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     

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     

Stability of clinohumite in the system MgO-SiO2-H2O

The low-pressure stability of clinohumite has been investigated in phase-equilibrium experiments on the reaction forsterite + brucite = clinohumite. The reaction was bracketed between 2.45 and 2.84 GPa at 650 °C, extending to between 1.37 and 1.57 GPa at 850 °C. At temperatures above the reaction brucite = periclase + vapour, the reaction clinohumite = forsterite + vapour was bracketed between 1.27 and 1.52 GPa at 900 °C, rising to between 1.90 and 2.00 GPa at 1000 °C. The position of the reaction forsterite + brucite = clinohumite is ∼0.5 GPa below the position determined in previous work, the difference arising either from pressure uncertainties in both studies, from enhanced reaction to clinohumite in this study due to the presence of excess brucite in the starting material, or from different concentrations of defects in the two samples. The brackets on the reaction were combined with other measured and estimated thermodynamic data for clinohumite to determine its enthalpy of formation and entropy, in a revised version of the thermodynamic dataset of Holland and Powell (1998). The values obtained were ΔH _f =−9607.29±3.05 kJ mol⁻¹, S=445 J mol⁻¹ K⁻¹. These data were used to calculate positions of other reactions involving clinohumite. The calculations suggest a larger stability field for clinohumite than implied by the results of previous experimental studies, indicating a need for more high-pressure phase-equilibrium studies to provide better thermodynamic data. Received: 30 April 1999 / Accepted: 8 November 1999     

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 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.     

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.     

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     

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.     

Pressure dependence of hydroxyl solubility in coesite

 The solubility of hydroxyl in coesite was investigated in multianvil experiments performed at 1200 °C over the nominal pressure range 5–10 GPa, at an f _O2 close to the Ni-NiO buffer. The starting material for each experiment was a cylinder of pure silica glass plus talc, which dehydrates at high P and T to provide a source of water and hydrogen (plus enstatite and excess SiO₂). Fourier-transform infrared (FTIR) spectra of the recovered coesite crystals show five sharp bands at 3606, 3573, 3523, 3459, and 3299 cm⁻¹, indicative of structurally bonded hydrogen (hydroxyl). The concentration of hydrogen increases with pressure from 285 H/10⁶ Si (at 5 GPa) to 1415 H/10⁶ Si (at 10 GPa). Assuming a model of incorporation by (4H)_Si defects, the data are fit well by the equation C _OH=Af ² _H2<\INF>Oexp(−PΔV/RT), with A=4.38 H/10⁶ Si/GPa, and ΔV=20.6 × 10⁻⁶ m³ mol⁻¹. An alternative model entailing association of hydrogen with cation substitution can also be used to fit the data. These results show that the solubility of hydroxyl in coesite is approximately an order of magnitude lower than in olivines and pyroxenes, but comparable to that in pyropic garnet. However, FTIR investigations on a variety of ultrahigh pressure metamorphic rocks have failed in all cases to detect the presence of water or hydrogen in coesite, indicating either that it grew in dry environments or lost its hydrogen during partial transformation to quartz. On the other hand, micro-FTIR investigations of quartz crystals replacing coesite show that they contain varying amounts of H₂O. These results support the hypothesis that preservation of coesite is not necessarily linked to fast exhumation rates but is crucially dependent on limited fluid infiltration during exhumation. Received: 23 August 1999 / Accepted: 10 April 2000     

The enthalpy of transformation of Ca(OH)2-I (portlandite) to Ca(OH)2-II (EuI2 structure) by low-temperature DSC

 Thermodynamic properties of high-pressure minerals that are not recoverable from synthesis experiments by conventional quenching methods (“unquenchable” phases) usually are calculated from equation of state data and phase diagram topologies. The present study shows that, with cryogenic methods of recovery and sample treatment, phases with a suitable decomposition rate can be made accessible to direct thermodynamic measurements. A set of samples of Ca(OH)₂-II has been synthesized in a multianvil device and subsequently recovered by cooling the high-pressure assembly with liquid nitrogen. Upon heating from liquid nitrogen to room temperature, the material transformed back to Ca(OH)₂-I. The heat effect of this backtransformation was measured by differential scanning calorimetry. A commercial differential scanning calorimeter (Netzsch DSC 404), modified to allow sample loading at liquid nitrogen temperature was used to heat the material from −150 to +200 °C at rates varying between 5 and 15 °C min⁻¹. The transformation started around −50 °C very gradually, and peaked at about 0 °C. To obtain a baseline correction, each sample was scanned under exactly the same conditions after the backtransformation was complete. Because of the relative sluggishness, onset and offset temperatures were not well defined as compared to fast (e.g., melting) reactions. To aid in integration, the resulting signals were successfully fitted using a generic asymmetric peak model. The enthalpy of backtransformation was determined to be ΔH =−10.37 ± 0.50 kJ mol⁻¹. From previous in situ X-ray diffraction experiments, the location of the direct transformation in P-T space has been constrained to 5.7 ± 0.4 GPa at 500 °C (Kunz et al. 1996). With the reaction volume known from the same study, and assuming that ΔC _p of the transformation remains negligible between the conditions of our measurements and 500 °C, our result gives an estimate of the entropy of transition and the P-T slope of the reaction curve. To a first approximation, the values ΔS = −16.00 ± 0.65 J(mol · K)⁻¹ and dP/dT = 0.0040 ± 0.0002 GPa/K have been determined. These results need to be refined by equation of state data for Ca(OH)₂-II. Received: 30 December 1999 / Accepted: 10 April 2000     

The thermodynamic properties of H2O in magnesium and iron cordierite

 The equilibrium water content of cordierite has been measured for 31 samples synthesized at pressures of 1000 and 2000 bars and temperatures from 600 to 750° C using the cold-seal hydrothermal technique. Ten data points are presented for pure magnesian cordierite, 11 data points for intermediate iron/magnesium ratios from 0.25 to 0.65 and 10 data points for pure iron cordierite. By representing the contribution of H₂O to the heat capacity of cordierite as steam at the same temperature and pressure, it is possible to calculate a standard enthalpy and entropy of reaction at 298.18° K and 1 bar for, (Mg,Fe)₂Al₄Si₅O₁₈+H₂O ⇄ (Fe,Mg)₂Al₄Si₅O₁₈.H₂O Combining the 31 new data points with 89 previously published experimental measurements gives: ΔH ^° _r =–37141±3520 J and ΔS ^° _r =–99.2±4 J/degree. This enthalpy of reaction is within experimental uncertainty of calorimetric data. The enthalpy and entropy of hydration derived separately for magnesian cordierite (–34400±3016 J, –96.5±3.4 J/degree) and iron cordierite (–39613±2475, –99.5±2.5 J/degree) cannot be distinguished within the present experimental uncertainty. The water content as a function of temperature, T(K), and water fugacity, f(bars), is given by n _H2O=1/[1+1/(K ⋅ f _H2O)] where the equilibrium constant for the hydration reaction as written above is, ln K=4466.4/T–11.906 with the standard state for H₂O as the gas at 1 bar and T, and for cordierite components, the hydrous and anhydrous endmembers at P and T. Received: 2 August 1994/Accepted: 7 February 1996     

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     

The low-pressure stability of phase A,Mg7Si2O8(OH)6

 Phase A, Mg₇Si₂O₈(OH)₆, is a dense hydrous magnesium silicate whose importance as a host of H₂O in the Earth’s mantle is a subject of debate. We have investigated the low-pressure stability of phase A in experiments on the reaction phase A=brucite+forsterite. Experiments were conducted in piston-cylinder and multi-anvil apparatus, using mixtures of synthetic phase A, brucite and forsterite. The reaction was bracketed between 2.60 and 2.75 GPa at 500° C, between 3.25 and 3.48 GPa at 600° C and between 3.75 and 3.95 GPa at 650^° C. These pressures are much lower than observed in the synthesis experiments of Yamamoto and Akimoto (1977). At 750^° C the stability field of brucite + chondrodite was entered. The enthalpy of formation and entropy of phase A at 1 bar (10⁵ Pa), 298 K, were derived from the experimental brackets on the reaction phase A=brucite+forsterite using a modified version of the thermodynamic dataset THERMOCALC of Holland and Powell (1990), which includes a new equation of state of H₂O derived from the molecular dynamics simulations of Brodholt and Wood (1993). The data for phase A are: ΔH ^o _f =−7126±8 kJ mol^-1, S ^o=351 J K^-1 mol^-1. Incorporating these data into THERMOCALC allows the positions of other reactions involving phase A to be calculated, for example the reaction phase A + enstatite=forsterite+vapour, which limits the stability of phase A in equilibrium with enstatite. The calculated position of this reaction (753° C at 7 GPa to 937° C at 10 GPa) is in excellent agreement with the experimental brackets of Luth (1995) between 7 and 10 GPa, supporting the choice of equation of state of H₂O used in THERMOCALC. Comparison of our results with calculated P-T paths of subducting slabs (Peacock et al. 1994) suggests that, in the system MgO–SiO₂–H₂O, phase A could crystallise in compositions with Mg/Si>2 at pressures as low as 3 GPa. In less Mg rich compositions phase A could crystallise at pressures above approximately 6 GPa. Received: 3 July 1995/Accepted: 14 December 1995     

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.     

Cation diffusion in aluminosilicate garnets: experimental determination in pyrope-almandine diffusion couples

Diffusion couples made from homogeneous gem quality natural pyrope and almandine garnets were annealed within graphite capsules under anhydrous conditions at 22–40 kbar, 1057–1400 °C in a piston-cylinder apparatus. The concentration profiles that developed in each couple were modeled to retrieve the self diffusion coefficients [D(I)] of the divalent cations Fe, Mg, Mn and Ca. Because of their usually low concentrations and lack of sufficient compositional change across the interface of the diffusion couples, only a few reliable data can be obtained for D(Ca) and D(Mn) from these experiments. However, nine sets of D(Fe) and D(Mg) data were retrieved in the above P-T range, and cast in the form of Arrhenian relation, D=D ₀exp{−[Q(1 bar)+PΔV ⁺]/RT}. The values of the activation energy (Q) and activation volume (ΔV ⁺) depend on whether f _O2 is constrained by graphite in the system C-O or held constant. For the first case, we have for Fe:Q(1 bar)=65,532±10,111 cal/mol, D ₀=3.50 (±2.30)×10⁻⁵ cm²/s, ΔV ⁺=5.6(±2.9) cm³/mol, and for Mg:Q(1 bar)=60,760±8,257 cal/mol, D ₀=4.66 (±2.48)×10⁻⁵ cm²/s, ΔV ⁺=5.3(±3.0) cm³/mol. Here the ΔV ⁺ values have been taken from Chakraborty and Ganguly (1992). For the condition of constant f _O2, the Q values are ∼9 kcal lower and ΔV ⁺ values are ∼4.9 cm³/mol larger than the above values. Lower temperature extrapolation of the Arrhenian relation for D(Mg) is in good agreement with the Mg tracer diffusion data (D ^* _Mg) of Chakraborty and Rubie (1996) and Cygan and Lasaga (1985) at 1 bar, 750–900 °C, when all data are normalized to the same pressure and to f _O2 defined by graphite in the system C-O. The D ^* _Mg data of Schwandt et al. (1995), on the other hand, are lower by more than an order of magnitude than the low temperature extrapolation of the present data, when all data are normalized to the same pressure and to f _O2 defined by the graphite buffer. Comparison of the D(Fe), D(Mg) and D(Mn) data in the pyrope-almandine diffusion couple with those in the spessartine-almandine diffusion couple of Chakraborty and Ganguly (1992) shows that the self diffusion of Fe and Mn are significantly enhanced with the increase in Mn/Mg ratio; the enhancement effect on D(Mg) is, however, relatively small. Proper application of the self diffusion data to calculate interdiffusion coefficient or D matrix elements for the purpose of modeling of diffusion processes in natural garnets must take into account these compositional effects on D(I) along with the effects of thermodynamic nonideality, f _O2, and pressure. Received: 8 May 1997 / Accepted: 2 October 1997     

Toward an Understanding of Biogenic-silica Dissolution in Seawater – An Initial Rate Approach Applied between 40 and 90 °C

Summary The kinetics of phytoplankton frustule dissolution has generally been studied as the appearance of silicic acid in a batch reactor. Unfortunately, this approach, though often illuminating, has not so far been successful because of the difficulty of parameterising the full reaction curve. This current study shows how the initial rate approach to chemical kinetics offers a way around this bottleneck, thereby allowing much chemical kinetics information about frustule dissolution to be collected. The technique is shown to be flexible and suited to short reaction times which facilitate detailed quantitative kinetics investigation, indeed, as would be expected in a solution phase, kinetics study. The technique is exemplified by a dissolution study of uncleaned frustules of Cyclotella crypticaat 40 °C and above. The frustules were found to yield the same dissolution rate after 5 weeks dark storage, at 4 °C. Meanwhile, log dissolution rate was found to vary linearly with pH, with gradient 0.38 ± 0.01 (r ²=0.990). Linearity was upheld even at pHs as high as 14. Finally, a robust Arrhenius plot was established between 40 and 90 °C yielding an activation energy for dissolution of 84 ± 3 kJ mol ⁻¹. Follow through with the Eyring equation yielded an activation enthalpy, ΔH ^‡, and an activation entropy, ΔS ^‡, of 81 and 85 J mol ⁻¹ K ⁻¹, respectively. The discussion brings salient aspects of existing knowledge about diatom frustule dissolution kinetics into the wider context of silicate mineral dissolution.     

High-temperature heat capacity and thermodynamic properties for end-member titanite (CaTiSiO5)

 The heat capacity of end-member titanite and (CaTiSiO₅) glass has been measured in the range 328–938 K using differential scanning calorimetry. The data show a weak λ-shaped anomaly at 483 ± 5 K, presumably associated with the well-known low-pressure P2₁/a ⇆ A2/a transition, in good agreement with previous studies. A value of 0.196 ± 0.007 kJ mol⁻¹ for the enthalpy of the P2₁/a ⇆ A2/a transition was determined by integration of the area under the curve for a temperature interval of 438–528 K, bracketing the anomaly. The heat capacity data for end-member titanite and (CaTiSiO₅) glass can be reproduced within <1% using the derived empirical equations (temperature in K, pressure in bars):

Iron Diffusion in Single-Crystal Diopside

 Iron tracer diffusion experiments in diopside have been performed using natural and synthetic single crystals of diopside, and stable iron tracers enriched in ⁵⁴Fe, at temperatures in the range 950–1100 °C, total pressure 1 atm, for times up to 29 days. Iron isotope diffusion profiles were determined with an ion microprobe. For experiments performed at log pO₂ = −13, in directions parallel to the c axis and the b axis of two natural, low iron (Fe ∼ 1.8 at %) diopsides, the data obey a single Arrhenius relationship of the form D = 6.22_−5.9 ^+49.6×10⁻¹⁵ exp(−161.5 ± 35.0 kJ mol⁻¹/RT) m² s⁻¹. A single datum for iron diffusion in iron-free, single-crystal diopside at 1050 °C, is approximately 1 order of magnitude slower than in the natural crystals. The pO₂ dependence of iron diffusion in natural crystals at 1050 °C (power exponent = 0.229 ± 0.036) indicates a vacancy mechanism; this is consistent with the results of unpublished atomistic simulation studies. There is no evidence of anisotropy for iron diffusion in diopside. Received: 16 March 1999 / Accepted: 10 April 2000     

The high-pressure stability of zoisite and phase relationships of zoisite-bearing assemblages

The fluid-absent reaction 12 zoisite = 3 lawsonite + 7 grossular + 8 kyanite + 1 coesite was experimentally reversed in the model system CaO-Al₂O₃-SiO₂-H₂O (CASH) using a multi-anvil apparatus. The upper pressure stability limit for zoisite was found to extend to 5.0 GPa at 700 °C and to 6.6 GPa at 950 °C. Additional experiments both in the H₂O-SiO₂-saturated and in the H₂O-Al₂O₃-saturated portions of CASH provide further constraints on high pressure phase relationships of lawsonite, zoisite, grossular, kyanite, coesite, and an aqueous fluid. Consistency of the present experiments with the H₂O-saturated breakdown of lawsonite is demonstrated by thermodynamic analysis using linear programming techniques. Two sets of data consistent with databases of Berman (1988) and Holland and Powell (1990) were retrieved combining experimental phase relationships, calorimetric constraints, and recently measured elastic properties of solid phases. The best fits result in G _{f ,1,298} ^∘,zoisite=−6,499,400 J and S _1,298 ^∘,zoisite=302 J/K, and G _{f ,1,298} ^{∘,lawsonite}=−4,514,600 J and S _1,298 ^{∘,lawsonite}=220 J/K for the dataset of Holland and Powell, and G _{f ,1,298} ^∘,zoisite=−6,492,120 J and S _1,298 ^∘,zoisite=304 J/K, and G _{f ,1,298} ^{∘,lawsonite}=−4,513,000 J and S _1,298 ^{∘,lawsonite}= 218 J/K for the dataset of Berman. Examples of the usage of zoisite as a geohygrometer and as a geobarometer in rocks metamorphosed at eclogite facies conditions are worked, profiting from the thermodynamic properties retrieved here. Received: 23 December 1996 / Accepted: 29 August 1997     

Oxygen and hydrogen isotope study of high-pressure metagabbros and metabasalts (Cyclades, Greece): implications for the subduction of oceanic crust

Oxygen and hydrogen stable isotope ratios of eclogite-facies metagabbros and metabasalts from the Cycladic archipelago (Greece) document the scale and timing of fluid–rock interaction in subducted oceanic crust. Close similarities are found between the isotopic compositions of the high-pressure rocks and their ocean-floor equivalents. High-pressure minerals in metagabbros have low δ¹⁸O values: garnet 2.6 to 5.9‰, glaucophane 4.3 to 7.1‰; omphacite 3.5 to 6.2‰. Precursor actinolite that was formed during the hydrothermal alteration of the oceanic crust by seawater analyses at 3.7 to 6.3‰. These compositions are in the range of the δ¹⁸O values of unaltered igneous oceanic crust and high-temperature hydrothermally altered oceanic crust. In contrast, high-pressure metabasalts are characterised by ¹⁸O-enriched isotopic compositions (garnet 9.2 to 11.5‰, glaucophane 10.6 to 12.5‰, omphacite 10.2 to 12.8‰), which are consistent with the precursor basalts having undergone low-temperature alteration by seawater. D/H ratios of glaucophane and actinolite are also consistent with alteration by seawater. Remarkably constant oxygen isotope fractionations, compatible with isotopic equilibrium, are observed among high-pressure minerals, with Δ_{glaucophane−garnet} = 1.37 ± 0.24‰ and Δ_{omphacite−garnet} = 0.72 ± 0.24‰. For the estimated metamorphic temperature of 500 °C, these fractionations yield coefficients in the equation Δ = A * 10⁶/T ² (in Kelvin) of A_{glaucophane−garnet} = 0.87 ± 0.15 and A_{omphacite−garnet} = 0.72 ± 0.24. A fractionation of Δ_{glaucophane–actinolite} = 0.94 ± 0.21‰ is measured in metagabbros, and indicates that isotopic equilibrium was established during the metamorphic reaction in which glaucophane formed at the expense of actinolite. The preservation of the isotopic compositions of gabbroic and basaltic oceanic crust and the equilibrium fractionations among minerals shows that high-pressure metamorphism occurred at low water/rock ratios. The isotopic equilibrium is only observed at hand-specimen scale, at an outcrop scale isotopic compositional differences occur among adjacent rocks. This heterogeneity reflects metre-scale compositional variations that developed during hydrothermal alteration by seawater and were subsequently inherited by the high-pressure metamorphic rocks. Received: 4 January 1999 / Accepted: 7 July 1999