How to estimate isotope fractionations of a Rayleigh-like but diffusion-limited disequilibrium process?

The Rayleigh distillation isotope fractionation(RDIF) model is one of the most popular methods used in isotope geochemistry. Numerous isotope signals observed in geologic processes have been interpreted with this model. The RDIF model provides a simple mathematic solution for the reservoir-limited equilibrium isotope fractionation effect. Due to the reservoir effect, tremendously large isotope fractionations will always be produced if the reservoir is close to being depleted. However, in real situations, many prerequisites assumed in the RDIF model are often difficult to meet. For instance, it requires the relocated materials, which are removed step by step from one reservoir to another with different isotope compositions(i.e., with isotope fractionation), to be isotopically equilibrated with materials in the first reservoir simultaneously. This ‘‘quick equilibrium requirement’’ is indeed hard to meet if the first reservoir is sufficiently large or the removal step is fast. The whole first reservoir will often fail to re-attain equilibrium in time before the next removal starts.This problem led the RDIF model to fail to interpret isotope signals of many real situations. Here a diffusion-coupled and Rayleigh-like(i.e., reservoir-effect included) separation process is chosen to investigate this problem. We find that the final isotope fractionations are controlled by both the diffusion process and the reservoir effects via the disequilibrium separation process. Due to its complexity, we choose to use a numerical simulation method to solve this problem by developing specific computing codes for the working model.According to our simulation results, the classical RDIF model only governs isotope fractionations correctly at the final stages of separation when the reservoir scale(or thickness of the system) is reduced to the order of magnitude of the quotient of the diffusivity and the separation rate. The RDIF model fails in other situations and the isotope fractionations will be diffusion-limited when the reservoir is relatively large, or the separation rate is fast. We find that the effect of internal isotope distribution inhomogeneity caused by diffusion on the Rayleigh-like separation process is significant and cannot be ignored. This method can be applied to study numerous geologic and planetary processes involving diffusion-limited disequilibrium separation processes including partial melting,evaporation, mineral precipitation, core segregation, etc.Importantly, we find that far more information can be extracted through analyzing isotopic signals of such ‘‘disequilibrium’’processes than those of fully equilibrated ones, e.g., reservoir size and the separation rate. Such information may provide a key to correctly interpreting many isotope signals observed from geochemical and cosmochemical processes.

Simulation Experiments on the Reaction of CH_4-CaSO_4 and Its Carbon Kinetic Isotope Fractionation

Thermochemical sulfate reduction (TSR) in geological deposits can account for the accumulation of H2S in deep sour gas reservoirs. In this paper, thermal simulation experiments on the reaction of CH4-CaSO4 were carried out using an autoclave at high temperatures and high pressures. The products were characterized with analytical methods including carbon isotope analysis. It is found that the reaction can proceed to produce H2S, H2O and CaCO3 as the main products. Based on the experimental results, the carbon kinetic isotope fractionation was investigated, and the value of Ki (kinetic isotope effect) was calculated. The results obtained in this paper can provide useful information to explain the occurrence of H2S in deep carbonate gas reservoirs.

Hydrogen and Oxygen Isotope Fractionation Mechanism in the Hydrothermal System and Its Geologic Significance

The geochemical behaviors of hydrogen and oxygen isotopes in the hydrothermal system and their inher-ent relationship with the water / rock exchange are discussed in this paper In addition to the temperature con-ditions, the effective W / R ratio is another factor controlling the changes in H and O isotope compositions ofthe altered rock and hydrothermal water. Besides, the application and geological significance of the water-rockexchange theory are also discussed in the light of the H and O isotope compositions and their variation charac-teristics of the mineralizing hydrothermal water and altered rocks from several mineral deposits. Finally, abrief evolutional model of H and O istotope compositions of meteoric and magmatic hydrothermal waters in ahydrothermal system is given.

First-principles Study on Equilibrium Sn Isotope Fractionations in Hydrothermal Fluids

Tin(Sn)isotope geochemistry has great potential in tracing geological processes.However,lack of equilibrium Sn isotope fractionation factors of various Sn species limits the development of Sn isotope geochemistry.Equilibrium Sn isotope fractionation factors(124Sn/116Sn and 122Sn/116Sn)among various Sn(II,IV)complexes in aqueous solution were calculated using first-principles calculations.The results show that the oxidation states and the change of Sn(II,IV)species in hydrothermal fluids are the main factors leading to tin isotope fractionation in hydrothermal systems.For the Sn(IV)complexes,Sn isotope fractionation factors depend on the number of H2O molecules.For the Sn(II)complexes,the Sn isotope fractionation between Sn(II)−F,Sn(II)−Cl and Sn(II)−OH complexes is mainly affected by the bond length and the coordination number of anion,whereas the difference in 1000lnβvalues of Sn(II)−SO4 and Sn(II)−CO_(3) complexes is insignificant with the change of anion coordination number.By comparing the 1000lnβvalues of all Sn(II,IV)complexes,the enrichment trend in heavy Sn isotopes is Sn(IV)complexes>Sn(II)complexes.The equilibrium Sn isotopic fractionation factors enhance our understanding of the tin transportation and enrichment processes in hydrothermal systems.

Phase transformation-induced Mg isotope fractionation in Mgmediated CaCO_(3)mineralization

The biomineralization of CaCO_(3)often involves the transformation of amorphous precursors into crystalline phases,which is regulated by various proteins and inorganic ions such as Mg^(2+)ions.While the effects of Mg^(2+)ions on the polymorph and shape of the crystalline CaCO_(3)have been observed and studied,the interplay between Mg^(2+)ions and CaCO_(3)during the mineralization remains unclear.This work focuses on the mechanism of Mg^(2+)ion-regulated mineralization of CaCO_(3).By tracing the Mg isotope fractionation,the different mineralization pathways of CaCO_(3)under different Mg^(2+)ion concentrations had been clarified.Detailed regulatory role of Mg^(2+)ions at the different stages of mineralization had been proposed through combining the fractionation data with the analyses of the CaCO_(3)polymorph and shape evolution.These results provide a clear view of the Mg-mediated crystallization process of amorphous CaCO_(3),which can be used to finely control the phase of the crystalline products according to different needs.

Assessment of aerobic biodegradation of lower-chlorinated benzenes in contaminated groundwater using field-derived microcosms and compound-specific carbon isotope fractionation

Biodegradation of lower chlorinated benzenes(tri-, di-and monochlorobenzene) was assessed at a coastal aquifer contaminated with multiple chlorinated aromatic hydrocarbons. Field-derived microcosms, established with groundwater from the source zone and amended with a mixture of lower chlorinated benzenes, evidenced biodegradation of monochlorobenzene(MCB) and 1,4-dichlorobenzene(1,4-DCB) in aerobic microcosms,whereas the addition of lactate in anaerobic microcosms did not enhance anaerobic reductive dechlorination. Aerobic microcosms established with groundwater from the plume consumed several doses of MCB and concomitantly degraded the three isomers of dichlorobenzene with no observable inhibitory effect. In the light of these results, we assessed the applicability of compound stable isotope analysis to monitor a potential aerobic remediation treatment of MCB and 1,4-DCB in this site. The carbon isotopic fractionation factors(ε) obtained from field-derived microcosms were-0.7‰ ± 0.1 ‰ and-1.0‰ ± 0.2 ‰ for MCB and1,4-DCB, respectively. For 1,4-DCB, the carbon isotope fractionation during aerobic biodegradation was reported for the first time. The weak carbon isotope fractionation values for the aerobic pathway would only allow tracing of in situ degradation in aquifer parts with high extent of biodegradation. However, based on the carbon isotope effects measured in this and previous studies, relatively high carbon isotope shifts(i.e., Δδ13C > 4.0 ‰) of MCB or 1,4-DCB in contaminated groundwater would suggest that their biodegradation is controlled by anaerobic reductive dechlorination.

Copper Isotope Fractionation during Basalt Leaching at 25℃ and pH=0.3,2

The geochemical cycling of copper in the hydrosphere and soil environments primarily involves the transport of Cu from rocks to rivers via weathering.Understanding the factors controlling Cu isotope fractionation during weathering is crucial for the purpose of using Cu isotopes as a tracer of geochemical cycling.Here,we performed acid-leaching experiments on natural basalts (BHVO-2 and GBW07105) and chalcopyrite in Erlenmeyer flasks at T=25℃ and different pH values (0.3 and 2).Our results reveal substantial Cu isotope fractionations (△^(65)Cu_(solution-initial)) between leachates (Cu_(solution)) and starting materials (Cu_(initial)).The leachates released from GBW07105 and chalcopyrite are consistently enriched in heavier Cu isotopes relative to the starting materials at pH=2.However,the δ^(65)Cu_(solution)values decrease to about-0.6‰first,then increase to>0 for BHVO-2 at pH=2 and GBW07105 at pH=0.3.Our results indicate that leaching of natural rocks by acidic liquids can produce both positive and negative Cu isotope fractionation,depending on pH values and the types of minerals in starting materials.X-ray power diffraction analysis (XRD) patterns reveal similar mineral assemblages between starting basalts and residues after each reaction round.The most likely mechanisms responsible for such Cu isotope fractionation are the relative rates of Cu oxidation at the surface and Cu release into solution,and the sequence of mineral dissolution.Our study represents an important step for future studies to use Cu isotopes to explain Cu isotopic variations in natural rocks and waters.

New insight into iron biogeochemical cycling in soil-rice plant system using iron isotope fractionation

Iron (Fe) migration in soil-plants is a critical part of Fe biogeochemical cycling in the earth surface system. Fe isotope fractionation analysis in the soil-rice system is promising for quantitatively assessing various pathways and clarifying Fe transformation processes. However, the mechanisms of Fe isotope fractionation in the soil-rice system are not well understood. In this study, the Fe isotopic compositions (δ^(56)Fe) of rhizosphere soils, pore water, Fe plaque, and rice plant tissues at the jointing and mature stages of the plants were determined. The rice plants were slightly enriched in heavier δ^(56)Fe by 0.3‰ relative to the soil, and the stele and cortex showed similar δ^(56)Fe values, indicating that the uptake of Fe by rice plants predominantly occurred via Fe(III)-phytosiderophores (Fe(III)-PS) chelation, but not Fe(III) reduction. Additionally, at both the jointing and mature stages, the rice plant tissues showed similar δ^(56)Fe values. However, the Fe isotope fractionation between the roots and stems (Δ56Feroot−stem) was 1.39 ± 0.13‰, which is similar to the previously Ab initio-calculated values between Fe(III)-citrate and Fe(III)- 2-deoxymugineic acid (DMA), indicating that both the phloem and xylem have similar δ^(56)Fe values, and the major Fe-chelating substances in the phloem of the rice plants are Fe(III)-DMA and Fe(II)- Nicotianamine (NA). Therefore, this study demonstrates that Fe isotope fractionation can be used as a signature for interpreting the Fe uptake and translocation mechanism in the soil-rice system.

Oxygen Isotope Fractionation of Common RE Fluorocarbonate

Fluorocarbonate is one of the most important RE minerals in the earth With the increment model developed by Zheng, oxygen isotope fractionation of RE fluorocarbonates is discussed and the 18 O enrichment order is obtained as follows: bastnaesite>cordylite>Ca 0 5 BaCe 2(CO 3) 4F>baiyuneboite>huangheite>cebaite Combining with the calculated equation, the oxygen isotopic compositions in RE fluorocarbonate from Bayan Obo ore deposit is discussed, and a better accordance of 18 O enrichment order with actual data on ore forming temperature with the ore deposit geology are found Because Ba RE fluorocarbonate could be considered as a stacking of CeCO 3F and BaCO 3 layers in the direction c , oxygen isotope fractionation in this stacking is discussed, and I in zhonghuacerite and cordylite is predicted with this model

HYDROGEN ISOTOPE FRACTIONATION BETWEEN ILVAITE AND WATER

A lot of experimental studies have been made on hydrogen isotope fractionation for hydrous minerals, such as mica, amphibole, epidote-group minerals, serpentine, aluminous-chlorite etc., since the 1970s. This plays an important role in the development of hydrogen isotope geochemistry. We have first made the experimental study on

Research progress on isotopic fractionation in the process of shale gas/coalbed methane migration

The research progress of isotopic fractionation in the process of shale gas/coalbed methane migration has been reviewed from three aspects: characteristics and influencing factors, mechanism and quantitative characterization model, and geological application. It is found that the isotopic fractionation during the complete production of shale gas/coalbed methane shows a four-stage characteristic of “stable-lighter-heavier-lighter again”, which is related to the complex gas migration modes in the pores of shale/coal. The gas migration mechanisms in shale/coal include seepage, diffusion, and adsorption/desorption. Among them, seepage driven by pressure difference does not induce isotopic fractionation, while diffusion and adsorption/desorption lead to significant isotope fractionation. The existing characterization models of isotopic fractionation include diffusion fractionation model, diffusion-adsorption/desorption coupled model, and multi-scale and multi-mechanism coupled model. Results of model calculations show that the isotopic fractionation during natural gas migration is mainly controlled by pore structure, adsorption capacity, and initial/boundary conditions of the reservoir rock. So far, the isotope fractionation model has been successfully used to evaluate critical parameters, such as gas-in-place content and ratio of adsorbed/free gas in shale/coal etc. Furthermore, it has shown promising application potential in production status identification and decline trend prediction of gas well. Future research should focus on:(1) the co-evolution of carbon and hydrogen isotopes of different components during natural gas migration,(2) the characterization of isotopic fractionation during the whole process of gas generation-expulsion-migration-accumulation-dispersion, and(3) quantitative characterization of isotopic fractionation during natural gas migration in complex pore-fracture systems and its application.

Carbon isotopic fractionation during vaporization of low molecular weight hydrocarbons(C6–C12)

Three series of laboratory vaporization experiments were conducted to investigate the carbon isotope fractionation of low molecular weight hydrocarbons（LMWHs）during their progressive vaporization.In addition to the analysis of a synthetic oil mixture,individual compounds were also studied either as pure single phases or mixed with soil.This allowed influences of mixing effects and diffusion though soil on the fractionation to be elucidated.The LMWHs volatilized in two broad behavior patterns that depended on their molecular weight and boiling point.Vaporization significantly enriched the ^13C present in the remaining components of the C6–C9 fraction,indicating that the vaporization is mainly kinetically controlled;the observed variations could be described with a Rayleigh fractionation model.In contrast,the heavier compounds（n-C10–n-C12）showed less mass loss and almost no significant isotopic fractionation during vaporization,indicating that the isotope characteristics remained sufficiently constant for these hydrocarbons to be used to identify the source of an oil sample,e.g.,the specific oil field or the origin of a spill.Furthermore,comparative studies suggested that matrix effects should be considered when the carbon isotope ratios of hydrocarbons are applied in the field.

Iron Isotopic Fractionation and Origin of Chromitites in the Paleo-Moho Transition Zone of the Kop Ophiolite, NE Turkey

The Kop ophiolite in NE Turkey is a fragment of Neo-Tethyan forearc.It can be mainly divided into a paleo-Moho transition zone(MTZ)in the North and a harzburgitic mantle sequence in the South.Dunites are predominant in the MTZ of the Kop ophiolite,and they are locally interlayered with chromitites and enclose minor bodies of harzburgites near the petrological Moho boundary.Large Fe isotopic variations were observed for magnesiochromite(-0.14‰to 0.06‰)and olivine(-0.12‰to 0.14‰)from the MTZ chromitites,dunites and harzburgites.In individual dunite samples,magnesiochromite usually has lighter Fe isotopic compositions than olivine,which was probably caused by subsolidus Mg-Fe exchange between the two mineral phases.Both magnesiochromite and olivine display an increasing trend ofδ56Fe along a profile from chromitite todunite.This trend reflects continuous fractional crystallization in a magma chamber,which resulted in heavier Fe isotopes concentrated in the evolved magmas.In each cumulative cycle of chromitite and dunite,dunite was formed from relatively evolved melts after massive precipitation of magnesiochromite.Mixing of more primitive and evolved melts in the magma chamber was a potential mechanism for triggering the crystallization of magnesiochromite,generating chromitite layers in the cumulate pile.Before mixing happened,the primitive melts had reacted with mantle harzburgites during their ascendance;whereas the evolved melts may lie on the olivine-chromite cotectic near the liquidus field of pyroxene.Variable degrees of magma mixing and differentiation are expected to generate melts with differentδ56Fe values,accounting for the Fe isotopic variations of the Kop MTZ.

Geochemical Trace of Silicon Isotopes of Intrusions and Ore Veins Related to Alkali-rich Porphyry Deposits in Western Yunnan, China

Western Yunnan is the well-known polymetallic province in China. It is characterized by copper-gold mineralization related to Cenozoic alkali-rich porphyry. This paper analyzes the silicon isotope data obtained from four typical alkali-rich porphyry deposits based on the dynamic fractionation principle of silicon isotope. The study shows that the ore materials should originate mainly from alkali-rich magmas, together with silicon-rich mineralizing fluids. The process of mineralization was completed by auto-metasomatism, i.e. silicon-rich mineralizing fluids (including alkali-rich porphyry and wall-rock strata) replaced and altered the country rocks and contaminated with crustal rocks during the crystallization of alkali-rich magmas. Such a process is essentially the continuance of the metasomatism of mantle fluids in crust's mineralization. This provides important evidence of silicon isotopic geochemistry for better understanding the mineralization of the Cenozoic alkali-rich porphyry polymetallic deposits

Experimental study of relationship between average isotopic fractionation factor and evaporation rate

Isotopic fractionation is the basis of tracing the water cycle using hydrogen and oxygen isotopes. Isotopic fractionation factors in water evaporating from free water bodies are mainly affected by temperature and relative humidity, and vary significantly with these atmospheric factors over the course of a day. The evaporation rate （E） can reveal the effects of atmospheric factors. Therefore, there should be a certain functional relationship between isotopic fractionation factors and E. An average isotopic fractionation factor （ t~＊ ） was defined to describe isotopic differences between vapor and liquid phases in evaporation with time intervals of days. The relationship between or＊ and E based on the isotopic mass balance was investigated through an evaporation pan experiment with no inflow. The experimental results showed that the isotopic compositions of residual water were more enriched with time; tr＊ was affected by air temperature, relative humidity, and other atmospheric factors, and had a strong functional relation with E. The values of 0~＊ can be easily calculated with the known values of E, the initial volume of water in the pan, and isotopic compositions of residual water.

First-principle study of Ba isotopic fractionation during ion exchange processes

The potential utilization and development of the Ba isotope tool depend on an accurateδ^(137/134)Ba determination of the samples.During the chemical purification,whether the adsorption process on the surface of the ionexchange resin could lead to the Ba isotopic fractionation and the degree of fractionation directly influence the accurateδ^(137/134)Ba determination.In the present work,first-principles calculations based on the density functional theory were used to quantify the Ba isotopic equilibrium fractionation factor between the aqueous solution and the resin in the acid leaching process.By constructing and optimizing the geometric configurations of Ba-containing species,Ba(H_(2)O)_(n)^(2+),Ba(H_(2)O)_(n)Cl_(2),Ba(H_(2)O)_(n)(NO_(3))2,and the adsorbed Ba^(2+)on the surface of the resin,extracting the harmonic vibrational frequencies,we finally at 298 K obtained the fractionations,Δ^(137/134)Ba_(soln-ads)=0.07‰,Δ^(137/134)Ba_(Ba(H_(2)O)_(n)Cl_(2)-ads)=0.05‰,andΔ^(137/134)-Ba^(Ba(H_(2)O)_(n)(NO_(3))2-ads)=0.02‰.Overall,there were almost no Ba isotope fractionations during leaching.Although the Ba isotope fractionation can be magnified by the Rayleigh fractionation process in purification,the difference inδ137/134Ba between the initial and final stages did not exceed0.060‰(or 0.045‰)when leaching the standard sample with HCl or HNO_(3),which is equal to or less than the accuracy of Ba isotopic analysis.At a common yield of89.75%,Ba isotopic fractionation induced by incomplete recovery was 0.015‰for HCl(or 0.011‰for HNO_(3)).Finally,if the influence of an incomplete recovery on theδ137/134Ba determination needs to be ignored,the recovery is suggested to be not less than 67%for HCl(or 46%for HNO_(3)).

Nitrogen isotopic fractionation of particulate organic matter production and remineralization in the Prydz Bay and its adjacent areas

During the 29 th Chinese National Antarctic Research Expedition,spatial variations in nitrogen isotopic composition of particulate nitrogen(δ15NPN)and their controlling factors were examined in detail with regard to nitrate drawdown by phytoplankton and particulate nitrogen(PN)remineralization in the Prydz Bay and its adjacent areas.To better constrain the nitrogen transformations,the physical and chemical parameters,including temperature,salinity,nutrients,PN andδ15NPN in seawater column were measured from surface to bottom.In addition,the nitrogen isotopic fractionation factor of nitrate assimilation by phytoplankton in the mixed layer,and the nitrogen isotopic fractionation factor of PN remineralization below the mixed layer were estimated using Rayleigh model and Steady State model,respectively.Our results showed that suspended particles had its lowestδ15NPN in the surface layer,which was due to the preferential assimilation of 14 N in nitrate by phytoplankton.Theδ15NPN in the mixed layer of the Prydz Bay and its adjacent areas decreased from the inner shelf to the outer basin,ascribing to the effect of isotope fractionation during phytoplankton assimilation.In mixed layer,the spatial distribution ofδ15NPN associated with particulate organic matter(POM)production can be well interpreted according to Rayleigh model and Steady State model.The nitrogen isotope fractionation factor during phytoplankton assimilating nitrate was estimated as 10.0‰by Steady State model,which was more reasonable than that calculated by Rayleigh model.These results validate the previous reports of fractionation factor during nitrate assimilation by phytoplankton.Increasingδ15NPN with depth below the euphotic zone correlated with the decreasing PN contents,and it was attributed to preferential remineralization of 14 N in PN by bacteria.In subsurface and deep layer,theδ15NPN distributions also conformed to Rayleigh model and Steady State model during PN remineralization,with a fractionation factor of about 3.6‰and 3.2‰,respectively.It is the first time to estimate the fractionation factor during POM production and remineralization in the Prydz Bay and its adjacent areas.Such fractionation may provide a useful tool for the follow-up study of the nitrogen dynamics in the Southern Ocean.

Simulations of an isotopic fractionation by freezing in an open system

This paper presents a model of isotopic fractionation by freezing under near equilibrium conditions in an open system and uses the model to predict the fractionation curve and slope gradient of δ 18 O versus δD. The simulation results show that 1) the fractionation curve and slope gradient are determined by the ratio of freezing rate to input rate, 2) the isotopic value in the initial stage of freezing is determined by the isotopic value of initial water; 3) in the latter half of freezing in an open system, the isotopic value converges to a certain value determined by that of input water. These results suggest that the shape of the fractionation curve is the method to distinguish whether freezing occurred in a closed or open system. This analysis is applied to an isotopic curve observed in basal ice of Hamna Glacier, Sya drainage, East Antarctica. The isotopic curve indicates formation by regelation in an open system with a ratio of freezing/input rates of about 10/4.

Carbon Isotope Fraction during Subduction Zone Metamorphism

Carbon isotope derived from mantle rocks and diamonds occurring worldwide show a narrow interval of-8‰to-2‰,with a very broad distribution to lower values（;41‰）and higher values（;‰）(Cartigny et al.,2014).

A Study of the Migration and Accumulation Efficiency and the Genesis of Hydrocarbon Natural Gas in the Xujiaweizi Fault Depression

In order to investigate the migration and accumulation efficiency of hydrocarbon natural gas in the Xujiaweizi fault depression, and to provide new evidence for the classification of its genesis, a source rock pyrolysis experiment in a closed system was designed and carried out. Based on this, kinetic models for describing gas generation from organic matter and carbon isotope fractionation during this process were established, calibrated and then extrapolated to geologic conditions by combining the thermal history data of the Xushen-1 Well. The results indicate that the coal measures in the Xujiaweizi fault depression are typical ＂high-efficiency gas sources＂, the natural gas generated from them has a high migration and accumulation efficiency, and consequently a large-scale natural gas accumulation occurred in the area. The highly/over matured coal measures in the Xujiaweizi fault depression generate coaliferous gas with a high δ^13C1 value （〉 -20‰） at the late stage, making the carbon isotope composition of organic alkane gases abnormally heavy. In addition, the mixing and dissipation through the caprock of natural gas can result in the negative carbon isotope sequence （δ^13C1 〉δ^13C2 〉δ^13C3 〉δ^13C4） of organic alkane gases, and the dissipation can also lead to the abnormally heavy carbon isotope composition of organic alkane gases. As for the discovery of inorganic nonhydrocarbon gas reservoirs, it can only serve as an accessorial evidence rather than a direct evidence that the hydrocarbon gas is inorganic. As a result, it needs stronger evidence to classify the hydrocarbon natural gas in the Xujiaweizi fault depression as inorganic gas.