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1.
自然界中矿物多以固溶体形式存在,据其晶体化学特征计算热力学性质是开展矿物成因理论研究的基础。本文引入描述二元矿物固溶体热力学性质的假三元模型,计算得到了透辉石-硬玉固溶体系列的热力学性质。该模型通过构造一种高度有序的中间相,同时考虑长程和短程有序效应,基于热力学平衡态矿物固溶体自由能最低的规律,可以计算特定组分下矿物的平衡自由能、焓和熵等热力学参数。本文针对透辉石-硬玉固溶体体系,取绿辉石为其中间有序态,计算了其活度-成分关系和温度-组分相图等,发现绿辉石随温度升高的有序无序相变为一级相变,相变温度为1 148±25 K,与实验研究结果一致。本文获得的透辉石-绿辉石-硬玉体系的热力学参数可用于视剖面图方法研究MORB成分的岩石的榴辉岩相变质作用过程。 相似文献
2.
Pierre-Yves F. Robin 《Geochimica et cosmochimica acta》1978,42(9):1383-1389
Whereas much petrographic evidence for pressure solution, in sedimentary rocks has been accumulated since Sorby's work, its thermodynamic justification has never been clearly established, and has been challenged by some authors. Difficulties disappear when it is recognized that in the most general case migration of chemical components proceeds down chemical-potential gradients rather than down concentration gradients. Along a grain contact a chemical-potential gradient is produced by variations in contact pressure and by local variations in Helmholtz energy of the solid. For example, in a sand made up of even-sized spherical grains buried 500 m, the ratio of the diameter (D) of the grains to that of a spherical elastic contact circle (a) is D/a ～- 26. The chemical potential at the center of such an elastic contact is ～- 14kcal mol?1 higher than in surrounding pore water saturated with respect to quartz. For comparison, at a temperature of 30°C, saturation with respect to amorphous silica rather than quartz raises the chemical potential by only 1.6 kcal mol?1. If the diameter of the contact circle has enlarged to e.g. a = D/5, the chemical potential at its center is still 0.5 kcal mol ?1 greater than that of free quartz under hydrostatic pressure. The corresponding potential gradients are the driving force of pressure solution. The concept of pressure solution thus does not contradict any thermodynamic principle; in particular, it does not require that the chemical component of the solid have a smaller partial volume in solution than in the solid state. Petrographic and experimental evidence can therefore be accepted without reservation. 相似文献
3.
We report in this paper results of lattice dynamical calculations of the thermodynamic properties, namely, the equation of
state and the melting point of forsterite. The root mean square displacements of atoms and thermal parameters are also evaluated.
It is observed from our results, that, a modified Lindemann criterion for melting may be proposed for an ionic ‘molecular’
solid like forsterite. Agreement among various theoretical and experimental results is satisfactory indicating that lattice
dynamical studies based on microscopic quasiharmonic formulations help in understanding the macroscopic properties of forsterite,
over a wide range of temperature and pressure. 相似文献
4.
Shanqi Liu Yongbing Li Junli Yang Huiquan Tian Bojing Zhu Yaolin Shi 《Physics and Chemistry of Minerals》2014,41(3):189-196
The pressure-dependent elastic properties of the Fe–S system are important to understand the dynamic properties of the Earth’s interior. We have therefore undertaken a first-principles study of the structural and elastic properties of FeS2 polymorphs under high pressure using a method based on plane-wave pseudopotential density function theory. The lattice constants, elastic constants, zero-pressure bulk modulus, and its pressure derivative of pyrite are in good agreement with the previous experiments and theoretical approaches; the lattice constants of marcasite are also consistent with the available experimental data. Calculations of the elastic constants of pyrite and marcasite have been determined from 0 to 200 GPa. Based on the relationship between the calculated elastic constants and the pressure, which can provide the stability of mineral, it would appear that pyrite is stable, whereas marcasite is unstable when the pressure rises above 130 GPa. Static lattice energy calculations predict the marcasite-to-pyrite phase transition to occur at 5.4 GPa at 0 K. 相似文献
5.
Robert G. Berman 《Geochimica et cosmochimica acta》1984,48(4):661-678
A thermodynamic model is proposed for calculation of liquidus relations in multicomponent systems of geologic interest. In this formulation of mineral-melt equilibria, reactions are written in terms of the liquid oxide components, and balanced on the stoichiometry of liquidus phases. In order to account for non-ideality in the liquid, a ‘Margules solution’ is derived in a generalized form which can be extended to systems of any number of components and for polynomials of any degree. Equations are presented for calculation of both the excess Gibbs free energy of a solution and the component activity coefficients.Application to the system CaO-Al2O3-SiO2 at one atmosphere pressure is achieved using linear programming. Thermodynamic properties of liquidus minerals and the melt are determined which are consistent with adopted error brackets for available calorimetric and phase equilibrium data. Constraints are derived from liquidus relations, the CaO-SiO2 binary liquid immiscibility gap, solid-solid reactions, and measured standard state entropies, enthalpies, and volumes of minerals in this system.Binary and ternary liquidus diagrams are recalculated by computer programs which trace cotectic boundaries and isothermal sections while checking each point on a curve for metastability. The maximum differences between calculated and experimentally determined invariant points involving stoichiometric minerals are 17°C and 1.5 oxide weight per cent. Because no solid solution models have been incorporated, deviations are larger for invariant points which involve non-stoichiometric minerals.Calculated heats of fusion, silica activities in the melt, and heats of mixing of liquids compare favorably with experimental data, and suggest that this model can be used to supplement the limited amount of available data on melt properties. 相似文献
6.
The SW96 formulation explicit in Helmholtz free energy proposed by Span and Wagner (1996) is the most accurate multifunction equation of state of CO2 fluid, from which all thermodynamic properties can be obtained over a wide temperature-pressure range from 216.592 to 1100 K and from 0 to 8000 bar with or close to experimental accuracy. This paper reports the applications of the SW96 formulation in fluid inclusions and mineral-fluid equilibria. A reliable and highly efficient algorithm is presented for the saturated properties of CO2 so that the formulation can be conveniently applied in the study of fluid inclusions, such as calculation of homogenization pressures, homogenization densities (or molar volumes), volume fractions of vapor phase and isochores. Meanwhile, the univariant curves of some typical decarbonation reactions of minerals are calculated with the SW96 formulation and relevant thermodynamic models of minerals. The computer code of the SW96 formulation can be obtained from the corresponding author. 相似文献
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8.
J. Amossé 《Physics and Chemistry of Minerals》1981,7(4):190-193
Oscillatory zoning in (Mn, Fe)WO4 solid solutions of wolframite consists of a crystalline arrangement of successive Mn-rich and Fe-rich layers. Thermochemical data show that during crystal growth the Mn/Fe ratio in the mineral is greater than in the mineralizing medium. If a diffusion process affects the Mn ion in the solution, a continuous zoning should occur as observed for other solid solutions. The theory developed in this paper emphasises that a continuous zoning cannot appear because the elastic energy needed to adjust two cells with different lattice parameters is greater than the thermodynamic energy required to deposit a cell with the same composition but with a solution of a different Mn/Fe ratio. The reversal of the two energies due to a large depletion in Mn of the solution entails an abrupt change in composition. The relevance of the theory can be checked with the help of a compositional profile found in literature, by calculating with a good approximation the Mn molar value of one layer, if the Mn molar value of the other is known. 相似文献
9.
Three‐dimensional time‐harmonic fundamental solutions for a fluid‐saturated poroelastic half‐space with partially permeable free surface 
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下载免费PDF全文 By virtue of a pair of scalar potentials for the displacement of the solid skeleton and the pore fluid pressure field of a saturated poroelastic medium, an alternative solution method to the Helmholtz decomposition is developed for the wave propagation problems in the framework of Biot's theory. As an application, a comprehensive solution for three‐dimensional response of an isotropic poroelastic half‐space with a partially permeable hydraulic free surface under an arbitrarily distributed time‐harmonic internal force field and fluid sources is developed. The Green's functions for the poroelastic fields, corresponding to point, ring, and disk loads, are reduced to semi‐infinite complex‐valued integrals that can be evaluated numerically by an appropriate quadrature scheme. Analytical and numerical comparisons are made with existing elastic and poroelastic solutions to illustrate the quality and features of the solution. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
10.
矿物在超临界溶液中的溶解度理论计算 总被引：10，自引：0，他引：10
本文概述了矿物在超临界溶液中的溶解度理论计算。讨论了平衡常数法和自由能法的热力学原理和计算机方法。两种方法都需要热力学数据,所不同的是平衡常数法需要的是反应平衡常数,而自由能法需要物种自由能数据。方法确定以后这些数据具备与否及其精度是这项研究的关键。此外当溶液中离子强度较大时,寻求一种适当的活度系数算法对溶解度理论计算也至关重要。 相似文献
11.
Michel Henricus Gerardus Jacobs Bernard H. W. S. de Jong 《Physics and Chemistry of Minerals》2009,36(7):365-389
We use a lattice vibrational technique to derive thermophysical and thermochemical properties of fayalite, Fe2SiO4. This semi-empirical technique is based on an extension of Kieffer’s model to incorporate details of the phonon spectrum.
It includes treatment of intrinsic anharmonicity and electronic effects based on crystal field theory. We extend it to predict
thermodynamic mixing properties of olivine (Mg,Fe)2SiO4
solid solutions by using results of our previous work on the system MgO–SiO2. Achieving this requires a relation between phonon frequency and composition and a composition relation for the energy of
the static lattice. Directed by experimental Raman spectroscopic data for specific optic modes in magnesium–iron solid solutions
of olivine and pyroxene we use an empirical relation for the composition dependence for phonon frequencies. We show that lattice
vibrations have a large effect on the excess entropy and that the static lattice contribution and lattice vibrations have
a large impact on excess enthalpy and excess Gibbs energy. Our model indicates that compositional effects in electronic and
magnetic properties are negligible. The compositional variation the Néel temperature has a large impact on excess heat capacity
for temperatures below 100 K. 相似文献
12.
C. A. McCammon I. Jackson A. E. Ringwood J. D. Cashion 《Physics and Chemistry of Minerals》1984,11(4):182-193
(Fe, Mn)S and (Fe, Mg)S solid solutions are examined to study and compare the properties of Fe2+ in two different B1-structured hosts, and also to study the relative stability of the B1 (NaCl) and B8 (NiAs) structures at high pressure. The Mössbauer spectra of (Fe, Mn)S and (Fe, Mg)S B1 solid solutions are quadrupole doublets at 298 K with parameters which vary smoothly with Fe2+ concentration. At 4.2 K the Mössbauer spectra of (Fe, Mn)S and Fe-rich (Fe, Mg)S B1 solid solutions are magnetically split into eight lines, but the spectra of Mg-rich (Fe, Mg)S solid solutions are quadrupole doublets. The line widths of the magnetic spectra are broad, consistent with a multiaxial spin arrangement. Some properties of the hypothetical phase FeS(B1) are calculated from the solid solution data; the phase is inferred to be relatively ionic compared to FeS(B8) and has a molar volume that is 7.2 percent larger than the B8 phase at 298 K. The large inferred volume difference between FeS(B1) and FeS(B8) should cause exsolution of a B8-structured phase from (Fe, Mn)S and (Fe, Mg)S B1 solid solutions at high pressure. This behaviour is confirmed experimentally at high pressure using X-ray diffraction and Mössbauer spectroscopy, and the results are correlated with thermodynamic calculations of the phase boundaries based on estimates of the volume and free energy differences between the B1 and B8 phases of FeS derived from atmospheric pressure data. The absence of an increase in solubility of Mg and Mn in the B8 phase with pressure suggests that any polymorphism in MnS and MgS at high pressure is unlikely to involve the B8 phase. Shock wave data for MgO and Fe0.94O reported in the literature suggest similar behaviour in the system FeO-MgO at high pressure, namely exsolution of essentially pure FeO(hpp) from (Fe, Mg)O B1 solid solutions. 相似文献
13.
广西拉么Zn—Cu矿床中夕卡岩的主要矿物特点与Ca—Fe—Si—C—O体系T—lgfO2图解 总被引：1，自引：0，他引：1
用电子探针数据研究了该矿床中主要夕卡岩矿物特点及其变化规律。采用理想结晶溶液固溶体位置混合模式,计算了石榴子石和辉石矿物对中钙铁榴石和钙铁辉石的摩尔分数。在计算纯固相和流体相参加的反应抵达平衡时的边界方程中,加上理想结晶固溶体中端元组分摩尔分数的修正项后,我们便可以计算出有纯固相、流体相和理想结晶溶液固溶体参加反应的在给定T、P条件下的lgfo_2值。计算结果表明:无变度点4周围的Hed+And+Wol组合对本矿区具有重要的地质地球化学意义。 相似文献
14.
15.
《Chemical Geology》2006,225(3-4):336-346
We present results of high temperature, high pressure atomistic simulations aimed at determining the thermodynamic mixing properties of key binary garnet solid solutions. Computations cover the pressure range 0–15 GPa and the temperature range 0–2000 K. Through a combination of Monte-Carlo and lattice-dynamics calculations, we derive thermodynamic mixing properties for garnets with compositions along the pyrope–almandine and pyrope–grossular joins, and compare these with existing experimental data. Across the pressure–temperature range considered, simulations show virtually ideal mixing behaviour in garnet on the pyrope–almandine join, while large excess volumes and enthalpies of mixing are predicted for garnet along the pyrope–grossular join. Excess heat capacities and entropies are also examined. These simulations shed additional light on the link between the behaviour at the atomic level and macroscopic thermodynamic properties: we illustrate the importance of certain atomistic Ca–Mg contacts in the pyrope–grossular solid solutions. For simulation techniques of this type to become sufficiently accurate for direct use in geological applications such as geothermobarometry, there is an urgent need for improved experimental determinations of several key quantities, such as the enthalpies of mixing along both joins. 相似文献
16.
徐有生 《矿物岩石地球化学通报》1997,(4)
高温高压下水和氯化钠溶液的物理化学性质研究徐有生（中国科学院地球化学研究所，贵阳５５０００２）关键词高温高压水和ＮａＣｌ溶液物理化学性质水和ＮａＣｌ溶液是地质上最常见的溶液，了解其物理化学性质有助于研究水溶液在地球内部各种地质作用和地质过程中所起的作... 相似文献
17.
Thermodynamics of sodium feldspar II: Experimental results and numerical calculations 总被引：1，自引：0，他引：1
The free energy, entropy and enthalpy of sodium feldspar in thermal equilibrium and in metastable states are derived from investigations of the heat capacities of albite, analbite, ordered and disordered Or31. The lattice strains of all stable and metastable states are calculated from the two-order parameter theory published in the preceding paper. This approach also allows one to distinguish between the influence of Al, Si order and of the displacive lattice distortion on the thermodynamic behaviour of albite. The thermal cross-over between high albite and low albite is found to be a smooth function of temperature. 相似文献
18.
Ferdinand F. Hingerl Georg Kosakowski Thomas Wagner Dmitrii A. Kulik Thomas Driesner 《Computational Geosciences》2014,18(2):227-242
GEMSFIT, a parallelized open-source tool for fitting thermodynamic activity models has been developed. It is the first open-source implementation of a generic geochemical-thermodynamic fitting tool coupled to a chemical equilibrium solver which uses the direct Gibbs energy minimization (GEM) approach. This enables speciation-based fitting of complex solution systems such as solid solutions and mixed solvents. The extendable framework of GEMSFIT provides a generic interface for fitting geochemical activity models at varying system compositions, temperatures and pressures. GEMSFIT provides the most common tools for statistical analysis which allow thorough evaluation of the fitted parameters. The program can receive input of measured data from a PostgreSQL database server or exported spreadsheets. The fitting tool allows for bound, linear, and nonlinear (in)equality-constrained minimization of weighted squared residuals of highly nonlinear systems over a wide temperature and pressure interval only limited by user-supplied thermodynamic data. Results from parameter regression as well as from statistical analysis can be visualized and directly printed to various graphical formats. Efficient use of the code is facilitated by a graphical user interface which assists in setting up GEMSFIT input files. The usage and resulting output of GEMSFIT is demonstrated by results from parameter regression of the extended universal quasichemical aqueous activity model for geothermal brines. 相似文献
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20.
N. N. Eremin R. A. Talis A. E. Grechanovskii V. S. Urusov 《Moscow University Geology Bulletin》2013,68(2):72-78
An original methodology for the atomistic computer modeling of solid solutions was applied for the study of the mixing properties and local structure of the grossular-uvarovite, i.e., Ca3Al2[SiO4]3 Ca3Cr2][SiO4]3, garnet series. The parameters of the interatomic potentials for end members of this series were optimized using experimental data on their structural, elastic, and thermodynamic characteristics. The optimized model of the potentials allowed us to describe the elastic, structural, and thermodynamic characteristics of grossular and uvarovite and estimate the energy of point defects in these crystal structures. Calculations of the mixing properties and local structure for seven different compositions of the solid solution were carried out on a “Chebyshev” supercomputer (Moscow State University) in a 2 × 2 × 4 supercell of the garnet-type structure containing 2560 atoms. Mixing properties, such as the enthalpy of mixing, parameters of interaction, excess mixing volume, deviation of bulk modulus from additivity, and the vibrational and configuration contribution to the entropy of mixing, were determined. This allowed us to estimate the stability field for the grossular-uvarovite solid solution. Histograms of the interatomic distances M-O (M = Ca, Al, Cr, Si) and O-O in supercells were plotted and the parameters of relaxation and changes of the CrO6 and AlO6 octahedron volumes were estimated. The data of the simulation are quite consistent with the experimental data on this system and supplement it significantly. 相似文献