Experimental calibration of clumped isotope reodering in dolomite

Dolomite clumped isotope compositions are indispensable for determining the temperatures and fluid sources of dolomitizing environments, but can be misleading if they have modified since formation. Carbonate Δ_(47) values are susceptible to resetting by recrystallization during diagenesis, and, even in the absence of dissolution and reprecipitation reactions, alteration by solid-state reordering during prolonged residences at elevated temperatures. In order to understand the potential of dolomite Δ_(47) values to preserve the conditions of dolomitizationin ancient sections, the kinetic parameters of solid-state reordering in this phase must be determined. We heated mm-sized crystals of near-stoichiometric dolomite in a René-type cold seal apparatus at temperatures between 409 and 717 °C for 0.1–450 h. In order to prevent the decarbonation of dolomite to calcite, periclase, and CO_2 at these conditions, the system was pressurized with CO_2 to 0.45–0.8 kbar. Over the course of 31 temperature-time points and 128 individual Δ_(47) measurements of powdered dolomite crystals from these points, we observed the evolution of dolomite Δ_(47) values from the initial (unheated) composition of the crystals (0.452 ± 0.004‰, corresponding to a formation temperature of ∼145 °C) towards high-temperature equilibrium distributions. Complete re-equilibration occurred in the 563–717 °C experiments. As with previous heating experiments using calcite and apatite, dolomite Δ_(47) exhibited complex reordering behavior inadequately described by first-order Arrhenian-style models. Instead, we fit the data using two published models for clumped isotope reordering: the transient defect/equilibrium defect model of Henkes et al. (2014), and the exchange-diffusion model of Stolper and Eiler (2015). For both models, we found optimal reordering parameters by using global least-squares minimization algorithms and estimated uncertainties on these fits with a Monte Carlo scheme that resampled individual Δ_(47) measurements and re-fit the dataset of these new mean values. Because the exact Δ_(47)–T relationship between 250 and 800 °C is uncertain, we repeated these fitting exercises using three published high-temperature Δ_(47)–T calibrations. Regardless of calibration choice, dolomite Δ_(47) rate constants determined using both models are resolvably slower than those of calcite and apatite, and predict that high-grade dolomite crystals should preserve apparent equilibrium blocking temperatures of between ∼210 and 300 °C during cooling on geologic timescales. Best agreement between model predictions and natural dolomite marbles was found when using the exchange-diffusion model and the ab initio Δ_(63)–T calibration of Schauble et al. (2006), projected into the Δ_(47) reference frame by Bonifacie et al. (2017). Therefore, we recommend modeling dolomite Δ_(47) reordering using the exchange-diffusion model and this parameter set. In simple heating scenarios, the two models disagree. The transient defect/equilibrium defect model suggests that dolomite fabrics resist detectable reordering at ambient temperatures as high as 180 °C for tens of millions of years, while the exchange-diffusion model predicts incipient partial reordering perhaps as low as 150 °C. In either case, barring later recrystallization, dolomite Δ_(47) values should be faithful recorders of the conditions of dolomitization in sedimentary sections buried no hotter than ∼150 °C for tens of millions of years

Clumped Isotope Thermometry Of Calcite And Dolomite In A Contact Metamorphic Environment

Clumped isotope compositions of slowly-cooled calcite and dolomite marbles record apparent equilibrium temperatures of roughly 150-200 °C and 300-350 °C, respectively. Because clumped isotope compositions are sensitive to the details of T-t path within these intervals, measurements of the Δ_(47) values of coexisting calcite and dolomite can place new constraints on thermal history of low-grade metamorphic rocks over a large portion of the upper crust (from ∼5 to ∼15 km depth). We studied the clumped isotope geochemistry of coexisting calcite and dolomite in marbles from the Notch Peak contact metamorphic aureole, Utah. Here, flat-lying limestones were intruded by a pluton, producing a regular, zoned metamorphic aureole. Calcite Δ_(47) temperatures are uniform, 156 ± 12 ˚C (2σ s.e.), across rocks varying from high-grade marbles that exceeded 500 °C to nominally unmetamorphosed limestones >5 km from the intrusion. This result appears to require that the temperature far from the pluton was close to this value; an ambient temperature just 20 ˚C lower would not have permitted substantial re-equilibration, and should have preserved depositional or early diagenetic Δ_(47) values several km from the pluton. Combining this result with depth constraints from overlying strata suggests the country rock here had an average regional geotherm of 22.3–27.4 ˚C/km from the late Jurassic Period until at least the middle Paleogene Period. Dolomite Δ_(47) in all samples above the talc+tremolite-in isograd record apparent equilibrium temperatures of 328^(+13)_(-12) °C (1σ s.e.), consistent with the apparent equilibrium blocking temperature we expect for cooling from peak metamorphic conditions. At greater distances, dolomite Δ_(47) records temperatures of peak (anchi)metamorphism or pre-metamorphic diagenetic conditions. The interface between these domains is the location of the 330 ˚C isotherm associated with intrusion. Multiple-phase clumped isotope measurements are complemented by bulk δ^(13)C and δ^(18)O dolomite-calcite thermometry. These isotopic exchange thermometers are largely consistent with peak temperatures in all samples within 4 km of the contact, indicating that metamorphic recrystallization can occur even in samples too low-grade to produce growth of conventional metamorphic index minerals (i.e., talc and tremolite). Altogether, this work demonstrates the potential of these methods to quantify the conditions of metamorphism at sub-greenschist facies

Experimental calibration of clumped isotope reodering in dolomite

Dolomite clumped isotope compositions are indispensable for determining the temperatures and fluid sources of dolomitizing environments, but can be misleading if they have modified since formation. Carbonate Δ_(47) values are susceptible to resetting by recrystallization during diagenesis, and, even in the absence of dissolution and reprecipitation reactions, alteration by solid-state reordering during prolonged residences at elevated temperatures. In order to understand the potential of dolomite Δ_(47) values to preserve the conditions of dolomitizationin ancient sections, the kinetic parameters of solid-state reordering in this phase must be determined. We heated mm-sized crystals of near-stoichiometric dolomite in a René-type cold seal apparatus at temperatures between 409 and 717 °C for 0.1–450 h. In order to prevent the decarbonation of dolomite to calcite, periclase, and CO_2 at these conditions, the system was pressurized with CO_2 to 0.45–0.8 kbar. Over the course of 31 temperature-time points and 128 individual Δ_(47) measurements of powdered dolomite crystals from these points, we observed the evolution of dolomite Δ_(47) values from the initial (unheated) composition of the crystals (0.452 ± 0.004‰, corresponding to a formation temperature of ∼145 °C) towards high-temperature equilibrium distributions. Complete re-equilibration occurred in the 563–717 °C experiments. As with previous heating experiments using calcite and apatite, dolomite Δ_(47) exhibited complex reordering behavior inadequately described by first-order Arrhenian-style models. Instead, we fit the data using two published models for clumped isotope reordering: the transient defect/equilibrium defect model of Henkes et al. (2014), and the exchange-diffusion model of Stolper and Eiler (2015). For both models, we found optimal reordering parameters by using global least-squares minimization algorithms and estimated uncertainties on these fits with a Monte Carlo scheme that resampled individual Δ_(47) measurements and re-fit the dataset of these new mean values. Because the exact Δ_(47)–T relationship between 250 and 800 °C is uncertain, we repeated these fitting exercises using three published high-temperature Δ_(47)–T calibrations. Regardless of calibration choice, dolomite Δ_(47) rate constants determined using both models are resolvably slower than those of calcite and apatite, and predict that high-grade dolomite crystals should preserve apparent equilibrium blocking temperatures of between ∼210 and 300 °C during cooling on geologic timescales. Best agreement between model predictions and natural dolomite marbles was found when using the exchange-diffusion model and the ab initio Δ_(63)–T calibration of Schauble et al. (2006), projected into the Δ_(47) reference frame by Bonifacie et al. (2017). Therefore, we recommend modeling dolomite Δ_(47) reordering using the exchange-diffusion model and this parameter set. In simple heating scenarios, the two models disagree. The transient defect/equilibrium defect model suggests that dolomite fabrics resist detectable reordering at ambient temperatures as high as 180 °C for tens of millions of years, while the exchange-diffusion model predicts incipient partial reordering perhaps as low as 150 °C. In either case, barring later recrystallization, dolomite Δ_(47) values should be faithful recorders of the conditions of dolomitization in sedimentary sections buried no hotter than ∼150 °C for tens of millions of years

Mechanism of Solid-State Clumped Isotope Reordering in Carbonate Minerals from Aragonite Heating Experiments

The clumped isotope compositions of carbonate minerals are subject to alteration at elevated temperatures. Understanding the mechanism of solid-state reordering in carbonate minerals is important in our interpretations of past climates and the thermal history of rocks. The kinetics of solid-state isotope reordering has been previously studied through controlled heating experiments of calcite, dolomite and apatite. Here we further explore this issue through controlled heating experiments on aragonite. We find that Δ_(47) values generally decrease during heating of aragonite, but increase by 0.05–0.15‰ as aragonite starts to transform into calcite. We argue that this finding is consistent with the presence of an intermediate pool of immediately adjacent singly-substituted carbonate ion isotopologues (‘pairs’), which back-react to form clumped isotopologues during aragonite to calcite transformation, revealing the existence of kinetically preferred isotope exchange pathways. Our results reinforce the ‘reaction-diffusion’ model as the mechanism for solid-state clumped isotope reordering in carbonate minerals. Our experiments also reveal that the reordering kinetics in aragonite is faster than in calcite and dolomite, making its clumped isotope composition highly susceptible to alteration during early diagenesis, even before conversion to calcite

Clumped Isotope Thermometry Of Calcite And Dolomite In A Contact Metamorphic Environment

Clumped isotope compositions of slowly-cooled calcite and dolomite marbles record apparent equilibrium temperatures of roughly 150-200 °C and 300-350 °C, respectively. Because clumped isotope compositions are sensitive to the details of T-t path within these intervals, measurements of the Δ_(47) values of coexisting calcite and dolomite can place new constraints on thermal history of low-grade metamorphic rocks over a large portion of the upper crust (from ∼5 to ∼15 km depth). We studied the clumped isotope geochemistry of coexisting calcite and dolomite in marbles from the Notch Peak contact metamorphic aureole, Utah. Here, flat-lying limestones were intruded by a pluton, producing a regular, zoned metamorphic aureole. Calcite Δ_(47) temperatures are uniform, 156 ± 12 ˚C (2σ s.e.), across rocks varying from high-grade marbles that exceeded 500 °C to nominally unmetamorphosed limestones >5 km from the intrusion. This result appears to require that the temperature far from the pluton was close to this value; an ambient temperature just 20 ˚C lower would not have permitted substantial re-equilibration, and should have preserved depositional or early diagenetic Δ_(47) values several km from the pluton. Combining this result with depth constraints from overlying strata suggests the country rock here had an average regional geotherm of 22.3–27.4 ˚C/km from the late Jurassic Period until at least the middle Paleogene Period. Dolomite Δ_(47) in all samples above the talc+tremolite-in isograd record apparent equilibrium temperatures of 328^(+13)_(-12) °C (1σ s.e.), consistent with the apparent equilibrium blocking temperature we expect for cooling from peak metamorphic conditions. At greater distances, dolomite Δ_(47) records temperatures of peak (anchi)metamorphism or pre-metamorphic diagenetic conditions. The interface between these domains is the location of the 330 ˚C isotherm associated with intrusion. Multiple-phase clumped isotope measurements are complemented by bulk δ^(13)C and δ^(18)O dolomite-calcite thermometry. These isotopic exchange thermometers are largely consistent with peak temperatures in all samples within 4 km of the contact, indicating that metamorphic recrystallization can occur even in samples too low-grade to produce growth of conventional metamorphic index minerals (i.e., talc and tremolite). Altogether, this work demonstrates the potential of these methods to quantify the conditions of metamorphism at sub-greenschist facies

Position-Specific Hydrogen Isotope Equilibrium in Propane

Intramolecular isotope distributions can constrain source attribution, mechanisms of formation and destruction, and temperature-time histories of molecules. In this study, we explore the D/H fractionation between central (-CH_2-) and terminal (-CH_3) positions of propane (C_3H_8)- a percent level component of natural gases. The temperature dependenceof position-specific D/H fractionation of propane could potentially work as a geo-thermometer for natural gas systems, and a forensic identifier of specific thermogenic sources of atmospheric or aquatic emissions. Moreover, kinetically controlled departures from temperature dependent equilibrium might constrain mechanisms of thermogenic production, or provide indicators of biological or photochemical destruction. We developed a method to measure position-specific D/H differences of propane with high-resolution gas source mass spectrometry. We performed laboratory exchange experiments to study the exchange ratesfor both terminal and central positions, and used catalysts to drive the hydrogen isotopedistribution of propane to thermodynamic equilibrium. Experimental results demonstrate that D/H exchange between propane and water happens easily in the presence of either Pd catalyst or Ni catalyst. Exchange rates are similar between the two positions catalyzed by Pd. However, the central position exchanges 2.2 times faster than the terminal position in the presence of Ni catalyst. At 200 °C in the presence of Pd catalyst, the e-folding time of propane-water exchange is 20 days and of homogeneous exchange (i.e., equilibrium between central and terminal positions) is 28 min. An equilibrated (bracketed and time-invariant) intramolecular hydrogen isotope distribution was attained for propane at three temperatures, 30 °C, 100 °C and 200 °C; these data serve as an initial experimental calibration of a new position-specific thermometer with a temperature sensitivity of 0.25‰ per °C at 100 °C. We use this calibration to test the validity of prior published theoretical predictions. Comparison of data with models suggest the most sophisticated of these discrepant models (Webb and Miller, 2014) is most accurate; this conclusion implies that there is a combined experimental and theoretical foundation for an ‘absolute reference frame’ for position-specific H isotope analysis of propane, following principles previously used for clumped isotope analysis of CO_2, CH_4 and O_2 (Eiler and Schauble, 2004; Yeung et al., 2014; Stolper et al., 2014)

Comparison of Experimental vs Theoretical Abundances of ¹³CH₃D and ¹²CH₂D₂ for Isotopically Equilibrated Systems from 1 to 500 °C

Methane is produced and consumed via numerous microbial and chemical reactions in atmospheric, hydrothermal, and magmatic reactions. The stable isotopic composition of methane has been used extensively for decades to constrain the source of methane in the environment. A recently introduced isotopic parameter used to study the formation temperature and formational conditions of methane is the measurement of molecules of methane with multiple rare, heavy isotopes (‘clumped’) such as ¹³CH₃D and ¹²CH₂D₂. In order to place methane clumped-isotope measurements into a thermodynamic reference frame that allows calculations of clumped-isotope based temperatures (geothermometry) and comparison between laboratories, all past studies have calibrated their measurements using a combination of experiment and theory based on the temperature dependence of clumped isotopologue distributions for isotopically equilibrated systems. These have previously been performed at relatively high temperatures (>150˚C). Given that many natural occurrences of methane form below these temperatures, previous calibrations require extrapolation when calculating clumped-isotope based temperatures outside of this calibration range. We provide a new experimental calibration of the relative equilibrium abundances of ¹³CH₃D and ¹²CH₂D₂ from 1–500˚C using a combination of γ-Al₂O₃ and Ni-based catalysts and compare them to new theoretical computations using Path Integral Monte Carlo (PIMC) methods and find 1:1 agreement (within ± 1 standard error) for the observed temperature dependence of clumping between experiment and theory over this range. This demonstrates that measurements, experiments, and theory agree from 1–500°C providing confidence in the overall approaches. Polynomial fits to PIMC computations, which are considered the most rigorous theoretical approach available, are given as follows (valid T ≥ 270 K): ∆¹³CH₃D≅1000×ln(K¹³CH₃D)= 1.47348×10¹⁹/T⁷ - 2.08648×10¹⁷/T⁶ + 1.19810×10¹⁵/T⁵ - 3.54757×10¹²/T⁴ +5.54476×10⁹/T³ – 3.49294×10⁶/T² + 8.89370×10₂/T ∆¹²CH₂D₂≅1000×ln(8/3×K¹²CH₂D₂)= -9.67634×10¹⁵/T⁶ + 1.71917×10¹⁴/T⁵ - 1.24819×10¹²/T⁴ + 4.30283×10⁹/T3 -4.48660×10⁶/T² + 1.86258×10³/T. We additionally compare PIMC computations to those performed utilizing traditional approaches that are the basis of most previous calibrations (Bigeleisen, Mayer, and Urey model, BMU) and discuss the potential sources of error in the BMU model relative to PIMC computations

Mechanism of Solid-State Clumped Isotope Reordering in Carbonate Minerals from Aragonite Heating Experiments

The clumped isotope compositions of carbonate minerals are subject to alteration at elevated temperatures. Understanding the mechanism of solid-state reordering in carbonate minerals is important in our interpretations of past climates and the thermal history of rocks. The kinetics of solid-state isotope reordering has been previously studied through controlled heating experiments of calcite, dolomite and apatite. Here we further explore this issue through controlled heating experiments on aragonite. We find that Δ_(47) values generally decrease during heating of aragonite, but increase by 0.05–0.15‰ as aragonite starts to transform into calcite. We argue that this finding is consistent with the presence of an intermediate pool of immediately adjacent singly-substituted carbonate ion isotopologues (‘pairs’), which back-react to form clumped isotopologues during aragonite to calcite transformation, revealing the existence of kinetically preferred isotope exchange pathways. Our results reinforce the ‘reaction-diffusion’ model as the mechanism for solid-state clumped isotope reordering in carbonate minerals. Our experiments also reveal that the reordering kinetics in aragonite is faster than in calcite and dolomite, making its clumped isotope composition highly susceptible to alteration during early diagenesis, even before conversion to calcite

Decentralized Estimation over Orthogonal Multiple-access Fading Channels in Wireless Sensor Networks - Optimal and Suboptimal Estimators

Optimal and suboptimal decentralized estimators in wireless sensor networks (WSNs) over orthogonal multiple-access fading channels are studied in this paper. Considering multiple-bit quantization before digital transmission, we develop maximum likelihood estimators (MLEs) with both known and unknown channel state information (CSI). When training symbols are available, we derive a MLE that is a special case of the MLE with unknown CSI. It implicitly uses the training symbols to estimate the channel coefficients and exploits the estimated CSI in an optimal way. To reduce the computational complexity, we propose suboptimal estimators. These estimators exploit both signal and data level redundant information to improve the estimation performance. The proposed MLEs reduce to traditional fusion based or diversity based estimators when communications or observations are perfect. By introducing a general message function, the proposed estimators can be applied when various analog or digital transmission schemes are used. The simulations show that the estimators using digital communications with multiple-bit quantization outperform the estimator using analog-and-forwarding transmission in fading channels. When considering the total bandwidth and energy constraints, the MLE using multiple-bit quantization is superior to that using binary quantization at medium and high observation signal-to-noise ratio levels

Position-Specific Hydrogen Isotope Equilibrium in Propane

Intramolecular isotope distributions can constrain source attribution, mechanisms of formation and destruction, and temperature-time histories of molecules. In this study, we explore the D/H fractionation between central (-CH_2-) and terminal (-CH_3) positions of propane (C_3H_8)- a percent level component of natural gases. The temperature dependenceof position-specific D/H fractionation of propane could potentially work as a geo-thermometer for natural gas systems, and a forensic identifier of specific thermogenic sources of atmospheric or aquatic emissions. Moreover, kinetically controlled departures from temperature dependent equilibrium might constrain mechanisms of thermogenic production, or provide indicators of biological or photochemical destruction. We developed a method to measure position-specific D/H differences of propane with high-resolution gas source mass spectrometry. We performed laboratory exchange experiments to study the exchange ratesfor both terminal and central positions, and used catalysts to drive the hydrogen isotopedistribution of propane to thermodynamic equilibrium. Experimental results demonstrate that D/H exchange between propane and water happens easily in the presence of either Pd catalyst or Ni catalyst. Exchange rates are similar between the two positions catalyzed by Pd. However, the central position exchanges 2.2 times faster than the terminal position in the presence of Ni catalyst. At 200 °C in the presence of Pd catalyst, the e-folding time of propane-water exchange is 20 days and of homogeneous exchange (i.e., equilibrium between central and terminal positions) is 28 min. An equilibrated (bracketed and time-invariant) intramolecular hydrogen isotope distribution was attained for propane at three temperatures, 30 °C, 100 °C and 200 °C; these data serve as an initial experimental calibration of a new position-specific thermometer with a temperature sensitivity of 0.25‰ per °C at 100 °C. We use this calibration to test the validity of prior published theoretical predictions. Comparison of data with models suggest the most sophisticated of these discrepant models (Webb and Miller, 2014) is most accurate; this conclusion implies that there is a combined experimental and theoretical foundation for an ‘absolute reference frame’ for position-specific H isotope analysis of propane, following principles previously used for clumped isotope analysis of CO_2, CH_4 and O_2 (Eiler and Schauble, 2004; Yeung et al., 2014; Stolper et al., 2014)