Thermal expansion of gehlenite, Ca2Al[AlSiO7], and the related aluminates LnCaAl[Al2O7] with Ln=Tb, Sm

The thermal expansion of gehlenite, Ca₂Al[AlSiO₇], (up to T=830 K), TbCaAl[Al₂O₇] (up to T=1,100 K) and SmCaAl[Al₂O₇] (up to T=1,024 K) has been determined. All compounds are of the melilite structure type with space group Thermal expansion data was obtained from in situ X-ray powder diffraction experiments in-house and at HASYLAB at the Deutsches Elektronen Synchrotron (DESY) in Hamburg (Germany). The thermal expansion coefficients for gehlenite were found to be: α₁=7.2(4)×10⁻⁶ K⁻¹+3.6(7)×10⁻⁹ΔT K⁻² and α₃=15.0(1)×10⁻⁶ K⁻¹. For TbCaAl[Al₂O₇] the respective values are: α₁=7.0(2)×10⁻⁶ K⁻¹+2.0(2)×10⁻⁹ΔT K⁻² and α₃=8.5(2)×10⁻⁶ K⁻¹+2.0(3)×10⁻⁹ΔT K⁻², and the thermal expansion coefficients for SmCaAl[Al₂O₇] are: α₁=6.9(2)× 10⁻⁶ K⁻¹+1.7(2)×10⁻⁹ΔT K⁻² and α₃=9.344(5)×10⁻⁶ K⁻¹. The expansion-mechanisms of the three compounds are explained in terms of structural trends obtained from Rietveld refinements of the crystal structures of the compounds against the powder diffraction patterns. No structural phase transitions have been observed. While gehlenite behaves like a ’proper’ layer structure, the aluminates show increased framework structure behaviour. This is most probably explained by stronger coulombic interactions between the tetrahedral conformation and the layer-bridging cations due to the coupled substitution (Ca²⁺+Si⁴⁺)-(Ln ³⁺+Al³⁺) in the melilite-type structure. Electronic Supplementary Material Supplementary material is available for this article at     

Thermal expansion of gehlenite, Ca2Al[AlSiO7], and the related aluminates LnCaAl[Al2O7] with Ln = Tb, Sm

The thermal expansion of gehlenite, Ca₂Al[AlSiO₇], (up to T=830 K), TbCaAl[Al₂O₇] (up to T=1100 K) and SmCaAl[Al₂O₇] (up to T=1024 K) has been determined. All compounds are of the melilite structure type with space group Thermal expansion data were obtained from in situ X-ray powder diffraction experiments in-house and at HASYLAB at the Deutsches Elektronen Synchrotron (DESY) in Hamburg (Germany). The thermal expansion coefficients for gehlenite were found to be: α₁=7.2(4)×10⁻⁶×K⁻¹+3.6(7)×10⁻⁹ΔT×K⁻² and α₃=15.0(1)×10⁻⁶×K⁻¹. For TbCaAl[Al₂O₇] the respective values are: α₁=7.0(2)×10⁻⁶×K⁻¹+2.0(2)×10⁻⁹ΔT×K⁻² and α₃=8.5(2)×10⁻⁶×K⁻¹+2.0(3)×10⁻⁹ΔT×K⁻², and the thermal expansion coefficients for SmCaAl[Al₂O₇] are: α₁=6.9(2)×10⁻⁶×K⁻¹+1.7(2)×10⁻⁹ΔT×K⁻² and α₃=9.344(5)×10⁻⁶×K⁻¹. The expansion mechanisms of the three compounds are explained in terms of structural trends obtained from Rietveld refinements of the crystal structures of the compounds against the powder diffraction patterns. No structural phase transitions have been observed. While gehlenite behaves like a ‘proper’ layer structure, the aluminates show increased framework structure behavior. This is most probably explained by stronger coulombic interactions between the tetrahedral conformation and the layer-bridging cations due to the coupled substitution (Ca²⁺+Si⁴⁺)–(Ln ³⁺+Al³⁺) in the melilite-type structure. This article has been mistakenly published twice. The first and original version of it is available at .     

Calorimetric study of perovskite solid solutions in the CaSiO3–CaGeO3 system

 Enthalpies of drop solution (ΔH _drop-sol) of CaGeO₃, Ca(Si_0.1Ge_0.9)O₃, Ca(Si_0.2Ge_0.8)O₃, Ca(Si_0.3Ge_0.7)O₃ perovskite solid solutions and CaSiO₃ wollastonite were measured by high-temperature calorimetry using molten 2PbO · B₂O₃ solvent at 974 K. The obtained values were extrapolated linearly to the CaSiO₃ end member to give ΔH _drop-sol of CaSiO₃ perovskite of 0.2 ± 4.4 kJ mol⁻¹. The difference in ΔH _drop-sol between CaSiO₃, wollastonite, and perovskite gives a transformation enthalpy (wo → pv) of 104.4 ± 4.4 kJ mol⁻¹. The formation enthalpy of CaSiO₃ perovskite was determined as 14.8 ± 4.4 kJ mol⁻¹ from lime + quartz or −22.2 ± 4.5 kJ mol⁻¹ from lime + stishovite. A comparison of lattice energies among A²⁺B⁴⁺O₃ perovskites suggests that amorphization during decompression may be due to the destabilizing effect on CaSiO₃ perovskite from a large nonelectrostatic energy (repulsion energy) at atmospheric pressure. By using the formation enthalpy for CaSiO₃ perovskite, phase boundaries between β-Ca₂SiO₄ + CaSi₂O₅ and CaSiO₃ perovskite were calculated thermodynamically utilizing two different reference points [where ΔG(P,T )=0] as the measured phase boundary. The calculations suggest that the phase equilibrium boundary occurs between 11.5 and 12.5 GPa around 1500 K. Its slope is still not well constrained. Received: 20 September 2000 / Accepted: 17 January 2001     

The reaction MgCr2O4 + SiO2 = Cr2O3 + MgSiO3 and the free energy of formation of magnesiochromite (MgCr2O4)

Low-temperature heat capacity measurements for MgCr₂O₄ have only been performed down to 52 K, and the commonly quoted third-law entropy at 298 K (106 J K⁻¹ mol⁻¹) was obtained by empirical extrapolation of these measurements to 0 K without considering the magnetic or electronic ordering contributions to the entropy. Subsequent magnetic measurements at low temperature reveal that the Néel temperature, at which magnetic ordering of the Cr³⁺ ions in MgCr₂O₄ occurs, is at ∼15 K. Hence a substantial contribution to the entropy of MgCr₂O₄ has been missed. We have determined the position of the near-univariant reaction MgCr₂O₄+SiO₂=MgSiO₃+Cr₂O₃. The reaction, which has a small positive slope in P-T space, has been bracketed at 100 K intervals between 1273 and 1773 K by reversal experiments. The reaction is extremely sluggish, and lengthy run times with a flux (H₂O, BaO-B₂O₃ or K₂O-B₂O₃) are needed to produce tight reversal brackets. The results, combined with assessed thermodynamic data for Cr₂O₃, MgSiO₃ and SiO₂, give the entropy and enthalpy of formation of MgCr₂O₄ spinel. As expected, our experimental results are not in good agreement with the presently available thermodynamic data. We obtain Δ _f H ^∘ ₂₉₈=−1759.2±1.5 kJ mol⁻¹ and S ^∘ ₂₉₈=122.1±1.0 J K⁻¹ mol⁻¹ for MgCr₂O₄. This entropy is some 16 J K⁻¹ mol⁻¹ more than the calorimetrically determined value, and implies a value for the magnetic entropy of MgCr₂O₄ consistent with an effective spin quantum number (S') for Cr³⁺ of 1/2 rather than the theoretical 3/2, indicating, as in other spinels, spin quenching. Received: 9 May 1997 / Accepted: 28 July 1997     

Thermodynamic functions of eskolaite Cr<Subscript>2</Subscript>O<Subscript>3</Subscript>(c) at 0–1800 K

The heat capacity of eskolaite Cr₂O₃(c) was determined by adiabatic vacuum calorimetry at 11.99–355.83 K and by differential calorimetry at 320–480 K. Experimental data of the authors and data compiled from the literature were applied to calculate the heat capacity, entropy, and the enthalpy change of Cr₂O₃ within the temperature range of 0–1800 K. These functions have the following values at 298.15 K: C _p ⁰ (298.15) = 121.5 ± 0.2 J K⁻¹mol⁻¹, S ⁰(298.15) = 80.95 ± 0.14 J K⁻¹mol⁻¹, and H ⁰(298.15)-H ⁰(0) = 15.30±0.02 kJ mol⁻¹. Data were obtained on the transitions from the antiferromagnetic to paramagnetic states at 228–457 K; it was determined that this transition has the following parameters: Neel temperature T _N = 307 K, Δ _tr S = 6.11 ± 0.12 J K⁻¹mol⁻¹ and δ _tr H = 1.87 ± 0.04 kJ mol⁻¹.     

Experimental study of the K2ZrSi3O9 (wadeite)–K2TiSi3O9 and K2(Zr,Ti)Si3O9–phlogopite systems at 2–3 GPa

Experiments ranging from 2 to 3 GPa and 800 to 1300 °C and at 0.15 GPa and 770 °C were performed to investigate the stability and mutual solubility of the K₂ZrSi₃O₉ (wadeite) and K₂TiSi₃O₉ cyclosilicates under upper mantle conditions. The K₂ZrSi₃O₉–K₂TiSi₃O₉ join exhibits complete miscibility in the P–T interval investigated. With increasing degree of melting the solid solution becomes progressively enriched in Zr, indicating that K₂ZrSi₃O₉ is the more refractory end member. At 2 GPa, in the more complex K₂ZrSi₃O₉–K₂TiSi₃O₉–K₂Mg₆Al₂Si₆O₂₀(OH)₄ system, the presence of phlogopite clearly limits the extent of solid solution of the cyclosilicate to more Zr-rich compositions [Zr/(Zr + Ti) > 0.85], comparable to wadeite found in nature, with TiO₂ partitioning strongly into the coexisting mica and/or liquid. However, at 1200 °C, with increasing pressure from 2 to 3 GPa, the partitioning behaviour of TiO₂ changes in favour of the cyclosilicate, with Zr/(Zr + Ti) of the K₂(Zr,Ti)Si₃O₉ phase decreasing from ∼0.9 to ∼0.6. The variation in the Ti content of the coexisting phlogopite is related to its degree of melting to forsterite and liquid, following the major substitution ^VITi+^VI□=2^VIMg. Received: 26 January 1999 / Accepted: 10 January 2000     

Thermodynamic data of the high-pressure phase Mg5Al5Si6O21(OH)7 (Mg-sursassite)

 Calorimetric and P–V–T data for the high-pressure phase Mg₅Al₅Si₆O₂₁(OH)₇ (Mg-sursassite) have been obtained. The enthalpy of drop solution of three different samples was measured by high-temperature oxide melt calorimetry in two laboratories (UC Davis, California, and Ruhr University Bochum, Germany) using lead borate (2PbO·B₂O₃) at T=700 ^∘C as solvent. The resulting values were used to calculate the enthalpy of formation from different thermodynamic datasets; they range from −221.1 to −259.4 kJ mol⁻¹ (formation from the oxides) respectively −13892.2 to −13927.9 kJ mol⁻¹ (formation from the elements). The heat capacity of Mg₅Al₅Si₆O₂₁(OH)₇ has been measured from T=50 ^∘C to T=500 ^∘C by differential scanning calorimetry in step-scanning mode. A Berman and Brown (1985)-type four-term equation represents the heat capacity over the entire temperature range to within the experimental uncertainty: C _P (Mg-sursassite) =(1571.104 −10560.89×T ^−0.5−26217890.0 ×T ⁻²+1798861000.0×T ⁻³) J K⁻¹ mol⁻¹ (T in K). The P V T behaviour of Mg-sursassite has been determined under high pressures and high temperatures up to 8 GPa and 800 ^∘C using a MAX 80 cubic anvil high-pressure apparatus. The samples were mixed with Vaseline to ensure hydrostatic pressure-transmitting conditions, NaCl served as an internal standard for pressure calibration. By fitting a Birch-Murnaghan EOS to the data, the bulk modulus was determined as 116.0±1.3 GPa, (K ^′=4), V _T,0 =446.49 ³ exp[∫(0.33±0.05) × 10⁻⁴ + (0.65±0.85)×10⁻⁸ T dT], (K _T/T) _P  = −0.011± 0.004 GPa K⁻¹. The thermodynamic data obtained for Mg-sursassite are consistent with phase equilibrium data reported recently (Fockenberg 1998); the best agreement was obtained with Δ_f H ⁰ ₂₉₈ (Mg-sursassite) = −13901.33 kJ mol⁻¹, and S ⁰ ₂₉₈ (Mg-sursassite) = 614.61 J K⁻¹ mol⁻¹. Received: 21 September 2000 / Accepted: 26 February 2001     

Heat capacity and thermodynamic properties of GdPO<Subscript>4</Subscript> in the temperature range 0–1600 K

The heat capacity of gadolinium orthophosphate (GdPO₄) measured in the temperature range 11.15–344.11 K by adiabatic calorimetry and available literature data were used to calculate its thermodynamic functions at 0–1600 K. At 298.15 K, these functions are as follows: C _p ⁰(298.15 K) = 101.85 ± 0.05 J K⁻¹ mol⁻¹, S ⁰(298.15 K) = 123.82 ± 0.18 J K⁻¹ mol⁻¹, H ⁰(298.15 K)–H ⁰(0) = 17.250 ± 0.012 kJ mol⁻¹, and Φ ⁰(298.15 K) = 65.97 ± 0.18 J K⁻¹ mol⁻¹ The calculated Gibbs free energy of formation from the elements of GdPO₄ is Δ _f G ⁰ (298.15 K) = −1844.3 ± 4.7 kJ mol⁻¹.     

Heat capacity and thermodynamic functions of xenotime YPO<Subscript>4</Subscript>(c) at 0–1600 K

The heat capacity of xenotime YPO₄(c) was measured by adiabatic calorimetry at 4.78–348.07 K. Our experimental and literature data on H ⁰(T)-H ⁰(298.15 K) of Y orthophosphate were utilized to derive the C _p ⁰(T) function of xenotime at 0–1600 K, which was then used to calculate the values of thermodynamic functions: entropy, enthalpy change, and reduced Gibbs energy. These functions assume the following values at 298.15 K: C _p ⁰ (298.15 K) = 99.27 ± 0.02 J K⁻¹ mol⁻¹, S ⁰(298.15 K) = 93.86 ± 0.08 J K⁻¹ mol⁻¹, H ⁰(298.15 K) − H ⁰(0) = 15.944 ± 0.005 kJ mol⁻¹, Φ⁰(298.15 K) = 40.38 ± 0.08 J K⁻¹ mol⁻¹. The value of the free energy of formation Δ _f G ⁰(YPO₄, 298.15 K) is −1867.9 ± 1.7 kJ mol⁻¹.     

Heat capacity and phase equilibria of wadeite-type K2Si4O9

The low-temperature heat capacity (C _p) of Si-wadeite (K₂Si₄O₉) synthesized with a piston cylinder device was measured over the range of 5–303 K using the heat capacity option of a physical properties measurement system. The entropy of Si-wadeite at standard temperature and pressure calculated from the measured heat capacity data is 253.8 ± 0.6 J mol⁻¹ K⁻¹, which is considerably larger than some of the previous estimated values. The calculated phase transition boundaries in the system K₂O–Al₂O₃–SiO₂ are generally consistent with previous experimental results. Together with our calculated phase boundaries, seven multi-anvil experiments at 1,400 K and 6.0–7.7 GPa suggest that no equilibrium stability field of kalsilite + coesite intervenes between the stability field of sanidine and that of coesite + kyanite + Si-wadeite, in contrast to previous predictions. First-order approximations were undertaken to calculate the phase diagram in the system K₂Si₄O₉ at lower pressure and temperature. Large discrepancies were shown between the calculated diagram compared with previously published versions, suggesting that further experimental or/and calorimetric work is needed to better constrain the low-pressure phase relations of the K₂Si₄O₉ polymorphs. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Heat capacity and thermodynamic functions of pretulite ScPO<Subscript>4</Subscript>(c) at 0–1600 K

The heat capacity of synthetic pretulite ScPO₄(c) was measured by adiabatic calorimetry within a temperature range of 12.13–345.31 K, and the temperature dependence of the pretulite heat capacity at 0–1600 K was derived from experimental and literature data on H ⁰(T)-H ⁰(298.15 K) for Sc orthophosphate. This dependence was used to calculate the values of the following thermodynamic functions: entropy, enthalpy change, and reduced Gibbs energy. They have the following values at 298.15 K: C _p ⁰ (298.15 K) = 97.45 ± 0.06 J K⁻¹ mol⁻¹, S ⁰(298.15 K) = 84.82 ± 0.18 J K⁻¹ mol⁻¹, H ⁰(298.15 K)-H ⁰(0) = 14.934 ± 0.016 kJ mol⁻¹, and Φ ⁰(298.15 K) = 34.73 ± 0.19 J K⁻¹mol⁻¹. The enthalpy of formation Δ _f H ⁰(ScPO₄, 298.15 K) = − 1893.6 ± 8.4 kJ mol⁻¹.     

High-pressure transitions and thermochemistry of MGeO3 (M=Mg, Zn and Sr) and Sr-silicates: systematics in enthalpies of formation of A2+B4+O3 perovskites

Phase transitions in MgGeO₃ and ZnGeO₃ were examined up to 26 GPa and 2,073 K to determine ilmenite–perovskite transition boundaries. In both systems, the perovskite phases were converted to lithium niobate structure on release of pressure. The ilmenite–perovskite boundaries have negative slopes and are expressed as P(GPa)=38.4–0.0082T(K) and P(GPa)=27.4−0.0032T(K), respectively, for MgGeO₃ and ZnGeO₃. Enthalpies of SrGeO₃ polymorphs were measured by high-temperature calorimetry. The enthalpies of SrGeO₃ pseudowollasonite–walstromite and walstromite–perovskite transitions at 298 K were determined to be 6.0±8.6 and 48.9±5.8 kJ/mol, respectively. The calculated transition boundaries of SrGeO₃, using the measured enthalpy data, were consistent with the boundaries determined by previous high-pressure experiments. Enthalpy of formation (ΔH _f°) of SrGeO₃ perovskite from the constituent oxides at 298 K was determined to be −73.6±5.6 kJ/mol by calorimetric measurements. Thermodynamic analysis of the ilmenite–perovskite transition boundaries in MgGeO₃ and ZnGeO₃ and the boundary of formation of SrSiO₃ perovskite provided transition enthalpies that were used to estimate enthalpies of formation of the perovskites. The ΔH _f° of MgGeO₃, ZnGeO₃ and SrSiO₃ perovskites from constituent oxides were 10.2±4.5, 33.8±7.2 and −3.0±2.2 kJ/mol, respectively. The present data on enthalpies of formation of the above high-pressure perovskites were combined with published data for A²⁺B⁴⁺O₃ perovskites stable at both atmospheric and high pressures to explore the relationship between ΔH _f° and ionic radii of eightfold coordinated A²⁺ (R _A) and sixfold coordinated B⁴⁺ (R _B) cations. The results show that enthalpy of formation of A²⁺B⁴⁺O₃ perovskite increases with decreasing R _A and R _B. The relationship between the enthalpy of formation and tolerance factor ( R _o: O²⁻ radius) is not straightforward; however, a linear relationship was found between the enthalpy of formation and the sum of squares of deviations of A²⁺ and B⁴⁺ radii from ideal sizes in the perovskite structure. A diagram showing enthalpy of formation of perovskite as a function of A²⁺ and B⁴⁺ radii indicates a systematic change with equienthalpy curves. These relationships of ΔH _f° with R _A and R _B can be used to estimate enthalpies of formation of perovskites, which have not yet been synthesized.     

Heat capacity of wadeite-type K2Si4O9 and the pressure-induced stable decomposition of K-feldspar

The heat capacity of synthetic, stoichiometric wadeite-type K₂Si₄O₉ has been measured by DSC in the 195≤T(K)≤598 range. Near the upper temperature limit of our data, the heat capacity observed by DSC agrees with that reported by Geisinger et al. (1987) based on a vibrational model of their infrared and Raman spectroscopic data. However, with decreasing temperature, the Cp observed by DSC is progressively higher than that predicted from the vibrational model, suggesting that the standard entropy of K₂Si₄O₉ is likely to be larger than 198.9 ± 4.0 J/K · mol computed from the spectroscopic data. A fit to the DSC data gave: Cp(T) = 499.13 (±1.87) − 4.35014 · 10³(±3.489 · 10¹) · T ^−0.5, with T in K and average absolute percent deviation of 0.37%. The room-temperature compressibilities of kalsilite and leucite, hitherto unknown, have been measured as well. The data, fitted to the Murnaghan equation of state, gave K _o = 58.6 GPa, K _o ^′ = 0.1 for kalsilite and K _o = 45 GPa, K _o ^′ = 5.7 for α-leucite. Apart from the above mentioned data on the properties of the individual phases, we have also obtained reaction-reversals on four equilibria in the system K₂O-Al₂O₃-SiO₂. The Bayesian method has been used simultaneously to process the properties of 13 phases and 15 reactions between them to derive an internally consistent thermodynamic dataset for the K₂O-Al₂O₃-SiO₂ ternary. The enthalpy of formation of K₂Si₄O₉ wadeite is in perfect agreement with its revised calorimetric value, the standard entropy is 232.1 ± 10.4 J/K · mol, ∼15% higher than that implied by vibrational modeling. The phase diagram, generated from our internally consistent thermodynamic dataset, shows that for all probable P-T trajectories in the subduction regime, the stable pressure-induced decomposition of K-feldspar will produce coesite + kalsilite rather than coesite + kyanite + K₂Si₄O₉ (cf. Urakawa et al. 1994). Received: 11 June 1997 / Accepted: 2 December 1997     

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.     

Pressure–volume–temperature equation of state of andradite and grossular, by high-pressure and -temperature powder diffraction

 The thermoelastic parameters of natural andradite and grossular have been investigated by high-pressure and -temperature synchrotron X-ray powder diffraction, at ESRF, on the ID30 beamline. The P–V–T data have been fitted by Birch-Murnaghan-like EOSs, using both the approximated and the general form. We have obtained for andradite K ₀=158.0(±1.5) GPa, (dK/dT )₀=−0.020(3) GPa K⁻¹ and α₀=31.6(2) 10⁻⁶ K⁻¹, and for grossular K ₀=168.2(±1.7) GPa, (dK/dT)₀=−0.016(3) GPa K⁻¹ and α₀=27.8(2) 10⁻⁶ K⁻¹. Comparisons between the present issues and thermoelastic properties of garnets earlier determined are carried out. Received: 7 July 2000 / Accepted: 20 October 2000     

(Na,Ca)(Ti3+,Mg)Si2O6-clinopyroxenes at high pressure: influence of cation substitution on elastic behavior and phase transition

A compressional study of (Na,Ca)(Ti³⁺,Mg)Si₂O₆-clinopyroxenes was carried out at high pressures between 10⁻⁴ and 10.2 GPa using in situ single-crystal X-ray diffraction, Raman spectroscopy and optical absorption spectroscopy. Compressional discontinuities accompanied by structural changes, in particular, the appearance of two distinct Ti³⁺–Ti³⁺ distances within the octahedral chains at 4.37 GPa, provide evidence for the occurrence of a phase transition in NaTi³⁺Si₂O₆. Equation-of-state parameters are K ₀ = 115.9(7) GPa with K′ = −0.9(3) and K ₀ = 102.7(8) GPa with K′ = 4.08(5) for the low- and high-pressure range, respectively. The transition involves a C2/c–P [`1] \overline{1} symmetry change, which can be confirmed by the occurrence of new modes in Raman spectra. Since no significant discontinuity in the evolution of the unit-cell volume with pressure has been observed, the transition appears to be second-order in character. The influence of the coupled substitution Na⁺Ti³⁺↔Ca²⁺Mg²⁺ on the static compression behavior and the structural stability has been investigated using a sample of the intermediate composition (Na_0.54Ca_0.46)(Mg_0.46Ti_0.54)Si₂O₆. No evidence for a deviation from continuous compression behavior has been found, neither in lattice parameter nor in structural data and the fit of a third-order Birch–Murnaghan equation-of-state to the pressure–volume data yields a bulk modulus of K ₀ = 109.1(5) GPa and K′ = 5.02(13). Raman and polarized absorption spectra have been compared to NaTiSi₂O₆ and reveal major similarities. The main driving force for the phase transition in NaTi³⁺Si₂O₆ is the localization of the Ti³⁺ d-electron and the accompanying distortion, which is suppressed in the (Na,Ca)(Ti³⁺,Mg)Si₂O₆-clinopyroxene.     

Transport properties of low-sanidine single-crystals, glasses and melts at high temperature

Thermal diffusivity (D) was measured using laser-flash analysis from oriented single-crystal low-sanidine (K_0.92Na_0.08Al_0.99Fe³⁺ _0.005Si_2.95O₈), and three glasses near KAlSi₃O₈. Viscosity measurements of the three supercooled liquids, in the range 10^6.8 to 10^12.3 Pa s, confirm near-Arrhenian behavior, varying subtly with composition. For crystal and glass, D decreases with T, approaching a constant near 1,000 K: D _sat ∼ 0.65 ± 0.3 mm² s⁻¹ for bulk crystal and ∼0.53 ± 0.03 mm² s⁻¹ for the glass. A rapid decrease near 1,400 K is consistent with crossing the glass transition. Melt behavior is approximated by D = 0.475 ± 0.01 mm² s⁻¹. Thermal conductivity (k _lat) of glass, calculated using previous heat capacity (C _P) and new density data, increases with T because C _P strongly increases with T. For melt, k _lat reaches a plateau near 1.45 W m⁻¹ K⁻¹, and is always below k _lat of the crystal. Melting of potassium feldspars impedes heat transport, providing positive thermal feedback that may promote further melting in continental crust.     

Experimental study of Pd hydrolysis in aqueous solutions at 25–70°C

The hydrolysis of the Pd²⁺ ion in HClO₄ solutions was examined at 25–70°C, and the thermodynamic constants of equilibrium K ₍₁₎⁰ and K ₍₂₎⁰were determined for the reactions Pd²⁺ + H₂O = PdOH⁺ + H⁺ and Pd²⁺ + 2H₂O = Pd(OH)₂⁰ + 2H⁺, respectively. The values of log K ₍₁₎⁰ = −1.66 ± 0.5 (25°C) and −0.65 ± 0.25 (50°C) and log K ₍₂₎⁰ = −4.34 ± 0.3 (25°C) and −3.80 ± 0.3 (50°C) were derived using the solubility technique at 0.95 confidence level. The values of log K ₍₁₎⁰ = −1.9 ± 0.6 (25°C), −1.0 ± 0.4 (50°C), and −0.5 ± 0.3 (70°C) were obtained by spectrophotometric techniques. The palladium ion is significantly hydrolyzed at elevated temperatures (50–70°C) even in strongly acidic solutions (pH 1–1.5), and its hydrolysis is enhanced with increasing temperature.     

In search of the mixed derivative ?2 M /? P ? T ( M = G , K ): joint analysis of ultrasonic data for polycrystalline pyrope from gas- and solid-medium apparatus

Elastic wave velocities for dense (99.8% of theoretical density) isotropic polycrystalline specimens of synthetic pyrope (Mg₃Al₂Si₃O₁₂) were measured to 1,000 K at 300 MPa by the phase comparison method of ultrasonic interferometry in an internally heated gas-medium apparatus. The temperature derivatives of the elastic moduli [(∂Ks/∂T) _P = −19.3(4); (∂G/∂T) _P = −10.4(2) MPa K⁻¹] measured in this study are consistent with previous acoustic measurements on both synthetic polycrystalline pyrope in a DIA-type cubic anvil apparatus (Gwanmesia et al. in Phys Earth Planet Inter 155:179–190, 2006) and on a natural single crystal by the rectangular parallelepiped resonance (RPR; Suzuki and Anderson in J Phys Earth 31:125–138, 1983) method but |(∂Ks/∂T) _P | is significantly larger than from a Brillouin spectroscopy study of single-crystal pyrope (Sinogeikin and Bass in Phys Earth Planet Inter 203:549–555, 2002). Alternative approaches to the retrieval of mixed derivatives of the elastic moduli from joint analysis of data from this study and from the solid-medium data of Gwanmesia et al. in Phys Earth Planet Inter 155:179–190 (2006) yield ∂² G/∂P∂T = [0.07(12), 0.20(14)] × 10⁻³ K⁻¹ and ∂² K _S /∂P∂T = [−0.20(24), 0.22(26)] × 10⁻³ K⁻¹, both of order 10⁻⁴ K⁻¹ and not significantly different from zero. More robust inference of the mixed derivatives will require solid-medium acoustic measurements of precision significantly better than 1%.     

Standard thermodynamic data for Rhodochrosite from equilibrium decomposition curve

Hydrothermal equilibrium decomposition curve for MnCO₃⇌MnO + CO₂ in the total CO₂ pressure range of 100–1700 bars and temperature range of 500–800°C was studied. The standard thermodynamic data obtained are: ΔH⁰ _f= − 894.382 ± 0.74 kj/mol and ΔG⁰ _f = − 822.170 ± 0.74 kj/mol. These values are more negative than the reported calorimetric data.