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1.
The theory of divariant reactions is investigated in some detail and approaches involving simultaneously operating reactions and X Mg isopleths are combined. Using the Gibbs' method (Spear et al. 1982), a general equation is derived for X Mg isopleth slopes in FMAS and CFMAS, which may be applied to any divariant assemblage in these systems. Isopleth slopes are calculated for a number of divariant FMAS and CFMAS reactions inferred to have operated in Sri Lankan granulites, giving more rigorous constraints on the local P-T path. Isopleth slopes are also calculated for the trivariant CFMAS reaction orthopyroxene + plagioclase = garnet + quartz. The resulting dP/dT range from +8 to +18 bar/K. Application to Sri Lankan granulites confirms an earlier hypothesis (Faulhaber and Raith 1991) that a retrograde path with a dP/dT of ～10–15 bar/K may cause garnet growth in charnockites and garnet breakdown in metabasites. It is shown here that dP/dT depends primarily on the Ca contents of garnet and plagioclase. Large variations in isopleth and reaction line slopes are possible, due to the thermodynamic effect of additional components in solid solutions, e.g. albite in plagioclase. This has a good potential for the assessment of the exact form of P-T paths. Equations to calculate isopleth slopes could be included in software packages aimed at defining P-T estimates, enabling geologists to derive realistic P-T paths.  相似文献   

2.
The Newtonian viscosity of synthetic rhyolitic liquids with 0.15-5.24 wt% dissolved water was determined in the interval between 580 and 1640 °C and pressures of 1 atm and 5-25 kbar. Measurements were performed by combining static and accelerated (up to 1000g) falling sphere experiments on water-bearing samples, with high temperature concentric cylinder experiments on 0.15 wt% H2O melts. These methods allowed viscosity determinations between 102 and 107 Pa s, and cover the complete range of naturally occurring magmatic temperatures, pressures, and H2O-contents for rhyolites.Our viscosity data, combined with those from previous studies, were modeled by an expression based on the empirical Vogel-Fulcher-Tammann equation, which describes viscosities and derivative properties (glass transition temperature Tg, fragility m, and activation volume of viscous flow Va) of silicic liquids as a function of P-T-X(H2O). The fitted expressions do not account for composition-dependent parameters other than X(H2O) and reproduce the entire viscosity database for silicic liquids to within 3.0% average relative error on log η (i.e. std. error of estimate of 0.26 log units).The results yield the expected strong decrease of viscosity with temperature and water content, but show variable pressure dependencies. Viscosity results to be strongly affected by pressure at low pressures; an effect amplified at low temperatures and water contents. Fragility, as a measure for the deviation from Arrhenian behavior, decreases with H2O-content but is insensitive to pressure. Activation volumes are always largely negative (e.g., less than −10 cm3/mol) and increase strongly with H2O-content. Variations in melt structure that may account for the observed property variations are discussed.  相似文献   

3.
The resonance bond number n, as defined in this paper, is designed to describe the strength of an XO bond as a function of the kinds of atoms present and which atoms are bonded. The calculation of n is made on a fragment extracted from the crystal encompassing the XO bond. If this fragment consists of only the X atom and its coordinating O atoms, then n is numerically equal to the Pauling bond strength, s. In this study a graph-theoretic algorithm is developed permitting the calculation of n using fragments including up to 50 atoms. This algorithm was used to calculate n for all of the bonds in ten silicate crystals. Since bond strength is be inversely related to bond length, we examined the relationship between these two variables and found that n can be used to explain over 70 percent of the variation of XO bond lengths from their average values in the crystals. A fit of the parameter n/r, where r is the row number in the periodic table of the metal atom X, to the observed bond lengths in these crystals yielded the equation R(XO)=1.39(n/r)?0.22 which explains over 95.5 percent of the variation of bond lengths in the crystals. The fact that the same formula with s replacing n was found in an earlier study to be a good estimator of average bond lengths in crystals shows that n relates to individual variations in bond lengths in crystals in the same way that s relates to average bond lengths in crystals. Using minimum energy SiO, AlO and MgO bond lengths and harmonic force constant data calculated for these bonds in hydroxyacid molecules, theoretical equations similar to those used by Pauling to explain bond length variations in hydrocarbons are derived. Bond lengths calculated with these equations for the 10 crystals shows that 95 percent of the variation of the observed bond lengths in these crystals can be explained in terms of n by this purely theoretical model.  相似文献   

4.
A new model for the evolution of substellar objects is proposed, which enables computation of their internal structure and evolution in an adiabatic approximation without allowance for axial rotation, magnetic fields, and nuclear reactions. The basic set of differential equations in the model contains a new equation for the gradient of the electron degeneracy parameter and adiabatic coefficients of the new type. The results of numerical simulations of evolutionary sequences of hydrogen (X = 1), helium (Y = 1), and hydrogen-helium (X = 0.75, Y = 0.25) substellar objects with masses M < 0.08 M ⊙ during the evolutionary stage 106 yr < t < 1010 yr are reported. Luminosity-effective temperature, mass-radius, radius-time, central temperature-central density, and central temperature-age relations are analyzed for the indicated chemical composition.  相似文献   

5.
The equilibrium activities and concentrations of N chemical species in a multicomponent system may be calculated given M independent equilibrium constants relating these species and N-M mass balances. These N equations are solved by Newton-Raphson iteration. Where initial concentration estimates are poor or the number of species large, an additional curve crawler technique introduces components by stepwise infinitesimal increments.  相似文献   

6.
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7.
A simple method is developed to determine seismic moments of earthquakes. The method is qualified through criteria such as simplicity of calculations, coverage of wide magnitude range, and insensitivity to detailed instrumental response. The method is applied to 163 major earthquakes which occurred underneath Japan and the Japan Sea in the time from 1926 to 1977. Magnitudes of these earthquakes, which have been determined by the Japan Meteorological Agency, (MJMA) cover the range from 4.3 to 7.5. At first, source spectra are analyzed through a very simple way introducing two new parameters: characteristic period Tc and seismic-moment factor Mc. The former is defined as an average value of apparent periods of seismic waves with the maximum trace amplitude at many stations. The latter is an average of products of maximum trace amplitude and its apparent period multiplied by epicentral distance. It is shown that Tc corresponds to the period of the corner frequency of an earthquake and Mc to the seismic-moment density at the period of Tc. A scaling model of earthquake source spectra is presented which satisfies the empirical relations between the surface-wave magnitude Ms and MJMA, and MJMA and the body-wave magnitude mb. Those relations are independent of the Gutenberg and Richter relation between Ms and mb, because MJMA is determined from maximum amplitudes of seismic waves with a period of about 4 sec. The static seismic moment of each earthquake can be estimated from calculated Mc using the source spectra of the scaling model. Seismic moments of 18 earthquakes determined by conventional analyses from near- and/or far-field observations are consistent with static seismic moments thus estimated over the range from 2 × 1023 to 3 × 1027 dyne cm. This shows the potential in practice of the present method, especially in the routine processing of seismic data.  相似文献   

8.
A probabilistic seismic hazard assessment is developed here using maximum credible earthquake magnitude statistics and earthquake perceptibility hazard. Earthquake perceptibility hazard is defined as the probability a site perceives ground shaking equal to or greater than a selected ground motion level X, resulting from an earthquake of magnitude M, and develops estimates for the most perceptible earthquake magnitude, M P(max). Realistic and usable maximum magnitude statistics are obtained from both whole process and part process statistical recurrence models. These approaches are extended to develop relationships between perceptible earthquake magnitude hazard and maximum magnitude recurrence models that are governed by asymptotic and finite return period properties, respectively. Integrated perceptibility curves illustrating the probability of a specific level of perceptible ground motion due to all earthquakes over the magnitude range extending from ?∞ to a magnitude M i are then developed from reviewing site-specific magnitude perceptibility. These lead on to achieving site-specific annual probability of exceedance hazard curves for the example cities of Sofia and Thessaloniki for both horizontal ground acceleration and ground velocity. Both the maximum credible earthquake magnitude M 3 and the most perceptible earthquake magnitude M P(max) are of importance to the earthquake engineer when approaching anti-seismic building design. Both forms of hazard are illustrated using contoured hazard maps for the region bounded by 39°–45°N, 19°–29°E. Patterns are observed for these magnitude hazard estimates—especially M P(max) specific to horizontal ground acceleration and horizontal ground velocity—and compared to inferred patterns of crustal deformation across the region. The full geographic region considered is estimated to be subject to a maximum credible earthquake magnitude M 3—estimated using cumulative seismic moment release statistics—of 7.53 M w, calculated from the full content of the adopted earthquake catalogue, while Bulgaria’s capital, Sofia, is estimated a comparable value of 7.36 M w. Sofia is also forecast most perceptible earthquake magnitudes for the lowest levels considered for horizontal ground acceleration of M PA(50) = 7.20 M w and horizontal ground velocity of M PV(5) = 7.23 M w for a specimen focal depth of 15 km.  相似文献   

9.
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   

10.
Changes in temperature, pressure and composition cause changes in the ratios of polyhedral sizes in oxygen-based minerals. Polyhedra with large, high-coordination, low-valence cations expand and compress more than polyhedra with small, low-coordination, high-valence cations. Changes in cation composition alter the ratios of polyhedral sizes by changing mean cation radii. Thus temperature, pressure and composition are structurally analogous variables. Since temperature, pressure and composition change structures in similar ways, it is possible to construct isostructural surfaces in P-T-X space. For structures in which stability is limited to specific ranges of polyhedral size ratios (e.g. octahedral-tetrahedral layers in mica), certain P-T-X isostructural surfaces may coincide with phase boundaries. If geometrical constraints on mineral stability are known, then phase equilibria may be predicted. Examples of stability limit calculations are given for several major oxygen-based mineral groups.  相似文献   

11.
本文通过研究青海尕林格矽卡岩型铁矿床内成矿阶段富Cl角闪石的矿物学特征,来反演岩浆-流体-矿物三者间的演化关系。尕林格富Cl角闪石应属于镁绿钙闪石亚族,化学成分特征显示:0.3Mg/(Mg+Fe2+)0.69,Si6.25apfu,0.681%Cl3.161%。XCl与XMg显示具有很好的负相关性,而XK和X2+Fe则与XCl显示具有正相关性。这些阴阳离子间的线性关系与角闪石的晶体结构特征密切相关。对于Cl-交代OH-进入角闪石分子结构可以用经验公式表示为ln(XCl/XOH)amp=ln(fCl/fOH)fluid+A·[4]Al·Fe2+/RT+B/RT,其中A和B为常数。因此,当所有富Cl角闪石的成分与流体在同一温度和相对不变fCl/fOH下平衡时,则角闪石中的ln(XCl/XOH)对其成分[4]Al·Fe2+投影应为线性关系,这一特点可理解为阳离子成分对Cl的加入的影响随流体成分的改变而改变。尕林格富Cl角闪石环带成分从核部到边部具有XCl先降低后升高的特点,这与OH-比Cl-更易交代进入分子结构有关。当角闪石和与之平衡的流体进入相对封闭环境时,随着角闪石的结晶,流体中Cl的含量逐渐增加导致角闪石环带边缘XCl明显比核部高。晶体和液体间的微量元素分异不仅受到晶体结构的控制,而且流体中的挥发分也是控制微量元素分异的主要因素。富Cl角闪石中Cl的含量对REE的分异同样也有影响,REE元素的分配系数随着流体中Cl含量的降低而升高。通常认为硅酸质岩浆早期结晶分异出来的高温高盐度流体是重要的载矿流体,因其含有大量的Cl-并且pH值较低,有利于Fe的Cl络合物进行长期迁移。当流体遇到偏碱性的碳酸盐地层导致流体pH值升高,或与天水混合形成低温低盐度流体时,Fe的Cl络合物就会发生解离沉淀。而此时流体中fOH升高,从而导致OH-交代进入早期矽卡岩矿物中形成角闪石等退化蚀变矿物。  相似文献   

12.
Evaluating the feasibility of CO2 geologic sequestration requires the use of pressure-temperature-composition (P-T-X) data for mixtures of CO2 and H2O at moderate pressures and temperatures (typically below 500 bar and below 100°C). For this purpose, published experimental P-T-X data in this temperature and pressure range are reviewed. These data cover the two-phase region where a CO2-rich phase (generally gas) and an H2O-rich liquid coexist and are reported as the mutual solubilities of H2O and CO2 in the two coexisting phases. For the most part, mutual solubilities reported from various sources are in good agreement. In this paper, a noniterative procedure is presented to calculate the composition of the compressed CO2 and liquid H2O phases at equilibrium, based on equating chemical potentials and using the Redlich-Kwong equation of state to express departure from ideal behavior. The procedure is an extension of that used by King et al. (1992), covering a broader range of temperatures and experimental data than those authors, and is readily expandable to a nonideal liquid phase. The calculation method and formulation are kept as simple as possible to avoid degrading the performance of numerical models of water-CO2 flows for which they are intended. The method is implemented in a computer routine, and inverse modeling is used to determine, simultaneously, (1) new Redlich-Kwong parameters for the CO2-H2O mixture, and (2) aqueous solubility constants for gaseous and liquid CO2 as a function of temperature. In doing so, mutual solubilities of H2O from 15 to 100°C and CO2 from 12 to 110°C and up to 600 bar are generally reproduced within a few percent of experimental values. Fugacity coefficients of pure CO2 are reproduced mostly within one percent of published reference data.  相似文献   

13.
Hydrothermal experiments on the reaction: rutile + calcite + quartz = sphene + CO2, suggest equilibrium at: Pfluid = 2 kbar, 500 ± 5°C, XCO2 = 0.5 ± 0.006; Pfluid = 3.45 kbar, 535 ± 10°C, XCO2 = 0.5 ± 0.006; Pfluid = 5 kbar, <580°C, XCO2 = 0.5 ± 0.006; Pfluid = 5 kbar, <635°C, XCO2 = 0.97 ± 0.035.The resultant stability field of sphene is much larger than that suggested by Schuiling and Vink (1967). Calculation of the reaction in P-T space directly from free energy data indicates a discrepancy in Δr of about 1.5 kcal/gfw when compared to our experimental data. In addition, P-T extrapolation of the reaction using thermochemical data disagrees with the constraints of the two experimental brackets, indicating possible errors in the entropy of one or more solid phases and/or in CO2 free energy data.The combination of these experimental results with published data on reactions involving additional minerals allows the recognition of sphene and/or rutile-bearing assemblages which can be used as indicators of P-T-XCO2 conditions at various grades of metamorphism. In particular, mineral assemblages useful in delimiting P-T-XCO2 conditions are: muscovite-sphene (H2O-rich fluids), diopside-rutile-quartz (high temperatures or a CO2-rich fluid at low temperatures), epidote-rutile-quartz (low temperatures, H2O-rich conditions), prehnite-rutile (very low temperatures, very H2O-rich conditions).  相似文献   

14.
Calculations on a new empirical solution model, constructed as a Kohler oxide solution with special oxide coefficients and nearly symmetrical binary interaction parameters, reproduce the simple geometry found for silicate liquid immiscibility in synthetic systems. Both ordinary regular and subregular solutions are unsuitable for these calculations because, as components are added, these solutions result in complicated liquid immiscibility with many extraneous solvii. The geometry of immiscibility is determined by spinodal calculation followed by a graphical construction. Spinodal calculation produces a vector R which must be roughly parallel to tie lines and is used to compare the real with modelled partitioning. The results agree very well with the available experimental work for SiO2-M(1)O-M(2)O systems M = Fe, Mg, Ca, Mn, Zn, Ba, Pb) and reasonably well for the quartz-fayalite-leucite section with minor Fe2O3, TiO2 and P2O5. The new model predicts that the flattened liquidus of diopside, in the diopside-leucite-quartz and diopside-nepheline-quartz systems, is due to the metastable extension of the diopside-quartz melt solvus, only 100–150°C below the liquidus of diopside. Preliminary attempts to extend the coefficient model to natural examples of magma immiscibility are not very successful.  相似文献   

15.
In this research, the equilibrium sorption of Zn(II) and Cu(II) by kaolinite was explained using the Freundlich, Langmuir and Redlich–Peterson isotherms, via both linear and non-linear regression analyses. In the case of non-linear regression method, the best-fitting model was evaluated using six different error functions, namely coefficient of determination (r 2), hybrid fractional error function (HYBRID), Marquardt’s percent standard deviation (MPSD), average relative error (ARE), sum of the errors squared (SSE) and sum of the absolute errors (EABS). The examination of error estimation methods showed that the Langmuir model provides the best fit for the experimental equilibrium data for both linear and non-linear regression analyses. The SSE function was found to be a better option to minimize the error distribution between the experimental equilibrium data and predicted two-parameter isotherms. In the case of three-parameter isotherm, HYBRID was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. Non-linear method was found to be more appropriate method for estimating the isotherm parameters.  相似文献   

16.
Compression index Ccis an essential parameter in geotechnical design for which the effectiveness of correlation is still a challenge.This paper suggests a novel modelling approach using machine learning(ML)technique.The performance of five commonly used machine learning(ML)algorithms,i.e.back-propagation neural network(BPNN),extreme learning machine(ELM),support vector machine(SVM),random forest(RF)and evolutionary polynomial regression(EPR)in predicting Cc is comprehensively investigated.A database with a total number of 311 datasets including three input variables,i.e.initial void ratio e0,liquid limit water content wL,plasticity index Ip,and one output variable Cc is first established.Genetic algorithm(GA)is used to optimize the hyper-parameters in five ML algorithms,and the average prediction error for the 10-fold cross-validation(CV)sets is set as thefitness function in the GA for enhancing the robustness of ML models.The results indicate that ML models outperform empirical prediction formulations with lower prediction error.RF yields the lowest error followed by BPNN,ELM,EPR and SVM.If the ranges of input variables in the database are large enough,BPNN and RF models are recommended to predict Cc.Furthermore,if the distribution of input variables is continuous,RF model is the best one.Otherwise,EPR model is recommended if the ranges of input variables are small.The predicted correlations between input and output variables using five ML models show great agreement with the physical explanation.  相似文献   

17.
Analysis of E||X-polarized optical absorption spectra of natural olivines of various origin in the range of electronic spin-allowed dd-transitions of Fe2+ evidences that in some crystals, there is a weak ordering of Fe2+ as in M1, as in M2 structural sites. The samples of three different depth facies seem showing a vague tendency of lowering of k D -values from spinel-pyroxene (Sp-Px) through graphite-pyrope (G-Py) to diamond-pyrope (D-Py) facies, but the statistics are too poor (24 samples only) to be certain of it. Weak relations between Mg, Fe2+-distribution and iron content were found for the samples of Sp-Px- and G-Py-facies, while there is practically no one for those of the deepest D-Py facie.  相似文献   

18.
In the present study, the modified Sverjensky–Molling equation, derived from a linear-free energy relationship, is used to predict the Gibbs free energies of formation of crystalline phases of α-MOOH (with a goethite structure) and α-M2O3 (with a hematite structure) from the known thermodynamic properties of the corresponding aqueous trivalent cations (M3+). The modified equation is expressed as ΔG0f,MVX=aMVXΔG0n,M3++bMVX+βMVXγM3+, where the coefficients aMVX, bMVX, and βMVX characterize a particular structural family of MvX (M is a trivalent cation [M3+] and X represents the remainder of the composition of solid); γ3+ is the ionic radius of trivalent cations (M3+); ΔG0f,MVX is the standard Gibbs free energy of formation of MvX; and ΔG0n,M3+ is the non-solvation energy of trivalent cations (M3+). By fitting the equation to the known experimental thermodynamic data, the coefficients for the goethite family (α-MOOH) are aMVX=0.8838, bMVX=?424.4431 (kcal/mol), and βMVX=115 (kcal/mol.?), while the coefficients for the hematite family (α-M2O3) are aMVX=1.7468, bMVX=?814.9573 (kcal/mol), and βMVX=278 (kcal/mol.?). The constrained relationship can be used to predict the standard Gibbs free energies of formation of crystalline phases and fictive phases (i.e. phases that are thermodynamically unstable and do not occur at standard conditions) within the isostructural families of goethite (α-MOOH) and hematite (α-M2O3) if the standard Gibbs free energies of formation of the trivalent cations are known.  相似文献   

19.
To enhance the computer simulation of hydrothermal processes using the HCh program package, an external ZnS_FeS module has been created on the basis of a nonideal asymmetric model of sphalerite solid solution. FeS and ZnS activity coefficients computed in line with this model within a temperature range 200?C350°C lead to the decrease in FeS mole fraction (X FeS) in sphalerite by 3.0?C1.5 times as compared with the ideal model. The calculated data on composition of sphalerite at the pyrite-pyrrhotite buffer with allowance for pyrrhotite nonideality are consistent with experimental results within the limits of 2% X FeS of its value (0.215). A nonlinear relationship logX FeS versus $\left( {\log f_{S_2 } } \right)$ . has been established, involving additional calculated data on equilibria of sphalerite with pyrite and magnetite, as well as pyrite and barite. With transition from pyrrhotite to magnetite and barite, a FeS mole fraction in sphalerite decreases to 0.1 and 0.006, respectively, because of increase in sulfur fugacity. The feasibility of using the calculation results based on the nonideal model of sphalerite for interpretation of natural data is exemplified in the Rainbow ore occurrence at the Mid-Atlantic Ridge (MAR). The computed pyrite-pyrrhotite and pyrite-cubanite-chalcopyrite buffer equilibria (X FeS = 0.215 and 0.10?C0.12, respectively) are consistent with compositions of sphalerite in the pyrrhotite-cubanite-sphalerite and sphalerite ores (X FeS = 0.20?C0.33 and 0.05?C0.14, respectively).  相似文献   

20.
Chun-Ming Wu  Jian Zhang 《Lithos》2004,78(4):319-332
Based on the net transfer reactions among garnet, muscovite, plagioclase, and quartz (for both Mg and Fe end-member models), the garnet-muscovite-plagioclase-quartz (GMPQ) geobarometry was empirically calibrated under the physical conditions of P=1.0-11.4 kbar and T=505-745 °C for 128 natural metapelitic rock samples collected from the literature. The input temperatures and pressures were simultaneously determined by the garnet-biotite thermometer and the garnet-aluminosilicate-plagioclase-quartz (GASP) barometer. The GMPQ calibrations adopted the same asymmetric quaternary solid solution model of garnet and the same Al-avoidance asymmetric ternary model of plagioclase as the calibrations of the garnet-biotite geothermometer and the GASP geobarometer. A symmetric Fe-Mg-AlVI ternary solid solution model of muscovite was adopted, and the Margules parameters of muscovite were obtained through regression. The Mg and Fe model reactions, along with the assumption of whether the ferric iron content in muscovite is 0% or 50%, resulted in four GMPQ barometry formulae. The GMPQ barometry formulae reproduce the input GASP pressures well within ±1.0 kbar (mostly within ±0.5 kbar). For both aluminosilicate-bearing and aluminosilicate-absent samples, the GMPQ barometry formulae yield identical pressures for every sample, whether the sample was included or not in calibrating the barometers. For each of the Mg or Fe model reaction, the formulae gave identical pressures within ±40 bars. The random error of the GMPQ barometry may be expected as ±1.4 kbar. The dP/dT slopes of these GMPQ formulae are close to that of the GASP barometer in the P-T space. Applications of the GMPQ barometry to aluminosilicate-absent metapelites within a limited geographic area without postmetamorphic structural discontinuity generally show no pressure difference. It may be concluded that the GMPQ barometry formulae derived in this work may be used as practical tools for metamorphic pelites under the conditions of 505-745 °C and 1-11.4 kbar, in the composition range of Xgros>3% in garnet and XAn>17% in plagioclase.  相似文献   

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