Thomas Fockenberg

Thermodynamic modeling of solubility and speciation of silica in H2O-SiO2 fluid up to 1300°C and 20 kbar based on the chain reaction formalism

Recent systematic studies of mineral solubilities in water to high pressures up to 50 kbar call for a suitable thermodynamic formalism to allow realistic fitting of the experimental data and the establishment of an internally consistent data base. The very extensive low-pressure ( 2 in H 2 O has in the last few years been extended to 20 kbar and 1300°C, providing an excellent experimental basis for testing new approaches. In addition, solubility experiments with different SiO 2 -buffering phase assemblages and in situ determinations of Raman spectra for H 2 O-SiO 2 fluids have provided both qualitative and quantitative constraints on the stoichiometry and quantities of dissolved silica species. We propose a thermodynamic formalism for modeling both absolute silica solubility and speciation of dissolved silica using a combination of the chain reaction approach and a new Gibbs free energy equation of water based on a homogeneous reaction formalism. For a given SiO 2 -buffer ( e.g. , quartz) and the coexisting H 2 O-SiO 2 fluid both solubility and speciation of silica can be described by the following two reactions: - monomer-forming standard reaction: \[\mathrm{SiO_{2(s)}\ {+}\ 2(H_{2}O)L\ {=}\ (SiO_{2}){\bullet}(H_{2}O)_{2}}\] - polymer-forming chain reaction: \[\mathrm{(SiO_{2})_{n{-}1}{\bullet}(H_{2}O)_{n}\ {+}\ (SiO_{2}){\bullet}(H_{2}O)_{2}\ {=}\ (SiO_{2})_{n}{\bullet}(H_{2}O)_{n{+}1}\ {+}\ (H_{2}O)_{L},}\] where 2 ≤ n ≤ ∞, and (H 2 O) L stands for “liquid-like” (associated, clustered) water molecules in the aqueous fluid. We show that reactions (A) and (B) lead to the simplified relationships Δ G ° (mono)r, P,T = Δ H ° (mono),r − T Δ S ° (mono),r + Δ Cp ° (mono),r [ T − 298.15 - T ln( T /298.15)] + Δ V ° (mono),r ( P − 1), and Δ G ° (poly),r, P,T = Δ H ° (poly),r − T Δ S (poly),r + Δ V ° (poly),r ( P − 1) (where the Δ G ° r, P,T , are the standard molar Gibbs free energy changes in reactions (A) and (B) as a function of pressure P and temperature T ; the Δ H ° r , Δ S ° r , Δ Cp ° r , and Δ V ° r are standard molar enthalpy, entropy, isobaric heat capacity and volume changes, respectively, in reactions (A) and (B) at reference temperature T o = 298.15 K and pressure T o = 1 bar) that provide excellent descriptions of the available H 2 O-SiO 2 data set in terms of both SiO 2 solubility and silica speciation. Discrepancies between directly determined solubility data and data obtained from in situ Raman spectra are ascribed to (i) possible experimental problems of equilibration and (ii) inherent difficulties of interpreting Raman spectra of dilute H 2 O-SiO 2 solutions. In agreement with recent findings, our model indicates that dissolved silica in quartz-buffered aqueous solutions is considerably polymerized, exceeding 20–25 % at all temperatures above 400°C.

An experimental study of the pressure-temperature stability of MgMgAl-pumpellyite in the system MgO-Al 2 O 3 -SiO 2 -H 2 O

Abstract The stability field of MgMgAl-pumpellyite. Mg5Al5Si6O21(OH)7, was determined in the system MgO-Al2O3-SiO2-H2O in reversal experiments at pressures between 34 and 100 kbar and temperatures in the range of 597 to 1050 °C. Brackets were obtained on five breakdown reactions (in order of increasing pressure): This phase becomes stable only at pressures of more than 34 kbar and temperatures up to 820 °C. Thus, MgMgAl-pumpellyite may be an H2O-containing phase at depths greater than 100 km in the coldest parts of subduction zones.

Melting of metasedimentary rocks at ultrahigh pressure—Insights from experiments and thermodynamic calculations

Diamondiferous quartzofeldspathic rocks from the Kokchetav Massif, Kazakhstan, and the Erzgebirge, central Europe, are rare witnesses of melting of sedimentary material at great depths. To better understand the melting process, two powdered samples from these localities were objects of experiments conducted in a piston-cylinder apparatus at pressures of 3–5 GPa. In addition, thermodynamic calculations in the system Na 2 O-CaO-K 2 O-FeO-MgO-Al 2 O 3 -SiO 2 -H 2 O using a haplogranitic melt model yielded isochemical phase equilibria diagrams (i.e., pseudosections) at ultrahigh pressure. The solidus for both rocks was located close to 1000 °C and 1100 °C at 3 GPa and 5 GPa, respectively, in the experiments. Initial potassic to ultrapotassic melts form by phengite breakdown. At ∼200 °C above the solidus, clinopyroxene disappears from the restite assemblage, and coexisting melts are granitic. The restite consists of garnet + coesite (±kyanite) up to temperatures close to the liquidus, which occurs at a temperature ∼350 °C above the solidus. The results of the thermodynamic calculations approximate the pressure-temperature conditions and phase relations around the solidus but increasingly deviate from the experimental results with rising temperature. According to the experiments, the melt that crystallized to diamondiferous saidenbachite from the Erzgebirge should have been as hot as 1400 °C, whereas the ultrahigh-pressure rocks from the Kokchetav Massif experienced temperatures of at least 1200 °C. These high melting temperatures are derived for rocks with no free water, which is the most likely scenario for continental crust taken to mantle depths where diamond forms.

Crystal structure of the high-pressure phase Mg 4 (MgAl)Al 4 [Si 6 O 21 /(OH) 7 ]

The crystal structure of the synthetic high-pressure phase Mg 4 (MgAl)Al 4 [Si 6 O 21 /(OH) 7 ], presently referred to as MgMgAl-pumpellyite in the literature, has been determined by the Rietveld method, and found to be isostructural with sursassite rather than pumpellyite. This phase is therefore a slightly modified Mg-analogue of sursassite Mn 2+ 4 Al 2 Al 4 [Si 6 O 22 /(OH) 6 ], with Mg for Mn and one Al replaced by Mg+H. For material synthesized at 5 GPa and 600°C, the following monoclinic cell-dimensions (Z = 1, space group = P 2 1 / m ) were derived: a = 8.5424(8) A, b = 5.7117(3) A, c = 9.6484(6) A, β = 108.298(4)°, V = 447.0(1) A 3 . Besides domain boundaries the material was well crystallized and HRTEM investigations did not suggest any stacking disorder along [001] or sursassite-pumpellyite intergrowth.

The solubility of natural grossular-rich garnet in pure water at high pressures and temperatures

The solubility of a natural grossular-rich garnet of composition Ca 2.86 Fe 2+ 0.07 Mg 0.07 Fe 3+ 0.10 Al 1.90 Si 3.00 O 12 has been experimentally determined in pure water at pressures from 1 to 5 GPa and temperatures ranging from 400 to 800 °C with the weight-loss technique in piston–cylinder apparatus. Grossular dissolves congruently in this pressure–temperature region. The amount of dissolved grossular increases with both increasing pressure and temperature and ranges from 0.1 to 7.0 wt.%. In comparison to available data on other phases in the CaO–Al 2 O 3 –SiO 2 system, the solubility of grossular is considerably lower than that of quartz (SiO 2 ) or wollastonite (CaSiO 3 ), but higher than that of corundum (Al 2 O 3 ) at comparable pressure–temperature conditions. Using a model based on the familiar correlation between the equilibrium constant of a dissolution reaction and the density of water, ρ H 2 O, we suggest that the following expression provides an acceptable description of the solubility of pure grossular, Ca 3 Al 2 Si 3 O 12 , in water for the above pressure–temperature range: \[log\ (\mathit{m}_{grs})\ =\ 0.8639\ {-}\ 3519.71{\ast}\mathit{T}^{{-}1}\ +\ 676921.07{\ast}\mathit{T}^{{-}2}\ +\ 4502.85{\ast}\mathit{T}^{{-}3}\ +\ log{\rho}_{H_{2}O}{\ast}\ (7.2557\ +\ 773.65{\ast}\mathit{T}^{{-}1}\ {-}\ 106080.98{\ast}\mathit{T}^{{-}2}),\] where m grs is the molality of dissolved grossular and T is in °C. Uncertainties estimated from the outer bounds of experimental data scatter indicate a maximum of ±0.045 mol grs /kg H 2 O. Comparison with available experimental solubility data on quartz, wollastonite, corundum and kyanite provides indirect evidence for the presence of aqueous Al–Si-species.

Pressure–temperature stability of pyrope in the system MgO–Al2O3–SiO2–H2O

The pressure–temperature stability field of pyrope was experimentally determined in reversed equilibrium experiments up to 10 GPa within the system MgO–Al 2 O 3 –SiO 2 –H 2 O. The lower pressure limit of pyrope is defined by reactions to aluminous enstatite + sapphirine + kyanite (1.5 GPa, 950–1050 °C) and to aluminous enstatite + corundum (1.5–1.7 GPa, 800–950 °C). Between 1.7 and 1.8 GPa pyrope is formed from the assemblage enstatite + chlorite + Mg-staurolite. The curve talc + Mg-staurolite + kyanite = pyrope + H 2 O marks the pyrope in field between 1.8 and 1.9 GPa, and at higher pressures up to 4 GPa pyrope forms from chlorite + talc + kyanite. Beyond 4 GPa, the assemblage talc + chlorite + Mg-chloritoid defines the lower temperature limit around 600 °C. At pressures higher than 5 GPa, pyrope forms via the reactions low-clinoenstatite + chlorite + Mg-sursassite = pyrope + H 2 O and high-clinoenstatite + forsterite + Mg-sursassite = pyrope + H 2 O (with increasing pressure). The bracketing results indicate that all these reactions have a high positive d P /d T -slope. Pyrope is a high-pressure phase stable only at mantle depths.

The enthalpy of formation and internally consistent thermodynamic data of Mg-staurolite

Abstract The enthalpies of drop solution in lead borate (2 PbO·B2O3) of four Mg-staurolite samples, synthesized at 720 °C and pressures between 2 and 5 GPa, were measured by high-temperature oxidemelt calorimetry at 702 °C. Staurolite compositions, determined by electron microprobe analysis, Karl-Fischer titration, and thermogravimetry, are: Mg3.71Al18.17Si7.60O44.31(OH)3.69, Mg3.87Al17.65Si7.75O43.68(OH)4.32, Mg3.66Al17.76Si7.68O43.31(OH)4.69, and Mg3.58Al18.05Si7.43O43.01(OH)4.99. The enthalpy of drop solution of the bulk samples (as well as the calculated values for the enthalpy of formation from the elements of Mg-staurolite) are strongly correlated to the H content of the samples. The enthalpy of formation from the elements is best described by the linear relation ΔfH0298 (Mgstaurolite) = (-25357.58 + 87.35 N) kJ/mol, where N = number of H atoms per formula unit in Mgstaurolite. The enthalpy of drop solution of two partially dehydrated Mg-staurolite samples is in a good agreement with the linear relation. Phase-equilibrium data for Mg-staurolite (Fockenberg 1998) were recalculated using the stoichiometric formula Mg3.5Al18Si7.75O44(OH)4. Based on these mineral equilibria and the internally consistent data set of Berman (1988), a mathematical programming analysis of the thermodynamic data of Mg-staurolite gave ΔfH0298 [Mg3.5Al18Si7.75O44(OH)4] = -25005.14 kJ/mol, and S0298 [Mg3.5Al18Si7.75O44(OH)4] = 937.94 J/(K·mol). Thus, for the first time, reliable thermodynamic data for Mg-staurolite, based on experimental constraints, are provided.

Modelling high-pressure aqueous fluids in the system CaO–SiO2–H2O: A comprehensive semi-empirical thermodynamic formalism

There is a distinct need for predictive equations of state for supercritical aqueous solutions, both for understanding fluids in deeper levels of Earth’s crust or in subduction zones, as well as in experimental work on mineral solubility. Here we develop a semi-empirical approach introduced by Gerya & Perchuk (1997) based on the P-T partition function of statistical thermodynamics, using experimental data on quartz and wollastonite solubility, as well as data on speciation of dissolved solution components derived from first principles molecular dynamics simulations. Two approaches are possible, differing in the degree of explicit information provided on the nature of the solution modelled and also in the amount of basic data needed to implement them. Both have their potential fields of application. A “simple” model using only the semi-empirical formulation for the H 2 O solvent is useful if independent data on speciation are lacking, overall neutrality of the dissolving species can be assumed, and the number of components is relatively low. Computation is fairly straightforward, because the system can be treated as a simple “mixing” problem, and adopted effective dissolved species are characterized by conventional thermodynamic properties that allow interpolation and extrapolation of fitted experimental solubility data. Application to the system CaO–SiO 2 –H 2 O shows that experimental data on fluids coexisting with wollastonite + quartz/coesite can be successfully modelled up to 900 °C and 4 GPa. This simple semi-empirical formulation can lay the groundwork for an “internally consistent data set” allowing descriptions of fluids in relatively simple fluid-rock systems at high pressures. With the addition of independent data on actual speciation, and an optimized model for the dissociation of H 2 O from available literature data, the semi-empirical approach can be extended to a comprehensive description of aqueous solutions in the CaO–SiO 2 –H 2 O system. Both models have one positive feature in common. Because standard thermodynamic properties for dissolved species, oxides or fictive aggregates/clusters can be derived, solutions of arbitrary compositions can be modelled from data obtained from experiments in which fluids are saturated with a given solid phase or phases.

Ca2+ solvation as a function of p, T, and pH from ab initio simulation.

First principles molecular dynamics simulations have been carried out at various temperatures and pressures starting with either Ca(2+) or CaO in a reactive volume of 63 H(2)O molecules. In the case of aqueous Ca(2+), the ion is surrounded by six H(2)O molecules in the first hydration shell at 300 K/0.3 GPa, with rare exchange between first and second hydrations shells. At 900 K/0.9 GPa, the coordination number in the first hydration shell fluctuates between six and eight, the average being 7.0. CaO immediately reacts with the surrounding H(2)O molecules to form Ca(2+) + 2OH(-). The hydroxyl ions form transient Ca(OH)(+) and Ca(OH)(2) complexes and have a mean residence time in the first coordination shell of Ca(2+) of 6 ± 4 ps at 500 K and 3 ± 3 ps at 900 K, respectively. At 500 K/0.5 GPa, the time-averaged relative concentrations of the transient Ca(2+), Ca(OH)(+), and Ca(OH)(2) species are 14%, 55%, and 29%, while at 900 K/0.9 GPa, they are 2%, 34%, and 63%.

Thermodynamic properties of magnesiochloritoid

Calorimetric and P-V-T data of synthetic magnesiochloritoid (MgAl 2 SiO 5 (OH) 2 ) have been obtained. The P-V-T behaviour of monoclinic and triclinic magnesiochloritoid has been determined in situ up to 8.5 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 of the triclinic polytype was determined as 127.9 ± 2.1 GPa, ( K’ = 4), V T,0 = 456.58 A 3 exp [∫(0.304 ± 0.022) × 10 −4 dT], (∂ K T /∂ T ) P = −0.017 ± 0.009 GPa K −1. The resulting fit parameters for the monoclinic polytype are very similar. The enthalpy of drop-solution was measured by high-temperature oxide melt calorimetry in two laboratories (UC Davis, California, and Ruhr-University Bochum, Germany) using lead borate (2 PbO·B 2 O 3 ) at 700°C as solvent. The resulting values were used to calculate the enthalpy of formation from the elements;-3538.9 ± 4.9 kJ mol −1 (Davis) and −3543.4 ± 6.2 kJ mol −1 (Bochum) were obtained. Heat capacity measurements of MgAl 2 SiO 5 were obtained by differential scanning calorimetry (DSC) in the temperature range from −10°C to 295°C. Two runs confirmed heat capacity data of Koch-Muller et al. (2002), represented by the Berman & Brown (1985) type four-term equation: C P = (391.75 - 2585.00 × T −0.5 - 8240000.0 × T −2 + 967000000.0 × T −3 ) J K −1 mol −1 . Consistency of the thermodynamic data obtained for magnesiochloritoid with phase equilibrium data reported in the literature was checked by mathematical programming analysis. The best agreement was obtained with Δ f H 0 298 (magnesiochloritoid) = −3551.7 kJ mol −1 , and S 0 298 (magnesiochloritoid) = 142.2 J K −1 mol −1 .