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1.
Ivanov  M. V.  Bushmin  S. A.  Aranovich  L. Y. 《Doklady Earth Sciences》2018,481(2):1086-1090
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2.
The heat capacity of praseodymium orthophosphate PrPO4 was measured by adiabatic and relaxation calorimetric techniques at 5.12–345.54 K, and these data were utilized to calculate thermodynamic functions of PrPO4 at 6–350 K. The Gibbs free energy of PrPO4 formation ΔfG0(298.15 K) is evaluated at 1851.8 ± 4.7 kJ mol–1.  相似文献   

3.
Atomistic model was proposed to describe the thermodynamics of mixing in the diopside-K-jadeite solid solution (CaMgSi2O6-KAlSi2O6). The simulations were based on minimization of the lattice energies of 800 structures within a 2 × 2 × 4 supercell of C2/c diopside with the compositions between CaMgSi2O6 and KAlSi2O6 and with variable degrees of order/disorder in the arrangement of Ca/K cations in M2 site and Mg/Al in Ml site. The energy minimization was performed with the help of a force-field model. The results of the calculations were used to define a generalized Ising model, which included 37 pair interaction parameters. Isotherms of the enthalpy of mixing within the range of 273–2023 K were calculated with a Monte Carlo algorithm, while the Gibbs free energies of mixing were obtained by thermodynamic integration of the enthalpies of mixing. The calculated T-X diagram for the system CaMgSi2O6-KAlSi2O6 at temperatures below 1000 K shows several miscibility gaps, which are separated by intervals of stability of intermediate ordered compounds. At temperatures above 1000 K a homogeneous solid solution is formed. The standard thermodynamic properties of K-jadeite (KAlSi2O6) evaluated from quantum mechanical calculations were used to determine location of several mineral reactions with the participation of the diopside-K-jadeite solid solution. The results of the simulations suggest that the low content of KalSi2O6 in natural clinopyroxenes is not related to crystal chemical factors preventing isomorphism, but is determined by relatively high standard enthalpy of this end member.  相似文献   

4.
New experimental data on the solubility of NaCl in gaseous CO2 were obtained at pressures (P) of 30–70 MPa and temperatures of 623 and 673 K on experimental equipment making possible to sample a portion of the gas in the course of the experiment. The new measures have demonstrated that the NaCl solubility increases with increasing temperature (T) and pressure and is approximately four to five orders of magnitude higher than the saturated vapor pressure of NaCl at the corresponding temperature. The paper also reports newly obtained experimental data on the equilibrium conditions of the reaction of talc decomposition into enstatite and quartz at a variable H2O/NaCl ratio in the fluid. The results of the experiments validate the empirical equations previously suggested for H2O and NaCl activities in concentrated aqueous salt solutions that can be used in describing silica-saturated fluids at high T-P parameters. A new empirical equation is suggested for the Gibbs free mixing energy in the H2O-CO2-NaCl ternary system, with the parameters of the equation calibrated against experimental data on phase equilibria in marginal binary systems and on the location of the boundary of the region of homogeneous three-component fluid according to data on synthetic fluid inclusions in quartz.  相似文献   

5.
The formulas for thermodynamic functions for minerals are presented, couched in terms of the important thermodynamic variable KT= (P/T)v, where is the volume thermal expansivity and KT is the isothermal bulk modulus. Presenting the formulas in this way leads to simplification since KT as a product varies only slightly with volume, and is close to being independent of temperature at high temperature. Using our equations, we present as examples some computed data in the form of graphs on the entropy, internal energy, Helmholtz free energy, and Gibbs free energy in the high temperature regime (up to 2000 K) and for high compression (up to 0.7), for MgO. For entropy, knowledge of the V, T dependence of KT is sufficient. For enthalpy and internal energy, the equation of state is needed in addition.  相似文献   

6.
A semi-empirical model for gas solubilities in high temperature brines was developed by modification of the Pitzer interaction model (Pitzer, 1973) and evaluated by least-squares fitting to available P-T-X data for carbon dioxide, hydrogen sulfide, and methane in pure water and in aqueous sodium chloride solutions. Over the range of experimental data used (25°–350°C, NaCl concentration 0–6 m, PCO2 1–150 atm. PCH4 1–30 atm, PCH4 1–1700 atm), standard deviations of fit in the natural logarithm of the Henry's law ratio were 0.096 for CO2, 0.093 for H2S and 0.116 for CH4.The model has several advantages. First, it has a theoretical basis which can easily be extended for the inclusion of more than one salt or gas. Second, the equations simplify to the empirically derived equation of Setschenow, in the limit of infinite dilution. Finally, the model is easily integrated into a framework of equations which can yield all of the thermodynamic properties of the system.An example in which values of the model parameters for interaction of gas with salt may be used to estimate the effect of dissolved gas or salt solubility is given.  相似文献   

7.
Vibrational density of states of the NaAlSi2O6 jadeite and NaAlSiO4 calcium ferrite (CF)-type, and SiO2 stishovite is calculated as a function of pressure up to 50 GPa using density functional perturbation theory. The calculated frequencies are used to determine the thermal contribution to the Helmholtz free energy within the quasi-harmonic approximation and to derive the equation of state and several thermodynamic properties of interest. A dissociation of jadeite into a mixture of a CF-type phase and stishovite is predicted to occur at 23.4 GPa and 1,800 K with a positive Clapeyron slope of 2.8 MPa/K. Elastic anisotropy for jadeite, the CF-type phase, and stishovite also computed clearly shows that stishovite and the CF-type phase are the most anisotropic and isotropic in these three phases, respectively.  相似文献   

8.
This article presents methods for predicting the standard partial molar Gibbs energy (standard chemical potential) and related derivative properties of aqueous hydroxy and aminoderivatives of (alkyl)benzenes over a wide range of temperatures and pressures. A thorough literature overview was conducted for collecting all available experimental data resulting from phase equilibrium, calorimetric and volumetric measurements that allow calculation of the thermodynamic properties of hydration. New experimental values are presented for solubility in water of isomeric toluidines and for the partial molal volume of phenol and cresols at high temperatures. Building upon the acquired database several prediction schemes were developed and tested for calculating the standard thermodynamic properties (and namely the Gibbs energy of hydration) of aqueous alkylphenols and alkylanilines as a function of temperature and pressure. First, a simple group contribution method was proposed for estimations at 298.15 K and 0.1 MPa using the simultaneous treatment of all available data on hydration properties at near ambient conditions. Second, this group contribution method allowed re-adjustment of the parameters of the Helgeson-Kirkham-Flowers model (HKF) using a new procedure proposed recently by Plyasunov and Shock [Plyasunov, A.V., Shock, E.L., 2001b. Correlation strategy for determining the parameters of the revised Helgeson-Kirkham-Flowers model for aqueous nonelectrolytes. Geochim. Cosmochim. Acta65, 3879-3900]. Third, using the Sedlbauer-O’Connell-Wood equation of state for aqueous species (SOCW), group contributions were determined for predictions at high temperatures and pressures by simultaneous correlation of all available thermodynamic data on hydration properties. The latter method was constrained by the group contributions at 298.15 K and 0.1 MPa making both group contribution schemes consistent at near ambient conditions. The calculations from the HKF and SOCW equations of state and those from the simple thermodynamic integration of the data at 298.15 K and 0.1 MPa were compared for several alkylphenols and alkylanilines. Equilibrium constants for hydration reactions obtained from the three approaches are in very good agreement at temperatures to at least 400 K. At higher temperatures we assess the accuracy of different predictive schemes and their associated uncertainties. The reliable predictions of the standard chemical potentials to at least 573 K and 100 MPa are possible by the group contribution method using the SOCW equation of state.  相似文献   

9.
《Chemical Geology》2003,193(3-4):257-271
A thermodynamic model for the solubility of carbon dioxide (CO2) in pure water and in aqueous NaCl solutions for temperatures from 273 to 533 K, for pressures from 0 to 2000 bar, and for ionic strength from 0 to 4.3 m is presented. The model is based on a specific particle interaction theory for the liquid phase and a highly accurate equation of state for the vapor phase. With this specific interaction approach, this model is able to predict CO2 solubility in other systems, such as CO2–H2O–CaCl2 and CO2–seawater, without fitting experimental data from these systems. Comparison of the model predictions with experimental data indicates that the model is within or close to experimental uncertainty, which is about 7% in CO2 solubility.  相似文献   

10.
This paper describes four programs for Windows, designed to obtain the thermodynamic properties of aqueous species from experimental data and reporting them in the Unitherm database format (HCh software package). Programs OptimA and OptimS allow users to derive the standard Gibbs free energies of aqueous species from the results of chemical experiments (e.g., potentiometry or solubility) and from ultraviolet–visible (UV–Vis) absorption spectra, respectively; programs OptimB and OptimC enable optimization of the parameters of the revised Helgeson–Kirkham–Flowers equation of state and the modified Ryzhenko–Bryzgalin electrostatic model, respectively, for an aqueous species from its standard Gibbs free energy or stability constant as a function of temperature and pressure.  相似文献   

11.
A thermodynamic model is presented to calculate methane solubility, liquid phase density and gas phase composition of the H2O-CH4 and H2O-CH4-NaCl systems from 273 to 523 K (possibly up to 573 K), from 1 to 2000 bar and from 0 to 6 mol kg−1 of NaCl with experimental accuracy. By a more strict theoretical approach and using updated experimental data, this model made substantial improvements over previous models: (1) the accuracy of methane solubility in pure water in the temperature range between 273 and 283 K is increased from about 10% to about 5%, but confirms the accuracy of the Duan model [Duan Z., Moller N., Weare J.H., 1992a. Prediction of methane solubilities in natural waters to high ionic strength from 0 to 250 °C and from 0 to 1600 bar. Geochim. Cosmochim. Acta56, 1451-1460] above 283 K up to 2000 bar; (2) the accuracy of methane solubility in the NaCl aqueous solutions is increased from >12% to about 6% on average from 273 K and 1 bar to 523 K and 2000 bar; (3) this model is able to calculate water content in the gas phase and liquid phase density, which cannot be calculated by previous models; and (4) it covers a wider range of temperature and pressure space. With a simple approach, this model is extended to predict CH4 solubility in other aqueous salt solutions containing Na+, K+, Mg2+, Ca2+, Cl− and , such as seawater and geothermal brines, with excellent accuracy. This model is also able to calculate homogenization pressure of fluid inclusions (CH4-H2O-NaCl) and CH4 solubility in water at gas-liquid-hydrate phase equilibrium. A computer code is developed for this model and can be downloaded from the website: www.geochem-model.org/programs.htm.  相似文献   

12.
Recent Mars missions have stimulated considerable thinking about the surficial geochemical evolution of Mars. Among the major relevant findings are the presence in Meridiani Planum sediments of the mineral jarosite (a ferric sulfate salt) and related minerals that require formation from an acid-salt brine and oxidizing environment. Similar mineralogies have been observed in acidic saline lake sediments in Western Australia (WA), and these lakes have been proposed as analogues for acidic sedimentary environments on Mars. The prior version of the equilibrium chemical thermodynamic FREZCHEM model lacked Al and Si chemistries that are needed to appropriately model acidic aqueous geochemistries on Earth and Mars. The objectives of this work were to (1) add Al and Si chemistries to the FREZCHEM model, (2) extend these chemistries to low temperatures (<0 °C), if possible, and (3) use the reformulated model to investigate parallels in the mineral precipitation behavior of acidic Australian lakes and hypothetical Martian brines.FREZCHEM is an equilibrium chemical thermodynamic model parameterized for concentrated electrolyte solutions using the Pitzer approach for the temperature range from <−70 to 25 °C and the pressure range from 1 to 1000 bars. Aluminum chloride and sulfate mineral parameterizations were based on experimental data. Aluminum hydroxide and silicon mineral parameterizations were based on Gibbs free energy and enthalpy data. New aluminum and silicon parameterizations added 12 new aluminum/silicon minerals to this Na-K-Mg-Ca-Fe(II)-Fe(III)-Al-H-Cl-Br-SO4-NO3-OH-HCO3-CO3-CO2-O2-CH4-Si-H2O system that now contain 95 solid phases.There were similarities, differences, and uncertainties between Australian acidic, saline playa lakes and waters that likely led to the Burns formation salt accumulations on Mars. Both systems are similar in that they are dominated by (1) acidic, saline ground waters and sediments, (2) Ca and/or Mg sulfates, and (3) iron precipitates such as jarosite and hematite. Differences include: (1) the dominance of NaCl in many WA lakes, versus the dominance of Fe-Mg-Ca-SO4 in Meridiani Planum, (2) excessively low K+ concentrations in Meridiani Planum due to jarosite precipitation, (3) higher acid production in the presence of high iron concentrations in Meridiani Planum, and probably lower rates of acid neutralization and hence, higher acidities on Mars owing to colder temperatures, and (4) lateral salt patterns in WA lakes. The WA playa lakes display significant lateral variations in mineralogy and water chemistry over short distances, reflecting the interaction of acid ground waters with neutral to alkaline lake waters derived from ponded surface runoff. Meridiani Planum observations indicate that such lateral variations are much less pronounced, pointing to the dominant influence of ground water chemistry, vertical ground water movements, and aeolian processes on the Martian surface mineralogy.  相似文献   

13.
A generalized cubic equation of state is given. The Peng-Robinson and the Soave-Redlich-Kwong equations are special cases of this equation. The generalized equation of state is precisely as simple and computationally efficient as these classical equations. Through comparison with the Span-Wagner equation for CO 2, we obtain an improved density accuracy in predefined temperature-pressure domains. The generalized equation is then verified through two relevant examples of CO 2 injection and migration. Comparisons are made with other standard cubic EOS in order to show the range of solutions obtained with less accurate EOS.  相似文献   

14.
Non-ideality in mineral solid solutions affects their elastic and thermodynamic properties, their thermobaric stability, and the equilibrium phase relations in multiphase assemblages. At a given composition and state of order, non-ideality in minerals is typically modelled via excesses in Gibbs free energy which are either constant or linear with respect to pressure and temperature. This approach has been extremely successful when modelling near-ideal solutions. However, when the lattice parameters of the solution endmembers differ significantly, extrapolations of thermodynamic properties to high pressures using these models may result in significant errors. In this paper, I investigate the effect of parameterising solution models in terms of the Helmholtz free energy, treating volume (or lattice parameters) rather than pressure as an independent variable. This approach has been previously applied to models of order–disorder, but the implications for the thermodynamics and elasticity of solid solutions have not been fully explored. Solid solution models based on the Helmholtz free energy are intuitive at a microscopic level, as they automatically include the energetic contribution from elastic deformation of the endmember lattices. A chemical contribution must also be included in such models, which arises from atomic exchange within the solution. Derivations are provided for the thermodynamic properties of n-endmember solutions. Examples of the use of the elastic model are presented for the alkali halides, pyroxene, garnet, and bridgmanite solid solutions. Elastic theory provides insights into the microscopic origins of non-ideality in a range of solutions, and can make accurate predictions of excess enthalpies, entropies, and volumes as a function of volume and temperature. In solutions where experimental data are sparse or contradictory, the Helmholtz free energy approach can be used to assess the magnitude of excess properties and their variation as a function of pressure and temperature. The formulation is expected to be useful for geochemical and geophysical studies of the Earth and other planetary bodies.  相似文献   

15.
The compositions of liquids coexisting with experimentally grown crystals of olivine, plagioclase, clinopyroxene, orthopyroxene, leucite, spinel, rhombohedral oxide, melilite and potassium feldspar are used to define, through mass action expressions of liquid/solid equilibrium, compositional derivatives of the Gibbs free energy of mixing of naturally occuring silicate liquids as a function of temperature, pressure and the fugacity of oxygen. The available experimental data describe these derivatives over a range of compositions which includes basic magmas. Therefore, for silicate liquids in this composition range, the topology of the Gibbs free energy of mixing can be approximated from experimental determinations of its derivatives. The majority of the existing thermodynamic data on the liquid phase is consistent with the application of regular solution theory to model the free energy of mixing. Strictly symmetric, temperature and pressure independent, regular solution interaction parameters are calibrated from this phase equilibrium data using regression techniques which have their basis in inverse theory. These techniques generate numerically stable interaction parameters which incorporate inter-variable correlation and account for experimental uncertainty. The regular solution model fits the available data on anhydrous silicate liquids to within the accuracy of the thermodynamic database +/?550 cals). Extensions to regular solution theory allow water solubility in more silica rich liquids to be modelled somewhat less accurately (+/?750 cals). The topology of the excess free energy of mixing surface is strongly asymmetric, possessing a single multicomponent saddle point which defines a spinodal locus. Given this prediction of a multicomponent spinode, a mathematical procedure based upon minimisation of the Gibbs free energy of mixing is developed for the calculation of the compositions of coexisting immiscible liquids. Predicted binodal compositions substantially agree with elemental liquid/liquid partitioning trends observed in lavas. Calculations suggest that an immiscible dome, in temperature-composition space, intersects the liquidus field of the magma type tholeiite. Immiscible phenomena are predicted at sub-liquidus temperatures for the bulk compositions of more basic or alkalic lavas, but are absent in more siliceous rock types for temperatures of the metastable liquid down to 900 K. The regular solution model is used in four petrological applications. The first concerns a prediction of the binary olivine-liquid phase diagram. The calculated geometry exhibits a minimum near Fa75, which, though not in accord with experimental results on the pseudobinary system, compares quite favorably with olivine-liquid phase equilibria interpreted from rhyolites, namely that the olivine phenocrysts of rhyolites are more iron rich than their coexisting liquids. The second petrological example concerns estimating the depth of the source regions of several basic lavas whose compositions cover a range from ugandite to basaltic andesite. The third application is a calculation of the saturation temperatures and compositions of plagioclase and olivine in four experimental basaltic liquids and a prediction of the liquidus temperatures and first phenocryst compositions of the Thingmuli lava series of Eastern Iceland. Lastly, enthalpies of fusion are computed for a variety of stoichiometric compounds of geologic interest. These demonstrate good agreement with calorimetrically measured quantities  相似文献   

16.
根据水的高精度热力学模型IAPWS-95和IAPWS-IF97产生的压力-体积-温度(PVT)数据,本文建立了超临界水的一种高精度立方型状态方程。在723.15~2273.15K和0~1.4GPa范围内,该方程的平均体积偏差只有0.26%;在此范围之外,直到4273.15K和2GPa,方程的平均体积偏差不到2%。该方程在精度和适用范围方面均明显优于以前的立方型方程。在可比的温压条件下,该方程也明显优于一些常用的多参数非立方型方程(多数是高次维里型方程)。本文根据上述立方型方程和有关的热力学原理导出了膨胀系数、压缩系数、逸度系数、剩余焓和剩余熵的解析表达式,其计算结果与IAPWS-95模型的结果均吻合得很好。在此基础上很容易计算出许多其它的热力学性质。  相似文献   

17.
We propose a thermodynamic approach to model the stepwise dehydration with increasing temperature or decreasing H2O activity of K, Na, Ca and Mg-smectite. The approach relies on the relative stability of the different solid-solutions that describe the hydration of di- or trioctahedral-smectites containing 0, 1, 2 or 3 interlayer water layers. The inclusion of anhydrous mica end-members makes it possible to cover, with the same solid-solution model, the entire range of composition from low-charge smectite to mica, through high-charge smectite and illite. Non-ideal Margules parameters were used to describe the non-ideality of the solid solutions between the hydrated and dehydrated smectite end-members. Standard state properties of all smectite end-members as well as Ca- and Mg-muscovite and -phlogopite were initially estimated by oxide summation. These values were then refined and the other non-ideal interactions were estimated on the basis of different experimental data. The stepwise dehydration of smectite, and its stability and compatibility relations were calculated by Gibbs free energy minimising. Our results account for the progressive evolution of smectite to interlayered illite/smectite and then to mica, as observed in nature and experiments, and our model provides an explanation for the thermodynamic stability of smectite and illite/smectite compared to mica + kaolinite or pyrophyllite assemblages. The results suggest that the enthalpic contribution of interlayer water is a function of the ionic potential of the interlayer cation and the number of interlayer water molecules. This evolution makes possible to estimate the standard-state thermodynamic parameters and hydration-temperature behaviour of smectite of virtually all possible compositions. For the four-interlayer cations considered in the study, our model reproduces the 3 → 2 → 1 water-layer transitions that accompany a reduction of water activity or an increase of temperature at ambient pressure. The range of water content and interlayer distance calculated for the 3w, 2w and 1w states are also in fair agreement with the experimental values at ambient pressure.  相似文献   

18.
We propose a thermodynamic model for the mixing of gases in aqueous sodium chloride solutions valid to high pressures, high temperatures, and high ionic strength solutions. Our model couples Henry's Law with any equation of state to reproduce experimental data in the aqueous-rich liquid and gas-rich vapor region. In our model, the chemical potential of the solute in the brine is related to the chemical potential of the solute in pure water through salting-out coefficients. The model reproduces all crucial phenomena of binary (gas–water) and pseudo-binary (gas–water–salt) vapor–liquid mixtures below their critical point. We applied the model to reproduce the phase behavior of nitrogen in water and NaCl brines. Results and discussions are shown.  相似文献   

19.
Gibbs energy minimization is the means by which the stable state of a system can be computed as a function of pressure, temperature and chemical composition from thermodynamic data. In this context, state implies knowledge of the identity, amount, and composition of the various phases of matter in heterogeneous systems. For seismic phenomena, which occur on time-scales that are short compared to the timescales of intra-phase equilibration, the Gibbs energy functions of the individual phases are equations of state that can be used to recover seismic wave speeds. Thermodynamic properties relevant to modelling of slower geodynamic processes are recovered by numeric differentiation of the Gibbs energy function of the system obtained by minimization. Gibbs energy minimization algorithms are categorized by whether they solve the non-linear optimization problem directly or solve a linearized formulation. The former express the objective function, the total Gibbs energy of the system, indirectly in terms of the partial molar Gibbs energies of phase species rather than directly in terms of the Gibbs energies of the possible phases. The indirect formulation of the objective function has the consequence that although these algorithms are capable of attaining high precision they have no generic means of treating phase separation and expertise is required to avoid local minima. In contrast, the solution of the fully linearized problem is completely robust, but offers limited resolution. Algorithms that iteratively refine linearized solutions offer a compromise between robustness and precision that is well suited to the demands of geophysical modeling.  相似文献   

20.
The P–T partition function in statistical thermodynamics can be used to derive semi-empirical formulations of the Gibbs free energy G for minerals and fluids. Parameterization of these equations includes simultaneous regression of experimental heat capacity and molar volume data, allowing fitting, appraisal and optimization of various data sources, as required in the construction of internally consistent petrological data bases. This approach can also be extended to minerals with -transitions and to fluids by considering the Gibbs free energy as a function of pressure P, temperature T and an ordering parameter X, so that accurate modelled representation and extrapolation of the thermodynamic properties of large numbers of petrologically significant minerals and coexisting fluids can be attained. The ordering parameter is chosen to denote the equilibrium mole fraction (thermodynamic probability) of ordered clusters (structural units) in a substance when G(T,P, X)=min. The procedure is tested on existing experimental data for the system MgO–SiO2–H2O. The proposed Gibbs free energy formulation permits thermodynamic properties of minerals, fluids and phase equilibria to be described and extrapolated over a wide range of pressure (0–800 kbar) and temperature (20–3000 K), thus allowing effective use in thermodynamic data bases of petrological interest.  相似文献   

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