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1.
The properties of the regular solution are described. A solid solution is assigned certain theoretical values of the heat of mixing and the results of the distribution of a component between two coexisting solutions are shown graphically on Roozeboom diagrams. Such representations may be useful in explaining the distribution of elements observed in natural mineral assemblages.  相似文献   

2.
Mixing properties for muscovite–celadonite–ferroceladonite solid solutions are derived from combining available experimental phase equilibrium data with tabulated thermodynamic data for mineral end‐members. When a partially ordered solution model is assumed, the enthalpy of mixing among the end‐members muscovite–celadonite–ferroceladonite is nearly ideal, although the Gibbs energies of muscovite–celadonite and muscovite–ferroceladonite solutions are asymmetric due to an asymmetry in the entropy of mixing. Thermodynamic consistency is achieved for data on phengite compositions inassemblages with (a) pyrope+kyanite+quartz/coesite (b) almandine+kyanite+quartz/coesite (c)talc+kyanite+quartz/coesite and (d) garnet–phengite pairs equilibrated both experimentally at high temperatures and natural pairs from low‐grade schists. The muscovite–paragonite solvus has been reanalysed using the asymmetric van Laar model, and the effects of the phengite substitution into muscovite have been quantitatively addressed in order to complete the simple thermodynamic mixing model for the solid solution among the mica end‐members. Results are applied to a natural pyrope–coesite–phengite–talc rock from the Western Alps, and to investigate the conditions under which biotite‐bearing mica schists transform to whiteschist‐like biotite‐absent assemblages for average pelite bulk compositions.  相似文献   

3.
Approximate mixing properties of the end-member components of the quarternary garnet solid solution, (Fe,Mg,Ca,Mn)3Al2Si3O12, have been derived through theoretical analysis of observational data, combined with certain experimental results and crystal chemical considerations. The results suggest that the mixing of pyrope with grossularite, spessartite, and almandine would involve significant positive excess free energies of mixing leading to the critical mixing temperatures of 694±55, 535±140, and 479±63 °C respectively. Spessartite would mix with almandine nearly ideally, and with grossularite with small positive deviation from ideality. The quarternary solution reduces essentially to a ternary mixture of pyrope, grossularite, and almandine + spessartite. The solid solubility relation, and tie line coordinates in this ternary system has been calculated as a function of temperature; the solid solution is found to be intrinsically stable for practically all ternary compositions at 600 °C.  相似文献   

4.
A quasi-chemical model for illites has been derived, and local electrostatic balance has been added to a random regular solution site-mixing model for illites (Stoessell, 1979). Each model assumes similar order-disorder conditions for both the end-members micas and the solid solution. Thermodynamic properties of illites predicted by the random, electrostatic, and quasi-chemical models are compared as a function of composition. For natural illite compositions, molar entropies of mixing in the electrostatic model are about 1 entropy unit less than those in the random model. Intermediate values are given by the quasi-chemical model. Each model predicts an increased entropy of mixing in dominantly trioctahedral illites as compared to dioctahedral illites. Each model also predicts destabilization of trioctahedral illites using absolute molar exchange energies greater than 2 RT/Zx, where Zx is the number of adjacent cation interactions per site in the Xth site class. The most negative free energies of mixing are predicted by the quasi-chemical model. Intermediate values predicted by the random model are apparently the result of error cancellation due to overestimation of both the entropy and enthalpy of mixing.  相似文献   

5.
Infrared powder-absorption spectra of nine natural and five synthetic olivine samples across the forsterite–fayalite join have been investigated at room temperature in the range 70–1400 cm–1. Variations of peak positions as a function of Fe content are close to linear for those vibrational bands whose trend could be followed across the solid solution. Line-broadening has been quantified by autocorrelation analysis. Positive deviations from linearity of the line-broadening parameter, corr, for groups of bands at low energies are consistent with the existence of local elastic strain heterogeneities at intermediate compositions in the solid solution. It also appears that the structure of forsterite is more homogeneous than Fe-rich olivines in relation to local elastic strain effects. Positive deviations from linearity of the line-broadening parameter for the low-energy regions scale linearly with calorimetric data for the enthalpy of mixing. This close correlation between line-broadening in IR spectra and calorimetric enthalpies of mixing has now been observed for four different binary solid solutions, and there is a further, qualitative correlation with bulk modulus.  相似文献   

6.
The partitioning of Fe2+ and Mn2+ between (Fe, Mn)TiO3 and (Fe, Mn)2SiO4 solid solutions in the system FeO-MnO-TiO2-SiO2 has been experimentally investigated at 1100 ∘C and pressures of 1 bar and 25 kbar, over a wide range of Fe/Mn ratios, using electron microprobe analysis of quenched run products. The ilmenite solid solution in this system is within analytical uncertainty a simple binary between FeTiO3 and MnTiO3, but the olivine solid solution appears to contain up to 2.5 wt% TiO2. The Fe-Mn partitioning results constrain precisely the difference in the thermodynamic mixing properties of the two solid solutions. If the mixing properties of (Fe, Mn)2SiO4 solid solutions are assumed to be ideal, as experimentally determined by Schwerdtfeger and Muan (1966), then the ilmenite is a regular, symmetric solution with W ilm Fe-Mn=1.8±0.1 kJ mol−1. The quoted uncertainty does not include the contribution from the uncertainty in the mixing properties of the olivine solution, which is estimated to be ±1.8 kJ mol−1, and which therefore dominates the uncertainty in the present results. Nevertheless, this result is in good agreement with the previous experimental study of O'Neill et al. (1989), who obtained W ilm Fe-Mn=2.2±0.3 kJ mol−1 from an independent method. The results provide another item of empirical evidence supporting the proposition that solid solutions between isostructural end-members, in which order-disorder effects are not important, generally have simple thermodynamic mixing properties, with little asymmetry, modest excess entropies, and excess enthalpies approximately proportional to the difference in the molar volumes of the end-members. Received: 11 February 1998 / Accepted: 29 June 1998  相似文献   

7.
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   

8.
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   

9.
The mixing properties and the local structure of the Ca-Sr fluorapatite isomorphic system were studied using the original atomistic computer modeling approach for solid solutions. Calculations were carried out for a 4 × 4 × 4 supercell (2688 atoms) in conjunction with the high-performance computer SKIF MSU Chebyshev. In order to find the most probable (energetically preferable) distribution of Sr over the M1 and M2 cation sites in the fluorapatite solid solution, eight different distributions were tested. Structures with the most preferable x(Sr1): x(Sr2) ratios were used for further investigation of the effect of mixing on the lattice parameters and elasticity of the Ca-Sr fluorapatite solid solution and for the detailed analysis of the local structure. The local structure analysis included investigation of the individual and average M1-O, M2-O, M2-F bond lengths distortions, changes in the M1 and M2 polyhedra volumes as function of Sr content as well as the estimation of the structural relaxation parameters for all compositions of the solid solutions considered in this work.  相似文献   

10.
The minerals of the ternary carbonate system CaCO3 - MgCO3 - FeCO3 represent a complex series of solid solutions and ordering states. An understanding of those complexities requires a solution model that can both duplicate the subsolidus phase relationships and generate correct values for the activities. Such a solution model must account for the changes in the total energy of the system resulting from a change in the ordering state of the individual constituents. Various ordering models have been applied to binary carbonate systems, but no attempts have previously been made to model the ordering in the ternary system. This study derives a new set of equations that allow for the equilibrium degree of order to be calculated for a system involving three cations mixing on two sites, as in the case of the ternary carbonates. The method is based on the Bragg-Williams approach. From the degree of order, the mole fractions of the three cations in each of the two sites can be determined. Once the site occupancies have been established, a Margules-type mixing model can be used to determine the free energy of mixing in the solid solution and therefore the activities of the various components.  相似文献   

11.
The Lippmann diagram for the system(Ba, Sr)SO4-H2O was computed at 25 °Cby determining the solid-phase activity coefficientsfrom first principles calculations. Directcalculations of the mixing properties of thebarite-celestite series indicate this solid solutionbehaves as non-ideal and non-regular. At 25 °C,the enthalpy of mixing shows a minimum around 50 mole% SrSO4 due to an ordering tendency. Thefree energy of mixing shows two minima that delimit awide and symmetric miscibility gap (from 2.1 to 97.9 mole% SrSO4) at this temperature. The excessfree energy of mixing requires a Guggenheim expansionseries of 5 terms to be described, where the termswith odd exponents are null as a consequence of thesymmetric distribution of the mixing properties withcomposition. The Lippmann diagram shows a peritecticpoint that corresponds to the composition of an aqueoussolution which is simultaneously at equilibrium withthe two extremes of the miscibility gap. The largedifference between the solubility products of theendmembers involves a strong preferential partitioningof the less soluble endmember towards the solid phase,which explains the extremely Ba-poor composition ofthe aqueous solution (aqueous activity fraction forBa2+ = 0.000446 ) at the peritectic point.  相似文献   

12.
Use of simple mixing models of orthopyroxene and garnet solid solutions enables extrapolation of experimentally determined equilibria in the MgSiO3-Al2O3 system to uninvestigated parts of pressure-temperature-composition space. Apparent discrepancies in the experimental data for simple and multicomponent systems may be explained by considering the effect of CaO and FeO on reducing pyrope activity in the garnet solid solutions. Equilibration pressures of natural garnet-orthopyroxene assemblages may be calculated, provided temperatures are known, from a combination of the experimental data on the MgSiO3-Al2O3 system and analyses of coexisting natural phases.Despite the presence of a compositional gap in the system, the solubility of enstatite in diopside coexisting with orthopyroxene can also be approximately treated by an ideal solution model. An empirical approach has been developed to take account of Fe2+ on the orthopyroxene-clinopyroxene miscibility gap in natural systems in order to calculate equilibration temperatures of 2-pyroxene assemblages. The model presented reproduces almost all of the available experimental data for multicomponent systems to within 60° C.  相似文献   

13.
 The volumes and enthalpies of mixing, ΔV Mix and ΔH Mix, of binary solid-solution aluminosilicate garnets have been studied by computer simulation. The use of “average atoms” to simulate solid solution was found to give results that are considerably different from those obtained by calculating and averaging over many configurations of cations at a given composition. Although we expect mineral properties calculated from model calculations to be correct only on a qualitative rather than a quantitative scale, fair agreement with experiment was obtained where carefully tested potential parameters were used. The results show that mixing behaviour in these materials is controlled by local strain and relaxation effects resulting from the atomic size mismatch of the mixing divalent cations. In particular, ΔV Mix and ΔH Mix are shown to scale quadratically with the volume difference between the end members, and to vary essentially symmetrically with composition, with a moderate dependence on the degree and nature of cation order. We conclude that computer modelling should be useful in providing detailed qualitative information about the mixing properties of solid solutions, which can help to better constrain and interpret experimental results. Received: 8 March 2000 / Accepted: 1 October 2000  相似文献   

14.
赵劲松 《矿物学报》1989,9(2):154-164
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   

15.
 We have experimentally determined the displacement of the equilibrium Grossular + 2 Kyanite + Quartz ⇆ 3 Anorthite (GASP) as a function of garnet composition in the systems Mg-Ca-Mn, Fe-Mg-Ca and Fe-Mg-Ca-Mn at 1000°C. The results were treated along with selected experimental and observational data available in the literature as well as binary parameters from other workers to obtain a set of mutually compatible binary mixing parameters of the quaternary (Fe,Mg,Ca,Mn)- aluminosilicate garnet solid solution. Attempts to determine equilibrium garnet composition in the GASP equilibrium in the Ca-Mg binary were unsuccessful due to the formation of pyroxene. Calculations of binary and ternary miscibility gaps show that the P,T,X combination required for unmixing of garnet solid solution is not realized by natural samples. The solution model was applied to account for compositional effects on Fe-Mg exchange between garnet and ortho- or clino-pyroxene. Applications of the revised thermometric formulations to selected natural assemblages yield P-T conditions which are much less sensitive to compositional effects compared to the other available formulations, and are consistent with independent constraints. Received: 21 April 1995 / Accepted: 17 May 1996  相似文献   

16.
《Chemical Geology》2006,225(3-4):304-313
Enthalpies of mixing and ordering in the binaries of the quaternary carbonate (Ca,Mg,Fe,Mn)CO3 solid solution have been modeled using static lattice energy minimization calculations. A set of self-consistent empirical potentials has been specially developed for this task. The calculations illustrate the importance of size mismatch in determining magnitudes of the enthalpies of mixing and ordering in the binaries. The enthalpy effects show positive correlation with the predicted temperatures of the order/disorder transitions in intermediate compounds with the dolomite structure. It is shown that the general behavior of the mixing enthalpy in high- and low-T limits can be constrained with a minimum set of sampled configurations.  相似文献   

17.
《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   

18.
Optimized standard state and solution properties of minerals   总被引：1，自引：0，他引：1  
 An internally consistent set of standard state and mixing properties has been derived for olivine, orthopyroxene, garnet, cordierite, and ilmenite in the system FeO-MgO-CaO-Al2O3-TiO2-SiO2-H2O from analysis of relevant phase equilibrium and thermophysical data. Solubility of Al2O3 in orthopyroxene is accounted for in addition to Fe-Mg mixing. Added confidence in the retrieved properties stems from the representation within reasonable uncertainties of data for seven linearly dependent Fe-Mg exchange equilibria, as well as net transfer equilibria, among the above phases. Critical to successful analysis was the extension of the mathematical programming technique to include bulk composition constraints which force an observed assemblage of fixed composition to be stable at experimentally studied conditions. The final optimization reproduces the extremely tight constraints on endmember properties while invoking very simple macroscopic solution models that afford an excellent opportunity for extrapolation beyond the data considered in this study. Compatibility among the experimental data is improved markedly by incorporation of recently published Cp data on pyrope and forsterite. Electrochemical data defining the oxygen fugacity of Fe-Fa-Qz, Fa-Mt-Qz, and Mt-Hm allow excellent compatibility of almandine thermochemical properties derived from phase equilibrium data obtained at both reducing (Fe-Wst) and oxidizing (Hm-Mt) conditions. Analysis of the combined data involving endmembers and solid solutions removes many of the ambiguities in mixing property magnitudes that arise in analyses of more restricted sets of data. In addition, the consideration of the solid solution data allows further refinement of some endmember properties. Nonideal mixing parameters, although correlated, are well defined by the combination of experimental data, with GOlex>GIlmex>GGtex >GOpxex>GCdex, and 0.7<WOlG<4.1 kJ/atom of isomorphous Fe-Mg at 1000 K. Experiments defining the Al2O3 solubility of Opx in equilibrium with Gt and Cd+Qz define negative Fe-Al interactions that have an important effect on Fe-Mg partitioning in Opx. Applications of this data set to high-grade metamorphic rocks are described in a companion paper, published as part II of the present work. Received: 14 September 1994 / Accepted: 20 March 1996  相似文献   

19.
 Thermodynamic properties of the barite–celestite solid solution were calculated using molecular principles. Cation–cation (Ba–Ba, Sr–Sr, and Ba–Sr) interaction energies were derived from a number of random and ordered cation distributions which were energy-optimized using force potentials as incorporated in the program package GULP. With these interaction energies, diagrams for the enthalpy and free energy of mixing could be computed for the entire range of the solid solution between the barite and celestite end members and for a number of annealing temperatures. These thermodynamic data show that the solid solution is nonideal. The system has a tendency for Ba2+ and Sr2+ cations to order onto alternating layers ||(100). However, this ordering scheme is thermodynamically only relevant for annealing temperatures below approximately 500 K and systems that are kinetically inhibited during crystal growth. For sufficiently long annealing times at room temperature, the solid solution tends to exsolve with barite–celestite interfaces ||(100). The cell parameters a and c were calculated to have almost linear behavior for the whole solid solution, suggesting close to ideal behavior according to Vegard's law. In contrast, b tends to deviate positively from linearity, in agreement with experimental values. Received: 6 April 1999 / Revised, accepted: 29 September 1999  相似文献   

20.
 The garnet (Grt)-clinopyroxene (Cpx) Fe-Mg exchange thermometer has been re-evaluated through analysis of phase equilibrium experiments defining the Fe-Mg exchange between Grt and Cpx, Grt and Ol (Ol=Olivine), and Cpx and Ol, together with thermophysical and other phase equilibrium constraints on solid solution and individual end-member properties. Results show that all data are mutually compatible if the heterogeneity range of Grt and Cpx in run products previously obtained by Pattison and Newton (PN) are accounted for in assessing equilibrium Grt-Cpx compositions. Derived mixing properties are in good agreement with results from numerous recent phase equilibrium studies. Application of the newly calibrated thermometer to a number of amphibolite to granulite facies terrains indicates temperatures between 70 and 200 ° C above PN’s thermometer, and general compatibility with independent temperature estimates. Received: 3 September 1993 / Accepted: 16 June 1994  相似文献   

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