Anharmonicity and asymmetry of Landau levels for a two-dimensional electron gas

We calculate the density of states of a two dimensional electron gas located at the interface of a GaAlAs/GaAs heterojunction. The disorder potential which is generally created by a single doping layer behind a spacer, is here enhanced by the presence of a second delta doped layer of scatterers which can be repulsive or attractive impurities. We have calculated the density of states by means of the Klauder's approximation, in the presence of a magnetic field of arbitrary strength. At low field either band tails or impurity bands are observed for attractive potentials, depending on the impurity concentration. At higher field, impurity bands are observed for both repulsive and attractive potentials. We discuss the effect of such an asymmetrical density of states on the transport properties in the quantum Hall effect regime.Comment: 22 pages, 12 figures. submitted to Phys. Rev.

A hydrothermal origin for isotopically anomalous cap dolostone cements from south China

The release of methane into the atmosphere through destabilization of clathrates is a positive feedback mechanism capable of amplifying global warming trends that may have operated several times in the geological past. Such methane release is a hypothesized cause or amplifier for one of the most drastic global warming events in Earth history, the end of the Marinoan ‘snowball Earth’ ice age, ~635 Myr ago. A key piece of evidence supporting this hypothesis is the occurrence of exceptionally depleted carbon isotope signatures (δ^(13)C_(PDB) down to −48‰; in post-glacial cap dolostones (that is, dolostone overlying glacial deposits) from south China; these signatures have been interpreted as products of methane oxidation at the time of deposition. Here we show, on the basis of carbonate clumped isotope thermometry, ^(87)Sr/^(86)Sr isotope ratios, trace element content and clay mineral evidence, that carbonates bearing the ^(13)C-depleted signatures crystallized more than 1.6 Myr after deposition of the cap dolostone. Our results indicate that highly ^(13)C-depleted carbonate cements grew from hydrothermal fluids and suggest that their carbon isotope signatures are a consequence of thermogenic methane oxidation at depth. This finding not only negates carbon isotope evidence for methane release during Marinoan deglaciation in south China, but also eliminates the only known occurrence of a Precambrian sedimentary carbonate with highly ^(13)C-depleted signatures related to methane oxidation in a seep environment. We propose that the capacity to form highly ^(13)C-depleted seep carbonates, through biogenic anaeorobic oxidation of methane using sulphate, was limited in the Precambrian period by low sulphate concentrations in sea water. As a consequence, although clathrate destabilization may or may not have had a role in the exit from the ‘snowball’ state, it would not have left extreme carbon isotope signals in cap dolostones

Calibration and applications of the dolomite clumped isotope thermometer to high temperatures

Carbonate clumped isotope paleothermometry is based on the temperature-dependent formation of ^(13)C^(18)O^(16)O_2 ^(2-) ion groups within solid carbonate minerals. This thermometer has now been calibrated for various synthetic and natural biogenic and abiogenic minerals (calcite, aragonite and carbonateapatites [e.g., 1, 2]) at temperatures below ~ 50°C. Here we extend the use of the carbonate clumped isotope thermometer to shallow crustal environments by determining the Δ_(47) values of CO_2 extracted from natural and synthetic dolomites grown at know temperatures from 25 to 350ºC. The experimental temperature dependance is not linear in the Δ_(47) vs T^(-2) plot and resembles the predicted theoretical temperature dependence, both in shape and absolute value [3]. These data for synthetic dolomites overlap the previous calibrations for inorganic calcite and some forms of biogenic carbonates between 25 and 50˚C, and are consistent with a single trend that also intersects data for synthetic calcite equilibrated at 1200˚C. These observations suggest that a single temperature dependant relationship reasonably approximates the calibration for both phases. Data from a variety of slowly-cooled (i.e., over geological timescales) natural marbles and rapid (i.e., laboratory timescales) heating experiments provide insights into the kinetics of solid-state ^(13)C-^(18)O bond reordering in carbonates and its closure temperature. More generally, our new calibration and constraints on high-temperature kinetics have implications for the application of this technique to burial and metamorphic processes. These issues will be illustrated through estimates of the thermal history and oxygen isotopic compositions and abundances of pore fluids for several suites of late Neoproterozoic carbonates [e.g., 4]

Calibration of the dolomite clumped isotope thermometer from 25 to 350°C, and implications for a universal calibration for all (Ca, Mg, Fe)CO_3 carbonates

Carbonate clumped isotope thermometry is based on the temperature-dependent formation of ^(13)C^(18)O^(16)O_2^(2-) ion groups within the lattice of solid carbonate minerals. At low temperatures the bonds between rare, heavy ^(13)C and ^(18)O isotopes are thermodynamically favored, and thus at equilibrium they are present in higher than random abundances. Here we calibrate the use of this temperature proxy in a previously uncalibrated carbonate phase — dolomite [CaMg(CO_3)_2] — over a temperature range that extends to conditions typical of shallow crustal environments, by determining the Δ_(47) values of CO_2 extracted from synthetic or natural (proto)dolomites grown at known temperatures from 25 to 350°C and analyzed in two different laboratories using different procedures for sample analysis, purification and post-measurement data treatment. We found that the Δ_(47) – 1/T^2 dependence for (proto)dolomite is linear between 25 and 350°C, independent of their Mg/Ca compositions or cation order (or the laboratory in which they were analyzed), and offset from, but parallel to, the theoretical predictions of the Δ_(63) dependence to temperature of the abundance of the ^(13)C^(18)O^(16)O_2 isotopologue inside the dolomite and calcite mineral lattices as expected from ab-initio calculations (Schauble et al., 2006). This suggests that neither the equilibrium constant for ^(13)C–^(18)O clumping in (proto)dolomite lattice, nor the experimental fractionation associated with acid digestion to produce CO_2, depend on their formation mechanism, degree of cation order and/or stoichiometry (ie., Mg/Ca ratio) and/or δ^(18)O and δ^(13)C compositions (at least over the range we explored). Thus, we suggest the following single Δ_(47) – 1/T^2 linear regression for describing all dolomite minerals: with T in kelvin and Δ_(47) in the Carbon Dioxide Equilibrium Scale (CDES) of Dennis et al. (2011) and referring to CO_2 extracted by phosphoric acid digestion at 90°C. The listed uncertainties on slope and intercept are 95% confidence intervals. The temperature sensitivity (slope) of this relation is lower than those based on low temperature acid digestion of carbonates, but comparable to most of those based on high temperature acid digestion (with however significantly better constraints on the slope and intercept values, notably due to the large range in temperature investigated and the large number of Δ_(47) measurements performed here, n = 67). We also use this dataset to empirically determine that the acid fractionation factor associated with phosphoric acid digestion of dolomite at 90°C (Δ∗_(dolomite90)) is about + 0.176‰. This is comparable to the Δ∗_(calcite90) experimentally obtained for calcite (Guo et al., 2009), suggesting that the acid fractionation Δ∗ for acid digestion of dolomite and calcite are the same within error of measurement, with apparently no influence of the cation identity. This hypothesis is also supported by the fact that our dolomite calibration data are indistinguishable from published calibration data for calcite, aragonite and siderite generated in similar analytical conditions (ie., carbonate digested at T ⩾ 70°C and directly referenced into CDES), demonstrating excellent consistency among the four (Ca,Mg,Fe)CO_3 mineral phases analyzed in seven different laboratories (this represents a total of 103 mean Δ_(47) values resulting from more than 331 Δ_(47) measurements). These data are used to calculate a composite Δ_(47)–T universal relation for those carbonate minerals of geological interest, for temperatures between -1 and 300°C, that is found to be statistically indistinguishable from the one described by dolomite only: Thus, in order to standardize the temperature estimates out of different laboratories running high temperature digestion of (Ca,Mg,Fe)CO_3 carbonate minerals, we recommend the use of this single Δ_(47)-T calibration to convert Δ_(47CDES) data into accurate and precise temperature estimates. More widely, this study extends the use of the Δ_(47) thermometry to studies of diagenesis and low-grade metamorphism of carbonates with unprecedented precision on temperature estimates based on Δ_(47) measurements — environments where many other thermometers are generally empirical or semi-quantitative

Distribution of recycled crust within the upper mantle : insights from the oxygen isotope composition of MORB from the Australian-Antarctic Discordance

Author Posting. © American Geophysical Union, 2009. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 10 (2009): Q12004, doi:10.1029/2009GC002728Geochemical heterogeneity within the mantle has long been recognized through the diversity of trace element and radiogenic isotopic compositions of mantle-derived rocks, yet the specific origin, abundance, and distribution of enriched material within the mantle have been difficult to quantify. In particular, the origin of the distinctive geochemical characteristics of Indian mantle has been debated for decades. We present new laser fluorination oxygen isotope measurements of mid-ocean ridge basalt from the Australian-Antarctic Discordance (AAD), an area where a particularly abrupt transition occurs between Pacific-type mid-ocean ridge basalts (MORB) and Atlantic-type MORB. These data show no distinction in average δ18O between Pacific- and Atlantic-type MORB, indicating that the origin of Indian-type mantle cannot be attributed to the presence of pelagic sediment. The combined radiogenic isotope, δ18O, and trace element characteristics of Indian-type MORB at the AAD are consistent with contamination of the Indian upper mantle by lower crustal material. We also present a compilation of available laser fluorination δ18O data for MORB and use these data to evaluate the nature and percentage of enriched material within the upper mantle globally. Data for each ocean basin fit a normal distribution, with indistinguishable means and standard deviations, implying that the variation in δ18O of MORB reflects a stochastic process that operates similarly across all ocean basins. Monte Carlo simulations show that the mean and standard deviation of the MORB data are robust indicators of the mean and standard deviation of the parent distribution of data. Further, although some skewness in the data cannot be ruled out, Monte Carlo results are most consistent with a normal parent distribution. This similarity in characteristics of the δ18O data between ocean basins, together with correlations of δ18O with radiogenic isotope and trace element characteristics of subsets of the data, suggest that the upper mantle globally contains an average of ∼5–10% recycled crustal material and that the depleted mantle in the absence of this component would have δ18O of ∼5.25‰. The Monte Carlo simulations also suggest that additional oxygen isotope data may be used in the future to test the ability of geodynamical models to predict the physical distribution of enriched domains within the upper mantle

Investigating magmatic processes in the early Solar System using the Cl isotopic systematics of eucrites

Generally, terrestrial rocks, martian and chondritic meteorites exhibit a relatively narrow range in bulk and apatite Cl isotope compositions, with δ37Cl (per mil deviation from standard mean ocean chloride) values between − 5.6 and + 3.8 ‰. Lunar rocks, however, have more variable bulk and apatite δ37Cl values, ranging from ∼ − 4 to + 40 ‰. As the Howardite-Eucrite-Diogenite (HED) meteorites represent the largest suite of crustal and sub-crustal rocks available from a differentiated basaltic asteroid (4 Vesta), studying them for their volatiles may provide insights into planetary differentiation processes during the earliest Solar System history. Here the abundance and isotopic composition of Cl in apatite were determined for seven eucrites representing a broad range of textural and petrological characteristics. Apatite Cl abundances range from ∼ 25 to 4900 ppm and the δ37Cl values range from − 3.98 to + 39.2 ‰. Samples with lower apatite H2O contents were typically also enriched in 37Cl but no systematic correlation between δ37Cl and δD values was observed across samples. Modelled Rayleigh fractionation and a strong positive correlation between bulk δ66Zn and apatite δ37Cl support the hypothesis that Cl degassed as metal chlorides from eucritic magmas, in a hydrogen-poor environment. In the case of lunar samples, it has been noted that δ37Cl values of apatite positively correlate with bulk La/Yb ratio. Interestingly, most eucrites show a negative correlation with bulk La/Yb ratio. Recently, isotopically light Cl values have been suggested to record the primary solar nebular signature. If this is the case then 4 Vesta, which accreted rapidly and early in Solar System history, could also record this primary nebular signature corresponding to the lightest Cl values measured here. The significant variation in Cl isotope composition observed within the eucrites are likely related to degassing of metal chlorides

InterCarb: a community effort to improve interlaboratory standardization of the carbonate clumped isotope thermometer using carbonate standards

Increased use and improved methodology of carbonate clumped isotope thermometry has greatly enhanced our ability to interrogate a suite of Earth-system processes. However, interlaboratory discrepancies in quantifying carbonate clumped isotope (Δ47) measurements persist, and their specific sources remain unclear. To address interlaboratory differences, we first provide consensus values from the clumped isotope community for four carbonate standards relative to heated and equilibrated gases with 1,819 individual analyses from 10 laboratories. Then we analyzed the four carbonate standards along with three additional standards, spanning a broad range of δ47 and Δ47 values, for a total of 5,329 analyses on 25 individual mass spectrometers from 22 different laboratories. Treating three of the materials as known standards and the other four as unknowns, we find that the use of carbonate reference materials is a robust method for standardization that yields interlaboratory discrepancies entirely consistent with intralaboratory analytical uncertainties. Carbonate reference materials, along with measurement and data processing practices described herein, provide the carbonate clumped isotope community with a robust approach to achieve interlaboratory agreement as we continue to use and improve this powerful geochemical tool. We propose that carbonate clumped isotope data normalized to the carbonate reference materials described in this publication should be reported as Δ47 (I-CDES) values for Intercarb-Carbon Dioxide Equilibrium Scale