Application of the cBΩ model to the calculation of diffusion parameters of He in olivine

The validity of the thermodynamic cBΩ model is tested in terms of the experimentally determined diffusion coefficients of He in a natural Fe-bearing olivine (Fo₉₀) and a synthetic end-member forsterite (Mg₂SiO₄) over a broad temperature range (250–950 °C), as reported recently by Cherniak and Watson (Geochem Cosmochim Acta 84:269–279, 2012). The calculated activation enthalpies for each of the three crystallographic axes were found to be (134 ± 5), (137 ± 13) and (158 ± 4) kJ mol^?1 for the [100], [010] and [001] directions in forsterite, and (141 ± 9) kJ mol^?1 for the [010] direction in olivine, exhibiting a deviation of <1 % with the corresponding reported experimental values. Additional point defect parameters such as activation volume, activation entropy and activation Gibbs free energy were calculated as a function of temperature. The estimated activation volumes (3.2–3.9 ± 0.3 cm³ mol^?1) of He diffusion in olivine are comparable with other reported results for hydrogen and tracer diffusion of Mg cations in olivine. The pressure dependence of He diffusion coefficients was also determined, based on single experimental diffusion measurements at 2.6 and 2.7 GPa along the [001] direction in forsterite at 400 and 650 °C.     

Identification of diffusion parameters in a nonlinear convection–diffusion equation using the augmented Lagrangian method

Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential equation arises as the saturation equation in the fractional flow formulation of the two-phase porous media flow equations. The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained minimization problem. We utilize the augmented Lagrangian method and transform the minimization problem into a coupled system of nonlinear algebraic equations, which is solved efficiently with the nonlinear conjugate gradient method. Numerical experiments are presented and discussed. This work was partially supported by the Research Council of Norway (NFR), under grant 128224/431.     

Review of the use of Péclet numbers to determine the relative importance of advection and diffusion in low permeability environments

In low permeability environments, transport by advection is often neglected based on a Péclet number criterion. Such a criterion usually states that if the Péclet number (Pe) is much smaller than 1, diffusion dominates over advection and transport may be modeled considering diffusion only. Unfortunately, up to 10 different Péclet number definitions exist and for a particular case these different definitions lead to very diverse Péclet number values, differing several orders of magnitude from each other. In this paper, the different Péclet number definitions are therefore evaluated on their ability to determine the relative importance of transport by advection and by diffusion in low permeability environments. This is done by comparing the results of the analytical solution for pure diffusion with the analytical solution for diffusion, advection and dispersion for a large number of different input parameter values. The relation between the different Péclet numbers and the difference between the calculated concentration considering diffusion only and the calculated concentration considering both diffusion and advection is studied. These calculations show that some Péclet number definitions are not well suited to decide whether advection may be neglected in low permeability media.

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Resumen Frecuentemente se descuida el transporte por avección en ambientes de baja permeabilidad sobre la base del criterio del número de Péclet. Dicho criterio usualmente sostiene que si el número de Péclet (Pe) es mucho menor a 1, la difusión domina sobre la avección y es posible modelar el transporte considerando la difusión únicamente. Desafortunadamente existen 10 definiciones diferentes del número de Péclet y para un caso en particular estas diferentes definiciones conducen a valores de número de Péclet muy diversos los cuales difieren entre sí en varias magnitudes. Por lo tanto, en este artículo se evalúan las diferentes definiciones en base a su habilidad para determinar la importancia relativa del transporte por avección y difusión en ambientes de baja permeabilidad. Esto se lleva a cabo mediante la comparación de los resultados de la solución analítica para difusión pura con los de la solución analítica por difusión, avección y dispersión para un número amplio de diferentes valores como parámetro. Se ha estudiado la relación entre los diferentes números de Péclet y las diferencias entre la concentración calculada considerando difusión únicamente y considerando tanto difusión como avección. Estos cálculos muestran que algunas de las definiciones de los números de Péclet no son muy apropiadas par decidir si se puede descuidar la avección en medios de baja permeabilidad.

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Résumé Dans les milieux à faible perméabilité, le transport par advection est souvent négligeable lorsquon se base sur le critère du nombre de Péclet. Un tel critère suggère habituellement que pour un nombre de Péclet beaucoup plus petit que 1, la diffusion domine sur ladvection et que le transport peut être modélisé par diffusion seulement. Malheureusement, il existe jusquà environ dix définitions du nombre de Péclet et pour un cas spécifique, ces différentes définitions mènent à des valeurs du nombre de Péclet très différentes, et qui varient entre elles de plusieurs ordres de grandeur. Dans cet article, les différentes définitions du nombre de Péclet sont évaluées en fonction de leur habileté à déterminer limportance relative du transport par advection et par diffusion dans les milieux à faible perméabilité. Ceci est fait en comparant les résultats de la solution analytique pour la diffusion pure à la solution analytique pour la diffusion, ladvection et la dispersion, et ce, pour un grand nombre de valeurs différentes comme paramètre dentrée. La relation entre les différents nombres de Péclet et la différence entre la concentration calculée en considérant la diffusion seulement et la concentration calculée considérant simultanément la diffusion et ladvection est étudiée. Ces calculs prouvent que certaines définitions de nombre de Péclet ne sont pas appropriées afin de décider si ladvection peut être négligée dans les milieux à faible perméabilité.

     

Constraints on the early cooling rates of Mt. Dabie from diffusion modeling of chemical zoning of garnet

Diffusion modeling of zoning profiles in eclogite garnets from three different tectonic units of Mt. Dabie, UHPM unit, HPM unit and northern Dabie, was used to estimate the relative time span and cooling rates of these rocks. Modeling result for the Huangzhen eclogite garnet shows that the maximal time span for the diffusion-adjustment process is about 22 Ma since the peak-temperature metamorphism, which is the maximum time span from amphibolite facies metamorphism to greenschist facies metamorphism. The Bixiling eclogites had subjected to a cooling process at a rate of - 10℃/Ma from 750℃ to 560℃ during 20 Ma. The second cooling stage of the Raobazhai eclogite following granulite-facies metamorphism is an initial fast cooling process at a rate of about 25℃/Ma and then slowed down gradually. All these belong to a coherent Dabie collision orogen with differences in subduction depth and exhumation/uplifting path.     

Pb−Sr−Nd−O isotopic constraints on the origin of rhyolites from the Taupo Volcanic Zone of New Zealand: evidence for assimilation followed by fractionation from basalt

A comprehensive Sr–Nd–Pb–O isotopic study is reported for rhyolites from the Maroa Volcanic Centre in the Taupo Volcanic Zone (TVZ) of New Zealand. The Sr–Nd isotopic compositions of the rhyolites (⁸⁷Sr/⁸⁶Sr=0.705236 to 0.705660 and _Nd = 2.0 to 0.2) are intermediate between those of primitive basalts (⁸⁷Sr/⁸⁶Sr=0.70387 and _Nd = 5.3) and the Torlesse basement (⁸⁷Sr/⁸⁶Sr=0.709 and _Nd = -4.5). The relatively low mantle-like oxygen isotopic compositions of ¹⁸ O = 7 ± 0.5 are consistent with the Nd-Sr isotopic constraints in that they can be accounted for by 15% to 25% crustal contamination of a basaltic parent by relatively ¹⁸ O-rich Torlesse metasediment. High precision Pb isotopic analyses of plagioclase separates from the Maroa rhyolites show that they have essentially the same compositions as the Torlesse metasedimentary terrane which is itself distinctive from the Western or Waipapa metasediments. Due to the high concentration of Pb in the Torlesse metasediments (>20 ppm) compared to the basalts (<2 ppm), the Pb isotopic composition of the volcanics may be controlled by relatively small amounts (>10%) of crustal contamination. All these results are shown to be consistent with derivation of the rhyolites by 15% to 25% contamination of relatively primitive basaltic magmas with Torlesse metasedimentary crust, followed by extensive, essentially closed system fractionation of the basalt to a magma of rhyolite composition. It is argued that the processes of assimilation and fractionation are separated in both space and time. The voluminous high silica rhyolites, which make up >97% of the exposed volcanism in the continental margin back-are basin environment of the TVZ, therefore appear to be a product of predominantly new additions to the crust with assimilation-recycling of pre-existing crust being of secondary importance.     

A re-examination of the role of hydrogen in Al−Si interdiffusion in feldspars

Recent experimental studies have shown that the rates of Al–Si order-disorder and interdiffusion in alkali feldspars at high pressures under dry conditions increase dramatically in the approximate pressure range 7–14 kb, depending on temperature and feldspar composition (Goldsmith 1987, 1988). Enhancement of Al–Si interdiffusion rates is ascribed to the involvement of hydrogen, but the species of hydrogen involved is undetermined.A simple kinetic analysis of the data of Goldsmith (1987) on disordering of dry albite at 800°–950° C and 6–24 kb in the solid media press is consistent with the NaCl pressure cell acting as a proton donor by enhancing dissociation of water in the pressure medium, generating a high in the experimental environment. The rate constant for disordering of albite is found to increase linearly with the estimated experimental and with the density of aqueous salt solution, implicating H⁺ as the rate-enhancing species.Further experimental studies confirm the importance of . At 16 kb and 850° C, dry albite in sealed Pt capsules in a NaCl cell containing tantalum powder (which reduces H₂O to H₂) remains highly ordered over the same time that complete disordering would occur in the absence of Ta. H₂ cannot therefore be the rate-enhancing species. At 1 kb and 850° C, the extent of Al–Si disorder in albite in direct contact with various NaCl–H₂O solutions increases from partially disordered for pure H₂O to completely disordered for saturated aqueous NaCl solution, giving strong support to the proton model. SIMS scanning ion imaging of albite run products demonstrates conclusively that solution-reprecipitation is not responsible for enhanced disordering rates.Results of disordering experiments in the solid media apparatus cannot be duplicated in Ar gas media internally-heated pressure vessels, even with the same experimental configuration around the albite-bearing capsules, due to the different proton-buffering capacities of the solid and gas media apparatus.     

Effects of grain dissolution–diffusion sliding and hydro-mechanical interaction on the creep deformation of soft rocks

Acta Geotechnica - The creep deformation behaviour of soft rocks is one of the most important research fields in geotechnical engineering. In this study, a theoretical model was developed to...     

Evaluation of the origin and fate of nitrate in the Abbotsford Aquifer using the isotopes of15N and18O in NO3−

Extensive NO₃⁻ contamination of groundwater in the Abbotsford aquifer to levels above drinking water limits is a major problem in the Fraser Lowlands of southwestern British Columbia, Canada. Nitrate concentrations in the aquifer ranged from 0 to 151 mg/l NO₃⁻, with a median concentration of 46 mg/l NO₃⁻. Of 117 wells sampled, 54% had NO₃⁻ concentrations exceeding the drinking water limit of 45 mg/1. Approximately 80% of the study area had groundwater NO₃⁻ concentrations exceeding 40 mg/1 NO₃⁻. Potential NO₃⁻ source materials were poultry manure N and synthetic NH₄ based fertilizers. Theδ¹⁵N of solid poultry manure samples ranged between + 7.9 and + 8.6‰ (AIR). Four brands of synthetic fertilizers commonly used hadδ¹⁵N values between −1.5 and −0.6‰. Ammonia volatilization caused theδ¹⁵N of groundwater NO₃⁻ produced from poultry manure N to range between +8 and +16‰. Theδ¹⁸O values of groundwater NO₃⁻, by contrast, mostly ranged between +2 and +5‰ (SMOW). This narrow range ofδ¹⁸O values fell within the expected range of NO₃⁻ produced by nitrification of reduced N forms such as poultry manure N and NH₄ fertilizers, and had a similar range ofδ¹⁸O values as NO₃⁻ in the upper part of the unsaturated zone below raspberry fields and beneath former manure piles. Theδ¹⁵N-NO₃⁻ andδ¹⁸O-NO₃⁻ data confirmed that NO₃⁻ in the aquifer was predominantly derived from poultry manure and to a lesser extent from synthetic fertilizers. Theδ¹⁸O-NO₃⁻ data further suggested the nitrification process occurred mainly in the summer months, with the soil NO₃⁻ produced subsequently flushed into the aquifer during fall recharge. Theδ¹⁵N-NO₃⁻andδ¹⁸O-NO₃⁻ data conclusively indicated that no significant bacterial denitrification is taking place in the Abbotsford aquifer.     

Origin of the inconsistent apparent Re–Os ages of the Jinchuan Ni–Cu sulfide ore deposit,China: Post-segregation diffusion of Os

Apparent Re–Os ages of some magmatic sulfide ore deposits are older than the zircon and baddeleyite U–Pb ages which are interpreted as the formation age of the host intrusions. The Jinchuan Ni–Cu–PGE deposit of China, the world's third largest, is such a case. We report apparent Re–Os isochron ages of 1117 ± 67 Ma, 1074 ± 120 Ma and 867 ± 75 Ma with initial ¹⁸⁷Os/¹⁸⁸Os ratios of 0.120 ± 0.012, 0.162 ±0.017 and 0.235 ± 0.027 for disseminated ores, sulfides from the disseminated ores and massive ores from Jinchuan, respectively. Using these data and Re–Os ages from the literature, we find that the oldest apparent Re–Os age and lowest initial Os isotope ratio are from disseminated ores which contain small amounts of sulfide minerals, the highest initial Os isotope ratios and youngest apparent Re–Os ages, consistent with the zircon and baddeleyite U–Pb ages, are from massive ores containing 90–100 modal% sulfide, and net-textured ores with about 25 modal% sulfides yield apparent Re–Os ages and initial Os ratios intermediate between those of the disseminated and massive ores.Because Os diffusion between sulfides is inhibited by the intervening silicates even at high temperatures, re-equilibration did not occur in the disseminated ore and the samples retained the Os ratios of the contaminated magma, leading to geologically meaningless ages that are older than the formation age of the rocks. While Os-bearing sulfide minerals and magnetite show low closure temperatures of Os diffusion and the sulfide minerals in the massive ore are closely connected with each other, facilitating fast diffusion of Os, re-equilibration of Os was achieved during cooling of the ore from about 850 °C after the segregation to about 400 °C. Thus, an age corresponding to the formation time and an elevated initial Os ratio were yielded by the massive ore. Os isotopes in the net-textured ore behave in the way intermediate between the disseminated and massive ores. Pb isotope data support the Os results. Disseminated ores have heterogeneous Pb isotope ratios whereas Pb in the massive ores is more uniform, consistent with Pb isotopic equilibration in the massive ores, but not in the disseminated ores.     

The Kovdor-2015 experiment: study of the parameters of a conductive layer of dilatancy–diffusion nature (DD Layer) in the Archaean crystalline basement of the Baltic Shield

This paper addresses the Kovdor-2015 Experiment involving frequency electromagnetic soundings of the Archaean basement of the Earth’s crust in the southwestern part of the Kola Peninsula. Eleven soundings were carried out using two transmitting arrangements, 85 km apart. Each arrangement consisted of two mutually orthogonal grounded electric dipoles of 1.5 km long. The distances between the source and the receiver were 25 and 50 km. Interpretation of the results took into account the influence of displacement currents and static distortions. It is found that there is an intermediate conductive layer of the dilatancy–diffusion nature (DD layer) with a longitudinal conductivity of about one siemens at depths ranging from 1.5–2 to 5–7 km. The results are interpreted in the terms of geodynamics.     

Distribution of trace and major elements in the −180 + 75 μm and −75 μm fractions of the sandveld regolith in northwest Ngamiland,Botswana

An orientation survey was undertaken in northwest Ngamiland to evaluate, among other criteria, an optimum size fraction for trace element analysis in the Kalahari sandveld regolith samples for a regional geochemical mapping project in the area. The most prominent geomorphological features of the region are the longitudinal rolling sand dunes and floodplain sediments adjacent to the unique, mid-continent Okavango Delta. Most of the dune sands were deposited in the Late Quaternary, and they show evidence of both pluvial and and environments. Presently the a lab dunes support varied shrub/grass vegetation with intermittent tree cover. Extensive forest fires have affected the region for generations, and the occurrences of remnants of large trees indicate that the region may have also supported large forests at some stage.The sandveld regolith comprises 70% quartz sand (−1000 + 63 μm) and 10–20% silt/clay (< 63 μm) material. There are no size variations between material from dune crests, dune depressions and down the soil profile to a depth of a metre. The process of regolith formation is relatively young and dynamic, being widely churned by a variety of boring animals, termites, ants and other insects. Hence no distinct zonation of soil horizons in the top 100 cm of the soil catena were observed. Remarkably, the significant proportion of the silt/clay fraction in the regolith indicates progressive weathering and possible deposition of precipitates.Trace element contents are invariably enhanced in the fine fractions, a characteristic widely observed elsewhere in residual soils. On the Xaxa-Cheracheraha traverse Zn values range from 2 to 98 ppm (mean 9 ppm); Pb varies from 1 to 101 ppm (mean 27 ppm) and Cu from 0 to 18 ppm (mean 5 ppm) in the −75 μm fraction. Contents in the −180 + 75 μm are, however, significantly lower than in the fine fractions. The variations in element concentrations along each of the orientation survey traverses at Qangwa-Nokaneng, Nxaunxau-Qurube and Nxaunxau-Ghane, in the coarse and fine fractions, generally remain sympathetic, showing that the enhanced values in the fines are a result of secondary dispersion, rather than mere compositional differences in the sandveld regolith.     

Fe–Mg diffusion in olivine II: point defect chemistry,change of diffusion mechanisms and a model for calculation of diffusion coefficients in natural olivine

Analysis of existing data and models on point defects in pure (Fe,Mg)-olivine (Phys Chem Miner 10:27–37,1983; Phys Chem Miner 29:680–694, 2002) shows that it is necessary to consider thermodynamic non-ideality of mixing to adequately describe the concentration of point defects over the range of measurement. In spite of different sources of uncertainties, the concentrations of vacancies in octahedral sites in (Fe,Mg)-olivine are on the order of 10⁻⁴ per atomic formula unit at 1,000–1,200 °C according to both the studies. We provide the first explicit plots of vacancy concentrations in olivine as a function of temperature and oxygen fugacity according to the two models. It is found that in contrast to absolute concentrations at ∼1,100 °C and dependence on fO₂, there is considerable uncertainty in our knowledge of temperature dependence of vacancy concentrations. This needs to be considered in discussing the transport properties such as diffusion coefficients. Moreover, these defect models in pure (Fe,Mg)-olivine need to be extended by considering aliovalent impurities such as Al, Cr to describe the behavior of natural olivine. We have developed such a formulation, and used it to analyze the considerable database of diffusion coefficients in olivine from Dohmen et al. (Phys Chem Miner this volume, 2007) (Part - I) and older data in the literature. The analysis documents unequivocally for the first time a change of diffusion mechanism in a silicate mineral—from the transition metal extrinsic (TaMED) to the purely extrinsic (PED) domain, at fO₂ below 10⁻¹⁰  Pa, and consequently, temperatures below 900 °C. The change of diffusion mechanism manifests itself in a change in fO₂ dependence of diffusivity and a slight change in activation energy of diffusion—the activation energy increases at lower temperatures. These are consistent with the predictions of Chakraborty (J Geophys Res 102(B6):12317–12331, 1997). Defect formation enthalpies in the TaMED regime (distinct from intrinsic defect formation) lie between −66 and + 15 kJ/mol and migration energies of octahedral cations in olivine are most likely ∼ 260 kJ/mol, consistent with previous inferences (Phys Chem 207:147–162, 1998). Plots are shown for diffusion at various constant fO₂ as well as along fO₂ buffers, to highlight the difference in behavior between the two. Considering all the diffusion data and constraints from the point defect models, (Fe–Mg) diffusion in olivine along [001] is best described by the Master equations: (1) At oxygen fugacities greater than 10⁻¹⁰ Pa:

Calculation of the effect of deprotonation on the Si NMR shielding for the series Si(OH)4 to SiO 4 4−

²⁹Si NMR shieldings have been calculated by ab initio coupled Hartree-Fock perturbation theory for the orthosilicate species Si(OH)₄, Si(OH)₃O^-, Si(OH)₂O ₂ ^2- , Si(OH)O ₃ ^3- and SiO ₄ ^4- using energy optimized geometries from ab initio Hartree-Fock calculations. The shielding of Si(OH)₃O^- is smaller than that of Si(OH)₄ by 2.7 ppm and the shielding trend along the Si(OH)₄ to SiO ₄ ^4- series is decidedly nonlinear. The unprotonated O in Si(OH)₃O^- is more shielded and has a much smaller electric field gradient than do the protonated oxygens. Calculated anisotropies show the largest components of the shielding to lie along or near the short Si-O bonds. Calculations employing point charges in place of H reproduce the shielding trends in T _d and S ₄ symmetry Si(OH)₄ semiquantitatively. The calculated trends in shielding with < si-o-h=" can=" also=" be=" correlated=" with=" the=" energies=" of=" the=" si3p,o2p="> bonding orbitals.     

Experimental measurements of the diffusion parameters of light hydrocarbons in water-saturated sedimentary rocks—I. A new experimental procedure

An automatic experimental set-up has been developed for the determination of diffusion parameters of hydrocarbon gases through water-saturated rock samples. Diffusive flow of hydrocarbons through rock slices is monitored by gas chromatography. Experiments are carried out according to the time lag method yielding diffusion coefficients, solubility coefficients, and diffusion permeabilities. Diffusion coefficients down to 10⁻¹² m² s⁻¹ (10⁻⁸ cm⁻² s⁻¹) may be determined routinely on rock samples of 2–10 mm thickness. Maximum errors in diffusion coefficients are estimated around 20% and reproducibility was found to range between 10 and 20%. Specific features of this set-up are automatic sampling and data acquistion, high sampling frequency, and maintenance of water-saturation of the rock samples throughout the experiment.     

Role of diffusion–precipitation reactions in authigenic pyritization

Models proposed for authigenic pyritization in the literature provide good indicators of the effect of very high concentrations of available iron on decaying organisms; however, the impact of lower concentrations of iron on an actively decaying system is not so well characterised. Gel-stabilised systems are used to model the effect of extremes of iron concentration on the precipitation of pyrite and the process of organic matter preservation. The experiments show the effect of sulphate reduction decay in an environment where iron is limited or dispersed, and in iron-rich environment where diffusion is limited. The formation of discrete sulphide bands in experiments where iron is limited indicates that negative feedback, or Liesegang, reactions play a role in the development of gaps between sites of organic matter preservation and pyrite precipitation, providing a mechanism for the formation of pyrite halos, concretion rims and overgrowths. In iron-rich environments, pyrite formation is confined to the decaying organism, and the Liesegang effect is limited due to the restricted diffusion of dissolved sulphide.     

Radon,Cl− and SO42− anomalies in hot spring water associated with the 1995 earthquake swarm off the east coast of the Izu Peninsula,Central Japan

Radon concentrations were continuously monitored in hot spring water in a 200-m-deep well in the Yugano hot spring area, Izu Peninsula, Japan from July to December 1995. Concentrations of Cl⁻ and SO₄²⁻ were measured in the hot spring water about once a month from May to December 1995. The Rn concentrations in the hot spring water increased significantly in September and October 1995, when the 1995 earthquake swarm off the E coast of the Izu Peninsula occurred at a distance of about 30 km from the observation well. The 1995 earthquake swarm began on 11 September and became most active from the end of September to the beginning of October. The Rn concentration rose gradually from 8 September, 3 days before the onset of the swarm activity, increasing by about 50% by 17 September. It remained high in October but had returned to normal by the end of November. However, Cl⁻ and SO₄²⁻ concentrations doubled suddenly from 22 to 23 September and remained high until the end of November. A good correlation between Cl⁻ and SO₄²⁻ concentrations suggests the same mechanism for their anomalous increases, probably mixing of water with high Cl⁻ and SO₄²⁻ concentrations caused by crustal deformation related to the seismic swarm activity. However, the anomalous increase in Rn concentration, which began 15 days before these anion increases, cannot be explained by the same water mixing mechanism. A possible mechanism for the anomalous Rn increase is the formation of microcracks caused by compressional stress, which preceded the onset of the earthquake swarm.     

Paragenesis and chemical characteristics of the celsian−hyalophane−K-feldspar series and associated Ba-Cr micas in barite-bearing strata of the Mesoarchaean Ghattihosahalli Belt,Western Dharwar Craton,South India

The upper greenschist - lower amphibolite facies, argillaceous to chemical-exhalative metasedimentary sequence of the Mesoarchaean Ghattihosahalli Schist Belt (GHSB), southern India, has been examined with a special focus on the paragenesis and solid solution characteristics of barian feldspars and associated dioctahedral Ba-Cr-bearing micas. Barian feldspars occur as untwinned porphyroblasts in a recrystallized finely banded matrix of barite, quartz and minor white mica. Idioblastic celsian (Cls_98-76Or_2-20Ab_1-8) and hyalophane (Cls_55-39Or_35-51Ab₁₀) predate the greenschist-facies foliation, whereas xenoblastic hyalophane (Cls_44-35Or_45-59Ab_8–17) and mantles on celsian (Cls_45-35Or_42-60Ab_13-5) as well as xenoblastic barian K-feldspar (Cls₆Or₉₀Ab₂) postdate the last fabric-defining event. The preservation of extremely complex zoning patterns down to the micron-scale shows that diffusional homogenization did not operate at fluid-present low to medium-grade conditions (350–550 °C, 3–5 kb). Microstructures indicate that at these conditions barian feldspars deform exclusively by brittle fracturing and do not undergo recrystallization. Barian feldspar compositions confirm the positive correlation of Na-content with temperature and the existence of a narrow asymmetric compositional gap (Cls_90-85?Cls₅₅, ~350 °C) which probably closes at lower amphibolite facies conditions (X_c ~Cls_75; T_c ~550 °C). White micas are solid solutions of the end-members muscovite, ganterite (Ba_0.5?K_0.5)Al₂(Al_1.5Si_2.5)O₁₀(OH)₂, paragonite, celadonite with a significant substitution of ^[VI]Al by Cr. Zoning is a common feature with cores being enriched in Ba. The data document extensive Ba substitution for K from muscovite to ganterite, exclusively controlled by the coupled substitution ^[XII]K + ^[IV]Si ? ^[XII]Ba + ^[IV]Al and strongly dependent on bulk composition. The extent of solid solution from (Ms+Gnt) towards paragonite and celadonite end-members is controlled by the miscibility gap in the (Ms+Gnt)–Pg–Cel pseudoternary, with the Pg-substitution depending on temperature and the Cel-substitution on pressure. ^[IV]Si values between 3.1 and 3.3 in Ba-poor micas indicate minimum pressures of chemical equilibration in the order of 3–5 kbar, while the most sodian compositions of low-celadonite micas provide an upper temperature estimate of ~550 °C, consistent with P-T estimates for assemblages of metapelites (500–550 °C, 4–5 kb).     

Evolution and composition of the lithospheric mantle underneath the western Arabian peninsula: constraints from Sr−Nd isotope systematics of mantle xenoliths

On the basis of their textures and mineral compositions spinel-peridotite xenoliths of the Cr-diopside group (group I) from Cenozoic volcanic fields of Arabia can be classified into different subtypes. Type IA is of lherzolitic to harzburgitic composition; mineral compositions are similar to those of group I mantle xenoliths from worldwide occurrences. Type IB xenoliths have lherzolitic to wehrlitic compositions; Mg/(Mg+Fe) ratios of the clinopyroxenes (0.862–0.916) and olivines (0.872–0.914) are similar too or slightly lower than those of typical IA minerals. Texturally, type IB xenoliths are distinguished from type IA rocks by the presence of intragranular spinel, intragranular relict Cr-pargasite, and subordinate intergranular Ba-phlogopite (11.1% BaO). The hydrous minerals in type IB xenoliths are interpreted to document an earlier metasomatism 1 which did not affect type IA lithospheric mantle. Subsequent recrystallization caused the partial replacement of Cr-pargasite in type IB materials and resulted in the formation of less hydrous mineral assemblages. Some of the type IA xenoliths are characterized by secondary intergranular amphibole which must have formed recently. The absence or presence of this intergranular amphibole is used to distinguish an anhydrous subtype IA1 from a hydrous subtype IA2. Type IB xenoliths may also contain secondary intergranular amphibole (similar to the one in subtype IA2) or they contain abundant formermelt patches now consisting of glass and phenocrysts of olivine, clinopyroxene, amphibole, and spinel. The secondary intergranular amphiboles and the former melt patches, both are interpreted as results of a second metasomatism (metasomatism 2). In their trace element and isotopic characteristics, type IA1 and type IA2 clinopyroxenes do not exhibit any systematic differences. Furthermore, type IA2 clinopyroxenes are in Sr isotopic disequilibrium with intergranular amphiboles. This suggests that type IA2 clinopyroxenes were not modified during the second metasomatism 2. All type IA clinopyroxenes have low Sr contents (100 ppm); most of them show Sm/Nd ratios higher than inferred for bulk earth. In their ⁸⁷Sr/⁸⁶Sr and ¹⁴³Nd/¹⁴⁴Nd ratios, type IA clinopyroxenes exhibit a large spread from 0.70226–0.70376 and from 0.51375–0.51251, respectively. Highly variable Sr/Nd ratios (5.0–79.3) and variable T_UR and T_CHUR model age relationships require different evolutions of the respective mantle portions. Nevertheless, all but two type IA clinopyroxenes form a linear array in a Sm–Nd isochron diagram which probably can not be explained by mixing. If taken as an isochron the slope of the array corresponds to an age of around 700 Ma. The mean initial _Nd of 5.8±1.7 (1) is similar to values for juvenile Pan-African (i.e. 850–650 Ma old) crust of the Arabian-Nubian shield. It is suggested that type IA lithospheric mantle and the juvenile Pan-African crust are two counterparts fractionated from a common source during the earlier stages of the Pan-African. Type IB clinopyroxenes have high Sr contents (200 ppm), variable Sr/Nd ratios (9–111) and Sm/Nd ratios generally below that inferred for bulk earth, and show a small spread in their Sr and Nd isotopic compositions (0.70299–0.70318 and 0.51285–0.51278, respectively). In a Sm–Nd isochron diagram the data points form a linear, horizontal array indicating a close-to-zero age for the earlier metasomatism 1 and suggesting a close genetic relationship to mantle processes related to the formation of the Red Sea.     

Stoichiometric saturation tests of NaCl1−xBrx and KCl1−xBrx

Stoichiometric saturation is examined as a possible control on Br contents of halite and sylvite during precipitation from binary salt solutions of NaCl-NaBr and KCl-KBr, respectively. Experimental data at 25°C, assumed to represent Stoichiometric saturation, were used to predict mole fractions of NaBr in halite and KBr in sylvite in thermodynamic equilibrium with fluids as a function of aqueous activity ratios of Br⁻:Cl⁻. The predictions are based on the additional assumption that the aqueous activity product of the major salt component in the precipitated salt was independent of the trace Br content in the salt lattice. The extension of the predictions to diagenetic pressures and temperatures is discussed.The predicted equilibrium Br content of halite at initial halite saturation of evaporating seawater is in close agreement with that computed from the distribution coefficient of Lutz (1975), measured in slowgrowth single crystal experiments. Fluid recrystallization of halite and sylvite at near-surface temperatures is predicted to generally deplete the Br contents in the solids. Bulk Br contents in halite in cap-rock of Gulf Coast salt domes generally agree with those predicted by the recrystallization of halite in the presence of evaporative-concentrated seawater. At a constant solution composition, increasing temperature results in increasing the equilibrium Br content of halite, making less efficient Br depletion in halite by recrystallization.     

Low-temperature thermodynamic model for the system Na2CO3−MgCO3−CaCO3−H2O

A comprehensive low-temperature thermodynamic model for the geochemically important Na₂CO₃−MgCO₃−CaCO₃−H₂O system is presented. The model is based on calorimetrically determined Δ_fH°₂₉₈ values, S°₂₉₈ values and C°_p(T) functions taken from the literature as well as on μ°₂₉₈ values of solids derived in this work from solubility measurements obtained in our laboratories or by others. When these thermodynamic quantities were combined with temperature-dependent Pitzer parameters taken from the literature, solubilities calculated for a wide range of conditions agree well with experimental data. The results for several subsystems were summarized by depicting the respective phase diagrams. For the MgO−CO₂−H₂O subsystem, it was found that the commonly believed stability relations must be revised, i.e., in the temperature range covered, nesquehonite never becomes more stable than hydromagnesite at p_CO2 ≤ 1 atm. Although the recommended set of thermodynamic data on sparingly soluble solids was derived from experimental results on mainly NaClO₄ systems, it can be incorporated in databanks containing additional Pitzer parameters for modeling more complex fresh- or seawater systems.