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     

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.     

Oxygen isotope variations in granulite-grade iron formations: constraints on oxygen diffusion and retrograde isotopic exchange

The oxygen isotope ratios of various minerals were measured in a granulite-grade iron formation in the Wind River Range, Wyoming. Estimates of temperature and pressure for the terrane using well calibrated geothermometers and geobarometers are 730±50° C and 5.5±0.5 kbar. The mineral constraints on fluid compositions in the iron formation during retrogression require either very CO₂-rich fluids or no fluid at all. In the iron formation, isotopic temperature estimates from quartz-magnetite fractionations are controlled by the proximity to the enclosing granitic gneiss, and range from 500° C ( _{qz – mt}=10.0) within 2–3 meters of the orthogneiss contact to 600° C ( _{qz – mt}=8.0) farther from the contact. Temperature estimates from other isotopic thermometers are in good agreement with those derived from the quartz-magnetite fractionations.During prograde metamorphism, the isotopic composition of the iron formation was lowered by the infiltration of an external fluid. Equilibrium was achieved over tens of meters. Closed-system retrograde exchange is consistent with the nearly constant whole-rock ¹⁸O_wr value of 8.0±0.6. The greater _qz-mt values in the iron formation near the orthogneiss contact are most likely due to a lower oxygen blocking temperature related to greater exchange-ability of deformed minerals at the contact. Cooling rates required to preserve the quartz-magnetite fractionations in the central portion of the iron formation are unreasonably high (800° C/Ma). In order to preserve the 600° C isotopic temperature, the diffusion coefficient D (for -quartz) should be two orders of magnitude lower than the experimentally determined value of 2.5×10^–16 cm²/s at 833 K. There are no values for the activation energy (Q) and pre-exponential diffusion coefficient (D ₀), consistent with the experimentally determined values, that will result in reasonable cooling rates for the Wind River iron formation. The discrepancy between the diffusion coefficient inferred from the Wind River terrane and that measured experimentally is almost certainly due to the enhancement of exchange by the presence of water in the laboratory experiments. Cooling rate estimates were also determined for iron formation retrograded under water-rich conditions. Application of the experimentally determined data to these rocks results in a reasonable cooling rate estimate, supporting the conclusion that the presence of water greatly enhances oxygen diffusion.Contribution 441 from the Mineralogical Laboratory, University of Michigan     

Granulite facies amphibole and biotite equilibria,and calculated peak-metamorphic water activities

Samples located near the Oregon Dome anorthosite massif in the south-central Adirondack Mountains, New York contain the fluid-buffering mineral assemblages: amphibole + clinopyroxene + orthopyroxene + quartz or biotite + quartz + orthopyroxene + K-feldspar. These rocks were metamorphosed under granulite-facies conditions (T=725°–750°C, P=7.5 kbar) during the Grenville orogeny. The Mg-rich nature of amphiboles, micas, and pyroxenes allow accurate calculation of water activities because corrections for the effects of solid solution are relatively small. The activity of water was low during the peak of granulite-facies metamorphism, with H₂O0.15±0.14. Wollastonite occurrences indicate that the CO₂ was low (<0.3) in nearby rocks, demonstrating that large quantities of CO₂ did not infiltrate in a pervasive manner. The combination of low H₂O with low CO₂ is consistent with the hypothesis that magmatic processes were dominant, generating dry, fluid-absent conditions.Abbreviations fi Fugacity of species i in a fluid - Xi mole fraction of component i in a phase - T temperature - P lithostatic pressure - P _F fluid pressure - _i ^x activity of component i phase X     

Basaltic glass with high-temperature equilibrated immiscible sulphide bodies with native iron from disko,central West Greenland

Immiscible sulphide bodies show eutectic quench textures in a basaltic glass rock (mg=66) from a native iron-bearing dyke chilled at T=1,200° C and P=250 bars. The sulphide bodies are composed of troilite (90–91%), iron (9–10%) and very scarce vanadium-rich chromite and approach a ternary cotectic in the Ni-poor part of the system Fe-Ni-S. Transition element partition between olivine (mg=83), silicate glass (mg=59) and sulphide blebs indicate that the phases were equilibrated at 1,200° C. D _{vanadium(olivine/glass)} is close to unity and reflect the reducing nature of the rock, for which estimates of f _O210^{–12 to –13} and f _S210^–5 have been made. D _{nickel, cobalt, copper (sulphide/glass)}=4,300, 230 and 380 respectively, are much higher than reported experimentally determined D's on_{monosulphide/basalt glass} at the same temperature and show increasing positive deviation (Ni>Co>Cu) with the increasingly siderophile character of the elements. K _{Dnickel-iron (sulphide/olivine)}=63 is much higher than an experimentally reported value (33) and comparison with published thermodynamic data on Ni-partition between olivine and iron metal suggests that the positive deviation is roughly proportional to the excess metal component in the sulphide melt. The occurrence of strongly Ni-depleted reduced basalts on Disko shows that fractionation of metal and sulphides was a common and geologically important process.     

An experimental study of the diffusion of oxygen in quartz and albite using an overgrowth technique

Diffusion rates of¹⁸O tracer in quartz ( c, 1 Kb H₂O) and Amelia albite ( 001, 2 Kb H₂O) have been measured, using Secondary Ion Mass Spectrometry (SIMS). A new technique involving hydrothermal deposition of labelled materials has removed the possibility of pressure solution-reprecipitation processes adversely affecting the experiments. Reported diffusion constants are:-quartz ( c), ,Q=98±7 KJ mol^–1 (600–825° C, 1 Kb); Amelia albite ( 001), ,Q=85±7 KJ mol^–1, (400–600° C, 2 Kb). Measured quartz¹⁸O diffusivities decrease discontinuously at the- transition, reflecting strong structural influences. The reported albite data agree with previously recorded studies, but-quartz data indicate significantly lower activation energies. Possible causes of this discrepancy, and some geological consequences, are noted.     

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     

Partition of Ni between olivine and sulfide: equilibria with sulfide-oxide liquids

The partition of Ni between olivine and monosulfide-oxide liquid has been investigated at 1300–1395° C, =10^–8-9–10^–6.8, and =10^–2.0–10^–0.9, over the composition range 20–79 mol. % NiS. The product olivine compositions varied from Fo98 to Fo59 and from 0.06 to 3.11 wt% NiO. The metal/sulfur ratio of the sulfide-oxide liquid increases with increase in , decrease in , and increase in NiS content. The Ni/Fe exchange reaction has been perfectly reversed using natural olivine and pure forsterite as starting materials. The FeO and NiO contents of olivine from runs equilibrated at the same and form isobaric distributions with NiS content, which, to a first approximation, are dependent at constant temperature and total pressure on a variable term, –0.5 log ( / ). The Ni/Fe distribution coefficient (K _D3) exhibits only a weak decrease from 35 to 29 with increase in from the IW buffer to close to the FMQ buffer. At values higher than FMQ, the sulfide-oxide liquid has the approximate composition (Ni,Fe)₃±_xS₂K _D358. The present K _D3 vs O/(S+O) data define a trend which extrapolates to K _D320 at 10 wt% oxygen in the sulfide-oxide liquid. The compositions of olivine and Ni-Cu sulfides associated with early-magmatic basic rocks and komatiites are consistent, at 1400° C, with a value of -log ( / ) of about 7.7, which is equivalent to 0.0 wt% oxygen in the hypothesized immiscible sulfide-oxide liquid. Therefore, K _D3 would not be reduced significantly from the 30 to 35 range for sulfide-oxide liquids with low oxygen contents.     

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.     

Thermal expansion of Neapolitan Yellow Tuff

Summary In saturated rocks and soils it is possible to define different coefficients of thermal expansion depending on the drainage conditions. This topic is first examined from the theoretical point of view with regard to an ideal isotropic thermo-elastic porous medium. Some special features of the behaviour of natural soils and rocks during thermal expansion tests are subsequently discussed. An experimental evaluation of some of these coefficients is presented in the second part of the paper. The material investigated is a pyroclastic rock, the so-called Neapolitan Yellow Tuff. Thermal expansion coefficient in drairend conditions has been evaluated, when this material is saturated with water. The e pressure increase induced by heating has been measured in undrained tes temperatures investigated range between room temperature up to 225°C.Different types of apparatus have been used and, when possible, a comparison between the results has been proposed. The results obtained in undrained thermal expansion tests are in agreement with theoretical predictions. This research is part of an on-going study of the complex phenomena known as Bradyseism, which is occurring in a volcanic area a few kilometers from Naples (Italy). Some considerations on this phenomenon are drawn in the last paragraph of the paper.List of Symbols _l linear thermal expansion coefficient - _s volumetric thermal expansion coefficient of the solid phase - _ss volumetric drained thermal expansion coefficient of the solid skeleton - _st volumetric drained thermal expansion coefficient that takes into account variations of porosity induced by heating - _t volumetric drained thermal expansion coefficient of the whole system - _u volumetric undrained thermal expansion coefficient of the whole system - _v volumetric thermal expansion coefficient - _w volumetric thermal expansion coefficient of the water - _l ^* volumetric thermal expansion coefficient of the distilled water - Biot's coefficient - _d dry specific gravity - _s specific gravity of the solid phase - _r ^' uniaxial compressive strength - _r ^' yield stress in isotropic compression - B _T parameter relating undrained thermally generated pore pressure with temperature change - d ₀ maximum uplift during Bradyseismic crises - d _f residual uplift during Bradyseismic crises - K _s compressibility modulus of the solid phase - K _ss compressibility modulus of the solid skeleton - K _w compressibility modulus of the water - n porosity - T temperature - T ₀ initial temperature in thermal expansion, tests performed in thermal expansion cell - T _m temperature at which the volume of waterV _Eexpelled from thermal expansion cell. is measured - V volume of the solid skeleton - V _E volume expelled from thermal expansion cell - V ₀ volume of the expansion cell at temperatureT ₀ - V _s volume of the solid phase     

Numerical modeling of three-dimensional contaminant migration from dissolution of multicomponent NAPL pools in saturated porous media

A three-dimensional model for contaminant transport resulting from the dissolution of multicomponent nonaqueous phase liquid (NAPL) pools in three-dimensional saturated subsurface formations is developed. The solution is obtained numerically by a finite-difference scheme, and it is suitable for homogeneous porous media with unidirectional interstitial velocity. Each dissolved component may undergo first-order decay and may sorb under local equilibrium conditions. It is also assumed that the dissolution process is mass transfer limited. The nonaqueous phase activity coefficients of the NAPL pool components are evaluated at each time step. The model behavior is illustrated through a synthetic example with a NAPL pool consisting of a mixture of TCA (1,1,2-trichloroethane) and TCE (trichloroethylene). The numerical solution presented in this work is in good agreement with a recently developed analytical solution for the special case of a single component NAPL pool. The results indicate the importance of accounting for the necessary changes in the organic phase activity which significantly affects the equilibrium aqueous solubility.Notation C liquid phase solute concentration (solute mass/liquid volume) (M L^–3) - C _s single component aqueous saturation concentration (solubility) (M L^–3) - C ^w equilibrium aqueous solubility (M L^–3) - D molecular diffusion coefficient (L² t ^–1) - D _e effective molecular diffusion coefficient (L² t ^–1) - D _x longitudinal hydrodynamic dispersion coefficient (L² t ^–1) - D _y lateral hydrodynamic dispersion coefficient (L² t ^–1) - D _z hydrodynamic dispersion coefficient in the vertical direction (L² t ^–1) - I() integer mode arithmetic operator - k local mass transfer coefficient (Lt ^–1) - k ^* average mass transfer coefficient (Lt ^–1) - L length - l _x ,l _y pool dimensions inx andy directions (L) - ll _x ,l _y x andy Cartesian coordinates of the pool origin (L) - M number of moles remaining in a pool (moles) - M initial number of moles (moles) - n finite-difference scheme time level - R retardation factor (dimensionless) - t time (t) - U _x average interstitial velocity (Lt ^–1) - x, y, z spatial Cartesian coordinates (L) - X dimensionless mole fraction - dimensionless activity coefficient - _w viscosity of water (=0.8904 cp at 25°C) - decay coefficient (t ^–1) - ^* tortuosity ( 1) - i,j, k finite-difference scheme grid indicators - p component number indicator - P total number of components - s pure single component - o nonaqueous phase - w aqueous phase     

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     

The potassic feldspar in metamorphic rocks from the western Hohe Tauern area,eastern Alps

Zusammenfassung Es wurden Kalifeldspäte aus Orthogneisen, Paragneisen und Glimmerschiefern des westlichen Tauemfensters (Hohe Tauern, Tirol) mit optischen und röntgenographischen Methoden im Hinblick auf ihren Strukturzustand untersucht.Es zeigte sich, daß in den Randbereichen des Tauemfensters in Gesteinen der Grünschieferfazies weitgehend geordneter Mikroklin mit einem optischen Achsenwinkel 2 V_x 80°, Auslöschungswinkel Z (010)=15–20°, Doppelbrechung n_z-n_x= 0,0065, Triklinität=0,90-–0,95, ca. 0,88 Al auf T₁O-Position und einem Ab-Gehalt von ca. 5 Gew.% auftritt. Dagegen wurden in Gesteinen der schwachtemperierten Amphibolitfazies des zentralen Bereichs Orthoklase bis intermediäre Mikrokline mit stark schwankenden optischen Eigenschaften, mit Triklinitäten zwischen 0 und 0,7, 0,8 bis 0,9 Al in T₁-Positionen, 0,45–0,8 Al auf T₁O und Ab-Gehalten von ca. 10 Gew.% festgestellt. Die Kalifeldspatkristalle zeigen ungleichmäßige Auslöschung mit Winkeln von Z (010) zwischen 0 und 15°, 2 V_x zwischen 50 und 75° und n_z-n_x=0,005 bis 0,006. Teilweise ist Zonarbau mit geringerer Triklinität am Kornrande erkennbar. Diese undulös auslöschenden Kalifeldspäte enthalten einzelne schmale Lamellen von maximal triklinem Mikroklin mit Z (010)=15–20° und n_z-n_x= 0,006–0,007.Die Grenze zwischen dem Verbreitungsgebiet von maximalem Mikroklin einerseits und Orthoklas bis intermediärem Mikroklin andererseits verläuft in den westlichen Hohen Tauern ungefähr konform mit der Albit-Oligoklas-Grenze (Morteani &Raase, 1974) und mit der aus Sauerstoff-Isotopen-Untersuchungen bestimmten 500° C-Isotherme (Hoernes &Friedrichsen, 1974).

---

The potassic feldspar in orthogneisses, paragneisses, and mica schists from the western Tauernfenster (Hohe Tauern, Tyrol) were studied by optical and X-ray methods with regard to their structural state and in relation to grade of metamorphism.In the peripheral region of the Tauernfenster in greenschist-facies rocks highly triclinic microcline occurs with an optic angle 2 V_x of about 80°, extinction angle Z (010) =15–20°, birefringence n_z-n_x=0.0065, triclinicity=0.90–0.95, approx. 0.88 Al in T₁O-site, and an Ab-content of about 5 wt.%. In the central area with rocks of the low-grade amphibolite facies, on the other hand, orthoclase to intermediate microcline with highly variable optical properties, triclinicities in the range of 0–0.7, 0.8–0.9 Al in T₁-sites, 0.45–0.8 Al in T₁O-site, and an Ab-content of about 10 wt.% was recognized. The K-feldspar grains have nonuniform extinction Z (010) scattering in the range of 0–15°, 2 V_x in the range of 50–75°, and n_z-n_x= 0.005–0.006. Sometimes a zonal structure with lower triclinicity exists at the rim. These undulatory K-feldspar grains usually contain small lamellae of highly triclinic microcline with Z (010) =15–20° and n_z-n_x=0.006–0.007.From the occurrence of maximum microcline and of orthoclase to intermediate microcline in the Hohe Tauern area an isograd was defined that is approximately conformable with the albite-oligoclase isograd (Morteani &Raase, 1974) and with the 500° C isotherm based on oxygen isotope analyses (Hoernes &Friedrïchsen, 1974).

---

Résumé Les feldspaths potassiques d'orthogneiss, de paragneiss et de micaschistes de la Fenêtre des Tauern occidental (Hohe Tauern, Tirol) ont été étudiés du point de vue de leur état structural.Dans les roches du faciès schistes verts de la région périphérique de la Fenêtre des Tauern les microclines sont caractérisés par un angle des axes optiques 2 V_p =80°, un angle d'extinction n_g (010)=15–20°, une biréfringence n_g-n_p=0,0065, une triclinicité= 0,90–0,95, 0,88 Al dans le site T₁O et par une teneur en albite d'environ 5%. Au contraire, dans les roches du faciès amphibolite à faible degré de la région centrale, ont été observées des orthoses allant à des microclines intermédiaires avec des propriétés optiques très variables, un degré de triclinicité de 0 à 0,7, 0,8–0,9 Al dans les sites T₁, 0,45–0,8 Al dans T₁O et avec une teneur en albite d'environ 10%.Les cristaux de feldspath montrent une extinction irrégulière avec des angles Z (010) variable de 0 à 15°, 2 V_p de 50 à 75° et n_g-n_p=0,005–0,006.On peut voir quelquefois une structure zonée avec une triclinicité moindre au bord des cristaux. Ces feldspaths potassiques contiennent de minces lamelles de microcline à triclinicité maximum, avec n_g (010)=15–20° et n_g-n_p 0,006–0,007.La limite entre les régions à microcline maximum d'une part, et à orthose ou microcline intermédiaire d'autre part, suit, dans les Hohe Tauern, sensiblement l'isograde albite-oligoclase (Morteani &Raase, 1974) et, l'isotherme de 500° C telle qu'elle fut determinée les isotopes de l'oxygène (Hoernes &Friedrichsen, 1974).

---

, ( , ) ., 2 V_x80°, Z (010)=15–20°, n_z–n_x=0,0065, =0,90–0,95, 0,88 l T₁O Ab 5 .-%. , 0 0,7, 0,8-0,9 1 T₁ l 10 .-%. Z V (010) 0 15°, 2 V_x 50 75° n_z–n_x=0,005–0,006. . Z V (010) =15-20° n_z–n_x=0,006–0,007. , Morteani & Raase (1974) 500° , Hoernes & Friedrichsen (1974).

     

Experimental determination of cation diffusivities in aluminosilicate garnets

Data from experimentally-induced diffusion profiles at approximately 40 Kbar, 1,300–1,500° C in spessartine-almandine couples and a pyrope-almandine couple at 40 Kbar, 1,440° C, described in Part I, were used to derive tracer diffusion coefficients (D ^*) of Fe, Mn and Mg in garnet. The experimental data were fitted by numerical simulations that model multicomponent, compositionally-dependent difussion, including the effects of nonideal thermodynamic mixing. The simulations use the formalism of irreversible thermodynamics and an eigenvector technique of solution. We were able to fit the asymmetrical spessartine-almandine profiles using constant D ^* and either the Darken/Hartley-Crank or Manning-Lasaga models relating D ^* and interdiffusion coefficients, and both models yielded D _Mg ^* consistent with the direct measurement of D _Mg ^* in by Cygan and Lasaga (1985) at lower temperatures (750–900° C). The results (equations 4.1–4.3 and Table 1) indicate that D _Fe ^* D _Mg ^* <D _Mn ^* and Q _FeQ _Mg>Q _Mn, where Q is the activation energy. In contrast, the asymmetry of pyrope-almandine profiles is too great to fit with either tracer model assuming constant D ^* and indicates that D _Mg ^* is similar to its value in spessartine-almandine couples but D _Fe ^* is an order of magnitude less. The fit also suggests that D _Ca ^* < D _Fe ^* Mg ^* in pyrope-almandine couples. Synthesis of data from the two types of diffusion couples suggests that D _Mg ^* is insensitive to compositional changes, whereas D _Fe ^* is affected by Mn/Mg and Fe/Mg ratios and probably by other factors. These compositional effects on tracer coefficients are compatible with those documented by Morioka (1983) for cation diffusion in olivine.     

H<Subscript>2</Subscript>O diffusion in peralkaline to peraluminous rhyolitic melts

The diffusion of water in a peralkaline and a peraluminous rhyolitic melt was investigated at temperatures of 714–1,493 K and pressures of 100 and 500 MPa. At temperatures below 923 K dehydration experiments were performed on glasses containing about 2 wt% H₂O _t in cold seal pressure vessels. At high temperatures diffusion couples of water-poor (<0.5 wt% H₂O _t ) and water-rich (~2 wt% H₂O _t ) melts were run in an internally heated gas pressure vessel. Argon was the pressure medium in both cases. Concentration profiles of hydrous species (OH groups and H₂O molecules) were measured along the diffusion direction using near-infrared (NIR) microspectroscopy. The bulk water diffusivity () was derived from profiles of total water () using a modified Boltzmann-Matano method as well as using fittings assuming a functional relationship between and Both methods consistently indicate that is proportional to in this range of water contents for both bulk compositions, in agreement with previous work on metaluminous rhyolite. The water diffusivity in the peraluminous melts agrees very well with data for metaluminous rhyolites implying that an excess of Al₂O₃ with respect to alkalis does not affect water diffusion. On the other hand, water diffusion is faster by roughly a factor of two in the peralkaline melt compared to the metaluminous melt. The following expression for the water diffusivity in the peralkaline rhyolite as a function of temperature and pressure was obtained by least-squares fitting:

Long-term prediction of intermediate depth earthquakes in the southern Aegean region based on a time-predictable model

Repeat times of strong intermediate depth (60 km h 180 km) earthquakes have been determined by the use of instrumental and historical data for six seismogenic sources in the Benioff zone of the southern Aegean area. For four of these sources, at least two interevent times (three mainshocks) are available for each source. By using the repeat times for these four sources, the following relation has been determined: logT _t = 0.20M _min + 0.19M _p +a, whereT _t is the repeat time (in years),M _min the surface wave magnitude of the smallest earthquake considered,M _p the magnitude of the preceding mainshock and a parameter which varies from source to source. A multilinear correlation coefficient equal to 0.91 was determined for this relation, which indicates that the time predictable model holds to a satisfactory degree for the strong mainshocks of intermediate focal depth in the southern Aegean.By assuming that the ratioT/T _t, whereT is the observed andT _t the calculated repeat time, follows a lognormal distribution, the conditional probabilities for the occurrence of strong (M _s 6.5) and very strong (M _s 7.5) earthquakes during the period 1991–2001 in these four seismogenic sources have been calculated. These probabilities are very high (P > 0.9) for the strong and high (P > 0.5) for the very strong intermediate depth earthquakes which occur in the three sources of the shallower (h < 100 km) part of the Benioff zone where coupling occurs between the front parts of the Mediterranean lithosphere (downgoing) and the Aegean lithosphere.     

Contrasting fluid/rock interaction between the Notch Peak granitic intrusion and argillites and limestones in western Utah: evidence from stable isotopes and phase assemblages

The Jurassic Notch Peak granitic stock, western Utah, discordantly intrudes Cambrian interbedded pure limestones and calcareous argillites. Contact metamorphosed argillite and limestone samples, collected along traverses away from the intrusion, were analyzed for ¹⁸O, ¹³C, and D. The ¹³C and ¹⁸O values for the limestones remain constant at about 0.5 (PDB) and 20 (SMOW), respectively, with increasing metamorphic grade. The whole rock ¹⁸O values of the argillites systematically decrease from 19 to as low as 8.1, and the ¹³C values of the carbonate fraction from 0.5 to –11.8. The change in ¹³C values can be explained by Rayleigh decarbonation during calcsilicate reactions, where calculated is about 4.5 permil for the high-grade samples and less for medium and low-grade samples suggesting a range in temperatures at which most decarbonation occurred. However, the amount of CO₂ released was not anough to decrease the whole rock ¹⁸O to the values observed in the argillites. The low ¹⁸O values close to the intrusion suggest interaction with magmatic water that had a ¹⁸O value of 8.5. The extreme lowering of ¹³C by fractional devolatilization and the lowering of ¹⁸O in argillites close to the intrusion indicates oxgen-equivalent fluid/rock ratios in excess of 1.0 and X(CO₂)_F of the fluid less than 0.2. Mineral assemblages in conjunction with the isotopic data indicate a strong influence of water infiltration on the reaction relations in the argillites and separate fluid and thermal fronts moving thru the argillites. The different stable isotope relations in limestones and argillites attest to the importance of decarbonation in the enhancement of permeability. The flow of fluids was confined to the argillite beds (argillite aquifers) whereas the limestones prevented vertical fluid flow and convective cooling of the stock.     

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

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     

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.     

Mean and turbulent velocity measurements of supersonic mixing layers

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