Equilibrium isotopic fractionation in the kaolinite, quartz, water system: Prediction from first-principles density-functional theory

Isotopic fractionation factors for oxygen, hydrogen and silicon have been calculated using first-principles methods for the kaolinite, quartz, water (ice and gas water) system. Good agreement between theory and experiment is obtained for mineral-water oxygen isotope fractionation. This approach gives reliable results on isotopic fractionation factors as a function of temperature, within a relative precision of typically 5%. These calculations provide independent quantitative constraints on the internal fractionation of oxygen in kaolinite, the fractionation of silicon isotopes at equilibrium, or hydrogen fractionation between kaolinite and water. Calculated fractionation factors at 300 K are 12.5‰ for the kaolinite internal-fractionation of oxygen, and 1.6‰ for silicon fractionation between quartz and kaolinite.     

Theoretical calculation of oxygen isotope fractionation factors in carbonate systems

Using established methods of statistical mechanical calculation and a recent compilation of vibrational frequency data, we have computed oxygen isotope reduced partition function ratios (β values) for a large number of carbonate minerals. The oxygen isotope β values of carbonates are inversely correlated to both the mass and radius of the cation bonded to the carbonate anion but neither correlation is good enough to be used as a precise and accurate predictor of β values. There is an approximately 0.6% relative increase in the β values of aragonite per 10 kbar increase in pressure. These estimates of the pressure effect on β values are broadly similar to those deduced previously for calcite using the methods of mineral physics. In comparing the β values of our study with those derived recently from first-principles lattice dynamics calculations, we find near-perfect agreement for calcite and witherite (<0.3% deviation), reasonable agreement for dolomite (<0.9% deviation) and somewhat poorer agreement for aragonite and magnesite (1.5-2% deviation). In the system for which we have the most robust constraints, CO₂-calcite, there is excellent agreement between our calculations and experimental data over a broad range of temperatures (0-900 °C). Similarly, there is good to excellent correspondence between calculation and experiment for most other low to moderate atomic mass carbonate minerals (aragonite to strontianite). The agreement is not as good for high atomic mass carbonates (witherite, cerussite, otavite). In the case of witherite and cerussite, the discrepancy may be due, in part, to our calculation methodology, which does not account for the effect of cation mass on the magnitude of vibrational frequency shifts associated with heavy isotope substitution. However, the calculations also reveal an incompatibility between the high- and low-temperature experimental datasets for witherite and cerussite. Specifically, the shapes of fractionation factor versus 1/T² curves in the calcite-witherite and calcite-cerussite systems do not conform to the robust constraints on the basic shape of these curves provided by theory. This suggests that either the high- or low-temperature datasets for both minerals is in error. Dolomite-calcite fractionation factors derived from our calculations fall within the wide range of fractionations for this system given by previous experimental and natural sample studies. However, our compilation of available low-temperature (25-80 °C) experimental data reveal an unusual temperature dependence of fractionations in this system; namely, the data indicate an increase in the magnitude of fractionations between dolomite (or proto-dolomite) and calcite with increasing temperature. Such a trend is incompatible with theory, which stipulates that fractionations between carbonate minerals must decrease monotonically with increasing temperature. We propose that the anomalous temperature dependence seen in the low-temperature experimental data reflect changes in the crystallinity and degree of cation ordering of the dolomite phase over this temperature interval and the effect these changes have on the vibrational frequencies of dolomite. Similar effects may be present in natural systems at low-temperature and must be considered in applying experimental or theoretical fractionation data to these systems. In nearly all cases, carbonate mineral-calcite fractionation factors given by the present calculations are in as good or better agreement with experimental data than are fractionations derived from semi-empirical bond strength methods.     

High-temperature Si isotope fractionation between iron metal and silicate

The Si stable isotope fractionation between metal and silicate has been investigated experimentally at 1800, 2000, and 2200 °C. We find that there is a significant silicon stable isotope fractionation at high temperature between metal and silicate in agreement with Shahar et al. (2009). Further we find that this fractionation is insensitive to the structure and composition of the silicate as the fractionation between silicate melt and olivine is insignificant within the error of the analyses. The temperature-dependent silicon isotope fractionation is Δ³⁰Si_{silicate-metal} = 7.45 ± 0.41 × 10⁶/T². We also demonstrate the viability of using laser ablation MC-ICPMS as a tool for measuring silicon isotope ratios in high pressure and temperature experiments.     

碳酸钙-水体系氧同位素分馏系数的低温实验研究

碳酸钙是古气候和沉积岩稳定同位素地球化学研究中最常用的矿物 ,因此对碳酸钙水体系氧同位素分馏系数的实验校准已成为稳定同位素地球化学诞生以来的热点和前沿课题。但由于碳酸钙在自然界存在 3种同质多象变体 (方解石、文石和六方方解石 ) ,使人们对碳酸钙矿物与水之间氧同位素分馏系数的实验测定结果存在较大差别 ,当应用到同位素地质测温时 ,会给出显著不同的温度值。正确选用合理的方解石水或文石水体系分馏曲线 ,对低温和环境地球化学研究和应用具有重要价值。文章系统总结和评述了碳酸钙水体系氧同位素分馏系数实验校准的历史、方法和结果 ,对前人在表达方式上的不一致进行了统一 ,对氧同位素分馏的盐效应、动力氧同位素分馏效应和同质多象转变过程中的氧同位素继承性进行了讨论。通过对前人大量实验数据的系统处理并与理论计算相比较 ,推荐了热力学上平衡的方解石水体系氧同位素分馏方程 ,而对于文石水体系 ,理论计算结果尚有待于实验证实。     

Comment on the studies of oxygen isotope fractionation between calcium carbonates and water at low temperatures by Zhou and Zheng (2003; 2005)

Experimental and theoretical aspects of oxygen isotope fractionation in the system calcite-water at low temperatures were critically examined. Contrary to the claim made by Zhou and Zheng [Zhou G.-T., and Zheng Y.-F. (2003) An experimental study of oxygen isotope fractionation between inorganically precipitated aragonite and water at low temperatures. Geochim. Cosmochim. Acta67, 387-399], there is excellent agreement between fractionation factors that were experimentally determined by means of slow, inorganic precipitation of calcite from solutions and those obtained largely from theoretical, statistical-mechanical calculations of the reduced partition function ratios. This agreement strongly suggests that calcite was precipitated from a solution very close to isotopic equilibrium. However, recently Zhou and Zheng [Zhou G.-T., and Zheng Y.-F. (2005) Effect of polymorphic transition on oxygen isotope fractionation between aragonite, calcite and water: a low-temperature experimental study. Am. Miner.90, 1121-1130] presented, without any explanation, conclusions on these major aspects that contradict the previous statements of Zhou and Zheng (2003). The apparent discrepancy in calcite-water oxygen isotope fractionation between experimental and theoretical studies discussed by Zhou and Zheng (2003) originates from the “mineral-water interaction” term in the modified increment method, which was developed by one of the authors (Y.-F. Zheng). We call for evidence for the theoretical nature of the modified increment method, which has never been presented in any of Zheng’s papers. Without such evidence, great caution must be exercised in using fractionation factors derived from the modified increment method.     

碳酸盐矿物氧同位素分馏的理论研究

应用增量方法系统地计算了碳酸盐矿物的同位素分馏系数，得到不同结构和成分的碳酸盐矿物的18O富集顺序为：菱铁矿〉铁白云石〉菱镁矿≥白云石≥方解石〉文石〉菱锶矿〉白铅矿〉碳钡矿。在0℃～1200℃范围内获得了一组内部一致的碳酸盐－水体系的理论分馏系数，这些计算结果与已知的实验和／或经验数据之间存在良好的一致性，因此本文对碳酸盐矿物氧同位素分馏系数的理论校准不仅可应用于共生矿物组合形成温度的确定，而且能够应用于其形成机理的示踪。 计算结果表明，白云石的氧同位素分馏行为与方解石相似，在25℃下白云石与方解石之间的平衡分馏为0.56‰ 。理论预测文石相对于方解石显著地亏损 δ18O，在25℃时方解石与文石之问的平衡分馏为4.47‰ 。文石向方解石的同质多相转变可能是通过一种没有同位素再造的惰性氧结构单元[CO3]2- 进行的，即只涉及Ca2+ 与[C03]2- 基团之间键的断裂和再组台而未出现[CO3]2- 基团内部C－O键的断裂和再组合。结果在自然界和实验室实验中，文石中氧同位索配分的温度关系能够传递副方解石中来。这种在同质多相转变形成方解石过程中的氧同位素继承性对于了解白云石－方解石－水体系分馏的难题至关重要。理论预测也能够用来解释对方解石分馏的经验估算与实验测定之间的分歧。     

An ab initio study of the O-H stretching frequency in tremolite

We have carried out a series of ab initio molecular orbital calculations for a cluster designed to model the OH site environment in tremolite to investigate the forces affecting the O-H stretch frequency in the crystal. The results of our calculations suggest that there are repulsive interactions between the hydrogen atom and silicon and oxygen atoms in the silicate ring adjacent to the OH site in tremolite. From our model calculations, we predict that the O-H stretching frequency of tremolite should first increase, then decrease, with applied pressure. This may affect the variation in H/D fractionation factors involving tremolite and other amphiboles with depth.     

On the Direction and Magnitude of Oxygen Isotope Fractionation Between Calcite and Aragonite at Thermodynamic Equilibrium

Oxygen isotope fractionation factors between calcium carbonates and water have been applied to ancient marine geochemistry principally for the purpose of geothermometry. The problem was encountered, however, with respect to the direction and magnitude of oxygen isotope fractionation between calcite and aragonite at thermodynamic equilibrium. This basically involves sound understanding of both thermodynamics and kinetics of oxygen isotope fractionation between inorganically precipitated carbonate and water at low temperatures. Thus the crucial issues are to acknowledge the processes of chemical reaction and isotopic exchange during precipitation of CaCO₃ minerals in solution, the kinetic mechanism of isotope equilibrium or disequilibrium, the effect of polymorphic transition from metastable aragonite to stable calcite under hydrous or anhydrous conditions, and the presence or absence of isotope salt effect on oxygen isotope exchange between carbonate and water in response to the hydrous or anhydrous conditions at thermodynamic equilibrium. Because good agreements exist in carbonate–water oxygen isotope fractionation factors between theoretical calculations and experimental determinations, it is encouraging to applying the thermodynamic and kinetic data to isotopic paleothermometry and geochemical tracing.     

DFT study of migration enthalpies in MgSiO<Subscript>3</Subscript> perovskite

The effect of pressure on ionic diffusion in orthorhombic MgSiO₃ perovskite has been investigated using density functional theory. An intensive investigation of possible silicon pathways revealed new positions of the saddle-points and an enthalpy of migration at 26.2 GPa of 4.7 eV that is in fair agreement with the experimental values of about 3.5 eV at 25 GPa. This is much lower than found in previous studies (~9 eV) and removes the need to explain silicon diffusion by a complicated process involving coupled oxygen vacancies, as has been previously proposed. Our migration enthalpies for oxygen and magnesium are in excellent agreement with experiments. We find that oxygen diffusion occurs via a chain of several inequivalent jumps along the octahedron edges, and that magnesium occurs via two inequivalent [110] jumps and one [001] jump. We also present activation volumes for all three species at 25 and 135 GPa.     

Fractionation of hydrogen and oxygen isotopes of gypsum hydration water and assessment of its geochemical indications

Fundamental knowledge of the isotopic fractionation between the hydration water and the mother solution and whether the primary information recorded in hydration water can be preserved or not in deposits or mines have long been unclear. In order to calculate the accurate hydrogen and oxygen isotopic fractionation factors between gypsum hydration water and its mother solution with new methods, to understand the mechanism of fractionation and synthetically assess the record-keeping abilities of the isotopic composition of hydration water during the process of diagenesis after deposition, experiments on the hydrogen and oxygen isotopic compositions of gypsum hydration water and its mother solution at different isothermal temperatures from 5 to 50°C were systematically conducted. In addition, samples from two typical gypsum deposits formed in different environmental conditions were also determined. Results show that during gypsum crystallisation, both hydrogen and oxygen isotopes show significant fractionation between the hydration water and the mother solution. The calculated hydrogen isotopic fractionation factors are <1, while the oxygen isotopic fractionation factors are >1 at temperatures from 5 to 50°C. The fractionation factors show no functional relationships with temperature. Isotopic compositions of gypsum hydration water in arid lake sediments can be used to trace the source of water and primary deposit environmental information. However, the isotopic composition of the gypsum hydration water can easily be altered by dissolution and secondary precipitation of gypsum during later diagenesis, particularly in areas with humid climate and abundant groundwater. A very careful assessment on record-keeping abilities of the primary isotopic composition of hydration water in gypsum during later diagenesis must be considered before application.     

First-principles calculations of equilibrium fractionation of O and Si isotopes in quartz,albite, anorthite,and zircon

In this study, we used first-principles calculations based on density functional theory to investigate silicon and oxygen isotope fractionation factors among the most abundant major silicate minerals in granites, i.e., quartz and plagioclase (including albite and anorthite), and an important accessory mineral zircon. Combined with previous results of minerals commonly occurring in the crust and upper mantle (orthoenstatite, clinoenstatite, garnet, and olivine), our study reveals that the Si isotope fractionations in minerals are strongly correlated with SiO₄ tetrahedron volume (or average Si–O bond length). The ³⁰Si enrichment order follows the sequence of quartz > albite > anorthite > olivine ≈ zircon > enstatite > diopside, and the ¹⁸O enrichment follows the order of quartz > albite > anorthite > enstatite > zircon > olivine. Our calculation predicts that measurable fractionation of Si isotopes can occur among crustal silicate minerals during high-temperature geochemical processes. This work also allows us to evaluate Si isotope fractionation between minerals and silicate melts with variable compositions. Trajectory for δ³⁰Si variation during fractional crystallization of silicate minerals was simulated with our calculated Si isotope fractionation factors between minerals and melts, suggesting the important roles of fractional crystallization to cause Si isotopic variations during magmatic differentiation. Our study also predicts that δ³⁰Si data of ferroan anorthosites of the Moon can be explained by crystallization and aggregation of anorthite during lunar magma ocean processes. Finally, O and Si isotope fractionation factors between zircon and melts were estimated based on our calculation, which can be used to quantitatively account for O and Si isotope composition of zircons crystallized during magma differentiation.     

A computer simulation approach to modelling the structure,thermodynamics and oxygen isotope equilibria of silicates

We use an atomistic model to simulate the structure, lattice dynamics and thermodynamics of silicate minerals. Our approach uses the Born model of a solid, in which the interaction between atoms is described by an interatomic pair potential. We have extended the study of thermodynamics to its very limit by looking at the subtle reaction of oxygen isotope exchange. We have modelled equilibria involving the important metamorphic minerals; albite, diopside, forsterite, pyrope, quartz and wollastonite. The predicted structural and thermodynamic data for these silicates are in very good agreement with the observed values. In addition, we predict not only the correct direction for the phase equilibria for oxygen isotope exchange, but also fractionation factors for the reaction to within a factor of two of the available experimental data. Hence, the potentials used in our approach have shown excellent transferability and have performed very well against the most stringent of tests.     

降水过程中氢氧稳定同位素理论关系研究

大气降水过程中氢氧稳定同位素比值呈现一定的规律,分析了瑞利分馏中分馏系数的影响因子,基于瑞利分馏原理和质量守恒定律,分别推导了开放系统和封闭系统降水过程中的稳定同位素微分方程模型,研究了大气降水过程中氢、氧稳定同位素变化规律,导出了云团水汽和降水氢、氧之间的相互关系,结果表明这一关系并非简单的线性关系。     

Oxygen isotope salt effects at high pressure and high temperature and the calibration of oxygen isotope geothermometers

The influence of NaCl, CaCl₂, and dissolved minerals on the oxygen isotope fractionation in mineral-water systems at high pressure and high temperature was studied experimentally. The salt effects of NaCl (up to 37 molal) and 5-molal CaCl₂ on the oxygen isotope fractionation between quartz and water and between calcite and water were measured at 5 and 15 kbar at temperatures from 300 to 750°C. CaCl₂ has a larger influence than NaCl on the isotopic fractionation between quartz and water. Although NaCl systematically changes the isotopic fractionation between quartz and water, it has no influence on the isotopic fractionation between calcite and water. This difference in the apparent oxygen isotope salt effects of NaCl must relate to the use of different minerals as reference phases. The term oxygen isotope salt effect is expanded here to encompass the effects of dissolved minerals on the fractionations between minerals and aqueous fluids. The oxygen isotope salt effects of dissolved quartz, calcite, and phlogopite at 15 kbar and 750°C were measured in the three-phase systems quartz-calcite-water and phlogopite-calcite-water. Under these conditions, the oxygen isotope salt effects of the three dissolved minerals range from ∼0.7 to 2.1‰. In both three-phase hydrothermal systems, the equilibrium fractionation factors between the pairs of minerals are the same as those obtained by anhydrous direct exchange between each pair of minerals, proving that the use of carbonate as exchange medium provides correct isotopic fractionations for a mineral pair.When the oxygen isotope salt effects of two minerals are different, the use of water as an indirect exchange medium will give erroneous fractionations between the two minerals. The isotope salt effect of a dissolved mineral is also the main reason for the observation that the experimentally calibrated oxygen isotope fractionations between a mineral and water are systematically 1.5 to 2‰ more positive than the results of theoretical calculations. Dissolved minerals greatly affect the isotopic fractionation in mineral-water systems at high pressure and high temperature. If the presence of a solute changes the solubility of a mineral, the real oxygen isotope salt effect of the solute at high pressure and high temperature cannot be correctly derived by using the mineral as reference phase.     

Structure of densified vitreous silica: Silicon and oxygen XANES spectra and multiple scattering calculations

The decrease of the mean Si-O-Si angle in vitreous silica upon densification from 2.20 to 2.36 gcm^-3 has been followed by oxygen and silicon K-edge XANES spectroscopy. Multiple scattering calculations using clusters of two shells around the oxygen and silicon atoms, respectively, are in good agreement with experimental absorption spectra and confirm mean Si-O-Si angles between 130 and 144° for these samples, and a decrease of the mean angle with densification. The experimental spectra also exhibit features due to scattering at outer (>2) shells around the photoabsorbers.     

Calculation of oxygen isotope fractionation in magmatic rocks

The increment method is applied to calculation of oxygen isotope fractionation factors for common magmatic rocks. The ¹⁸O-enrichment degree of the different compositions of magmatic rocks is evaluated by the oxygen isotope indices of both CIPW normative minerals and normalized chemical composition. The consistent results are obtained from the two approaches, pointing to negligible oxygen isotope fractionation between rock and melt of the same compositions. The present calculations verify the following sequence of ¹⁸O-enrichment in the magmatic rocks: felsic rocks>intermediate rocks>mafic rocks>ultramafic rocks. Two sets of internally consistent fractionation factors are acquired for phenocryst–lava systems at the temperatures above 1000 K and rock–water systems in the temperatures range of 0–1200 °C, respectively. The present calculations are consistent with existing data from experiments and/or empirical calibrations. The obtained results can be used to quantitatively determine the history of water–rock interaction and to serve geological thermometry for various types of magmatic rocks (especially extrusive rocks).     

滇西富碱斑岩型矿床岩体和矿脉同位素地球化学研究

选取马厂箐铜钼金矿、金厂箐金矿、北衙铅金矿和姚安铅银金矿四个典型的富碱斑岩型多金属矿床，对岩体和矿脉的铅、硅、氢、氧、硫、碳及氦、氩同位素分析。结果表明，富碱岩浆和富硅成矿流体的最初和主要铅源均来自地幔，但混染了部分地壳或地层铅；富碱岩浆起源于地幔交代作用形成的富集地幔源区，而富硅成矿流体则具有原始地幔流体性质，前者的硅同位素组成表现为经历强烈动力分馏的高正值；后者则为几乎未经动力分馏的低负值。综合研究表明，该类矿床的成矿作用是在富碱岩浆的成岩过程中，伴随富硅成矿流体对岩体和地层围岩的(自)交代蚀变作用，并与岩石一定程度混染而实现的。因此，富硅成矿流体作用实质上是地幔流体交代作用在地壳内成矿作用中的延续。     

Response to the Comment by J. Horita and R.N. Clayton on “The studies of oxygen isotope fractionation between calcium carbonates and water at low temperatures”

The apparent inconsistency in calcite-water fractionation does occur between the arithmetic combination of Zhou and Zheng [Zhou G.-T., and Zheng Y.-F. (2003) An experimental study of oxygen isotope fractionation between inorganically precipitated aragonite and water at low temperatures. Geochim. Cosmochim. Acta67, 387-399] and the experimental determination of Zhou and Zheng [Zhou G.-T., and Zheng Y.-F. (2005) Effect of polymorphic transition on oxygen isotope fractionation between aragonite, calcite and water: a low-temperature experimental study. Am. Mineral90, 1121-1130]. To resolve this issue is to acknowledge whether or not the isotope salt effect of dissolved minerals would occur on oxygen isotope exchange between water and the minerals of interest. The question is whether or not a term of mineral-water interaction should be taken into account when calculating mineral-water 10³ln α factors by an arithmetic combination between theoretical 10³ln β factors for mineral and water, respectively. The hydrothermal experiments of Hu and Clayton [Hu G.-X., and Clayton R.N. (2003) Oxygen isotope salt effects at high pressure and high temperature, and the calibration of oxygen isotope geothermometers. Geochim. Cosmochim. Acta67, 3227-3246] demonstrate the absence of isotope salt effect on the oxygen isotope fractionation between calcite and water, and this abnormal behavior reasonably explains the so-called inconsistency in the calcite-water fractionations of Zhou and Zheng (2003, 2005). We argue that the mineral-water correction is still necessary for calculation of fractionations in mineral-water systems. New experimental data for oxygen isotope fractionations involving dolomite and cerussite are consistent with the calculations of Zheng [Zheng Y.-F. (1999a) Oxygen isotope fractionation in carbonate and sulfate minerals. Geochem. J.33, 109-126], but also shed light on the assumptions used in modifying the increment method. We argue that the modified increment method has developed into a theoretical mean of predictive power for calculation of oxygen isotope fractionation factors for crystalline minerals of geochemical interest.     

Limits on the effect of pressure on isotopic fractionation

The equilibrium distribution of oxygen isotopes between calcium carbonate and water was determined at 500°C at pressures from 1 to 20 kbar and at 700°C at pressures of 0.5 and 1 kbar. At both temperatures, the pressure-dependence of the fractionation factor was below the limit of detection. The experimental results are consistent with theoretical estimates of the volume change due to isotope substitution. Application of the theory to silicate systems leads to the conclusion that pressure effects on oxygen isotopic fractionation between silicates are < 0.2% at pressures of tens of kilobars. Thus the observed large variations of O¹⁸/O¹⁶ ratio in kimberlitic eclogites cannot be attributed to the effect of pressure     

A laser fluorination method for oxygen isotope analysis of biogenic silica and a new oxygen isotope calibration of modern diatoms in freshwater environments

An empirical calibration for the oxygen isotope fractionation between biogenic silica and water was determined for diatom frustules sampled from living diatom communities in the Jemez Mountains of northern New Mexico, USA. Over a temperature range from 5.1 to 37.8 °C, the silica-water fractionation is defined by the equation 1000 ln α_{(silica-water)} = 2.39(±0.13) × 10⁶T⁻² + 4.23(±1.49). This relationship is in close agreement with other published silica-water fractionation factors for laboratory cultured diatom samples; however, it is as much as 8‰ lower than equilibrium quartz-water fractionations and 3-4‰ lower than observed silica-water fractionations in diatomaceous silica collected from sediment traps and sediment cores. There are three possible explanations for the disparate silica-water fractionation factors observed in diatom silica: (1) silica does not precipitate in equilibrium with ambient water, (2) silica does precipitate in equilibrium with ambient water, but the silica-water fractionation factor for diatom silica is considerably less than the equilibrium fractionation factor for quartz-water, or (3) silica precipitation is influenced by a ‘vital’ effect, where the δ¹⁸O value of the water inside the diatom cell walls is lower than the δ¹⁸O values of ambient water.Post-mortem loss of organic material results in an alteration or ‘maturation’ of diatom silica in which silica reequilibrates with a silica-water fractionation closer to the equilibrium quartz-water fractionation. Alteration is likely to occur rapidly after the diatom frustule loses its organic coating, either as it settles through the water column or at the sediment-water interface; δ¹⁸O values recorded by paleo-diatom silica therefore do not record growing conditions but more likely record conditions at the sediment-water interface. In the case of lacustrine environments, where the bottom water remains at a nearly constant 4 °C, the reequilibration of diatom silica with bottom conditions could reduce or remove the conflating effects of temperature on δ¹⁸O values recorded by paleo-diatom silica and provide direct information on the δ¹⁸O value of the lake water.