Matthias Gottschalk

Perturbation theory based equation of state for polar molecular fluids: I. Pure fluids

Based on the thermodynamic perturbation theory an equation of state (EOS) for molecular fluids has been formulated which can be used for many fluid species in geological systems. The EOS takes into account four substance specific parameters. These are the molecular dipole moment, the molar polarizability and the two parameters of the Lennard-Jones potential. For many fluids these parameters can be evaluated directly or indirectly from experimental measurements. In the absence of direct experimental determinations, as a first approximation, for a pure fluid the parameters of the Lennard-Jones potential can be evaluated using the critical temperature and the critical density if for polar molecules in addition the dipole moment is known with reasonable accuracy. The EOS with its model potential has the appropriate asymptotic behaviour at high pressures and temperatures and can be used to calculate both vapor-liquid equilibria and thermodynamic properties of single phase fluids up to at least 10 GPa and 2000 K. Currently, parameters for 98 inorganic and organic compounds are available. In this article the EOS for pure fluids is presented. In a further communication the EOS is extended to fluid mixtures (Churakov and Gottschalk, 2003).

Antigorite Pressure and temperature dependence of polysomatism and water content

The pressure and temperature dependence of antigorite polysomatism was investigated in the P,T-range of 350-710°C, 0.2-5.0 GPa within the system MgO-SiO2-H2O (MSH). TEM-study indicated that increasing temperature and decreasing pressure of MSH-antigorite formation are correlated with a shorter a-cell periodicity, i.e. smaller m- value (m = number of tetrahedra in a single chain along the wavelength a). For the P,T-conditions investigated, the compositional m-range of antigorite is rather narrow (14-18) corresponding to Mg2.79Si2O5(OH)3.57 - Mg2.83Si2O5(OH)3.67. The change in the crystal structure of antigorite is combined with a gradual partial dehydration process and loss of MgO. For the formulation of reactions that include antigorite, the P,T-dependence of the chemical composition of antig- orite has to be considered. However, our results support the conclusion of Mellini et al. (1987) of the limited appli- cability of a modulation-dependent geothermobarometer, because equilibrium states of antigorite modulation are rarely observed in natural occurrences and have not been reached in our experiments. The successive partial dehydration of antigorite during ongoing subduction of serpentine-bearing oceanic litho- sphere probably influences its rheological properties.

Perturbation theory based equation of state for polar molecular fluids: II. Fluid mixtures

The equation of state (EOS) for 98 pure organic and inorganic fluids formulated by Churakov and Gottschalk (2003) is extended to complex fluid mixtures. For the calculation of the thermodynamic properties of mixtures, theoretical combining rules from statistical mechanics are used. These mixing rules do not involve any empirical parameters. The properties of the fluid mixtures are directly derived from those of the pure constituents. As an example we show that the EOS describes accurately the thermodynamic relations in the H2O-CO2 binary at high pressures and temperatures. At subcritical conditions the EOS is able to reproduce accurately the phase relations within mixtures of non-polar fluids. In particular the EOS predicts phase separations within various fluid mixtures of polar and non-polar molecules.

A new semi-micro wet chemical method for apatite analysis and its application to the crystal chemistry of fluorapatite-chlorapatite solid solutions

Abstract A series of synthetic apatite crystals along the fluorapatite-chlorapatite Ca5(PO4)3(F,Cl) join have been synthesized at 1220 to 1375 °C from Ca3(PO4)2 dissolved in a CaF2-CaCl2 melt. The solid solutions have then been characterized both chemically and structurally. Because of well-known difficulties in measuring the chemical composition of apatites containing F and Cl by electron microprobe a new semi-micro wet chemical method has been developed. Apatite is relatively well dissolved in mineral acids including HNO3. Nitric acid digestion of apatite for analysis of F and Cl has not been applied in the past to our knowledge. One reason is the potential risk of losing gaseous HF and HCl during acid decomposition. We present an analytical procedure that enables the analyses of F, Cl, Ca, P, and trace elements after digestion of 10 mg apatite with a small amount of 1 N HNO3 in gas-tight PTFE tubes at 80 °C. Analytical results from three independent closed acid digestions of 20 synthetic fluor-chlorapatites are presented. The reliability of this method was tested on the basis of charge balance, the Ca/P, Ca/(F+Cl), and P/(F+Cl) ratios, and the total cation sum. Independently derived Cl/F ratios by XRD using Rietveld refinement of apatite crystals from the same synthesis experiments are additionally presented. The apatite solid solutions were characterized by IR spectroscopy, X-ray powder diffraction using Rietveld refinements (XRD), and single-crystal diffraction (SCXRD) structure determinations. IR spectra indicate no or only a very minor hydroxylapatite component in the solid solutions. Lattice parameters of the apatite solid solutions vary systematically with composition. The a-lattice parameter varies linearly. In contrast to F-, which occupies a special position at (0,0,1/4) in the unit cell, Cl- occupies split positions ranging from 0.346(4) to 0.4428(2) in the z-coordinate because of the larger ionic Cl- radius. Single-crystal structure determinations reveal that the Ca2 site is also split into Ca2A and Ca2B sites for F- and Cl- as nearest neighbors, respectively. In comparison to the Ca2A-F- arrangements, the larger Cl- ion presses the triangular arrangement of Ca-ions outward to facilitate an energetic more favorable constellation resulting in the formation of Ca2B-Cl- arrangements. The occupancies of the Ca2A and Ca2B sites, as determined by SCXRD, correlate strictly with the F-Cl content. Apatites rich in Cl (xCl > 0.5) show a deficiency in halogens, which is probably charge balanced by oxygen (Cl-+Cl- ↔ O2-+□) forming an oxyapatite component. The oxyapatite component prevents the F-absent, Cl-rich apatite from crystallizing with a monoclinic symmetry and stabilizes the observed hexagonal symmetry.

Crystal chemistry of K-richterite-richterite-tremolite solid solutions: a SEM, EMP, XRD, HRTEM and IR study

Solid solutions in the ternary K-richterite-richterite-tremolite (K x Na y □ 1-x-y )(Na x+y Ca 2-x-y ) 2 Mg 5 [Si 8 O 22 /(OH) 2 ] have been synthesized at 200 MPa and 800°C using cold-seal vessels, and at 1800 MPa and 800°C using a piston-cylinder apparatus. The amphiboles were synthesized from oxide and hydroxide mixtures in the presence of a 2-molal aqueous chloridic solution. Solid run products have been investigated by optical, electron scanning and high-resolution transmission electron microscopy, electron microprobe, X-ray powder diffraction and fourier transform infrared spectroscopy. The synthesized amphiboles are up to 1000 μm x 50 μm in size. The crystals are chemically homogeneous and structurally well-ordered. Complete solid solutions are observed in the ternary Kri-ri-tr, but compositions very close to pure richterite and K-richterite end-member could not be synthesized, always showing small but significant amounts of tremolite component. In addition, small amounts of cummingtonite component are present in most amphiboles. There are no indications for crystal chemical restrictions for complete solid solutions, however. The lattice parameters of the solid solutions correlate linearly with the cation occupancies on the A-and M4-sites and are therefore a linear combination of the lattice parameters of the end-members tremolite, cummingtonite, richterite and K-richterite. Two systems of OH-stretching bands are observed. The first band system at wavenumbers between 3669 and 3678 cm -1 is due to a vacant A-site and the second between 3721 and 3737 cm -1 due to a filled A-site. The observed fine structure of the bands can be attributed to distinct M4-site occupancies by Ca 2+ , Mg 2+ and Na + . Using pure tremolite as a standard, the vacancy concentration was determined quantitatively from normalized integral absorbances of the band system at 3669-3678 cm -1 . The derived vacancy concentrations are consistent with those derived by electron microprobe. Additional bands at 3659, 3695 and 3710 cm -1 are probably due to triple-chains or higher chain multiplicity faults in the amphibole. The integral absorbances of these bands may be used to determine, the concentration of chain multiplicity faults.

Experimental investigation of the kinetics of the reaction 1 tremolite+11 dolomite⇌8 forsterite+13 calcite+9 CO2+1 H2O

AbstractThe kinetics of the reaction of tremolite plus dolomite to give forsterite, calcite, CO2, and H2O were investigated by powder experiments at 500 MPa. In the first group of experiments, the mole fraction of CO2(

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

X_{\operatorname{CO} _2 }

The T-X dependence of the isosymmetric displacive phase transition in synthetic Fe3+-Al zoisite: A temperature-dependent infrared spectroscopy study

) of the carbon dioxide-H2O mixture (present in all runs) lay in the range of 0.60–0.69. At this