首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献，搜索用时 296 毫秒
1.
An analytical approach to the analysis of zoning profiles in minerals is presented that simultaneously accounts for all of the possible continuous reactions that may be operative in a given assemblage. The method involves deriving a system of simultaneous linear differential equations consisting of a Gibbs-Duhem equation for each phase, a set of linearly independent stoichiometric relations among the chemical potentials of phase components in the assemblage, and a set of equations describing the total differential of the slope of the tangent plane to the Gibbs free energy surface of solid solution phases. The variables are the differentials of T, P, chemical potentials of all phase components, and independent compositional terms of solid solution phases. The required input data are entropies, volumes, the compositions of coexisting phases at a reference P and T, and an expression for the curvature of the Gibbs functions for solid solution phases. Results derived are slopes of isopleths (dP/dT, dX/dT or dX/dP) which can be used to contour P-T diagrams with mineral composition.To interpret mineral zoning, T and P can be expressed as functions of n independent composition parameters, where n is the variance of the mineral assemblage. The total differentials of P and T are differential equations that can be solved by finite difference techniques using the derivatives obtained from the analytical formulation of phase equilibria.Results calculated from Zone I and Zone IV garnets of Tracy et al. (1976) indicate that Zone I garnets grew while T increased (T+72° C) and P decreased sharply (P–3 kb). Zone IV garnets zoned in response to decreasing T (T–17° C) and P (P–1 kb). A P-T path calculated for a zoned garnet from the Greinerschiefer series, western Tauern Window, Austria, also indicates growth during decompression (–3kb) and heating (T+15° C). A P-T path calculated for the Wissahickon schist (Crawford and Mark 1982) indicates growth during cooling and compression (T–25 C, P+2.2 kb). The calculated P-T paths differ according to structural environment and can be used to relate mineral growth to tectonic processes.  相似文献   

2.
The problem of determining capillary pressure functions from centrifuge data leads to an integral equation of the form a x K(x,t)f(t)dt=g(x),x[a,b],(1)where the kernel K is known exactly and given by the underlying mathematical model. g is only known with a limited degree of accuracy in a finite and discrete set of points x 1,...,x M . However, the sought function f(t) is continuous. By the nature of the right-hand side, g(x), equation (1) is a discrete inverse problem which is ill-posed in the sense of Hadamard [9]. By a parameterization of the sought function, equation (1) reduces to a system of linear equations of the form Ac=b+ ,where b is the observation vector and A arises from discretization of the forward problem. is the error vector associated with b, and c contains the model parameters. The matrix A is usually ill-conditioned. The ill-conditioning is closely connected to the parameterization of the problem [23].In this paper a semi-iterative regularization method for solving the Volterra integral equation in the 2-norm, namely, Brakhage's -method [2], is investigated. The iterative method is tested on synthetically generated, and on experimental data.  相似文献   

3.
We consider a two-phase incompressible immiscible flow, with neglected surface tension, in a thin domain. Using the method of asymptotic expansions with respect to the thickness of the domain, effective 1D equations are derived. Supposing that the fluids are strictly separated at t=0, we show that the derived equations equal the Buckley–Leverett equation for the saturation, in conjunction with the Reynolds law for each of the flowing phases. The fractional flow curve and corresponding relative permeabilities are determined explicitly and their heuristically observed properties verified.  相似文献   

4.
A single-crystal of composition CaNiSi2O6 (space group C2/c) was investigated at high pressure up to about 7.8 GPa by X-ray diffraction. The unit-cell parameters were measured at 18 different pressures. The P-V data were fitted by a third-order Birch-Murnaghan equation of state V0=435.21(1) Å3, K 0=117.6(3) GPa and K=6.4(1). The linear axial compressibilities a, b, c and a sin are 2.14(1), 3.00(1), 2.43(1) and 1.63(1) × 10–3 GPa–1. Comparing the compressibility data with other CaM1Si2O6 pyroxenes we suggest that the empirical K × V = constant relationships are followed in C2/c pyroxenes only if the same valence electron character is shared.  相似文献   

5.
Historically, the characterization of the internal energy of a simple gas is based on free expansion experiments and imprecise use of the word function, which is rigorously defined in mathematics. Univariable equations of state show that the internal energy of simple monatomic, diatomic, and polyatomic gases can be expressed as a function of temperature only. However, multivariable equations of state derived from composite functions confirm that the internal energy of these gases can in each situation also be expressed as a function of pressure and volume only. It is essential that the mathematical definition of the word function be adhered to in science because it is fundamental for the formulation of the calculus, a mathematical tool essential for solving a variety of thermodynamics problems.  相似文献   

6.
In this study, a database comprised of 30 pullout pile load tests was collected from geotechnical literature and analyzed to investigate the dependency of unit shaft resistance on effective vertical stress. The collected database consists of steel pipe, timber, and concrete piles, with varying normalized penetration depth with respect to pile diameter, driven into loose to very dense sand. Different correlations for the uplift lateral earth pressure coefficient K, Bjerrum-Burland ratio , and the average unit shaft resistance f ave were derived using different assumptions. A comparison between measured and predicted capacities of the collected piles using the developed correlations indicated that the assumption of values of K and that were constant with depth did not provide a reasonable fit for the measured capacities of the collected piles and thus this assumption is inappropriate. The best correlations for K and that yield a reasonable fit to the measured capacities of the collected piles were found to be functions of sand relative density, pile diameter, and level of effective vertical stress. This indicates that average unit shaft resistance does not reach a limiting value, but rather continues to increase with depth. Moreover, the correlations for K and in terms of effective stress revealed that average unit shaft resistance increases as pile diameter decreases and this increase depends on initial sand relative density. Comparisons of measured and predicted pullout capacities of the collected piles using the best-obtained correlations for K and were made and compared to predictionsobtained from other methods. On the basis of these comparisons, it is concluded that the correlations for K and in terms of effective stress give results comparable to those obtained from other methods, without stipulating limiting values for the average unit shaft resistance.  相似文献   

7.
The thermodynamic stability constants for the hydrolysis and formation of mercury (Hg2+) chloride complexes
have been used to calculate the activity coefficients for Hg(OH) n (2–n)+ and HgCl n (2–n)+ complexes using the Pitzer specific interaction model. These values have been used to determine the Pitzer parameters for the hydroxide and chloro complexes and C ML). The values of and have been determined for the neutral complexes (Hg(OH)2 and HgCl2). The resultant parameters yield calculated values for the measured values of log to  ±0.01 from I  =  0.1 to 3 m at 25°C. Since the activity coefficients of and are in reasonable agreement with the values for Pb(II), we have estimated the effect of temperature on the chloride constants for Hg(II) from 0 to 300°C and I = 0–6 m using the Pitzer parameters for complexes. The resulting parameters can be used to examine the speciation of Hg(II) with Cl− in natural waters over a wide range of conditions.  相似文献   

8.
A revised equation is proposed to represent and extrapolate the heat capacity of minerals as a function of temperature: C P=k0+k1 T –0.5+k2 T –2+k3 T –3 (where k1, k20).This equation reproduces calorimetric data within the estimated precision of the measurements, and results in residuals for most minerals that are randomly distributed as a function of temperature. Regression residuals are generally slightly greater than those calculated with the five parameter equation proposed by Haas and Fisher (1976), but are significantly lower than those calculated with the three parameter equation of Maier and Kelley (1932).The revised equation ensures that heat capacity approaches the high temperature limit predicted by lattice vibrational theory (C P=3R+2VT/). For 16 minerals for which and have been measured, the average C Pat 3,000 K calculated with the theoretically derived equation ranges from 26.8±0.8 to 29.3±1.9 J/(afu·K) (afu = atoms per formula unit), depending on the assumed temperature dependence of . For 91 minerals for which calorimetric data above 400 K are available, the average C Pat 3,000 K calculated with our equation is 28.3±2.0 J/(afu·K). This agreement suggests that heat capacity extrapolations should be reliable to considerably higher temperatures than those at which calorimetric data are available, so that thermodynamic calculations can be applied with confidence to a variety of high temperature petrologic problems.Available calorimetric data above 250 K are fit with the revised equation, and derived coefficients are presented for 99 minerals of geologic interest. The heat capacity of other minerals can be estimated (generally within 2%) by summation of tabulated oxide component C Pcoefficients which were obtained by least squares regression of this data base.  相似文献   

9.
Kyser, O'Neil, and Carmichael (1981, 1982) measured the 18O values of coexisting minerals from peridotite nodules in alkali basalts and kimberlites, interpreting the nodules as equilibrium assemblages. Using Ca-Mg-Fe element-partition geothermometric data, they proposed an empirical18O/16O geothermometer: T(°C)=1,151–173–68 2, where is the per mil pyroxene-olivine fractionation. However, this geothermometer has an unusual crossover at 1,150 °C, and in contrast to what might be expected during closed-system equilibrium exchange, the most abundant mineral in the nodules (olivine) shows a much greater range in 18O (+4.4 to +7.5) than the much less abundant pyroxene (all 50 pyroxene analyses from spinel peridotites lie within the interval +5.3 to +6.5). On 18O-olivinevs. 18O-pyroxene diagrams, the mantle nodules exhibit data arrays that cut across the 18O=zero line. These arrays strongly resemble the non-equilibrium quartzfeldspar and feldspar-pyroxene 18O arrays that we now know are diagnostic of hydrothermally altered plutonic igneous rocks. Thus, we have re-interpreted the Kyser et al. data as non-equilibrium phenomena, casting doubt on their empirical geothermometer. The peridotite nodules appear to have been open systems that underwent metasomatic exchange with an external, oxygen-bearing fluid (CO2, magma, H2O, etc.); during this event, the relatively inert pyroxenes exchanged at a much slower rate than did the coexisting olivines and spinels, in agreement with available exchange-rate and diffusion measurements on these minerals. This accounts for the correlation between 18O pyroxene-olivine and the whole-rock 18O of the peridotites, which is a major difficulty with the equilibrium interpretation.Contribution No. 3978, Publications of the Division of Geological and Planetary Sciences, California Institute of Technology  相似文献   

10.
The mechanism of earthquakes is presented by use of the elastic dislocation theory. With consideration of the continuous dislocation field, the general problem of medium deformation requires analysis based on non-Riemannian geometry with the concept of the continuum with a discontinuity (no-more continuum). Here we derive the equilibrium equation (Navier equation) for the continuous dislocation field by introducing the relation between the concepts of the continuous dislocation theory and non-Riemannian geometry. This equation is a generalization of the Laplace equation, which can describe fractal processes like diffusion limited aggregation (DLA) and dielectric breakdown (1313). Moreover, the kinematic compatibility equations derived from Navier equation are the Laplace equations and the solution of Navier equation can be put in terms of functions which satisfy the biharmonic equation, suggesting a close formal connection with fractal processes. Therefore, the relationship between the non-Riemannian geometry and the fractal geometry of fracturing (damage) in geomaterials as earthquakes can be understood by using the Navier equation. Moreover, the continuous dislocation theory can be applied to the problem of the earthquake formation with active folding related with faulting (active flexural-slip folding related to the continuous dislocation field).  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号