Cation diffusion in aluminosilicate garnets: experimental determination in spessartine-almandine diffusion couples,evaluation of effective binary diffusion coefficients,and applications   总被引：9，自引：1，他引：8  

Sumit Chakraborty  Jibamitra Ganguly 《Contributions to Mineralogy and Petrology》1992,111(1):74-86

We present new experimental data on diffusion of divalent cations in almandine-spessartine diffusion couples in graphite capsules in the P-T range of 14–35 kb, 1100–1200° C. The tracer diffusion coefficients of the major divalent cations, viz. Fe, Mg and Mn, retrieved from the multicomponent diffusion profiles, have been combined with earlier data from our laboratory at 29–43 kb, 1300–1480° C (Loomis et al. 1985) to derive expressions of the P-T dependence of the diffusion coefficients at fO₂ approximately corresponding to that defined by equilibrium in the system graphite-O₂. We review the conditions, discussed earlier by Cooper, under which the flux of a component in a multicomponent system becomes proportional to its concentration gradient (Fickian diffusion), as if the entire solvent matrix behaves as a single component, and also suggest a method of incorporating the thermodynamic effect on diffusion in the same spirit. Regardless of the magnitude or sign of the off-diagonal terms of the D matrix, it is always possible to define an effective binary diffusion coefficient (EBDC) of a component in a semi-infinite multicomponent diffusion-couple experiment such that it has the property of the Fickian diffusion coefficient, provided that there is no inflection on the diffusion profiles. It is shown that the success of Elphick et al. in fitting the experimental diffusion profiles of all components over a limited concentration range by a single diffusion coefficient is due to fortuitous similarity of the EBDCs of the components (Fe, Mg, Mn and Ca) in their diffusion couple experiments. In common metapelitic garnets showing compositional zoning, the EBDCs of the divalent cations do not differ from each other by more than a factor of 2.5. However, the EBDC of a component changes from core to rim by a factor of 3 to 12, depending on the composition. We suggest a method of volume averaging of the EBDC which should prove useful in approximate calculations of diffusion flux during relaxation of compositional zoning. The EBDC of Mn is found to reduce essentially to D _MnMn, the main diagonal term of the D matrix, and consequently can be calculated quite easily. Evaluation of EBDC of Fe, Mg and Mn in garnets from a prograde Barrovian sequence did not reveal any significant dependence on the extent of relaxation of garnet. The diffusion data have been applied to calculate the cooling rate of natural biotite-garnet diffusion couple from eastern Finland and diffusional modification of growth zoning in garnet in early Proterozoic Wopmay orogen, Canada. The results are in good agreement with geochronological and other independent constraints.Symbols and abbreviations a Radius of a spherical garnet crystal - BSE Back-scattered electron imaging - C Column vector of (n-1) independent components - D Diffusion coefficient matrix - D _ij An element of the diffusion matrix on the i th row and j th column - D _* ⁱ Tracer diffusion coefficient of component i - D(i) Effective interdiffusion coefficient (EIC) of various components in a multicomponent solution rich in the component i - D(i-j) Interdiffusion coefficient of components i and j in a binary solution - D _i (EB) Effective binary diffusion coefficient of component i in a multicomponent solution - D _i (EB:Ideal) D _i (EB) under condition of ideal thermodynamic mixing of the diffusing species - D _i (EB:thermo) Thermodynamic component of D _i(EB) - D _O ^A Interdiffusion coefficient at peak temperature T ₀ in the phase A - D ₀ Pre-exponential factor in an Arrhenius relation - EBDC Effective binary diffusion coefficient between a solute and a multicomponent solvent matrix - FEC Fixed edge composition model - EIC Effective interdiffusion coefficient - f _i Fugacity of component i - HM Hematite-magnetite oxygen fugacity buffer - kb Kilobars - P Pressure - Q Activation energy (enthalpy) of diffusion - Extent of relaxation defined as the difference between core and rim compositions normalized to the same difference in the initial zoning profile - R Gas constant - s Cooling rate - T ₀, T _Ch Peak temperature and characteristic temperature, respectively - t Time - VEC Variable edge composition model - V ⁺ Activation volume - W _ij Simple mixture interaction parameter between i and j - W _i(EB) Effective simple mixture interaction parameter of a component i in a multicomponent solution - _ij Margules interaction parameter between i and j - X _i Mole fraction of component i - _i Activity coefficient of component i - A dimensionless variable =D t/a ² - _ij Kronecker delta (i=j, _ij =1; ij, _ij =0) - Z_i Charge on the ion i  相似文献   

Transport of stable isotopes: I: Development of a kinetic continuum theory for stable isotope transport     

L. P. Baumgartner  D. Rumble III 《Contributions to Mineralogy and Petrology》1988,98(4):417-430

Equations are developed describing migration of stable isotopes via a fluid phase infiltrating porous media. The formalism of continuum fluid mechanics is used to deal with the problem of microscopic inhomogeneity. Provision is made explicitly for local equilibrium exchange of isotopes between minerals and fluids as well as for kinetic control of isotopic exchange. Changing characteristic parameters of transport systems such as porosity, permeability, and changes in modal proportions of minerals due to precipitation or dissolution are taken into account.The kinetic continuum theory (KCIT) is used to show how to deduce the dominant mechanism of mass transport in metasomatic rocks. Determination of the transport mechanism requires data on the spatial distribution of the reaction progress of exchange reactions between minerals and fluids involving at least two stable isotope systems such as ¹³C-¹²C and ¹⁸O-¹⁶O, for example. It is concluded that a combination of field and laboratory measurements of two or more stable isotope systems can be used to place constraints not only on the mechanism of transport but also on the magnitude of fluid fluxes, the identity of fluid sources, and the molecular species composition of fluids.Variables used C number of chemical components - D _i,j hydrodynamic dispersion tensor [m²/s] - D _i ^j diffusion coefficient matrix [m²/s] - D ^* apparent diffusion coefficient, includes sorption, dispersion, porosity and tortuosity [m²/s] - F number of degrees of freedom (variance) - f _i ^j mass or number of isotope j in fluid species i - g acceleration due to gravity [m/s²] - flow [m³/m² s] - j isotope species - j chemical element - k coefficient defined in Eq. 17 - K permeability of porous media [m²], [darcy] - L _ij phenomenological diffusion coefficient matrix [mol²/j m s] - m number of fluid species - n number of isotope exchange vectors - p number of phases - P pressure [Pa] - P ^* hydrological pressure potential [Pa] - R ^j ratio of concentration of rare to common isotope of element j - r number of restrictions imposed on system - s _i ^j mass or number of isotope j in one mole of mineral phase i - t time [s] - V volume [m³] - X _i number of moles of fluid species i in unit fluid volume - X _l number of moles of mineral l in unit volume - X _l ^j mole fraction of isotope j in one mole mineral l - X ^* mole fraction with respect to the whole system - z space coordinate [m] - z transformed space coordinate - z ^* location of an infiltration front [m] - _x–y ^j fractionation factor between two phases, x, y, for isotope j - porosity - fluid viscosity [Ns/m²] - fraction of porosity accessible to a specific mass transport mechanism - chemical potential [j/mole] - stoichiometric reaction coefficient - normalized reaction progress variable - mass, specific mass [gr/cm] - tortuosity - fluid velocity [m/s] - c common isotope - init initial - j isotope species - r rare isotope - tot sum of common and rare isotope - dif diffusive - disp dispersive - eq mineral composition in equilibrium with initial infiltration concentration of the fluid - f fluid - inf infiltrative - r rock, without fluid phase - samp sample - std standard - sys system - tot fluid and rock  相似文献   

Garnet-pyroxene equilibria in the system CaO-MgO-Al2O3-SiO2 (CMAS): prospects for simplified (‘T-independent’) lherzolite barometry and an eclogite-barometer     

G. P. Brey  K. G. Nickel  L. Kogarko 《Contributions to Mineralogy and Petrology》1986,92(4):448-455

New experimental data on compositions of garnets in two-pyroxene — garnet assemblages in the system CaO –MgO –Al₂O₃ –SiO₂ (CMAS) are presented for conditions between 1,100 and 1,570° C and 30 to 50 kb. Garnets in these assemblages become less calcic with increasing pressure. Garnet-orthopyroxene barometry (Al-solubility-barometry) pertinent to geobarometry for garnet lherzolites has been evaluated with a set of experimental data covering the range 900 to 1,570° C and 15 to 100 kb. Various formulations of this barometer work well to 75 kb. Phase equilibria are not sufficient to positively verify the thermodynamic validity of any of such models. Empirical garnet-orthopyroxene barometry at least in the system CMAS can be formulated to obtain a pressure estimate without previous temperature estimation (P(kb)=34.4-19.175 1n X _Al ^M1 +17.702 1n X _Ca ^M2 ). The potential application of an analogous garnetclinopyroxene equilibrium is limited because the amount of Ca-Tschermaks in natural clinopyroxenes is usually quite small in garnet lherzolites and many eclogites. The Ca-Mg exchange between garnet and clinopyroxene appears however sufficiently sensitive to pressure to allow calibration of a CMAS barometer. The reaction 3CaMgSi₂O₆+Mg₃Al₂Si₃O₁₂=3Mg₂Si₂O₆+Ca₃Al₂Si₃O₁₂ has a V ^o of 3.5 cm³. The total pressure dependency of this reaction is however closer to a theoretical V ^o of about 5 cm³ when excess volume properties of the phases involved are taken into account. We have calibrated such a barometer (mean error of estimate 2.8 kb) for assemblages with pyrope-rich (py>80) garnets and orthopyroxenes. This may provide the basis for a geobarometer for eclogites from kimberlites.Abbreviations Used in the Text CaTs Ca-tschermak's molecule, CaAl₂SiO₆ - cpx clinopyroxene - di diopside, CaMgSi₂O₆ - en enstatite, Mg₂Si₂O₆ - gr grossular, Ca₃Al₂Si₃O₁₂ - gt garnet - MgTs Mg-Tschermak's molecule, MgAl₂SiO₆ - opx orthopyroxene - px pyroxene - py pyrope, Mg₃Al₂Si₃O₁₂ - a _i ^j activity of component i in phase j - activity coefficient - G(I) molar Gibbs free energy difference of reaction (I) at standard state unless specified otherwise - H(I), (H _I) molar enthalpy (difference) of phase (reaction) (I) at standard state unless specified otherwise - S (I), (S _I) molar entropy (difference) of phase (reaction) (I) at standard state unless specified otherwise - V ^o, (V _I ^o) molar volume (difference) of phase (reaction) (I) at standard state - X _i ^j mole fraction of component i in phase j  相似文献   

A method for determining the reversibility of a Markov sequence   总被引：1，自引：0，他引：1  

David Richman  W. E. Sharp 《Mathematical Geology》1990,22(7):749-761

This paper describes, given a tally matrix with strictly positive entries, a method to determine whether the associated Markov process is reversible, and (for reversible Markov processes) methods to compute the reversibility matrix from the tally matrix. If the tally matrixN is symmetric, then it is shown that the Markov process must be reversible and the reversibility matrixC equalss (R ^–1NR^–1), whereR is the diagonal matrix whosei ^th diagonal entry is the sum of the entries of thei ^th row ofN (for everyi) ands denotes the sum of all the entries ofN. Because a symmetric tally matrix is of special importance in applications, a ² test is proposed for determining, in the presence of experimental errors, whether such a matrix is symmetric.  相似文献   

A case study of the amount and distribution of heat and fluid during metamorphism   总被引：1，自引：0，他引：1  

J. M. Ferry 《Contributions to Mineralogy and Petrology》1980,71(4):373-385

The volume of fluid and amount of heat involved in a portion of a metamorphic event around three synmetamorphic granitic stocks has been quantitatively estimated using mineral composition and modal data from carbonate rocks. Values of volumetric fluid-rock ratios range, with respect to a reference zoisite isograd, from 0.001 to 0.434. Amounts of heat involved range from –25 to 134 cal/cm³ rock. Contours of constant fluid-rock ratio and of constant amount of heat are generally concentric about the granitic stocks indicating that the stocks are foci of high heat and fluid fluxes during metamorphism. In addition, contours of fluid-rock ratios and amount of heat outline NE-SW-trending channelways of high fluid and heat fluxes that alternate with regions of lower fluid and heat fluxes. The NE-SW-trending vertical bedding and schistosity in the area — of premetamorphic origin — probably constrained fluid and heat transfer to occur preferentially in NE-SW directions. Large values of heat involved in metamorphism are strongly correlated with large fluid-rock ratios, suggesting that fluids are an important carrier of heat during metamorphism. Configurations of mapped isograds in the area mimic the patterns of contours of constant fluid-rock ratio and of heat content, indicating that configurations of isograds may contain useful information about regional patterns of heat and fluid transfer during metamorphism.Notation T Last temperature recorded by metacarbonate rocks (°C) - P Lithostatic pressure (bars) - Pi Partial pressure of component i (bars) - of last fluid in equilibrium with carbonate rocks during metamorphism - R 1.987 cal/bar-degree - K _s Activity constant for an assemblage of solid mineral phases - In Natural logarithm - c _v Volumetric heat capacity (cal/cm³-degree) - Q Heat added to or subtracted from a rock during metamorphism in the zoisite zone (kcal/100 cm³ rock; cal/cm³ rock) - Q{ibrxn} Heat added to or subtracted from a rock due to mineral reactions during metamorphism in the zoisite zone (kcal/100 cm³ rock; cal/cm³ rock) - Std. Dev. Standard Deviation - Average of fluid in equilibrium with carbonate rocks during their metamorphism in the zoisite zone - of fluid in equilibrium with carbonate rocks at the zoisite isograd - T Temperature at the zoisite isograd (°C) - X _i,j Mole fraction of component i in phase j - H _i Molar enthalpy of reaction i at 0 bars pressure - ¯V _i Change of molar volume due to reaction _ii - _i Measure of progress of reaction i - V Change in rock volume due to fluid-rock reactions - iV Initial rock volume before metamorphism within the zoisite zone - ¯V _s,i Change in molar volume of solid minerals due to reaction i Component notation an CaAl₂Si₂O₈ Phase notation Pl Plagioclase - Am Amphibole - Cc Calcite - Qz Quartz - Di Diopside - Zo Zoisite - Ga Garnet - Bi Biotite - Kf Microcline - Mu Muscovite  相似文献   

A distribution-free alternative to least-squares regression and its application to Rb/Sr isochron calculations     

Raymond G. Vugrinovich 《Mathematical Geology》1981,13(5):443-454

A distribution-free estimator of the slope of a regression line is introduced. This estimator is designated S_m and is given by the median of the set of n(n – 1)/2 slope estimators, which may be calculated by inserting pairs of points (X _i, Y_i)and (X _j, Y_j)into the slope formula S _i = (Y _i – Y_j)/(X _i – X_j),1 i < j n Once S _m is determined, outliers may be detected by calculating the residuals given by R_i = Y_i – S_mX_i where 1 i n, and chosing the median R_m. Outliers are defined as points for which |R_i – R_m| > k (median {|R _i – R_m|}). If no outliers are found, the Y-intercept is given by R_m. Confidence limits on R_m and S_m can be found from the sets of R_i and S_i, respectively. The distribution-free estimators are compared with the least-squares estimators now in use by utilizing published data. Differences between the least-squares and distribution-free estimates are discussed, as are the drawbacks of the distribution-free techniques.  相似文献   

Study on the compositional dependence of the apparent partition coefficient of iron and magnesium between coexisting garnet and clinopyroxene solid solution     

Yasutami Oka  Takashi Matsumoto 《Contributions to Mineralogy and Petrology》1974,48(2):115-121

Compositional dependence of apparent partition coefficient of iron and magnesium between coexisting garnet and clinopyroxene from Mt. Higasiakaisi is studied by means of a multicomponent regular solution model. It is shown that garnet and clinopyroxene solid solutions are positively non-ideal, and the non-ideal parameters according to the symmetric regular solution model are 2.58 kcal and 2.39 kcal, respectively, assuming the equilibration temperature of the mass to be 550° C.Notations a _i ^h activity of component i in phase h - _ij interaction parameter of component i and j in a solid solution - _i activity coefficient of component i - X _i mole fraction of component i - K partition coefficient of Fe and Mg between coexisting garnet and clinopyroxene - K apparent partition coefficient of Fe and Mg between coexisting garnet and clinopyroxene - G ⁰ difference in free energy of the partition reaction - H ⁰ difference in enthalpy of the partition reaction - S ⁰ difference in entropy of the partition reaction - R gas constant - G garnet - Alm almandine component - Py pyrope component - Gr grossular component - Sp spessartine component - CPx clinopyroxene - Hd hedenbergite component - Di diopside component - Jd jadeite component - Ts Tschermac's molecule component Deceased on April 17, 1974.  相似文献   

Fe-Mn partitioning between garnet and ilmenite: experimental calibration and applications   总被引：2，自引：0，他引：2  

Mark I. Pownceby  Victor J. Wall  Hugh St. C. O'Neill 《Contributions to Mineralogy and Petrology》1987,97(1):116-126

A new mineralogic geothermometer based on the partitioning of Fe and Mn between garnet and ilmenite has been calibrated by reversal experiments in the P-T range 600–900° C, 2 and 5 kbars and for fO₂=QFM. The results constitute a sensitive geothermometer applicable over a broad range of composition and conditions. Garnetilmenite thermometry has advantages relative to existing geothermometers because of its accurate calibration, marked temperature sensitivity and the chemical and structural simplicity of the crystalline solutions involved. Application to natural assemblages reveals that the garnet-ilmenite geothermometer yields temperatures that agree well with other estimates. The reactivity of, and relatively rapid Fe-Mn diffusion in ilmenite may lead to retrograde resetting of high temperature partition values, but these factors may be useful for estimating rock cooling rates. Analysis of the experimental data indicates minor positive deviations from ideality for Fe-Mn garnets and ilmenites. Absolute magnitudes of interaction parameters (W _AB) derived from a regression analysis are subject to considerable uncertainty. The partition coefficient is, however, strongly dependent on the difference between solution parameters. These differences are well constrained with a magnitude of W _FeMn ^ilm –W _FeMn ^gar 300 cal mol^–1. The accuracy and applicability of garnet-ilmenite thermometry will improve with the availability of better thermodynamic data for garnet crystalline solutions.Abbreviations and symbols used in text R universal gas constant (cal/mol/°K) - T absolute temperature (°K or °C) - P pressure (kbars) - V ⁰ volume change of reaction (1) - H _{1, T} ⁰ standard state enthalpy change of reaction (1) at 1 bar and the T of interest, in cal/mole - S _T ⁰ entropy change of reaction (1) at T of interest, in cal/mole/°K - G _P,T ⁰ standard free energy change of reaction (1) at the T and P of interest, in cal/mole - distribution coefficient for Fe-Mn partitioning between garnet and ilmenite - K apparent equilibrium coefficient for reaction (1) - _i ^j activity of component i in phase j - W _A-B binary A-B interaction (Margules) parameter - gar garnet - ilm ilmenite - biot biotite - ol olivine - opx orthopyroxene  相似文献   

Orthopyroxene-clinopyroxene equilibria in the system CaO-MgO-Al2O3-SiO2 (CMAS): new experimental results and implications for two-pyroxene thermometry     

K. G. Nickel  G. P. Brey  L. Kogarko 《Contributions to Mineralogy and Petrology》1985,91(1):44-53

A new set of reversal experiments for coexisting ortho- and clinopyroxenes in the system CMAS at conditions between 1,000–1,570° C and 30 to 50 kb is presented and combined with literature data. Pyroxene behaviour, particularly that of clinopyroxene, is very complicated and different styles of Al incorporation into the pyroxene structure for low and high concentrations of Al are indicated, strongly influencing the exchange of the enstatite component between ortho- and clinopyroxene. Thermodynamic modelling of this exchange is problematic because of the large number of unknown coefficients compared to the number of experiments. Thermometry based on such models becomes very dependent on accuracy of experimental data and analyses of small quantities of elements. Despite this complexity very simple empirical thermometric equations are capable of reproducing experimental conditions in the systems CMS and CMAS over a wide range of P, T conditions. We derived the equation which gives a mean error of estimate of 25° C when applied to CMS and CMAS data.Abbreviations Used in the Text cpx clinopyroxene - di diopside, CaMgSi₂O₆ - en enstatite, Mg₂Si₂O₆ - opx orthopyroxene - px Pyroxene - py pyrope - a _i ^j activity of component i in phase j - activity coefficient - G _P,T (A) molar Gibbs free energy difference of reaction (A) at P, T - X _i ^j mole fraction of component i in phase j  相似文献   

On the least-squares fit of small and great circles to spherically projected orientation data     

Norman H. Gray  Peter A. Geiser  James R. Geiser 《Mathematical Geosciences》1980,12(3):173-184

Given the direction cosines a _i ^′ = (a ₁ ⁱ , a ₂ ⁱ , a ₃ ⁱ )corresponding to a set of pspherically projected fabric poles, an initial estimate x′ = (x₁, x₂, x₃, x₄)for the angular radius x₄,and direction cosines of the center of the least-squares small circle which minimizes the sum of the squares of the angular residuals $$r = \sum\limits_p {\left[ {x_4 - \cos ^{ - 1} \left( {a_1^i x_1 + a_2^i x_2 + a_3^i x_3 } \right)} \right]} ^2 $$ can be iteratively improved by taking x_j+1 = x_j + Δxwhere x_j is the value of xat the jth iteration and $$\Delta x = - H_j^{ - 1} \left[ {q_j + x_j \left( {x'_j H_j^{ - 1} x_j } \right)\left( {q_j - x'_j H_j^{ - 1} q_j } \right)} \right],$$ where As an initial approximation for xwe have found it convenient to ignore the fact that the data are constrained to lie on the surface of the reference sphere and to use the parameters of a least-squares plane through the given poles. Generalization of this approach to fitting variously constrained great and small circles is easily made. The relative merits of differently constrained fits to the same data can be tested approximately if it is assumed that the errors in the location of the poles are isotropic and normally distributed. It is thus possible to statistically assess the relative significance of conflicting structural models which predict different geometrical patterns of fabric elements.  相似文献   

Detecting nonrandom associations between proportions by tests of remaining-space variables     

Felix Chayes 《Mathematical Geosciences》1983,15(1):197-206

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The relation between c dimension and exchange components in micas     

Embaie Asmerom Ferrow 《Mineralogy and Petrology》1990,43(1):23-35

Summary A number of micas of varying compositions and polytypism have been selected from the literature for multiple linear regression analysis. The c dimension in micas is found to depend on the sizes of the interlayer cation, d_i, and tetrahedral cation, d_t, as well as on the hydroxyl content, [OH]. The regression equation obtained: c_r = 5.415 + 0.071[OH] + 2.098d_i + 2.335d_t with R² = 90.5%, shows that the three variables affect the c-axis dimension in the order d_t > d_i [OH]. Addition of 2- and 3-layer polytypes to the regression analysis reduces R² to 87.2%. Application of the regression analysis to synthetic Al-rich biotites from the literature shows that the amount of [A1^IVA1^VI]_1Y[Fe²⁺, MgSi]_–1y in solid solution is limited and always less than [A1^VIO]_1z[Fe²⁺, MgOH]_–1z (i.e. 0.35 > y z). The maximum value of the vector y in solution is slightly higher than that reported for natural Al-rich biotites.

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Die Beziehung zwischen der Gitterkonstante c und den Austauschkomponenten in Glimmern

Zusammenfassung Eine Anzahl von Glimmern unterschiedlicher Zusammensetzung und Polytypie wurde aus der Literatur für eine multiple lineare Regressionsanalyse ausgewählt. Es stellte sich heraus, dass in Glimmern die Gitterkonstante c von den Grössen des Zwischenschicht-Kations d_i und des tetraedrischen Kations d_t abhängt, ferner vorn Hydroxylgehalt, [OH]. Die erhaltene Regressionsgleichung c_r = 5,415 + 0,071 [OH] + 2,098d_i + 2,335d_t mit R² = 90,5% zeigt, dass die drei Variablen die Grösse der c-Achse in der Reihenfolge d_t > d_i [OH] beeinflussen. Der Einschluss von 2- und 3-Schicht Polytypen in die Regressionsanalysen verkleinert R² auf 87,2%. Die Anwendung der Regressionsanalysen auf synthetische Al-reiche Biotite aus der Literatur zeigt, der Betrag von [A1^IVA1^VI]_1y[Fe²⁺, MgSi]_–1y beschränkt und immer kleiner als [A1^VIO]_1z[Fe²⁺, MgOH]_–1z (mit 0,35 < y z) ist. Der Maximalwert des Vektors y in Lösung ist etwas grösser als jener, der für natürliche Al-reiche Biotite angegeben wurde.

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With 1 Figure  相似文献   

Examination of the Chayes-Kruskal procedure for testing correlations between proportions     

John O. Kork 《Mathematical Geology》1977,9(6):543-562

The Chayes-Kruskal procedure for testing correlations between proportions uses a linear approximation to the actual closure transformation to provide a null value,p _ij , against which an observed closed correlation coefficient,r _ij , can be tested. It has been suggested that a significant difference betweenp _ij andr _ij would indicate a nonzero covariance relationship between theith andjth open variables. In this paper, the linear approximation to the closure transformation is described in terms of a matrix equation. Examination of the solution set of this equation shows that estimation of, or even the identification of, significant nonzero open correlations is essentially impossible even if the number of variables and the sample size are large. The method of solving the matrix equation is described in the appendix.  相似文献   

Fe-Zn mixing energetics of the Iss phase in the system Cu-Fe-Zn-S     

B. Mishra  M. K. Panigrahi 《Contributions to Mineralogy and Petrology》1990,105(5):562-568

A thermodynamic analysis of the intermediate solid solution (Iss) of near-cubanite composition has been attempted by considering an Fe–Zn exchange equilibrium between Iss and sphalerite. The interchange free-energy parameter of Fe–Zn mixing in Iss (W^Iss) and the free energy of the exchange equilibrium (G_1,T ) have been deduced at 500, 600, 700 and 723° C using the compositional data of sphalerite and Iss from phase equilibrium experiments and by the standard method of linear regression analysis. For sphalerite, two independent activity-composition models have been chosen. The extracted values of G_1,T and W^Iss, using both models, are compared. Although the values match, the errors in the extracted parameters are relatively larger when Hutcheon's model is used. Both G_1,T and W^Iss show linear variations with temperature, as given by the following relations: G^1,T = –35.41 + 0.033 T in kcal (SE=0.229)W^ISS= 48.451 – 0.041 T in kcal (SE=0.565) Activity-composition relations and different mixing parameters have been calculated for the Iss phase. A large positive deviation from ideality is observed in Iss on the join CuFe₂S₃–CuZn₂S₃. No geothermometric application has been attempted in this study, even though Iss of cubanite composition (isocubanite) in association with sphalerite, pyrite and pyrrhotite is reported from seafloor hydrothermal deposits. This is due to the fact that: (a) the temperatures of formation of these deposits are significantly lower than 500° C, the lower limit of appropriate experimental data base; (b) microprobe data of the coexisting isocubanite and sphalerite in the relevant natural assemblages are not available.Symbols a _J ⁱ activity of component i in phase J - G_{1, T} standard free energy change of reaction (cal) - G^IM free energy of ideal mixing (cal) - G^EM free energy of excess mixing (cal) - G _M ^ex free energy of mixing (cal) - G _i excess free energy of mixing at infinite dilution (cal) - _i ^J activity coefficient of component i in phase J - _i ^{J, 0} standard chemical potential of component i in phase J (cal) - ; _i ^J chemical potential of component i in phase J (cal) - R universal gas constant (1.98717 cal/K·mol) - T temperature in degree (K) - W^J interchange free energy of phase J in (cal) - X _J ⁱ mole fraction of component i in phase J  相似文献   

Mean and turbulent velocity measurements of supersonic mixing layers   总被引：1，自引：0，他引：1  

S. G. Goebel  J. C. Dutton  H. Krier  J. P. Renie 《Mineralium Deposita》1994,29(1):263-272

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some largescale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity ( _u /U).List of Symbols a speed of sound - b total mixing layer thickness betweenU ₁ – 0.1U andU ₂ + 0.1U - f normalized third moment ofu-velocity,f u ³/(U)³ - g normalized triple product ofu ² v,g u ² v/(U)³ - h normalized triple product ofu v ², h uv' ²/(U)³ - l _u axial distance for similarity in the mean velocity - l _u axial distance for similarity in the turbulence intensity - M Mach number - M _c convective Mach number (for ₁=₂),M _c (U ₁–U ₂)/(a ₁+a ₂) - P static pressure - r freestream velocity ratio,rU ₂/U ₁ - Re unit Reynolds number,Re U/ - s freestream density ratio,s ₂/ ₁ - T _t total temperature - u instantaneous streamwise velocity - u deviation ofu-velocity,u u–U - U local mean streamwise velocity - U ₁ primary freestream velocity - U ₂ secondary freestream velocity - U average of freestream velocities, ¯U (U ₁ +U ₂)/2 - U freestream velocity difference,U U ₁ –U ₂ - v instantaneous transverse velocity - v deviation ofv-velocity,v v – V - V local mean transverse velocity - x streamwise coordinate - y transverse coordinate - y ₀ transverse location of the mixing layer centerline - ensemble average - ratio of specific heats - boundary layer thickness (y-location at 99.5% of free-stream velocity) - similarity coordinate, (y –y ₀)/b - compressible boundary layer momentum thickness - viscosity - density - standard deviation - dimensionless velocity, (U –U ₂)/U - 1 primary stream - 2 secondary stream A version of this paper was presented at the 11th Symposium on Turbulence, October 17–19, 1988, University of Missouri-Rolla  相似文献   

Size and shape effects in point load tests of irregular rock fragments   总被引：1，自引：0，他引：1  

L. A. Panek  T. A. Fannon 《Rock Mechanics and Rock Engineering》1992,25(2):109-140

Summary Point-load tests were performed on three hard rocks of the Lake Superior district, ironformation, metadiabase, and ophitic basalt. More than 500 irregular, mine-run fragments ranging in diameter up to about 250 mm were tested in the field, using a specially designed, semi-portable test rig. Results were analyzed by multiple regression techniques, seeking a best expression for the point-load strength in terms of a size effect and shape effects. Standard unconfined compression tests and Brazilian tests were also performed on the metadiabase and the basalt, three core sizes of each, in order to determine their respective size effects. The size-effect exponents for compression were found to be a variable characteristic of rock type, as previously reported for other rocks by the senior author, whereas the size-effect exponent in the point-load test was constant over all three rocks.Notation A Load-bearing area of prismatic compression specimen, mm² - Probability level of a statistical significance test - b, w Long and short prism dimensions, mm, in plane perpendicular to load - c _i ,c _L Exponent in equation for strength (coefficient, in the log-linear form) - d Diameter, mm - D, H Initial and final (at rupture) distance between the load points, mm - E Young's modulus, MPa - F Axis of the fracture surface normal toD, mm, point-load test - G, J Semiminor, semimajor, specimen axis, mm, perpendicular to direction of point load - h Height of prismatic compression specimen, mm - K Constant in linear regression model, basic rock strength parameter - L, M, S Long, intermediate, and short axes, of point-load-test specimen - log Natural (Napierian) logarithm - n Number of tests - v Poisson's ratio - P Resistance of test specimen at rupture, Newtons - Q Compressive strength, MPa, determined from unconfined compression test - R Multiple correlation ratio for a multilinear regression analysis - SE Standard error of estimate for a multilinear regression analysis - T Tensile strength, MPa, determined from diametral compressive test of core - t Thickness, mm - U Geometric mean diameter, mm, of the minimum cross section through the load points=(DG)^1/2 - V Geometric mean diameter, mm, of point-load specimen=(LMS)^1/3 - W Geometric mean diameter, mm, of the specimen midsection perpendicular to the point-load direction=(GJ)^1/2 - X, Y Geometric mean diameter, mm, of the fracture surface, estimated by (DF)^1/2, by (HF)^1/2 - Z _LM ,Z _RA , ... Differences between values of logK, used to express category effects, those attributed to specimen orientation and/or rock type  相似文献   

Some parameters of rockbursts derived from underground seismological measurements   总被引：2，自引：0，他引：2  

Karel Holub  Vladimír Petro&#x; 《Tectonophysics》2008,456(1-2):67

A total of 240 three-component recordings from 80 rockbursts, which occurred in various coal mines in the Ostrava-Karviná Coal Basin (Czech Republic) between 1993 and 2005, was used to examine the decrease in maximum particle velocities u_i (m/s) with a scaled distance of d = d/√E (m/√J) or d/³√E (m/³√J) and the rate of predominant frequencies of body waves. The energetic span of rockbursts was within the interval of E = 6.2 × 10³ − 5.0 × 10⁸ J, while calculated hypocentral distances d of four underground seismic stations varied from 0.6 to 7 km. The slopes b of regression straight lines for the maximum particle velocities u_i (m/s) of P- and S-waves in the bilogarithmic scale correspond to the values of − 1.004, − 1.297, − 1.183 and − 1.527. The results of the linear regression are as follows:

P_max-waves u_i = 1.184 × 10^− 4 × d^− 1.004 (m/s) (square root scaling)

P_max-waves u_i = 3.055 × 10^− 3 × d^− 1.297 (m/s) (cube root scaling)

S_max-waves u_i = 5.280 × 10^− 4 × d^− 1.183 (m/s) (square root scaling)

S_max-waves u_i = 2.397 × 10^− 2 × d^− 1.527 (m/s) (cube root scaling).

The evaluation of the abovementioned dynamic parameters was based on seismic events data gathered in the database of the regional seismic array, and calculations were carried out either by using special programs applied as part of the automated data processing in the computation center, or by usual linear regression approaches. The aim of the detailed analysis of the maximum particle velocity and predominant frequencies was a) to set up input data from underground seismological observations for laboratory experiments dealing with the comparison of rock mass behaviour under modeled laboratory conditions simulating manifestation of rockbursts, and b) to incorporate particle velocity into the design of support in order to control damage and evident devastation of workings by rockbursts. The investigation of peak particle velocities was based on the recognition that they are the best criterion to assess vibration damage to surface structures and in mines.  相似文献   

Measurements in a heated turbulent wall jet on a concave wall     

S. Okamoto  M. M. Gibson 《Mineralium Deposita》1994,29(1):291-297

The paper contains the results of extensive single-point hot-wire and resistance-thermometer measurements in a wall jet on a heated concave wall with an external free stream. It is found that the turbulence in the inner (wall) and outer layers is sensitive to the distortion produced by the curved wall, broadly confirming current views of these effects. The effect on the turbulence of streamline curvature is stabilising in the outer layer, destabilising in the inner. Consequently the point of zero shear stress is closer to the point of maximum mean velocity than in flat and convex wall jets with which these new results are compared. The rate of growth is about 80% of that of the equivalent flat wall flow, and about half that of the convex wall flow. Changes in the wall shear stress and heat flux, which are increased relative to the flat wall flow, are significant but less than the changes in the corresponding convex wall flow. The greatest changes occur in the triple products.List of Symbols c _f skin friction coefficient, 2 _w / U _M ² - q ² u ² +v ²+w ² - R radius of curvature of wall - r radius of curvature - St Stanton number,-q _w /c _p U _M (T –T _w ) - T mean temperature - U streamwise mean velocity - U _J initial wall-jet velocity - U ₁ initial free-stream velocity - U ₀ U _M –U _PW - u, v, w fluctuating velocity components - x, y distances measured along and normal to the wall - y _0.5,y _M wall-jet thicknesses defined in the text - y _S ,y _T wall-jet thicknesses defined in the text - T T _W –T - shear-layer thickness - ₂ momentum thickness - temperature fluctuation - M point of maximum velocity - P potential flow - s point of zero shear stress - W wall value - free stream value  相似文献   

Improvement in the frequency response of the electrochemical wall shear stress meter     

B. Py 《Mineralium Deposita》1994,29(1):281-285

One of the very few disadvantages of the mass-transfer transducer when compared with the hot-film sensor, is a slightly diminished frequency-response due to the higher Prandtl number encountered. Mass or thermal balance and transfer equations were solved first by Fortuna and Hanratty (1971) for small fluctuations of the wall shear. The solutions allow to make accurate corrections on the frequency spectra and the power of the fluctuations, but in different time. In this paper, the author deduces the frequency response of split rectangular electrodes and shows how a combination of signals improves the response at higher frequencies and makes it comparable to the thermal transducer with the same size, in the same fluid. Two experimental devices are described and compared. With these devices, the measurement of the wall shear fluctuations is improved in real time. Accurate determinations of turbulent power fluctuations and probability density spectra are feasible and illustrate the subject.List of Symbols A total area of the electrode - A _j area of the partj of the electrode - a coefficient - C concentration - C bulk concentration - c fluctuation of concentration - D diffusion coefficient - F Faraday's constant - f(n ⁺) transfer function - g gain of the differential electrode - I _j electrolysis current on the partj of the electrode - K transfert coefficient - k fluctuation ofK - l electrode length - n frequency - P _r Prandtl number - S wall shear - s fluctuation of the wall-shear - t time - x direction of the flow - y direction normal to the wall - phase delay - kinematic viscosity A version of this paper was presented at the 11th Symposium on Turbulence, University of Missouri-Rolla, 17–19 October 1988  相似文献