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An internally consistent thermodynamic data set for phases of petrological interest

TL;DR: In this article, the authors presented a revised and updated data set of 154 mineral end-members, 13 silicate liquid endmembers and 22 aqueous fluid species, which is used for the calculation of uncertainties on mineral reactions to be performed.
Abstract: The thermodynamic properties of 154 mineral end-members, 13 silicate liquid end-members and 22 aqueous fluid species are presented in a revised and updated data set. The use of a temperature-dependent thermal expansion and bulk modulus, and the use of high-pressure equations of state for solids and fluids, allows calculation of mineral-fluid equilibria to 100 kbar pressure or higher. A pressure-dependent Landau model for order-disorder permits extension of disordering transitions to high pressures, and, in particular, allows the alpha-beta quartz transition to be handled more satisfactorily. Several melt end- members have been included to enable calculation of simple phase equilibria and as a first stage in developing melt mixing models in NCKFMASH. The simple aqueous species density model has been extended to enable speciation calculations and mineral solubility determination involving minerals and aqueous species at high temperatures and pressures. The data set has also been improved by incorporation of many new phase equilibrium constraints, calorimetric studies and new measurements of molar volume, thermal expansion and compressibility. This has led to a significant improvement in the level of agreement with the available experimental phase equilibria, and to greater flexibility in calculation of complex mineral equilibria. It is also shown that there is very good agreement between the data set and the most recent available calorimetric data. kinetics which apply to determining directly the greatest majority of such equilibria in the laboratory, for forming solid solutions, and inclusion of aqueous and silicate melt species), and provides uncertainties especially at lower temperatures, as well as the diYculty of establishing reversals of reactions involving solid allowing the likely uncertainties on the results of thermodynamic calculations to be estimated. This is a solutions. The levels of precision and accuracy required of thermodynamic data in order to be able to forward- critical issue in that calculations using data sets should always involve uncertainty propagation to help evalu- model synthetic and natural mineral assemblages mean that the continuing upgrading and expansion of the ate the results. Because the experimental phase equilib- ria involve overlapping subsets of compositional space, data set by incorporation of new phase equilibrium constraints, calorimetry and new measurements of the derived thermodynamic data are highly correlated, and it is only the inclusion of the correlations which molar volume, thermal expansion and compressibility are more than justified. enables the reliable calculation of uncertainties on mineral reactions to be performed. Earlier work on mineral thermodynamic data sets for rock-forming minerals includes compilations of The thermodynamic data extraction involves using weighted least squares on the diVerent types of data
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Journal ArticleDOI
TL;DR: In this article, an algorithm for the construction of phase diagram sections is formulated that is well suited for geodynamic problems in which it is necessary to assess the influence of phase transitions on rock properties or the evolution and migration of fluids.

1,780 citations

Journal ArticleDOI
TL;DR: In this paper, the authors show that the Zr content of rutile coexisting with zircon increases with decreasing the activity of SiO2 and demonstrate that the substitution of Ti in Zircon is primarily for Si.
Abstract: The models recognize that ZrSiO4, ZrTiO4, and TiSiO4, but not ZrO2 or TiO2, are independently variable phase components in zircon. Accordingly, the equilibrium controlling the Zr content of rutile coexisting with zircon is ZrSiO4 = ZrO2 (in rutile) + SiO2. The equilibrium controlling the Ti content of zircon is either ZrSiO4 + TiO2 = ZrTiO4 + SiO2 or TiO2 + SiO2 = TiSiO4, depending whether Ti substitutes for Si or Zr. The Zr content of rutile thus depends on the activity of SiO2 $$(a_{\text{SiO}_{2}})$$ as well as T, and the Ti content of zircon depends on $$a_{\text{SiO}_{2}}$$ and $$a_{\text{TiO}_{2}}$$ as well as T. New and published experimental data confirm the predicted increase in the Zr content of rutile with decreasing $$a_{\text{SiO}_{2}},$$ and unequivocally demonstrate that the Ti content of zircon increases with decreasing $$a_{\text{SiO}_{2}}$$ . The substitution of Ti in zircon therefore is primarily for Si. Assuming a constant effect of P, unit $$a_{\text{ZrSiO}_{4}},$$ and that $$a_{\text{ZrO}_{2}}$$ and $$a_{\text{ZrTiO}_{4}}$$ are proportional to ppm Zr in rutile and ppm Ti in zircon, [log(ppm Zr-in-rutile) + log $$a_{\text{SiO}_{2}}$$ ] = A1 + B1/T(K) and [log(ppm Ti-in-zircon) + log $$a_{\text{SiO}_{2}}$$ − log $$a_{\text{TiO}_{2}}$$ ] = A2 + B2/T, where the A and B are constants. The constants were derived from published and new data from experiments with $$a_{\text{SiO}_{2}}$$ buffered by either quartz or zircon + zirconia, from experiments with $$a_{\text{SiO}_{2}}$$ defined by the Zr content of rutile, and from well-characterized natural samples. Results are A1 = 7.420 ± 0.105; B1 = −4,530 ± 111; A2 = 5.711 ± 0.072; B2 = −4,800 ± 86 with activity referenced to α-quartz and rutile at P and T of interest. The zircon thermometer may now be applied to rocks without quartz and/or rutile, and the rutile thermometer applied to rocks without quartz, provided that $$a_{\text{SiO}_{2}}$$ and $$a_{\text{TiO}_{2}}$$ are estimated. Maximum uncertainties introduced to zircon and rutile thermometry by unconstrained $$a_{\text{SiO}_{2}}$$ and $$a_{\text{TiO}_{2}}$$ can be quantitatively assessed and are ≈60 to 70°C at 750°C. A preliminary assessment of the dependence of the two thermometers on P predicts that an uncertainty of ±1 GPa introduces an additional uncertainty at 750°C of ≈50°C for the Ti-in-zircon thermometer and of ≈70 to 80°C for the Zr-in-rutile thermometer.

1,578 citations

Journal ArticleDOI
TL;DR: The asymmetric formalism (ASF) as discussed by the authors is an extension to the symmetric formalisms that allows asymmetric energies to be accommodated via a simple extension, which turns it into a macroscopic van Laar formulation.
Abstract: For petrological calculations, including geothermobarometry and the calculation of phase diagrams (for example, P–T petrogenetic grids and pseudosections), it is necessary to be able to express the activity–composition (a–x) relations of minerals, melt and fluid in multicomponent systems Although the symmetric formalism—a macroscopic regular model approach to a–x relations—is an easy-to-formulate, general way of doing this, the energetic relationships are a symmetric function of composition We allow asymmetric energetics to be accommodated via a simple extension to the symmetric formalism which turns it into a macroscopic van Laar formulation We term this the asymmetric formalism (ASF) In the symmetric formalism, the a–x relations are specified by an interaction energy for each of the constituent binaries amongst the independent set of end members used to represent the phase In the asymmetric formalism, there is additionally a "size parameter" for each of the end members in the independent set, with size parameter differences between end members accounting for asymmetry In the case of fluid mixtures, for example, H2O–CO2, the volumes of the end members as a function of pressure and temperature serve as the size parameters, providing an excellent fit to the a–x relations In the case of minerals and silicate liquid, the size parameters are empirical parameters to be determined along with the interaction energies as part of the calibration of the a–x relations In this way, we determine the a–x relations for feldspars in the systems KAlSi3O8–NaAlSi3O8 and KAlSi3O8–NaAlSi3O8–CaAl2Si2O8, for carbonates in the system CaCO3–MgCO3, for melt in the melting relationships involving forsterite, protoenstatite and cristobalite in the system Mg2SiO4–SiO2, as well as for fluids in the system H2O–CO2 In each case the a–x relations allow the corresponding, experimentally determined phase diagrams to be reproduced faithfully The asymmetric formalism provides a powerful and flexible way of handling a–x relations of complex phases in multicomponent systems for petrological calculations

1,144 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a new compilation of physical properties of minerals relevant to subduction zones and new phase diagrams for mid-ocean ridge basalt, lherzolite, depleted LH, harzburgite, and serpentinite.
Abstract: [1] We present a new compilation of physical properties of minerals relevant to subduction zones and new phase diagrams for mid-ocean ridge basalt, lherzolite, depleted lherzolite, harzburgite, and serpentinite. We use these data to calculate H2O content, density and seismic wave speeds of subduction zone rocks. These calculations provide a new basis for evaluating the subduction factory, including (1) the presence of hydrous phases and the distribution of H2O within a subduction zone; (2) the densification of the subducting slab and resultant effects on measured gravity and slab shape; and (3) the variations in seismic wave speeds resulting from thermal and metamorphic processes at depth. In considering specific examples, we find that for ocean basins worldwide the lower oceanic crust is partially hydrated (<1.3 wt % H2O), and the uppermost mantle ranges from unhydrated to � 20% serpentinized (� 2.4 wt % H2O). Anhydrous eclogite cannot be distinguished from harzburgite on the basis of wave speeds, but its � 6% greater density may render it detectable through gravity measurements. Subducted hydrous crust in cold slabs can persist to several gigapascals at seismic velocities that are several percent slower than the surrounding mantle. Seismic velocities and VP/VS ratios indicate that mantle wedges locally reach 60–80% hydration. INDEX TERMS: 3040 Marine Geology and Geophysics: Plate tectonics (8150, 8155, 8157, 8158); 3660 Mineralogy and Petrology: Metamorphic petrology; 3919 Mineral Physics: Equations of state; 5199 Physical Properties of Rocks: General or miscellaneous; 8123 Tectonophysics: Dynamics, seismotectonics; KEYWORDS: subduction, seismic velocities, mineral physics, H2O

834 citations

Journal ArticleDOI
TL;DR: In this article, the problem of phase equilibrium is reduced to a linear optimization problem that is independent of the functional form used for the equations of state of individual phases of the aggregate.
Abstract: [1] Geodynamic models commonly assume equations of state as a function of pressure and temperature. This form is legitimate for homogenous materials, but it is impossible to formulate a general equation of state for a polyphase aggregate, e.g., a rock, as a function of pressure and temperature because these variables cannot distinguish all possible states of the aggregate. In consequence, the governing equations of a geodynamic model based on a pressure-temperature equation of state are singular at the conditions of low-order phase transformations. An equation of state as a function of specific entropy, specific volume, and chemical composition eliminates this difficulty and, additionally, leads to a robust formulation of the energy and mass conservation equations. In this formulation, energy and mass conservation furnish evolution equations for entropy and volume and the equation of state serves as an update rule for temperature and pressure. Although this formulation is straightforward, the computation of phase equilibria as a function of entropy and volume is challenging because the equations of state for individual phases are usually expressed as a function of temperature and pressure. This challenge can be met by an algorithm in which continuous equations of state are approximated by a series of discrete states: a representation that reduces the phase equilibrium problem to a linear optimization problem that is independent of the functional form used for the equations of state of individual phases. Because the efficiency of the optimization decays as an exponential function of the dimension of the function to be optimized, direct solution of the linearized optimization problem is impractical. Successive linear programming alleviates this difficulty. A pragmatic alternative to optimization as an explicit function of entropy and volume is to calculate phase relations over the range of pressure-temperature conditions of interest. Numerical interpolation can then be used to generate tables for any thermodynamic property as a function of any choice of independent variables. Regardless of the independent variables of the governing equations, a consistent definition of pressure, and the coupling of equilibrium kinetics to deformation, is only possible if the continuity equation accounts for dilational strain.

831 citations

References
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Journal ArticleDOI
TL;DR: In this paper, a series of experiments were performed in a large flume to determine the effect of slope and sediment load on channel patterns, and the results indicated that landforms may not always respond progressively to altered conditions and dramatic morphologic changes can occur abruptly when critical erosional and (or) depositional threshold values are exceeded.
Abstract: A series of experiments was performed in a large flume to determine the effect of slope and sediment load on channel patterns. Sediment loads and slopes were closely related, and as slope and sediment loads increased, threshold values of these variables were encountered, at which channel patterns altered significantly. At a very low slope and sediment load, the channels remained straight, but at a discharge of 0.15 cfs, a meandering-thalweg channel formed at slopes greater than 0.002. With increased slope and sediment loads, thalweg sinuosity increased to a maximum of 1.25. At slopes greater than 0.016, a braided channel formed. The model channels responded to increased sediment loads by maintaining steeper gradients and by major channel pattern changes, but at very gentle slopes and at steep slopes, the channel could not be forced to develop a meandering thalweg. These experiments suggest that landforms may not always respond progressively to altered conditions. Rather, dramatic morphologic changes can occur abruptly when critical erosional and (or) depositional threshold values are exceeded. The meandering-thalweg channel was not a meandering channel. A truly meandering channel with a sinuosity of 1.3 formed when a suspended-sediment load (3 percent concentrations of kaolinite) was introduced into the flow. The clay stabilized the alternate bars, and scour and deepening of the thalweg resulted. This in turn lowered the water level at constant discharge, and the alternate bars emerged o t form point bars. A meandering-thalweg channel was thus converted to a meandering channel by the type of sediment load change that has accompanied climatic and hydrologic changes of the recent geologic past.

755 citations

Book
01 Jan 1979

470 citations

Journal ArticleDOI
TL;DR: In this article, the partitioning of Fe and Mg between coexisting garnet and olivine has been studied at 30 kb pressure and temperatures of 900 ° to 1,400 °C.
Abstract: The partitioning of Fe and Mg between coexisting garnet and olivine has been studied at 30 kb pressure and temperatures of 900 ° to 1,400 °C. The results of both synthesis and reversal experiments demonstrate that K D (= (Fe/Mg)gt/(Fe/Mg)OI) is strongly dependent on Fe/Mg ratio and on the calcium content of the garnet. For example, at 1,000 °C/30 kb, K D varies from about 1.2 in very iron-rich compositions to 1.9 at the magnesium end of the series. Increasing the mole fraction of calcium in the garnet from 0 to 0.3 at 1,000 ° C increases K D in magnesian compositions from 1.9 to about 2.5. The observed temperature and composition dependence of K D has been formulated into an equation suitable for geothermometry by considering the solid solution properties of the olivine and garnet phases. It was found that, within experimental error, the simplest kind of nonideal solution model (Regular Solution) fits the experimental data adequately. The use of more complex models did not markedly improve the fit to the data, so the model with the least number of variables was adopted. Multiple linear regression of the experimental data (72 points) yielded, for the exchange reaction: 3Fe2SiO4+2Mg3Al2Si3O12 olivine garnet ⇌ 2Fe2Al2Si3O12+3Mg2SiO4 garnet olivine ΔH ° (30kb) of −10,750 cal and ΔS ° of −4.26 cal deg−1 mol−1. Absolute magnitudes of interaction parameters (W ij ) derived from the regression are subject to considerable uncertainty. The partition coefficient is, however, strongly dependent on the following differences between solution parameters and these differences are fairly well constrained: W FeMg ol -W FeMg gt ≃ 800 cal W CaMg gt -W CaFe gt ≃ 2,670 cal. The geothermometer is most sensitive in the temperature and composition regions where K D is substantially greater than 1. Thus, for example, peridotitic compositions at temperatures less than about 1,300 ° C should yield calculated temperatures within 60 °C of the true value. Iron rich compositions (at any temperature) and magnesian compositions at temperatures well above 1,300 °C could not be expected to yield accurate calculated temperatures. For a fixed K D the influence of pressure is to raise the calculated temperature by between 3 and 6 °C per kbar.

450 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed regression of experimental solubility data with theoretical equations providing for the intrinsic properties of SiO/sub 2/ and the calorimetric consequences of electrostriction collapse and solvation affords close approximation of the thermodynamic behavior of aqueous silica to 5 kb and 600/sup 0/C.
Abstract: Regression of experimental solubility data with theoretical equations providing for the intrinsic properties of SiO/sub 2/ and the calorimetric consequences of electrostriction collapse and solvation affords close approximation of the thermodynamic behavior of aqueous silica to 5 kb and 600/sup 0/C. The standard molal volume of aqueous silica (V/sup 0/) decreases as a sigmoid function of temperature at constant pressure but increases as pressure increases at constant temperature. In contrast, the standard molal heat capacity (C/sup 0//sub p/) maximizes with increasing pressure at intermediate temperatures. C/sup 0//sub p/, which is negative at low temperatures, exhibits a maximum also as a function of temperature at constant pressure. Owing to the behavior of the partial derivatives of the dielectric constant of H/sub 2/O with respect to pressure and temperature, both V/sup 0/ and C/sup 0//sub p/ approach -infinity at the critical point of H/sub 2/O, but at low temperatures where V/sup 0/ is positive, C/sup 0//sub p/ is negative and decreases dramatically with decreasing temperature at constant pressure. The broad extrema exhibited by curves representing the solubility of ..cap alpha..-quartz as a function of temperature at pressures less than or equal to a kilobar are a consequence of these variations in V/supmore » 0/ and C/sup 0//sub p/. At high temperatures and low pressures, changes in the thermodynamic properties of aqueous silica are controlled primarily by the electrostatic properties of H/sub 2/O, but at low temperatures the local solvent structure dominates the temperature and pressure dependence of V/sup 0/ and C/sup 0//sub p/. The geologic consequences of the thermodynamic behavior of aqueous silica can be predicted by combining the theoretical equations and regression coefficients with thermodynamic data for minerals and other aqueous species, which permits calculation of the distribution of SiO/sub 2/ among silicates and H/sub 2/O-rich hydrothermal solutions at high pressures and temperatures.« less

405 citations