The adaptation of Pearce element ratio diagrams to complex high silica systems

Pearce element ratios (PERs, of Pearce 1968) express geochemical data in a form where variations in absolute compositions of an igneous suite can be evaluated. Generally the denominator value in the ratio is taken as a major element abundance, but it is argued here that Zr provides a more suitable choice. Zr remains incompatible in magmatic systems up to 68 wt.% SiO₂ because zircon fractionation can be suppressed by high melt temperatures and increased volatile contents. The use of Zr thus permits PER modelling to be extended to much higher levels of silica than previously investigated. However, such systems are more complex than those just involving simple basaltic magmas. Besides fractionation, the processes of magma mixing, combined assimilation and fractional crystallization, and the initial degree of partial melting in the mantle source must also be considered. To distinguish and evaluate these processes a set of example suites are investigated from a complex synextensional calc-alkaline province in the western USA. Samples within most individual suites can be modelled by fractionation, however a significant trend orthogonal to the main fractionation vector is also apparent, and open system processes are inferred. Successful modelling is achieved on an inter-suite basis using diagrams with axis functions of ([4(Ca+Na)+0.5(Fe+Mg)]/Zr versus (Si+Al)/Zr). Potential open system evolution paths between mafic end members and crustal contaminants are also displayed and evaluated on these same diagrams. The encouraging results suggest that such PER diagrams may be employed as a versatile tool for investigating the systematics of related igneous suites over a wide area.     

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

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.     

The Variance-Based Cross-Variogram: You Can Add Apples and Oranges

The variance-based cross-variogram between two spatial processes, Z₁ (·) and Z₂ (·), is var (Z₁ ( u ) – Z₂ ( v )), expressed generally as a bivariate function of spatial locations uandv. It characterizes the cross-spatial dependence between Z₁ (·) and Z₂ (·) and can be used to obtain optimal multivariable predictors (cokriging). It has also been called the pseudo cross-variogram; here we compare its properties to that of the traditional (covariance-based) cross-variogram, cov (Z₁ ( u ) – Z₁ ( v ), Z₂ ( u ) – Z₂ ( v )). One concern with the variance-based cross-variogram has been that Z₁ (·) and Z₂ (·) might be measured in different units (apples and oranges). In this note, we show that the cokriging predictor based on variance-based cross-variograms can handle any units used for Z₁ (·) and Z₂ (·); recommendations are given for an appropriate choice of units. We review the differences between the variance-based cross-variogram and the covariance-based cross-variogram and conclude that the former is more appropriate for cokriging. In practice, one often assumes that variograms and cross-variograms are functions of uandv only through the difference u – v. This restricts the types of models that might be fitted to measures of cross-spatial dependence.     

Silicate melts at magmatic temperatures: in-situ structure determination to 1651°C and effect of temperature and bulk composition on the mixing behavior of structural units

The abundance of coexisting structural units in K-, Na-, and Li-silicate melts and glasses from 25° to 1654°C has been determined with in-situ micro-Raman spectroscopy. From these data an equilibrium constant, K_x, for the disproportionation reaction among the structural units coexisting in the melts, Si₂O₅(2Q³)SiO₃(Q²)+SiO₂(Q⁴), was calculated (K_x is the equilibrium constant derived by using mol fractions rather than activities of the structural units). From ln K_x vs l/T relationships the enthalpy (H_x) for the disproportionation reaction is in the range of-30 to 30 kJ/mol with systematic compositional dependence. In the potassium and sodium systems, where the disproportionation reaction shifts to the right with increasing temperature, the H_x increases with silica content (M/Si decreases, M=Na, K). For melts and supercooled liquids of composition Li₂O·2SiO₂ (Li/Si=1), the H_x is indistinguishable from 0. By decreasing the Li/Si to 0.667 (composition LS3) and beyond (e.g., LS4), the disproportionation reaction shifts to the left as the temperature is increased. For a given ratio of M/Si (M=K, Na, Li), there is a positive, near linear correlation between the H_x and the Z/r² of the metal cation. The slope of the H_x vs Z/r² regression lines increases as the system becomes more silica rich (i.e., M/Si is decreased). Activity coefficients for the individual structural units, _i, were calculated from the structural data combined with liquidus phase relations. These coefficients are linear functions of their mol fraction of the form _i=a lnX _i+b, where a is between 0.6 and 0.87, and X _i is the mol fraction of the unit. The value of the intercept, b, is near 0. The relationship between activity coefficients and abundance of individual structural units is not affected by temperature or the electronic properties of the alkali metal. The activity of the structural units, however, depend on their concentration, type of metal cation, and on temperature.     

Cation diffusion in aluminosilicate garnets: experimental determination in spessartine-almandine diffusion couples,evaluation of effective binary diffusion coefficients,and applications

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     

Spatial and multivariate analysis of geochemical data from metavolcanic rocks in the Ben Nevis area, Ontario

A study of the lithogeochemistry of metavolcanics in the Ben Nevis area of Ontario, Canada has shown that factor analysis methods can distinguish lithogeochemical trends related to different geological processes, most notably, the principal compositional variation related to the volcanic stratigraphy and zones of carbonate alteration associated with the presence of sulphides and gold. Auto- and cross-correlation functions have been estimated for the two-dimensional distribution of various elements in the area. These functions allow computation of spatial factors in which patterns of multivariate relationships are dependent upon the spatial auto- and cross-correlation of the components. Because of the anisotropy of primary compositions of the volcanics, some spatial factor patterns are difficult to interpret. Isotropically distributed variables such as CO ₂ are delineated clearly in spatial factor maps. For anisotropically distributed variables (SiO ₂ ), as the neighborhood becomes smaller, the spacial factor maps becomes better. Interpretation of spatial factors requires computation of the corresponding amplitude vectors from the eigenvalue solution. This vector reflects relative amplitudes by which the variables follow the spatial factors. Instability of some eigenvalue solutions requires that caution be used in interpreting the resulting factor patterns. A measure of the predictive power of the spatial factors can be determined from autocorrelation coefficients and squared multiple correlation coefficients that indicate which variables are significant in any given factor. The spatial factor approach utilizes spatial relationships of variables in conjunction with systematic variation of variables representing geological processes. This approach can yield potential exploration targets based on the spatial continuity of alteration haloes that reflect mineralization.List of symbols c _i Scalar factor that minimizes the discrepancy between andU _i - D Radius of circular neighborhood used for estimating auto- and cross-correlation coefficients - d Distance for which transition matrixU is estimated - d _ij Distance between observed valuesi andj - E Expected value - E _i Row vector of residuals in the standardized model - F(d _ij) Quadratic function of distanced _ij F(d _ij)=a+bd _ij+cd _ij ² - L Diagonal matrix of the eigenvalues ofU - _i Eigenvalue of the matrixU;ith diagonal element ofL - N Number of observations - p Number of variables - Q Total predictive power ofU - R Correlation matrix of the variables - R _0j Variance-covariance signal matrix of the standardized variables at origin;j is the index related tod andD (e.g.,j=1 ford=500 m,D=1000 m) - R _1j Matrix of auto- and cross-correlation coefficients evaluated at a given distance within the neighborhood - R _m ² Multiple correlation coefficient squared for themth variable - S _i Column vectori of the signal values - s _k ² Residual variance for variablek - T _i Amplitude vector corresponding toV _i;ith row ofT=V ^–1 - T Total variation in the system - U Nonsymmetric transition matrix formed by post-multiplyingR ₀₁ ^–1 byR _ij - U _i Componenti of the matrixU, corresponding to theith eigenvectorV _i;U _i= _iV_iT_i - U* _i ComponentU _i multiplied byc _i - U _ij Sum of componentsU _i+U _j - V _i Eigenvector of the matrixU;ith column ofV withUV=VL - w Weighting factor; equal to the ratio of two eigenvalues - X _i Random variable at pointi - x _i Value of random variable at pointi - y _i Residual ofx _i - Z _i Row vectori for the standardized variables - z _i Standardized value of variable     

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

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     

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

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     

Analytical expressions for three-phase generalized relative permeabilities in water- and oil-wet capillary tubes

We analyze three-phase flow of immiscible fluids taking place within an elementary capillary tube with circular cross-section under water- and oil-wet conditions. We account explicitly for momentum transfer between the moving phases, which leads to the phenomenon of viscous coupling, by imposing continuity of velocity and shear stress at fluid-fluid interfaces. The macroscopic flow model which describes the system at the Darcy scale includes three-phase effective relative permeabilities, K _{i j,r} , accounting for the flux of the ith phase due to the presence of the jth phase. These effective parameters strongly depend on phase saturations, fluid viscosities, and wettability of the solid matrix. In the considered flow setting, K _{i j,r} reduce to a set of nine scalar quantities, K _{i j,r} . Our results show that K _{i j,r} of the wetting phase is a function only of the fluid phase own saturation. Otherwise, K _{i j,r} of the non-wetting phase depends on the saturation of all fluids in the system and on oil and water viscosities. Viscous coupling effects (encapsulated in K _{i j,r} with i ≠ j) can be significantly relevant in both water- and oil-wet systems. Wettability conditions influence oil flow at a rate that increases linearly with viscosity ratio between oil and water phases.     

An ion microprobe study of anhydrous oxygen diffusion in anorthite: a comparison with hydrothermal data and some geological implications

The diffusion rate of ¹⁸O tracer atoms in anorthite (An₉₇Ab₀₃) under anhydrous conditions has been measured using SIMS techniques. The tracer source was ¹⁸O₂ 98.4% gas at 1 bar, in the temperature range 1300° C–850° C. The measured diffusion constants are D ₀=1 _–0.6 ⁺¹ ×10^–9 m²s^–1 Q=236±8 kJ mol^–1 Comparison of these values with published data for ¹⁸O diffusion in anorthite under hydrothermal conditions shows that dry oxygen diffusivities are orders of magnitude lower than equivalent wet values at similar temperatures. The effect of these differences on oxygen isotope equilibration during cooling is discussed.     

Calculations of activity-composition relations in multi-site solid solutions: the example of AB2O4 spinels

A model to calculate activities in multisite solutions like spinels, from a general expression of the Gibbs free energy is developped. The free energy is written as that of a solution with ideal mixing of cations on each sublattice corrected by any suitable higher order terms. It is shown that activities of i^th end-member can be simply written: $${\text{act (}}i{\text{) = (}}\gamma _i {\text{/}}\gamma _i^{\text{0}} {\text{)}}\mathop \prod \limits_j (N_j /N_j^0 )^{P(j,{\text{ }}i)} .$$ N _j are site occupancy fractions; the γ _i are equal to one for the ideal multisite model and depend only on the higher order corrections to this model; ⁰ indicate values for the i ^th end member. The exponents in the matrix P are integers and constants. The activities cannot be expressed explicitly as function of the macroscopic composition. The site occupancy fractions which minimize the Gibbs free energy must be calculated first solving a set of non linear equations which define the internal equilibrium conditions. The (Fe²⁺, Mg) (Al, Cr, Fe³⁺) spinel are used to illustrate these calculations. For multicomponent AB₂O₄ spinels activity expressions derived for the reference ideal multisite mixing model are: $${\text{act (AB}}_{\text{2}} {\text{O}}_{\text{4}} {\text{) = }}\frac{{({\text{A}})[{\text{B}}]^2 }}{{({\text{A}})_0 [{\text{B}}]_0^2 }}$$ (A): fraction of tetrahedral sites occupied by A²⁺; [B]: fraction of octahedral sites occupied by B³⁺. Because the site occupancy fractions at equilibrium are not independent (but related by the internal equilibrium relations) many equivalent expressions of the activities can be obtained. Finally approximations proposed in the literature to obtain simple explicit activity-concentration relationships are discussed.     

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

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.     

Cesstibtantite—a geologic introduction to the inverse pyrochlores

Summary The crystal structure of cesstibtantite has been solved from diffractometer data collected on samples from Leshaia, Russia and the Tanco pegmatite, Manitoba. Cesstibtantite from the Leshaia pegmatite (type locality) hasa 10.515(2) Å, space groupFd3m, composition Cs_0.31(Sb_0.57Na_0.31Pb_0.02Bi_0.01)_O.91(Ta_1.88Nb_0.12)₂(O_5.69[OH, F]_0.31)₆(OH, F)_0.69, Z 8; its structure was refined toR 3.8,wR 4.3% using 96 observed (F > 3[F]) reflections (MoK). Cesstibtantite from the Tanco pegmatite hasa 10.496(1) Å, space groupFd3m, composition (Cs_0.22K_0.01)_0.23(Na_0.45Sb_0.39Pb_0.14· Ca_0.06Bi_0.02)_1.06(Ta_1.95Nb_0.05)₂(O_5.78[OH,F]_0.22)₆(OH,F)_0.55,Z 8; its structure was refined toR 3.9w R 3.7% using 104 observed reflections. Cesstibtantite differs from the normal pyrochlores in that it contains significant amounts of very large cations such as Cs. As these cations are too large (^VIII[r] > 1.60 Å) for the conventional [8]-coordinated A site, they occupy the [18]-coordinated site, which normally contains monovalent anions. Natural cesstibtantite samples are non-ideal in that both Cs and monovalent anions occur at the site; thus cesstibtantite is intermediate to thenormal pyrochlores (with only monovalent anions at the site) and theinverse pyrochlores (with only large cations at the site).

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Cesstibtantit—eine geologische Einfiihrung in die inversen Pyrochlore

Zusammenfassung Die Kristallstruktur von Cesstibtantit wurde auf der Basis von Diffraktometerdaten von Proben von Leshaia, Russland and dem Tanco Pegmatit, Manitoba, gelöst. Cesstibtantit aus dem Leshaia Pegmatit (Typlokalität) hat a 10.515(2) Å, RaumgruppeFd3m, die Zusammensetzung CS_0.31(Sb_0.57Na_0.31Pb_0.02Bi_0.01)_0.91(Ta_1.88Nb_0.12)₂· (O_5.69OH, F_0.31)₆(OH, F)_0.69 Z 8; die Struktur wurde aufR 3.8,wR 4.3% verfeinert unter Benützung von 96 beobachteten Reflexen. Cesstibtantit vom Tanco Pegmatit hat a 10.496(1) Å, RaumgruppeFd3m, die Zusammensetzung (Cs_0.22K_0.01)_0.23(Na_0.45· Sb_0.39Pb_0.14Ca_0.06Bi_0.02)_1.06(Ta_1.95Nb_0.05)₂(O_5.78OH,F_0.22)₆(OH,F)_0.55,Z 8; seine Struktur wurde aufR 3.9wR 3.7% auf der Basis von 104 beobachteten Rettexen verfeinert. Cesstibtantit unterscheidet sich von normalen Pyrochloren insofern, als er signifikante Mengen von sehr großen Kationen, wie z.B. Cs enthält. Da these Kationen zu groß sind (^VIII r 1.60 Å) für eine konventionelle [8]-koordinierteA Stelle, nehmen she die [18]-koordinierten Positionen ein, welche normalerweise monovalente Anionen enthalten. Natürliche Cesstibtantitproben sind nicht ideal insofern als sowohl Cs als auch monovalente Anionen in der Position vorkommen. Somit ist Cesstibtantit intermediär zu den normalen Pyrochloren (mit nur monovalenten Anionen auf der Position) and den inversen Pyrochloren (mit ausschließlichen großen Kationen an der Position).

     

Über p-Veatehit,eine neue Veatehit-Varietät aus dem Zechsteinsalz

Zusammenfassung Im Älteren Steinsalz von Reyershausen bei Göttingen wurde eine neue Veatchit-Varietät gefunden mita ₀ = 6,721 Å,b ₀ = 20,81 Å,c ₀ = 6,64₇ Å, = 119° 4; Raumgruppe oderP2₁,Z = 4[(Sr, Ca) O · 3 B₂O₃ · 2 H₂O]. (010) ist die Ebene der vollkommenen Spalt-barkeit. Die Polymorphie der Veatehit-Minerale wird geometrisch durch geringfügige Deformationen der rhombischen Raumgruppe (bzw.A2₁ a m) erklärt.Der neue Vertreter wirdp-Veatehit (mit einfach-primitivem Raumgitter) genannt im Unterschied zum Original-Veatehit, der in die Raumgruppe gehört und dessen Symametrieebene senkrecht auf der vollkommenen Spaltebene steht.     

Graphical estimations of magma densities and compositional expansion coefficients

Assuming that the partial molar volume of each chemical component in a magma is constant, the magma density, _m , is expressed as 1/ _m =C _i / _fi , whereC _i is the weight fraction, and _fi is the fractionation density of thei ^th component. Using this linear relationship between 1/ and weight fraction, the density change due to addition or subtraction of any component can be graphically estimated on 1/ vs oxide wt% diagrams. The compositional expansion coefficient of thei ^th component, _fi , is expressed as _i = _m / _fi –1. The compositional expansion coefficient of H₂O has a much larger absolute value than those of any other oxide or mineral components, showing that addition of a small amount of H₂O can significantly decrease magma density. These simple expressions facilitate the estimation of magma densities during fractionation.     

On comparative probabilities for normal confidence intervals by pearson's Types III and VII, and the Edgeworth series models for biotite data

Biotite crystals were counted in standard thin sections which originated from the diamond drill core of the mafic norite formation at Strathcona mine, Sudbury Nickel Irruptive. Pearson's method of moments is suitable to fit Types III and VII to the biotite data and its log ₁₀ transformation values, as the number of samples (thin sections)is large (351).Based on the two models and the Edgeworth series (utilizing the log ₁₀ data)probability values p,that biotite occurrences lie in the interval mean ± Z standard deviations is derived. Results are compared with the usual normal probability values p_Z corresponding to Zand it is shown that the Edgeworth series generated the largest pvalues for intervals when p_Z values are large; for intermediate or lower p_Z s. Types VII and III models produced larger ps, relative to the Normal and the Edgeworth series.     

Orschallite,Ca3(SO3)2 · SO4 · 12H2O,a new calcium-sulfite-sulfate-hydrate mineral

Summary The new mineral orschallite, Ca₃(SO₃)₂SO₄ · 12H₂O, was found at the Hannebacher Ley near Hannebach, Eifel, Germany. Crystal structure analysis of the mineral, chemical analysis and water determination on synthetic material gave the composition Ca₃(SO₃)₂SO₄ · 12H₂O. The mineral crystallizes in space group with a = 11.350(1), c = 28.321(2) Å, V = 3159.7 ų, Z = 6, D_c = 1.87 Mg/m³, D_m = 1.90(3) Mg/m³. It is uniaxial positive with the optical constants = 1.4941, = 1.4960(4). The strongest lines in the powder pattern are (d-value (Å), I, hkl) 5.73, 100, 1 0 4/8.11, 80, 0 1 2/2.69, 80, 3 0 6/3.63, 60, 1 1 6/3.28, 40, 3 0 0. Refinement of the crystal structure led to a weighted residual of R_w = 0.043 for 600 observed reflections with I > 2(I) and 52 variable parameters.

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Orschallit, Ca₃(SO₃)₂SO₄ · 12H₂O, ein neues Kalzium-Sulfat-Sulfat-Hydrat-Mineral

Zusammenfassung Das neue Mineral Orschallit, Ca₃(SO₃)₂SO₄ · 12H₂O, wurde in der Hannebacher Ley bei Hannebach, Eifel, Deutschland gefunden. Eine Analyse der Kristallstruktur an einem Einkristall des natürlichen Materials, chemische Analyse und Wasserbestimmung an synthetischem Material ergaben die Zusammensetzung Ca₃(SO₃)₂SO₄ · 12H₂O. Das Mineral kristallisiert in der Raumgruppe mit a = 11.350(1), c = 28.321(2) Å, V = 3159.7 ų, Z = 6, D_c = 1.87 Mg/m³, D_m = 1.90(3) Mg/m³. Es ist optisch einachsig mit den optischen Konstanten = 1.4941, = 1.4960(4). Die stärksten Linien des Pulver-diagramms liegen bei (d-Wert (Å), I, hkl) 5.73, 100, 1 0 4/8.11, 80, 0 1 2/2.69, 80, 3 0 6/3.63, 60; 1 1 6/3.28, 40, 3 0 0. Die Verfeinerung der Kristallstruktur ergab einen gewichteten Residualwert R_w = 0.043 für 600 beobachtete Reflexe mit I > 2(I) und 52 variable Parameter.

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Upper crustal abundances of trace elements: A revision and update

We report new estimates of abundances of rarely analyzed elements (As, B, Be, Bi, Cd, Ge, In, Mo, Sb, Sn, Te, Tl, W) in the upper continental crust based on precise ICP-MS analyses of well-characterized upper crustal samples (shales, pelites, loess, graywackes, granitoids and their composites) from Australia, China, Europe, New Zealand and North American. Obtaining a better understanding of the upper crustal abundance and associated uncertainties of these elements is important in placing better constraints on bulk crust composition and, from that, whole Earth models of element cycling and crust generation. We also present revised abundance estimates of some more commonly analyzed trace elements (Li, Cr, Ni, and Tm) that vary by > 20% compared to previous estimates. The new estimates are mainly based on significant (r² > 0.6) inter-element correlations observed in clastic sediments and sedimentary rocks, which yield upper continental crust elemental ratios that are used in conjunction with well-determined abundances for certain key elements to place constraints on the concentrations of the rarely analyzed elements. Using the well-established upper crustal abundances of La (31 ppm), Th (10.5 ppm), Al₂O₃ (15.40%), K₂O (2.80%) and Fe₂O₃ (5.92%), these ratios lead to revised upper crustal abundances of B = 47 ppm, Bi = 0.23 ppm, Cr = 73 ppm, Li = 41 ppm, Ni = 34 ppm, Sb = 0.075, Te = 0.027 ppm, Tl = 0.53 ppm and W = 1.4 ppm. No significant correlations exist between Mo and Cd and other elements in the clastic sediments and sedimentary rocks, probably due to their enrichment in organic carbon. We thus calculate abundances of these elements by assuming the upper continental crust consists of 65% granitoid rocks plus 35% clastic sedimentary rocks. The validity of this approach is supported by the similarity of SiO₂, Al₂O₃, La and Th abundances calculated in this way with their upper crustal abundances given in Rudnick and Gao [Rudnick, R., Gao, S., 2003. Composition of the continental crust. In: Rudnick, R.L. (Ed.), The Crust. In: Holland, H.D., Turekian, K.K. (Eds.), Treatise on Geochemistry, vol. 3. Elsevier–Pergamon, Oxford, pp. 1–64.]. The upper crustal abundances thus obtained are Mo = 0.6 ppm and Cd = 0.06 ppm. Our data also suggest a  20% increase of the Tm, Yb and Lu abundances reported in Rudnick and Gao [Rudnick, R., Gao, S., 2003. Composition of the continental crust. In: Rudnick, R.L. (Ed.), The Crust. In: Holland, H.D., Turekian, K.K. (Eds.), Treatise on Geochemistry, vol. 3. Elsevier–Pergamon, Oxford, pp. 1–64.].     

The structure type of heulandite B (heat-collapsed phase)

Summary If heulandite is heated to 300–400°C for at least 12 hours it is transformed to heulandite B, the ideal composition of which is (Ca, Na₂)Al₂Si₇O₁₈·2H₂O. Heulandite B crystallizes monoclinic,C2/m being the most probable space group; lattice constants:a=16.95,b=16.42,c=7.28 , =117°47;Z=4. The most important alteration that heulandite undergoes during the change of phase is a rotation of its fundamental polyhedral unit (formed of 4- and 5-membered tetrahedral rings). As a result of this rotation the geometrical shape of the two kinds of channels parallel toc is changed considerably; their section, which in the low-temperature phase is practically circular, becomes markedly elliptical, with the major axis of the ellipse parallel to [102] for the larger channels, and parallel tob for the smaller channels.

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Der Strukturtyp des Heulandits B (wärmegeschrumpfte Phase)

Zusammenfassung Wenn Heulandit mindestens 12 Stunden auf 300–400°C erhitzt wird, wandelt er sich in Heulandit B um; dieser hat die ideale chemische Zusammensetzung (Ca, Na₂)Al₂Si₇O₁₈·2H₂O. Heulandit B kristallisiert monoklin, wahrscheinliche Raumgruppe istC2/m; Gitterkonstanten:a=16,95,b=16,42,c=7,28 , =117°47;Z=4. Die wichtigste Änderung des Heulandits bei dieser Phasenumwandlung ist eine Drehung seiner Hauptpolyedergruppe, die aus Vierer- und Fünferringen aufgebaut ist. Als Folge dieser Drehung ändert sich die geometrische Gestalt der beiden Arten von Kanälen parallelc beträchtlich; ihr Querschnitt, der in der Tieftemperatur-Phase praktisch kreisförmig ist, wird deutlich elliptisch, und zwar für die größeren Kanäle mit größerer Ellipsenachse parallel [102] und für die kleineren Kanäle mit größerer Ellipsenachse parallelb.

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