Calculation of the average travel distance in a low-level picker-to-part system considering any distribution function within the aisles

The estimation of the average travel distance in a low-level picker-to-part order picking system can be done by analytical methods in most cases. Often a uniform distribution of the access frequency over all bin locations is assumed in the storage system. This only applies if the bin location assignment is done randomly. If the access frequency of the articles is considered in the bin location assignment to reduce the average total travel distance of the picker, the access frequency over the bin locations of one aisle can be approximated by an exponential density function or any similar density function. All known calculation methods assume that the average number of orderlines per order is greater than the number of aisles of the storage system. In case of small orders this assumption is often invalid. This paper shows a new approach for calculating the average total travel distance taking into account that the average number of orderlines per order is lower than the total number of aisles in the storage system and the access frequency over the bin locations of an aisle can be approximated by any density function.

REE and Hf distribution among mineral phases in the CV-CK clan : a way to explain present-day Hf isotopic variations in chondrites

Chondrites are among the most primitive objects in the Solar System and constitute the main building blocks of telluric planets. Among the radiochronometers currently used for dating geological events, Sm–Nd and Lu–Hf are both composed of refractory, lithophile element. They are thought to behave similarly as the parent elements (Sm and Lu) are generally less incompatible than the daughter elements (Nd and Hf) during geological processes. As such, their respective average isotopic compositions for the solar system should be well defined by the average of chondrites, called Chondritic Uniform Reservoir (CHUR). However, while the Sm–Nd isotopic system shows an actual spread of less than 4% in the average chondritic record, the Lu–Hf system shows a larger variation range of 28% [Bouvier A., Vervoort J. D. and Patchett P. J. (2008) The Lu–Hf and Sm–Nd isotopic composition of CHUR: Constraints from unequilibrated chondrites and implications for the bulk composition of terrestrial planets. Earth Planet. Sci. Lett.273, 48–57]. To better understand the contrast between Sm–Nd and Lu–Hf systems, the REE and Hf distribution among mineral phases during metamorphism of Karoonda (CK) and Vigarano-type (CV) carbonaceous chondrites has been examined. Mineral modes were determined from elemental mapping on a set of five CK chondrites (from types 3–6) and one CV3 chondrite. Trace-element patterns are obtained for the first time in all the chondrite-forming minerals of a given class (CK chondrites) as well as one CV3 sample. This study reveals that REE are distributed among both phosphates and silicates. Only 30–50% of Sm and Nd are stored in phosphates (at least in chondrites types 3–5); as such, they are not mobilized during early stages of metamorphism. The remaining fraction of Sm and Nd is distributed among the same mineral phases; these elements are therefore not decoupled during metamorphism. Of the whole-rock total of Lu, the fraction held in phosphate decreases significantly as the degree of metamorphism increases (30% for types 3 and 4, less than 5% in type 6). In contrast to Lu, Hf is mainly hosted by silicates with little contribution from phosphates throughout the CK metamorphic sequence. A significant part of Sm and Nd are stored in phosphates in types 3–5, and these elements behave similarly during CK chondrite metamorphism. That explains the robustness of the Sm/Nd ratios in chondrites through metamorphism, and the slight discrepancies observed in the present-day isotopic Nd values in chondrites. On the contrary, Lu and Hf are borne by several different minerals and consequently they are redistributed during metamorphism–induced recrystallization. The Lu/Hf ratios are therefore significantly disturbed during chondrites metamorphism, leading to the high discrepancies observed in present-day Hf isotopic values in chondrites.

Geochemical synthesis for the Effingen Member in boreholes at Oftringen, Gösgen and Küttigen

The Effingen Member is a low-permeability rock unit of Oxfordian age (ca. 160 Ma) that occurs across northern Switzerland. It comprises sandy calcareous marls and (argillaceous) limestones. This report describes the hydrogeochemistry, mineralogy and supporting physical properties of the Effingen Member in three boreholes in the Jura-Südfuss area: Oftringen, Gösgen and Küttigen, where it is 220–240 m thick. The top of the Effingen Member is at 420, 66 and 32 m depths at the three sites. Core materials are available from Oftringen and Gösgen, whereas information from Küttigen is limited to cuttings, in-situ hydrogeological testing and geophysical logging. Hydrogeological boundaries of the Effingen Member vary between locations. Ground-water flows were identified during drilling at the top (Geissberg Member), but not at the base, of the Effingen Member at Oftringen, at the base (Hauptrogenstein Formation) of the Effingen Member at Gösgen, and in a limestone layer (Gerstenhübel unit) within the Effingen Member at Küttigen. The marls and limestones of the Effingen Member have carbonate contents of 46–91 wt.-% and clay-mineral contents of 5–37 wt.-%. Pyrite contents are up to 1.6 wt.-%, but no sulphate minerals were detected by routine analyses. Clay minerals are predominantly mixed-layer illite-smectite, illite and kaolinite, with sporadic traces of chlorite and smectite. Veins filled with calcite ± celestite occur through the Effingen Member at Oftringen but not at Gösgen or Küttigen. They formed at 50–70 ºC from externally derived fluids, probably of Miocene age. Water contents are 0.7–4.2 wt.-%, corresponding to a water-loss porosity range of 1.9–10.8 vol.-%. Specific surface areas, measured by the BET method, are 2–30 m2/g, correlating with clay-mineral contents. Water activity has been measured and yielded surprisingly low values down to 0.8. These cannot be explained by pore-water salinity alone and include other effects, such as changes in the fabric due to stress release or partial saturation. Observed variations in measurements are not fully understood. Cation exchange capacity (CEC) and exchangeable cation populations have been studied by the Ni-en method. CEC, derived from the consumption of the index cation Ni, is 9–99 meq/kgrock at a solid:liquid ratio of 1, correlating with the clay-mineral content. Cation concentrations in Ni-en extract solutions are in the order Na+≥Ca2+>Mg2+>K+>Sr2+. However, the analytical results from the Ni-en extractions have additional contributions from cations originating from pore water and from mineral dissolution reactions that occurred during extraction, and it was not possible to reliably quantify these contributions. Therefore, in-situ cation populations and selectivity coefficients could not be derived. A suite of methods have been used for characterising the chemical compositions of pore waters in the Effingen Member. Advective displacement was used on one sample from each Oftringen and Gösgen and is the only method that produces results that approach complete hydrochemical compositions. Aqueous extraction was used on core samples from these two boreholes and gives data only for Cl- and, in some cases, Br-. Out-diffusion was used on core samples from Oftringen and similarly gives data for Cl- and Br- only. For both aqueous extraction and out-diffusion, reaction of the experimental water with rock affected concentrations of cations, SO42 and alkalinity in experimental solutions. Another method, centrifugation, failed to extract pore water. Stable isotope ratios (δ18O and δ2H) of pore waters in core samples from Oftringen were analysed by the diffusive exchange method and helium contents of pore water in Oftringen samples were extracted for mass spectrometric analysis by quantitative outgassing of preserved core samples. Several lines of evidence indicate that drillcore samples might not have been fully saturated when opened and subsampled in the laboratory. These include comparisons of water-loss porosities with physical porosities, water-activity measurements, and high contents of dissolved gas as inferred from ground-water samples. There is no clear proof of partial saturation and it is unclear whether this might represent in-situ conditions or is due to exsolution of gas due to the pressure release since drilling. Partial saturation would have no impact on the recalculation of pore-water compositions from aqueous extraction experiments using water-loss porosity data. The largest uncertainty in the pore-water Cl- concentrations recalculated from aqueous extraction and out-diffusion experiments is the magnitude of the anion-accessible fraction of water-loss porosity. General experience of clay-mineral rich formations suggests that the anion-accessible porosity fraction is very often about 0.5 and generally in a range of 0.3 to 0.6 and tends to be inversely correlated with clay-mineral contents. Comparisons of the Cl- concentration in pore water obtained by advective displacement with that recalculated from aqueous extraction of an adjacent core sample suggests a fraction of 0.27 for an Oftringen sample, whereas the same procedure for a Gösgen sample suggests a value of 0.64. The former value for anion-accessible porosity fraction is presumed to be unrepresentative given the local mineralogical heterogeneity at that depth. Through-diffusion experiments with HTO and 36Cl- suggest that the anion-accessible porosity fraction in the Effingen Member at Oftringen and Gösgen is around 0.5. This value is proposed as a typical average for rocks of the Effingen Member, bearing in mind that it varies on a local scale in response to the heterogeneity of lithology and pore-space architecture. The substantial uncertainties associated with the approaches to estimating anion-accessible porosity propagate into the calculated values of in-situ pore-water Cl- concentrations. On the basis of aqueous extraction experiments, and using an anion-accessible porosity fraction of 0.5, Cl- concentrations in the Effingen Member at Oftringen reach a maximum of about 14 g/L in the centre. Cl- decreases upwards and downwards from that, forming a curved depth profile. Cl- contents in the Effingen Member at Gösgen increase with depth from about 3.5 g/L to about 14 g/L at the base of the cored profile (which corresponds to the centre of the formation). Out-diffusion experiments were carried out on four samples from Oftringen, distributed through the Effingen Member. Recalculated Cl- concentrations are similar to those from aqueous extraction for 3 out of the 4 samples, and somewhat lower for one sample. Concentrations of other components, i.e. Na+, K+, Ca2+, Mg2+, Sr2+, SO42- and HCO3- cannot be obtained from the aqueous extraction and out-diffusion experimental data because of mineral dissolution and cation exchange reactions during the experiments. Pore-water pH also is not constrained by those extraction experiments. The only experimental approach to obtain complete pore-water compositions for samples from Oftringen and Gösgen is advective displacement of pore water. The sample from Oftringen used for this experiment is from 445 m depth in the upper part of the Effingen Member and gave eluate with 16.5 g/L Cl- whereas aqueous extraction from a nearby sample indicated about 9 g/L Cl-. The sample from Gösgen used for advective displacement is from 123 m depth in the centre of the Effingen Member sequence and gave eluate with about 9 g/L Cl- whereas aqueous extraction gave 11.5 g/L Cl-. In both cases the pore waters have Na-(Ca)-Cl compositions and SO42- concentrations of about 1.1 g/L. The Gösgen sample has a Br/Cl ratio similar to that of sea water, whereas this ratio is lower for the Oftringen sample. Taking account of uncertainties in the applied experimental approaches, it is reasonable to place an upper limit of ca. 20 g/L on Cl- concentration for pore water in the Effingen Member in this area. There are major discrepancies between pore-water SO42- concentrations inferred from aqueous extraction or out-diffusion experiments and those obtained from advective displacement in both the Oftringen and Gösgen cases. A general conclusion is that all or at least part of the discrepancies are attributable to perturbation of the sulphur system and enhancement of SO42- by sulphate mineral dissolution and possibly minor pyrite oxidation during aqueous extraction and out-diffusion. Therefore, data for SO42- calculated from those pore-water sampling methods are considered not to be representative of in-situ conditions. A reference pore-water composition was defined for the Effingen Member in the Jura Südfuss area. It represents the probable upper limits of Cl- contents and corresponding anion and cation concentrations that are reasonably constrained by experimental data. Except for Cl- and possibly Na+ concentrations, this composition is poorly constrained especially with respect to SO42- and Ca2+ concentrations, and pH and alkalinity. Stable isotope compositions, δ18O and δ2H, of pore waters in the Effingen Member at Oftringen plot to the right of the meteoric water line, suggesting that 18O has been enriched by water-rock exchange, which indicates that the pore waters have a long residence time. A long residence time of pore water is supported by the level of dissolved 4He that has accumulated in pore water of the Effingen Member at Oftringen. This is comparable with, or slightly higher than, the amounts of 4He in the Opalinus Clay at Benken. Ground waters were sampled from flowing zones intersected by boreholes at the three locations. The general interpretation is that pore waters and ground-water solutes may have similar origins in Mesozoic and Cenozoic brackish-marine formations waters, but ground-water solutes have been diluted rather more than pore waters by ingress of Tertiary and Quaternary meteoric waters. The available hydrochemical data for pore waters from the Effingen Member at these three locations in the Jura-Südfuss area suggest that the geochemical system evolved slowly over geological periods of time, in which diffusion was an important mechanism of solute transport. The irregularity of Cl- and δ18O profiles and spatial variability of advective ground-water flows in the Malm-Dogger system suggests that palaeohydrogeological and hydrochemical responses to changing tectonic and surface environmental conditions were complex.

Prismatine: Revalidation for Boron-Rich Compositions in the Kornerupine Group

Kornerupine and prismatine were introduced independently by Lorenzen in 1884 (but published in 1886 and 1893) and by Sauer in 1886, respectively. Ussing (1889) showed that the two minerals were sufficiently close crystallographically and chemically to be regarded as one species. However, recent analyses of boron using the ion microprobe and crystal structure refinement, indicate that the boron content of one tetrahedral site in kornerupine ranges from 0 to 1. Kornerupine and prismatine, from their respective type localities of Fiskenaesset, Greenland and Waldheim, Germany, are distinct minerals, members of an isomorphic series differing in boron content. For this reason, we re-introduce Sauer's name prismatine for kornerupines with B > 0.5 atoms per formula unit (p.f.u.) of 22(O,OH,F), and restrict the name kornerupine sensu stricto to kornerupines with B < 0.5 p.f.u. Kornerupine sensu lato is an appropriate group name for kornerupine of unknown boron content. Kornerupine sensu stricto and prismatine from the type localities differ also in Fe2+/Mg ratio, Si - (Mg + Fe2+ + Mn) content, Al content, F content, colour, density, cell parameters, and paragenesis. Both minerals formed under granulite-facies conditions with sapphirine and phlogopite, but kornerupine sensu stricto is associated with anorthite and homblende or gedrite, whereas prismatine is found with oligoclase (An9-13), sillimanite, garnet, and/or tourmaline. Occurrences at other localities suggest that increasing boron content extends the stability range of prismatine relative to that of kornerupine sensu stricto.

Synagogue compositions

by Samuel Alman

The isotopic composition of pore-water from Tournemire argillite (France): An inter-comparison study.

The determination of stable isotope contents of pore-water from consolidated argillaceous rocks remains a critical issue. In order to understand the processes involved in techniques developed for acquiring stable isotope compositions of pore-water, a comparative study between different methods was based on core samples of the Tournemire argillite. It concerns two water extraction techniques based on vacuum distillation and two pore-water equilibration techniques (radial diffusion in liquid phase and diffusive exchange in vapor phase). The water-content values obtained from vacuum distillation at 50 °C are always the lowest, on average 8% lower than the values obtained by heating at 105 °C and 17% lower than the values obtained by heating at 150 °C. The amounts of pore-water estimated from vacuum distillation at 105 °C and 150 °C and from radial diffusion method are in good agreement with those determined by heating. On the contrary, the vapor exchange method provides the highest values of water contents. Concerning stable isotope data, a good agreement was found between those obtained by equilibration techniques and those of fracture water, especially for 2H. Vacuum distillation at high temperature (particularly at 150 °C) also provided results consistent with data of fracture fluids. On the other hand, distillation at 50 °C provides a systematic depletion in heavy isotopes (about –20‰ for 2H and –2.7‰ for 18O) that can be modelled by an incomplete Rayleigh-type distillation process.

The sacred musical compositions of the late Israel Lazarus Mombach : containing the services for Sabbaths and festivals, New Year and Day of Atonement, consecration hymns, psalms and choral wedding service

ed. by M. Keizer

Komatiites constrain molybdenum isotope composition of the Earth's mantle

In order to estimate the Mo isotope composition and Mo abundance in the Bulk Silicate Earth (BSE), a total of thirty komatiite samples from five localities on three continents were analyzed using an isotope dilution double spike technique. Calculated Mo concentrations of the emplaced komatiite lavas range from 25±325±3 to 66±22 ng/g66±22 ng/g, and the inferred Mo concentrations in the deep mantle sources of the komatiites range between 17±417±4 and 30±12 ng/g30±12 ng/g, with an average value of 23±7 ng/g23±7 ng/g (2SE). This average value represents our best estimate for the Mo concentration in the BSE; it is identical, within the uncertainty, to published previous estimates of 39±16 ng/g39±16 ng/g, but is at least a factor of 2 more precise. The Mo isotope compositions of the komatiite mantle sources overlap within uncertainty and range from View the MathML sourceδMo98=−0.04±0.28 to 0.11±0.10‰0.11±0.10‰, with an average of 0.04±0.06‰0.04±0.06‰ (2SE). This value is analytically indistinguishable from published Mo isotope compositions of ordinary and enstatite chondrites and represents the best estimate for the Mo isotope composition of the BSE. The inferred δ98Mo for the BSE is therefore lighter than the suggested average of the upper continental crust (0.3 to 0.4‰). Thus, from the mass balance standpoint, a reservoir with lighter Mo isotope composition should exist in the Earth's mantle; this reservoir can potentially be found in subducted oceanic crust. The similarity of δ98Mo between chondritic meteorites and estimates for the BSE from this study indicates that during the last major equilibration between Earth's core and mantle, i.e., the one that occurred during the giant impact that produced the Moon, chemical and isotopic equilibrium of Mo between Fe metal of the core and the silicate mantle was largely achieved.

Chemical compositions of solid particles present in the Greenland NEEM ice core over the last 110,000 years

This study reports the chemical composition of particles present along Greenland’s North Greenland Eemian Ice Drilling (NEEM) ice core, back to 110,000 years before present. Insoluble and soluble particles larger than 0.45 μm were extracted from the ice core by ice sublimation, and their chemical composition was analyzed using scanning electron microscope and energy dispersive X-ray spectroscopy and micro-Raman spectroscopy. We show that the dominant insoluble components are silicates, whereas NaCl, Na₂SO₄, CaSO ₄, and CaCO₃ represent major soluble salts. For the first time, particles of CaMg(CO₃)₂ and Ca(NO₃)₂ 4H₂O are identified in a Greenland ice core. The chemical speciation of salts varies with past climatic conditions. Whereas the fraction of Na salts (NaCl + Na₂SO₄) exceeds that of Ca salts (CaSO₄+ CaCO₃) during the Holocene (0.6–11.7 kyr B.P.), the two fractions are similar during the Bølling-Allerød period (12.9–14.6 kyr B.P.). During cold climate such as over the Younger Dryas (12.0–12.6 kyr B.P.) and the Last Glacial Maximum (15.0–26.9 kyr B.P.), the fraction of Ca salts exceeds that of Na salts, showing that the most abundant ion generally controls the salt budget in each period. High-resolution analyses reveal changing particle compositions: those in Holocene ice show seasonal changes, and those in LGM ice show a difference between cloudy bands and clear layers, which again can be largely explained by the availability of ionic components in the atmospheric aerosol body of air masses reaching Greenland.

Reconstruction of in-situ porosity and porewater compositions of low-permeability crystalline rocks: Magnitude of artefacts induced by drilling and sample recovery

Geological site characterisation programmes typically rely on drill cores for direct information on subsurface rocks. However, porosity, transport properties and porewater composition measured on drill cores can deviate from in-situ values due to two main artefacts caused by drilling and sample recovery: (1) mechanical disruption that increases porosity and (2) contamination of the porewater by drilling fluid. We investigated the effect and magnitude of these perturbations on large drill core samples (12–20 cm long, 5 cmdiameter) of high-grade, granitic gneisses obtained from 350 to 600 m depth in a borehole on Olkiluoto Island (SW Finland). The drilling fluid was traced with sodium–iodide. By combining out-diffusion experiments, gravimetry, UV-microscopy and iodide mass balance calculations, we successfully quantified the magnitudes of the artefacts: 2–6% increase in porosity relative to the bulk connected porosity and 0.9 to 8.9 vol.% contamination by drilling fluid. The spatial distribution of the drilling-induced perturbations was revealed by numerical simulations of 2D diffusion matched to the experimental data. This showed that the rims of the samples have a mechanically disrupted zone 0.04 to 0.22 cm wide, characterised by faster transport properties compared to the undisturbed centre (1.8 to 7.7 times higher pore diffusion coefficient). Chemical contamination was shown to affect an even wider zone in all samples, ranging from 0.15 to 0.60 cm, inwhich iodide enrichmentwas up to 180 mg/kgwater, compared to 0.5 mg/kgwater in the uncontaminated centre. For all samples in the present case study, it turned out that the magnitude of the artefacts caused by drilling and sample recovery is so small that no correction is required for their effects. Therefore, the standard laboratory measurements of porosity, transport properties and porewater composition can be taken as valid in-situ estimates. However, it is clear that the magnitudes strongly depend on site- and drilling-specific factors and therefore our results cannot be transferred simply to other locations. We recommend the approach presented in this study as a route to obtain reliable values in future drilling campaigns aimed at characterising in-situ bedrock properties.

Cessation of facial growth in subjects with short, average, and long facial types - Implications for the timing of implant placement

Placement of a single-tooth implant should be performed when a patient's facial growth has ceased. In this retrospective observational study, we evaluated if there was a difference in the timing of cessation of craniofacial growth in short, average, and long facial types. Based on the value of the angle between cranial base and mandibular plane (SN/MP angle), three groups comprising 48 subjects with short facial type (SF; SN/MP ≤28°), 77 with average facial type (AF; SN/MP ≥31.5° and ≤34.5°), and 44 with long facial type (LF; SN/MP ≥38°) were selected. Facial growth was assessed on lateral cephalograms taken at 15.4 years of age, and 2, 5, and 10 years later. Variables were considered to be stable when the difference between two successive measurements was less than 1 mm or 1°. We found no difference between facial types in the timing of cessation of facial growth. Depending on the variable, the mean age when variables became stable ranged from 18.0 years (Is-Pal in LF group) to 22.0 years (SN/MP in LF group). However, facial growth continued at the last follow-up in approximately 20% subjects. This study demonstrates that facial type is not associated with the timing of cessation of facial growth.

UHP Metamorphism Documented in Ti-chondrodite- and Ti-clinohumite-bearing Serpentinized Ultramafic Rocks from Chinese Southwestern Tianshan

The southwestern Tianshan (China) metamorphic belt records high-pressure (HP) to ultrahigh-pressure (UHP) conditions corresponding to a cold oceanic subduction-zone setting. Serpentinites enclosing retrogressed eclogite and rodingite occur as lenses within metapelites in the UHP unit, which also hosts coesite-bearing eclogites. Based on the petrology and petrography of these serpentinites, five events are recognized: (1) formation of a wehrlite–harzburgite–dunite association in the mantle; (2) retrograde metamorphism and partial hydration during exhumation of the mantle rocks close to the seafloor; (3) oceanic metamorphism leading to the first serpentinization and rodingitization; (4) UHP metamorphism during subduction; (5) retrograde metamorphism during exhumation together with a second serpentinization. The peak metamorphic mineral assemblage of the serpentinized wehrlite comprises Ti-chondrodite + olivine + antigorite + chlorite + magnetite + brucite. A computed pseudosection for this serpentinized wehrlite shows that the Al content in antigorite is mostly sensititive to temperature but can also be used to constrain pressure. The average XAl = 0·204 ± 0·026 of antigorite (XAl = Al (a.p.f.u.)/8, where Al is in atoms per formula unit for a structural formula M48T34O85(OH)62, and M and T are octahedral and tetrahedral sites, respectively) included in Ti-chondrodite and average XAl = 0·203 ± 0·019 of antigorite in the matrix result in a well-constrained peak metamorphic temperature of 510–530°C. Peak pressures are less precisely constrained at 37 ± 7 kbar. The Tianshan serpentinites thus record UHP metamorphic conditions and represent the deepest subducted serpentinites discovered so far. The retrograde evolution occurs within the stability field of brucite + antigorite + olivine + chlorite and formation of Ti-clinohumite at the expense of Ti-chondrodite has been observed, suggesting isothermal decompression. The resulting P–T path is in excellent agreement with the metamorphic evolution of country rocks, indicating that the UHP unit in Tianshan was subducted and exhumed as a coherent block. To refine the metamorphic path of the ultramafic rocks, we have investigated the stability fields of Ti-chondrodite and Ti-clinohumite using piston-cylinder experiments. A total of 11 experiments were conducted at 25–55 kbar and 600–750°C in a F-free natural system. Combined with previous experiments and information from natural rocks we constructed a petrogenetic grid for the stability of Ti-chondrodite and Ti-clinohumite in F-free peridotite compositions. The formation of Ti-chondrodite in serpentinites requires a minimum pressure of about 26 kbar, whereas in Ti-rich systems it can form at considerably lower pressures. A key finding is that at UHP conditions, F-free Ti-chondrodite or Ti-clinohumite breaks down in the presence of orthopyroxene between 700 and 750°C, at temperatures that are significantly lower than those of the terminal breakdown reactions of these humite minerals. These breakdown reactions are an additional source of fluid during prograde subduction of serpentinites.

Calibration of cosmogenic noble gas production based on ³⁶Cl-³⁶Ar ages. Part 2. The ⁸¹Kr-Kr dating technique

We calibrated the ⁸¹Kr-Kr dating system for ordinary chondrites of different sizes using independent shielding-corrected ³⁶Cl-³⁶Ar ages. Krypton concentrations and isotopic compositions were measured in bulk samples from 14 ordinary chondrites of high petrologic type and the cosmogenic Kr component was obtained by subtracting trapped Kr from phase Q. The thus-determined average cosmogenic ⁷⁸Kr/⁸³Kr, ⁸⁰Kr/⁸³Kr, ⁸²Kr/⁸³Kr, and ⁸4Kr/⁸³Kr ratiC(Lavielle and Marti 1988; Wieler 2002). The cosmogenic ⁷⁸Kr/⁸³Kr ratio is correlated with the cosmogenic 22Ne/21Ne ratio, confirming that ⁷⁸Kr/⁸³Kr is a reliable shielding indicator. Previously, ⁸¹Kr-Kr ages have been determined by assuming the cosmogenic production rate of ⁸¹Kr, P(⁸¹Kr)c, to be 0.95 times the average of the cosmogenic production rates of ⁸⁰Kr and ⁸²Kr; the factor Y = 0.95 therefore accounts for the unequal production of the various Kr isotopes (Marti 1967a). However, Y should be regarded as an empirical adjustment. For samples whose ⁸⁰Kr and ⁸²Kr concentrations may be affected by neutron-capture reactions, the shielding-dependent cosmogenic (⁷⁸Kr/⁸³Kr)c ratio has been used instead to calculate P(⁸¹Kr)/P(⁸³Kr), as for some lunar samples, this ratio has been shown to linearly increase with (⁷⁸Kr/⁸³Kr)c (Marti and Lugmair 1971). However, the ⁸¹Kr-Kr ages of our samples calculated with these methods are on average ~30% higher than their ³⁶Cl-³⁶Ar ages, indicating that most if not all the ⁸¹Kr-Kr ages determined so far are significantly too high. We therefore re-evaluated both methods to determine P(⁸¹Kr)c/P(⁸³Kr)c. Our new Y value of 0.70 ± 0.04 is more than 25% lower than the value of 0.95 used so far. Furthermore, together with literature data, our data indicate that for chondrites, P(⁸¹Kr)c/P(⁸³Kr)c is rather constant at 0.43 ± 0.02, at least for the shielding range covered by our samples ([⁷⁸Kr/⁸³Kr]c = 0.119–0.185; [22Ne/21Ne]c = 1.083–1.144), in contrast to the observations on lunar samples. As expected considering the method used, ⁸¹Kr-Kr ages calculated either directly with this new P(⁸¹Kr)c/P(⁸³Kr)c value or with our new Y value both agree with the corresponding ³⁶Cl-³⁶Ar ages. However, the average deviation of 2% indicates the accuracy of both new ⁸¹Kr-Kr dating methods and the precision of the new dating systems of ~10% is demonstrated by the low scatter in the data. Consequently, this study indicates that the ⁸¹Kr-Kr ages published so far are up to 30% too high.

Correlated cosmogenic W and Os isotopic variations in Carbo and implications for Hf-W chronology

An obstacle for establishing the chronology of iron meteorite formation using 182Hf-182W systematics (t1/2 = 8.9 Myr) is to find proper neutron fluence monitors to correct for cosmic ray modification of W isotopic composition. Recent studies showed that siderophile elements such as Pt and Os could serve such a purpose. To test and calibrate these neutron dosimeters, the isotopic compositions of W and Os were measured in a slab of the IID iron meteorite Carbo. This slab has a well-characterized noble gas depth profile reflecting different degrees of shielding to cosmic rays. The results show that W and Os isotopic ratios correlate with distance from the pre-atmospheric center. Negative correlations, barely resolved within error, were found between epsilo190Os-epsilo189Os and epsilo186Os-epsilo189Os with slopes of -0.64 ± 0.45 and -1.8(+1.9/-2.1), respectively. These Os isotope correlations broadly agree with model predictions for capture of secondary neutrons produced by cosmic ray irradiation and results reported previously for other groups of iron meteorites. Correlations were also found between epsilo182W-epsilo189Os (slope = 1.02 ± 0.37) and epsilo182W-epsilo190Os (slope = -1.38 ± 0.58). Intercepts of these two correlations yield pre-exposure epsilo182W values of -3.32 ± 0.51 and -3.62 ± 0.23, respectively (weighted average epsilo182W = -3.57 ± 0.21). This value relies on a large extrapolation leading to a large uncertainty but gives a metal-silicate segregation age of -0.5 ± 2.4 Myr after formation of the solar system. Combining the iron meteorite measurements with simulations of cosmogenic effects in iron meteorites, equations are presented to calculate and correct for cosmogenic effects on 182W using Os isotopes.