations (FC). Computer simulations have been performed to analyze the stability of specific associative complexes and to compare their bond lengths with experimental data.     

Pressure induced phase transition in Pb<Subscript>6</Subscript>Bi<Subscript>2</Subscript>S<Subscript>9</Subscript>

The crystal structure of Pb₆Bi₂S₉ is investigated at pressures between 0 and 5.6 GPa with X-ray diffraction on single-crystals. The pressure is applied using diamond anvil cells. Heyrovskyite (Bbmm, a = 13.719(4) Å, b = 31.393(9) Å, c = 4.1319(10) Å, Z = 4) is the stable phase of Pb₆Bi₂S₉ at ambient conditions and is built from distorted moduli of PbS-archetype structure with a low stereochemical activity of the Pb²⁺ and Bi³⁺ lone electron pairs. Heyrovskyite is stable until at least 3.9 GPa and a first-order phase transition occurs between 3.9 and 4.8 GPa. A single-crystal is retained after the reversible phase transition despite an anisotropic contraction of the unit cell and a volume decrease of 4.2%. The crystal structure of the high pressure phase, β-Pb₆Bi₂S₉, is solved in Pna2 ₁ (a = 25.302(7) Å, b = 30.819(9) Å, c = 4.0640(13) Å, Z = 8) from synchrotron data at 5.06 GPa. This structure consists of two types of moduli with SnS/TlI-archetype structure in which the Pb and Bi lone pairs are strongly expressed. The mechanism of the phase transition is described in detail and the results are compared to the closely related phase transition in Pb₃Bi₂S₆ (lillianite).     

Calorimetric study on high-pressure transitions in KAlSi<Subscript>3</Subscript>O<Subscript>8</Subscript>

KAlSi₃O₈ sanidine dissociates into a mixture of K₂Si₄O₉ wadeite, Al₂SiO₅ kyanite and SiO₂ coesite, which further recombine into KAlSi₃O₈ hollandite with increasing pressure. Enthalpies of KAlSi₃O₈ sanidine and hollandite, K₂Si₄O₉ wadeite and Al₂SiO₅ kyanite were measured by high-temperature solution calorimetry. Using the data, enthalpies of transitions at 298 K were obtained as 65.1 ± 7.4 kJ mol^–1 for sanidine wadeite + kyanite + coesite and 99.3 ± 3.6 kJ mol^–1 for wadeite + kyanite + coesite hollandite. The isobaric heat capacity of KAlSi₃O₈ hollandite was measured at 160–700 K by differential scanning calorimetry, and was also calculated using the Kieffer model. Combination of both the results yielded a heat-capacity equation of KAlSi₃O₈ hollandite above 298 K as C_p=3.896 × 10²–1.823 × 10³T^–0.5–1.293 × 10⁷T^–2+1.631 × 10⁹T^–3 (C_p in J mol^–1 K^–1, T in K). The equilibrium transition boundaries were calculated using these new data on the transition enthalpies and heat capacity. The calculated transition boundaries are in general agreement with the phase relations experimentally determined previously. The calculated boundary for wadeite + kyanite + coesite hollandite intersects with the coesite–stishovite transition boundary, resulting in a stability field of the assemblage of wadeite + kyanite + stishovite below about 1273 K at about 8 GPa. Some phase–equilibrium experiments in the present study confirmed that sanidine transforms directly to wadeite + kyanite + coesite at 1373 K at about 6.3 GPa, without an intervening stability field of KAlSiO₄ kalsilite + coesite which was previously suggested. The transition boundaries in KAlSi₃O₈ determined in this study put some constraints on the stability range of KAlSi₃O₈ hollandite in the mantle and that of sanidine inclusions in kimberlitic diamonds.     

IR calibrations for water determination in olivine,r-GeO<Subscript>2</Subscript>, and SiO<Subscript>2</Subscript> polymorphs

Mineral-specific IR absorption coefficients were calculated for natural and synthetic olivine, SiO₂ polymorphs, and GeO₂ with specific isolated OH point defects using quantitative data from independent techniques such as proton–proton scattering, confocal Raman spectroscopy, and secondary ion mass spectrometry. Moreover, we present a routine to detect OH traces in anisotropic minerals using Raman spectroscopy combined with the “Comparator Technique”. In case of olivine and the SiO₂ system, it turns out that the magnitude of ε for one structure is independent of the type of OH point defect and therewith the peak position (quartz ε = 89,000 ± 15,000  \textl \textmol_{\textH2\textO}^-1 \textcm^-2\text{l}\,\text{mol}_{{\text{H}_2}\text{O}}^{-1}\,\text{cm}^{-2}), but it varies as a function of structure (coesite ε = 214,000 ± 14,000  \textl \textmol_{\textH2\textO}^-1 \textcm^-2\text{l}\,\text{mol}_{{\text{H}_2}\text{O}}^{-1}\,\text{cm}^{-2}; stishovite ε = 485,000 ± 109,000  \textl \textmol_{\textH2\textO}^-1 \textcm^-2\text{l}\,\text{mol}_{{\text{H}_2}\text{O}}^{-1}\,\text{cm}^{-2}). Evaluation of data from this study confirms that not using mineral-specific IR calibrations for the OH quantification in nominally anhydrous minerals leads to inaccurate estimations of OH concentrations, which constitute the basis for modeling the Earth’s deep water cycle.     

Low-temperature heat capacities of MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> and spinels of the MgCr<Subscript>2</Subscript>O<Subscript>4</Subscript>–MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> solid solution

We present results from low-temperature heat capacity measurements of spinels along the solid solution between MgAl₂O₄ and MgCr₂O₄. The data also include new low-temperature heat capacity measurements for MgAl₂O₄ spinel. Heat capacities were measured between 1.5 and 300 K, and thermochemical functions were derived from the results. No heat capacity anomaly was observed for MgAl₂O₄ spinel; however, we observe a low-temperature heat capacity anomaly for Cr-bearing spinels at temperatures below 15 K. From our data we calculate standard entropies (298.15 K) for Mg(Cr,Al)₂O₄ spinels. We suggest a standard entropy for MgAl₂O₄ of 80.9 ± 0.6 J mol⁻¹ K⁻¹. For the solid solution between MgAl₂O₄ and MgCr₂O₄, we observe a linear increase of the standard entropies from 80.9 J mol⁻¹ K⁻¹ for MgAl₂O₄ to 118.3 J mol⁻¹ K⁻¹ for MgCr₂O₄.     

Hydrostatic compression of galenobismutite (PbBi<Subscript>2</Subscript>S<Subscript>4</Subscript>): elastic properties and high-pressure crystal chemistry

A single-crystal sample of galenobismutite was subjected to hydrostatic pressures in the range of 0.0001 and 9 GPa at room temperature using the diamond-anvil cell technique. A series of X-ray diffraction intensities were collected at ten distinct pressures using a CCD equipped 4-circle diffractometer. The crystal structure was refined to R1(|F₀| > 4σ) values of approximately 0.05 at all pressures. By fitting a third-order Birch-Murnaghan equation of state to the unit-cell volumes V ₀ = 700.6(2) ų, K ₀ = 43.9(7) GPa and dK/dP = 6.9(3) could be determined for the lattice compression. Both types of cations in galenobismutite have stereochemically active lone electron pairs, which distort the cation polyhedra at room pressure. The cation eccentricities decrease at higher pressure but are still pronounced at 9 GPa. Galenobismutite is isotypic with CaFe₂O₄ (CF) but moves away from the idealised CF-type structure during compression. Instead of the two octahedral cation sites and one bi-capped trigonal-prismatic site, PbBi₂S₄ attains a new high-pressure structure characterised by one octahedral site and two mono-capped trigonal-prismatic sites. Analyses of the crystal structure at high pressure confirm the preference of Bi for the octahedral site and the smaller one of the two trigonal-prismatic sites.     

Atomistic model of diopside-K-jadeite (CaMgSi<Subscript>2</Subscript>O<Subscript>6</Subscript>-KAlSi<Subscript>2</Subscript>O<Subscript>6</Subscript>) solid solution

Atomistic model was proposed to describe the thermodynamics of mixing in the diopside-K-jadeite solid solution (CaMgSi₂O6-KAlSi₂O₆). The simulations were based on minimization of the lattice energies of 800 structures within a 2 × 2 × 4 supercell of C2/c diopside with the compositions between CaMgSi₂O₆ and KAlSi₂O₆ and with variable degrees of order/disorder in the arrangement of Ca/K cations in M2 site and Mg/Al in Ml site. The energy minimization was performed with the help of a force-field model. The results of the calculations were used to define a generalized Ising model, which included 37 pair interaction parameters. Isotherms of the enthalpy of mixing within the range of 273–2023 K were calculated with a Monte Carlo algorithm, while the Gibbs free energies of mixing were obtained by thermodynamic integration of the enthalpies of mixing. The calculated T-X diagram for the system CaMgSi₂O₆-KAlSi₂O₆ at temperatures below 1000 K shows several miscibility gaps, which are separated by intervals of stability of intermediate ordered compounds. At temperatures above 1000 K a homogeneous solid solution is formed. The standard thermodynamic properties of K-jadeite (KAlSi₂O₆) evaluated from quantum mechanical calculations were used to determine location of several mineral reactions with the participation of the diopside-K-jadeite solid solution. The results of the simulations suggest that the low content of KalSi₂O₆ in natural clinopyroxenes is not related to crystal chemical factors preventing isomorphism, but is determined by relatively high standard enthalpy of this end member.