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.

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.

Rebuilding the theory of isotope fractionation for evaporation of silicate melts under vacuum condition

Isotope eff ects are pivotal in understanding silicate melt evaporation and planetary accretion processes.Based on the Hertz-Knudsen equation,the current theory often fails to predict observed isotope fractionations of laboratory experiments due to its oversimplified assumptions.Here,we point out that the Hertz-Knudsen-equation-based theory is incomplete for silicate melt evaporation cases and can only be used for situations where the vaporized species is identical to the one in the melt.We propose a new model designed for silicate melt evaporation under vacuum.Our model considers multiple steps including mass transfer,chemical reaction,and nucleation.Our derivations reveal a kinetic isotopic fractionation factor(KIFF orα)αour model=[m(^(1)species)/m(^(2)species)]^(0.5),where m(species)is the mass of the reactant of reaction/nucleation-limiting step or species of diffusion-limiting step and superscript 1 and 2 represent light and heavy isotopes,respectively.This model can eff ectively reproduce most reported KIFFs of laboratory experiments for various elements,i.e.,Mg,Si,K,Rb,Fe,Ca,and Ti.And,the KIFF-mixing model referring that an overall rate of evaporation can be determined by two steps jointly can account for the eff ects of low P_(H2)pressure,composition,and temperature.In addition,we find that chemical reactions,diffusion,and nucleation can control the overall rate of evaporation of silicate melts by using the fitting slope in ln(−ln f)versus ln(t).Notably,our model allows for the theoretical calculations of parameters like activation energy(E_(a)),providing a novel approach to studying compositional and environmental eff ects on evaporation processes,and shedding light on the formation and evolution of the proto-solar and Earth-Moon systems.

Application of Stable Isotope Techniques in Studies of Carbon and Nitrogen Biogeochemical Cycles of Ecosystem

Stable isotope techniques have been proved useful as tools for studying the carbon (C) and nitrogen (N) biogeochemical cycles of ecosystem. This paper firstly introduced the basic principles and the distribution characteristics of stable isotope, then reviewed the recent advances and applications of stable isotope in the C and N biogeochemical cycles of ecosystem. By applying the 13 C natural abundance technique, ecologists are able to understand the photosynthetic path and CO 2 fixation of plants, the CO 2 exchange and C balance status of ecosystem, the composition, distribution and turnover of soil organic C and the sources of organic matter in food webs, while by using the 13 C labeled technique, the effects of elevated CO 2 on the C processes of ecosystem and the sources and fate of organic matter in ecosystem can be revealed in detail. Differently, by applying the 15 N natural abundance technique, ecologists are able to analyze the biological N 2 -fixation, the N sources of ecosystem, the N transformation processes of ecosystem and the N trophic status in food webs, while by using the 15 N labeled technique, the sources, transformation and fate of N in ecosystem and the effects of N input on the ecosystem can be investigated in depth. The applications of both C and N isotope natural abundance and labeled techniques, combined with the elemental, other isotope ( 34 S) and molecular biomarker information, will be more propitious to the investigation of C and N cycle mechanisms. Finally, this paper concluded the problems existed in current researches, and put forward the perspective of stable isotope techniques in the studies on C and N biogeochemical cycles of ecosystem in the future.

Vital effects of K isotope fractionation in organisms： observations and a hypothesis

Compared with the measureable but limited K isotope variation in geological samples,biological samples have much larger variations in δ^41 values：from-1.3‰ to＋1.1‰ relative to the international K standard NIST SRM 3141a.Notably,higher plants generally have δ^41 values that are lower than igneous rocks,whereas sea plants（algae）have δ^41 values that are higher than seawater;the range in δ^41K values of plants encompasses the δ^41 values of both igneous rocks and seawater.Plant cells utilize different K uptake mechanisms in response to highand low-K conditions.In a low-K environment,plant cells use energy-consuming ion pumps for active uptake of K;plant cells in high-K environments use non-energy-consuming ion channels.Based on these facts and on K isotope data from sea and land plants,it is hypothesized that the different K uptake mechanisms are accompanied by distinct K isotope fractionation behaviors or vital effects.The enrichment of light K isotopes in terrestrial plants could be attributed to preferential transport of isotopically light K in the energy-consuming active uptake process by K ion pumps in the membranes of plant root cells.On the other hand,the enrichment of heavy K isotopes in algae may be caused by a combination of the lack of K isotope fractionation during K uptake from seawater via ion channels and the preferential efflux of light K isotopes across the cell membrane back to the seawater.The large variation of K isotope compositions in biological samples therefore may reflect the diversity of isotopic vital effects for K in organisms,which implies the great potential of K isotopes in biogeochemical studies.

Nuclear ?eld shift effects on stable isotope fractionation: a review

An anomalous isotope effect exists in many heavy element isotope systems （e.g., Sr, Gd, Zn, U）. This effect used to be called the ＂odd--even isotope effect＂ because the odd mass number isotopes behave differently from the even mass number isotopes. This mass-indepen- dent isotope fractionation driving force, which originates from the difference in the ground-state electronic energies caused by differences in nuclear size and shape, is cur- rently denoted as the nuclear field shift effect （NFSE）. It is found that the NFSE can drive isotope fractionation of some heavy elements （e.g., Hg, T1, U） to an astonishing degree, far more than the magnitude caused by the con- ventional mass-dependent effect （MDE）. For light ele- ments, the MDE is the dominant factor in isotope fractionation, while the NFSE is neglectable. Furthermore, the MDE and the NFSE both decrease as temperatures increase, though at different rates. The MDE decreases rapidly with a factor of 1/T2, while the NFSE decreases slowly with a factor of 1/T. As a result, even at high temperatures, the NFSE is still significant for many heavy element isotope systems. In this review paper, we begin with an introduction of the basic concept of the NSFE, including its history and recent progress, and follow with the potential implications of the inclusion of the NFSE into the kinetic isotope fractionation effect （KIE） and heavy isotope geochronology.

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.

Theoretical calculation of equilibrium Mg isotope fractionation between silicate melt and its vapor

Isotope fractionation during the evaporation of silicate melt and condensation of vapor has been widely used to explain various isotope signals observed in lunar soils, cosmic spherules, calcium-aluminum-rich inclu- sions, and bulk compositions of planetary materials. During evaporation and condensation, the equilibrium isotope fractionation factor （α） between high-temperature silicate melt and vapor is a fundamental parameter that can con- strain the melt＇s isotopic compositions. However, equilib- rium a is difficult to calibrate experimentally. Here we used Mg as an example and calculated equilibrium Mg isotope fractionation in MgSiO3 and Mg2SiO4 melt-vapor systems based on first-principles molecular dynamics and the high- temperature approximation of the Bigeleisen-Mayer equation. We found that, at 2500 K, 625Mg values in the MgSiO3 and Mg2SiO4 melts were 0.141 ±0.004 and 0.143 ±0.003‰ more positive than in their respective vapors. The corresponding 626Mg values were 0.270 ± 0.008 and 0.274 ± 0.006‰ more positive than in vapors, respectively. The general α - T equations describing the equilibrium Mg α in MgSiO3 and Mg2SiO4 melt-vapor systems were： αMg（l）-Mg（g） = 1 ＋ 5.264×10^5/T^2 （1/m - 1/m＇） and αmg（l）-Mg（g） = 1 ＋ 5.340×10^5/T^2 （1/m - 1/m＇）, respectively, Where m is the mass of light isotope, ^25Mg or ^26Mg. These results offer a necessary parameter for mechanistic under- standing of Mg isotope fractionation during evaporation and condensation that commonly occurs during the early stages of planetary formation and evolution.

Boron isotope geochemistry of Zigetang Co saline lake sediments,Tibetan Plateau

The origin of boron in boron-rich salt lakes in the Tibetan Plateau is highly controversial.In this study,we carried out a detailed study on boron geochemistry and isotope composition of lake sediments collected in Zigetang Co,central Tibet.Evaporites had high boron concentrations of 172.3–418.6 lg/g and δ^(11)B values of-8.2%to-3.3%,suggesting a non-marine origin for the saline lake.The boron isotopic fractionation factor,a,between evaporite and brackish water(a_(evaporite–brackish))decreased systematically with depth,from 0.9942 at the top of the drill core to 0.9893 at the bottom;the linear variation between α_(evaporite–brackish)and depth reflects boron isotopic fractionation associated with progressive crystallization.The positive correlation between δ^(11)B versus[B]and δ^(11)B versus depth in the evaporite phase reflects pH and boron speciation in the solution control on the adsorption of boron,and B(OH)_3 species incorporated preferentially into Mg(OH)_2 precipitation at high pH.

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

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.

Equilibrium and kinetic Si isotope fractionation factors and their implications for Si isotope distributions in the Earth's surface environments

Several important equilibrium Si isotope fractionation factors among minerals,organic molecules and the H_4SiO_4 solution are complemented to facilitate the explanation of the distributions of Si isotopes in Earth's surface environments.The results reveal that,in comparison to aqueous H_4SiO_4,heavy Si isotopes will be significantly enriched in secondary silicate minerals.On the contrary,quadra-coordinated organosilicon complexes are enriched in light silicon isotope relative to the solution.The extent of ^(28)Si-enrichment in hyper-coordinated organosilicon complexes was found to be the largest.In addition,the large kinetic isotope effect associated with the polymerization of monosilicic acid and dimer was calculated,and the results support the previous statement that highly ^(28)Sienrichment in the formation of amorphous quartz precursor contributes to the discrepancy between theoretical calculations and field observations.With the equilibrium Si isotope fractionation factors provided here,Si isotope distributions in many of Earth's surface systems can be explained.For example,the change of bulk soil δ^(30)Si can be predicted as a concave pattern with respect to the weathering degree,with the minimum value where allophane completely dissolves and the total amount of sesquioxides and poorly crystalline minerals reaches their maximum.When,under equilibrium conditions,the well-crystallized clays start to precipitate from the pore solutions,the bulk soil δ^(30)Si will increase again and reach a constant value.Similarly,the precipitation of crystalline smectite and the dissolution of poorly crystalline kaolinite may explain the δ^(30)Si variations in the ground water profile.The equilibrium Si isotope fractionations among the quadracoordinated organosilicon complexes and the H_4SiO_4solution may also shed light on the Si isotope distributions in the Si-accumulating plants.

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

UV Photolysis of N2O Isotopomers： Isotopic Fractionations and Product Rotational Quantum State Distributions

The time-dependent quantum wave packet method is used to study the dynamics of the pho- todissociation processes for the isotopomers 14N14N16O, 14N15N16O, 15N14N16O, 15N15N16O, 14N14N17O, and 14N14N18O. In general, the computed isotopic fractionation factors derived from the absorption cross sections of five heavy isotopomers are in good agreement with the experimental results. Relative to the 14NI4N16O isotopomer, the N2 rotational state distributions for the isotopically nitrogen substituted N2O are found to be entirely shifted to higher rotational states. Similar to its isotopic fractionation factors, the N2 rotational state distributions for the asymmetric isotopomers 14N15N16O and 15N14N16O are found to be observably different.

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.

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.

Water Role and Its Influence on Hydrogen Isotopic Composition of Natural Gas during Gas Generation

In order to discuss the role and influence of water during the generation of natural gas,the participation mechanism of water during the evolution of organic matter and its influences were summarized.In addition,we carried out an anhydrous cracking experiment of oil extracted from the Feixianguan Formation source rock in a closed system,which led to the establishment of the kinetic models for describing carbon and hydrogen isotopic fractionation during gas generation from organic matter.The models were calibrated and then applied to the northeastern Sichuan Basin.By combining a series of gas generation experiments from octadecane pyrolysis without water or with distilled water in varying mass proportions,several results were proved:(1) the hydrogen isotopic composition of natural gas becomes lighter with the participation of formation water;(2) we can quantitatively study the hydrogen isotopic fractionation with the kinetic model for describing carbon isotopic fractionation; (3) more abundant and reliable geological information can be obtained through the combined application of carbon and hydrogen isotopic indices.

Isotopic Geochemistry of Cadmium:A Review

Cadmium（Cd） is a scarce, but not an extremely rare element in the Earth＇s crust（crustal average： 0.2 ppm Cd）. Geochemically, Cd exhibits thiophile, lithophile, and volatile behavior in different geologic processes. Biologically, it is a nutrient-like element that is closely related to P and Zn and is toxic element to organisms. Presently, Cd isotopes have been successfully utilized to trace Cd sources and nutrient cycling in marine systems in addition to unearthing other geochemical processes. Using published studies and our recent work, this survey summarizes the chemical preparation and mass spectrometry of Cd isotopes. It also reviews Cd isotopic compositions and fractionation mechanisms in nature as well as experiments.

Kinetic Parameters of Methane Generated from Source Rocks in the Kuqa Depression of Tarim Basin and Their Application

In a thermal simulation experiment of gold tubes of closed-system, calculating with the KINETICS and GOR-ISOTOPE KINETICS software, kinetic parameters of gas generation and methane carbon isotopic fractionation from Triassic-Jurassic hydrocarbon source rocks in the Kuqa depression of Tarim Basin are obtained. The activation energies of methane generated from Jurassic coal, Jurassic mudstone and Triassic mudstone in the Kuqa Depression are 197-268 kJ/mol, 180-260 kJ/mol and 214-289 kJ/mol, respectively, and their frequency factors are 5.265×10^13 s^-1, 9.761×10^11 s^-1 and 2.270×10^14 s^-1. This reflects their differences of hydrocarbon generation behaviors. The kinetic parameters of methane carbon isotopic fractionation are also different in Jurassic coal, Jurassic mudstone and Triassic mudstone, whose average activation energies are 228 kJ/mol, 205 kJ/mol and 231 kJ/mol, respectively. Combined with the geological background, the origin of natural gas in the Yinan-2 gas pool is discussed, and an accumulation model of natural gas is thus established. The Yinan- 2 gas is primarily derived from Jurassic coal-bearing source rocks in the Yangxia Sag. Main gas accumulation time is 5-0 Ma and the corresponding Ro is in the range from 1.25 %-1.95 %. The loss rate of natural gas is 25 %-30 %.