Equilibrium Isotope Fractionation Research Articles

Comment on “experimental determination of carbon isotope equilibrium fractionation between dissolved carbonate and carbon dioxide”

Comment on “experimental determination of carbon isotope equilibrium fractionation between dissolved carbonate and carbon dioxide”

Reply to the comment by M. P. Verma on “Experimental determination of carbon isotope equilibrium fractionation between dissolved carbonate and carbon dioxide”

Reply to the comment by M. P. Verma on “Experimental determination of carbon isotope equilibrium fractionation between dissolved carbonate and carbon dioxide”

Hydrogen and oxygen isotope studies of metamorphic fluid-rock interactions in the Dabie Mountains

Hydrogen and oxygen isotope studies were carried out on mineral separates from high to ultrahigh pressure metamorphic rocks at Huangzhen and Shuanghe in the eastern Dabie Mountains, East China. The δ18O values of eclogites cover a wide range of −5‰ to+9‰, but the δD values of micas fall within a narrow range of −85% to −70‰. Both equilibrium and disequilibrium oxygen isotope fractionations were observed between quartz and the other minerals, with reversed fractionations between omphacite and garnet in some eclogite samples. The δ18 O values of −5‰ to −1‰ for some of the eclogites represent the oxygen isotope compositions of their protoliths which underwent meteoric water-rock interaction prior to plate subduction. The preservation of oxygen isotope heterogeneity in the eclogites implies a channelized flow of fluids during progressive metamorphism caused by rapid subduction. Retrograde metamorphism has caused oxygen and hydrogen isotope disequilibria between some of the minerals, but the fluid for retrograde reactions was internally buffered in the stable isotope compositions.

13C, 15N, and 18O equilibrium isotope effects and fractionation factors1

A listing of 13C, 15N, and 18O equilibrium isotope effects and fractionation factors for atoms in specific positions is provided. Empirical factors that can be used to adjust these fractionation factors for more complex structures are presented and discussed. While much work needs to be done to determine equilibrium isotope effects for these heavy atoms, the values tabulated here should be useful to anyone working with isotope effects involving these atoms.Key words: equilibrium isotope effects, fractionation factors, 13C, 15N, 18O.

Hydrogen and oxygen isotope evidence for fluid–rock interactions in the stages of pre- and post-UHP metamorphism in the Dabie Mountains

Hydrogen and oxygen isotope studies were carried out on high and ultrahigh pressure metamorphic rocks in the eastern Dabie Mountains, China. The δ 18 O values of eclogites cover a wide range of −4.2 to +8.8‰, but the δD values of micas from the eclogites fall within a narrow range of −87 to −71‰. Both equilibrium and disequilibrium oxygen isotope fractionations were observed between quartz and the other minerals, with reversed fractionations between omphacite and garnet in some eclogite samples. The δ 18 O values of −4 to −1‰ for some of the eclogites represent the oxygen isotope compositions of their protoliths which underwent meteoric water–rock interaction before the high to ultrahigh pressure metamorphism. Heterogeneous δ 18 O values for the eclogite protoliths implies not only the varying degrees of the water–rock interaction before the metamorphism at different localities, but also the channelized flow of fluids during progressive metamorphism due to rapid plate subduction. Retrograde metamorphism caused oxygen and hydrogen isotope disequilibria between some of the minerals, but the fluid for retrograde reactions was internally buffered in the stable isotope compositions and could be derived from structural hydroxyls dissolved in nominally anhydrous minerals.

Obtaining equilibrium oxygen isotope fractionations from rocks: theory and examples

A generalized approach for retrieving equilibrium isotope fractionations from natural rocks is proposed in which models of prograde reaction histories and retrograde diffusional exchange are used to identify coexisting minerals with similar isotope closure temperatures. Examples using literature data and new analyses from 32 natural amphibolite-facies schists demonstrate both the feasibility and limitations of obtaining equilibrium oxygen isotope fractionations from minerals in natural rocks. By screening samples according to the theoretical models, natural data are shown to have highly consistent mineral fractionations (±2σ reproducibilities of ±0.16 to 0.54‰) that within uncertainty reproduce experimental determinations among the minerals quartz, biotite, muscovite, and calcic amphibole. This correspondence indicates that the proposed theoretically-based selection criteria improve the likelihood of measuring equilibrium fractionations. The new data further corroborate the expected progressive enrichment of δ18O in the orthosilicates with increasing Al+Si relative to Fe+Mg: Δ(Ky-Grt) ∼1.05‰, Δ(St-Grt) ∼0.6‰, and Δ(St-Cld) ∼0.3‰ at 525–575 °C. In contrast, typical samples that fail to satisfy screening criteria exhibit fractionations involving quartz, biotite, and amphibole that are strongly disequilibrium because of exchange during cooling. Theoretical screening of samples prior to isotope analysis allows robust, independent assessment of theoretical and experimental determinations of equilibrium isotope fractionations.

Anharmonic and pressure effects on equilibrium isotope fractionation

Anharmonic and pressure effects on equilibrium isotope fractionation

Geochemistry of Jinman copper vein deposit, West Yunnan Province, China— II. Fluid inclusion and stable isotope geochemical characteristics

The Jinman deposit is a Ag-bearing copper vein deposit located at the north margin of the Lanping-Simao back-arc basin in West Yunnan. Systematic studies of fluid inclusions and stable isotopes are presented in this paper. The filling-replacement stage and the boiling-exhalative precipitation stage of mineralization took place atT1 = 140–280°3 andT2 = 94–204°C under pressure of (600 – 1200) x 105 Pa. The salinity of ore-forming solutions ranges from 5 wt% –20.8 wt% (NaCl). Sulphide δ34S(CDT) values are in the range of -9.6%.– +11.03%. with a range of 22. 66%. showing an apparent “pagoda”-shaped distribution in histogram. Meanwhile, the δ34S values of the various sulphides are consistent with the characters of isotope equilibrium fractionation, i.e., δ34 SPy>δ34SCp>δ34SBn. The TS/TOC ratios of the ores are widely variable between 0.16 and 5.54 with no correlation of any kind can be established. According to the model of Ohmoto, the oxidation-reduction ratios of sulfur species in ore-forming solutions at the two mineralization stages were calculated to be R′1 = 2.16 x 10-17 and R′2 = 1.55 x 104. δ13Coo2(PDB) values obtained from fluid inclusions in calcite and quartz are between -8.12%.-3.18%., averaging -5.26%., which are comparable with the isotopic composition of mantle-derived CO2. Inclusions in quartz yield δ13CCH4 (PEB) between -32. 11%. and -22.04%. (averaging -26.69%.), similar to that of methane in modern geothermal gases. For the ore-forming solutions, δ18 OH2O (SMOW) values are between -10.57%. and +9.77%. and δDH2O (SMOW) are between -51%. and -135%. Considering the effect of isotope exchange during water-rock reactions, most of the data are plotted along or close to the line defined by the reaction of meteoric water with clastic rocks, while a small part of the points fall near the reaction line of magmatic water with clastic rocks. In δ13C vs. δ18O diagram, the ore-forming solutions are plotted for the most part into the mixing area between the meteoric fluid and the deep-seated fluid and partially on the mixing line of P = 1.

98/00005 Coal structure study by oxidation of aromatic model compounds

Natural variations in 238U/235U of marine calcium carbonates might provide a useful way of constraining redox conditions of ancient environments. In order to evaluate the reliability of this proxy, we conducted aragonite and calcite coprecipitation experiments at pH ∼7.5 and ∼8.5 to study possible U isotope fractionation during incorporation into these minerals.Small but significant U isotope fractionation was observed in aragonite experiments at pH ∼8.5, with heavier U isotopes preferentially enriched in the solid phase. 238U/235U of dissolved U in these experiments can be fit by Rayleigh fractionation curves with fractionation factors of 1.00007 + 0.00002/−0.00003, 1.00005 ± 0.00001, and 1.00003 ± 0.00001. In contrast, no resolvable U isotope fractionation was observed in an aragonite experiment at pH ∼7.5 or in calcite experiments at either pH. Equilibrium isotope fractionation among different aqueous U species is the most likely explanation for these findings. Certain charged U species are preferentially incorporated into calcium carbonate relative to the uncharged U species Ca2UO2(CO3)3(aq), which we hypothesize has a lighter equilibrium U isotope composition than most of the charged species. According to this hypothesis, the magnitude of U isotope fractionation should scale with the fraction of dissolved U that is present as Ca2UO2(CO3)3(aq). This expectation is confirmed by equilibrium speciation modeling of our experiments. Theoretical calculation of the U isotope fractionation factors between different U species could further test this hypothesis and our proposed fractionation mechanism.These findings suggest that U isotope variations in ancient carbonates could be controlled by changes in the aqueous speciation of seawater U, particularly changes in seawater pH, PCO2, Ca2+, or Mg2+ concentrations. In general, these effects are likely to be small (<0.13‰), but are nevertheless potentially significant because of the small natural range of variation of 238U/235U.

98/00002 Analysis of sulfur forms in Polish coals

Natural variations in 238U/235U of marine calcium carbonates might provide a useful way of constraining redox conditions of ancient environments. In order to evaluate the reliability of this proxy, we conducted aragonite and calcite coprecipitation experiments at pH ∼7.5 and ∼8.5 to study possible U isotope fractionation during incorporation into these minerals.Small but significant U isotope fractionation was observed in aragonite experiments at pH ∼8.5, with heavier U isotopes preferentially enriched in the solid phase. 238U/235U of dissolved U in these experiments can be fit by Rayleigh fractionation curves with fractionation factors of 1.00007 + 0.00002/−0.00003, 1.00005 ± 0.00001, and 1.00003 ± 0.00001. In contrast, no resolvable U isotope fractionation was observed in an aragonite experiment at pH ∼7.5 or in calcite experiments at either pH. Equilibrium isotope fractionation among different aqueous U species is the most likely explanation for these findings. Certain charged U species are preferentially incorporated into calcium carbonate relative to the uncharged U species Ca2UO2(CO3)3(aq), which we hypothesize has a lighter equilibrium U isotope composition than most of the charged species. According to this hypothesis, the magnitude of U isotope fractionation should scale with the fraction of dissolved U that is present as Ca2UO2(CO3)3(aq). This expectation is confirmed by equilibrium speciation modeling of our experiments. Theoretical calculation of the U isotope fractionation factors between different U species could further test this hypothesis and our proposed fractionation mechanism.These findings suggest that U isotope variations in ancient carbonates could be controlled by changes in the aqueous speciation of seawater U, particularly changes in seawater pH, PCO2, Ca2+, or Mg2+ concentrations. In general, these effects are likely to be small (<0.13‰), but are nevertheless potentially significant because of the small natural range of variation of 238U/235U.

Hydrogen isotope fractionation and hydrogen diffusion in the tourmaline-water system

Hydrogen isotope exchange between tourmaline and water has been studied experimentally over the temperature range of 800-350°C. The hydrogen isotope equilibrium fractionation factor between tourmaline and water may be expressed as a function of temperature by the following linear equation: 10 3 ln α tourmaline-water e = −27.9(10 6/ T 2) + 2.3 A study of the kinetics of hydrogen isotope exchange between tourmaline and water indicates that exchange is dominated by hydrogen diffusion. Over the temperature range of 800-450°C, the relation between the hydrogen diffusion coefficient and temperature for the tourmaline-water system is as follows: Cylinder model: log D cyl = −5.96 − 6.68(10 3/ T) Plate model: log D plate = −5.64 − 6.42(10 3/ T) The activation energies for hydrogen diffusion are 128.0 kJ/mol (cylinder model) and 123.1 kJ/mol (plate model), respectively. For the temperature range 800-450 C, the relation of the hydrogen isotope equilibrium fractionation factor to the temperature (10 6/ T 2. chemical composition ( M), and hydroxyl-stretching frequency (ƒ) for systems of nonhydrogen-bonded hydroxyl minerals and water can be expressed as 10 3 ln α mineral-water e = − 14.7 10 3 × f − 3 (10 6/ T 2) + 26.4 + (2 M Al − 4 M Mg − 68 M Fe ) where M represents the mole fraction of designated cation in the mineral.

Equilibrium fractionation of the iron isotopes: Estimation from Mössbauer spectroscopy data

A close relationship between the second-order Doppler shift (SOD) of the Mössbauer resonant recoil-free frequency and the equilibrium stable isotope fractionation has been established. The reduced isotopic partition function ratios (β-factors) of the iron isotopes for a set of substances has been evaluated from appropriate experimental data on the SOD. The extent of the equilibrium stable iron isotope fractionation has been estimated. The equilibrium fractionation of the iron isotopes is notable at temperatures up to 1000 K and may be essential not only at surface conditions but in geothermal and metamorphic processes in the Earth's crust as well. This opens up new possibilities for applications of iron isotope fractionation in geochemistry and cosmochemistry.

Tansley Review No. 95 15 N natural abundance in soil-plant systems.

Equilibrium and kinetic isotope fractionations during incomplete reactions result in minute differences in the ratio between the two stable X isotopes, 15 N and 14 N, in various N pools. In ecosystems such variations (usually expressed in per mil [δ15 N] deviations from the standard atmospheric N2 ) depend on isotopic signatures of inputs and outputs, the input-output balance, N transformations and their specific isotope effects, and compartmentation of N within the system. Products along a sequence of reactions, e.g. the N mineralization-N uptake pathway, should, if fractionation factors were equal for the different reactions, become progressively depleted. However, fractionation factors van. For example, because nitrification discriminates against 15 N in the substrate more than does N mineralization, NH4 + can become isotopically heavier than the organic N from which it is derived. Levels of isotopic enrichment depend dynamically on the stoichiometry of reactions, as well as on specific abiotic and biotic conditions. Thus, the δ15 N of a specific N pool is not a constant, and 15 N of a N compound added to the system is not a conservative, unchanging tracer. This fact, together with analytical problems of measuring 15 N in small and dynamic pools of N in the soil-plant system, and the complexity of the X cycle itself (for instance the abundance of reversible reactions), limit the possibilities of making inferences based on observations of 15 N abundance in one or a few pools of N in a system. Nevertheless, measurements of δ15 N might offer the advantage of giving insights into the N cycle without disturbing the system by adding 15 N tracer. Such attempts require, however, that the complex factors affecting 15 N in plants be taken into account, viz. (i) the source(s) of N (soil, precipitation, NOX , NH3 , N2 -fixation), (ii) the depth(s) in soil from which N is taken up, (iii) the form(s) of soil-N used (organic N, NH4 + , NO3 - ), (iv) influences of mycorrhizal symbioses and fractionations during and after N uptake by plants, and (v) interactions between these factors and plant phenology. Because of this complexity, data on δ15 N can only be used alone when certain requirements are met, e.g. when a clearly discrete N source in terms of amount and isotopic signature is studied. For example, it is recommended that N in non-N2 -fixing species should differ more than 5% from N derived by N2 -fixation, and that several non-N2 -fixing references are used, when data on δ15 N are used to estimate Na -fixation in poorly described ecosystems. As well as giving information on N source effects, δ15 N can give insights into N cycle rates. For example, high levels of N deposition onto previously N-limited systems leads to increased nitrification, which produces 15 N-enriched NH4 and N-depleted NO3 . As many forest plants prefer NH4 - they become enriched in 15 N in such circumstances. This change in plant 15 N will subsequently also occur in the soil surface horizon after litter-fall, and might be a useful indicator of N saturation, especially since there is usually an increase in 15 N with depth in soils of N-limited forests. Generally, interpretation of 15 N measurements requires additional independent data and modelling, and benefits from a controlled experimental setting. Modelling will be greatly assisted by the development of methods to measure the 15 N of small dynamic pools of N in soils. Direct comparisons with parallel low tracer level 15 N studies will be necessary to further develop the interpretation of variations in 15 N in soil-plant systems. Another promising approach is to study ratios of 15 N: 14 N together with other pairs of stable isotopes, e.g. 13 C: 12 C or 18 O:16 O, in the same ion or molecules. This approach can help to tackle the challenge of distinguishing isotopic source effects from fractionations within the system studied. CONTENTS Summary 179 I. Introduction 180 II. Units, causes of isotope effects, stoichiometry, modelling 181 III. N dynamics and variations in 15 N abundance in soil-plant systems 183 IV. Applications 189 V. Conclusions and suggestions for future research 197 Acknowledgements 198 References 198.

Single cell gas flotation separator with filter media

Geochemical data from late Archean sedimentary rocks point to photosynthetic O2 production and at least intermittent occurrences of locally mild oxidative weathering and surface ocean oxygenation (“oxygen oases”) prior to the early Paleoproterozoic Great Oxidation Event. For example, distinctive authigenic enrichments of Mo and Re in euxinic (anoxic and sulfidic) black shales are best explained by the oxidative mobilization of these metals from crustal sulfide minerals and their accumulation as oxyanions in seawater. In contrast, it is not clear if low U enrichments in the same shales reflect negligible oxidation of U from the upper crust or a very small oceanic U inventory that was derived from oxidative U mobilization. Here, we report U isotope data for the 2.50 Ga Mt. McRae Shale (Hamersley basin, Western Australia), which provides a more sensitive test for the presence or absence of authigenic U compared to U concentrations and enrichment factors normalized to average shale or upper crustal compositions (that may not be representative of the local detrital composition). We find instances where the U isotope composition in the upper Mt. McRae Shale (δ238U = − 0.2 to 0.0‰ relative to standard SRM950a) is isotopically heavier than average upper crust (δ238U = − 0.31 ± 0.14 [2SD] based on granitoids and basalts). The high δ238U values point to U isotope fractionation in the late Archean marine environment and hence indicate the presence of a small amount of dissolved U in seawater and authigenic U in the Mt. McRae Shale. Volume-dependent equilibrium isotope fractionation during the reduction of dissolved UVI to insoluble UIV, like that observed in the modern Black Sea, may explain the high δ238U signatures if U removal from bottom waters was not quantitative. Alternatively, quantitative U removal would require that late Archean seawater had high δ238U, which could have arisen from the preferential sequestration of 235U to Fe (oxyhydr)oxide minerals elsewhere in the Hamersley basin. The supracrustal δ238U signatures are associated with some of the highest Mo and Re enrichments in the Mt. McRae Shale as well as distinctive Mo, S and N isotope signatures that are indicative of mild environmental oxygenation. Hence, our findings suggest that small amounts of U were oxidatively mobilized from the upper crust at 2.50 Ga. Unlike Mo and Re, however, U oxidation may not have occurred on land. Instead, we hypothesize that oxidative U mobilization occurred by submarine weathering in an oxygen oasis.

Process for treating iron-containing sulfidic rocks and ores

Geochemical data from late Archean sedimentary rocks point to photosynthetic O2 production and at least intermittent occurrences of locally mild oxidative weathering and surface ocean oxygenation (“oxygen oases”) prior to the early Paleoproterozoic Great Oxidation Event. For example, distinctive authigenic enrichments of Mo and Re in euxinic (anoxic and sulfidic) black shales are best explained by the oxidative mobilization of these metals from crustal sulfide minerals and their accumulation as oxyanions in seawater. In contrast, it is not clear if low U enrichments in the same shales reflect negligible oxidation of U from the upper crust or a very small oceanic U inventory that was derived from oxidative U mobilization. Here, we report U isotope data for the 2.50 Ga Mt. McRae Shale (Hamersley basin, Western Australia), which provides a more sensitive test for the presence or absence of authigenic U compared to U concentrations and enrichment factors normalized to average shale or upper crustal compositions (that may not be representative of the local detrital composition). We find instances where the U isotope composition in the upper Mt. McRae Shale (δ238U = − 0.2 to 0.0‰ relative to standard SRM950a) is isotopically heavier than average upper crust (δ238U = − 0.31 ± 0.14 [2SD] based on granitoids and basalts). The high δ238U values point to U isotope fractionation in the late Archean marine environment and hence indicate the presence of a small amount of dissolved U in seawater and authigenic U in the Mt. McRae Shale. Volume-dependent equilibrium isotope fractionation during the reduction of dissolved UVI to insoluble UIV, like that observed in the modern Black Sea, may explain the high δ238U signatures if U removal from bottom waters was not quantitative. Alternatively, quantitative U removal would require that late Archean seawater had high δ238U, which could have arisen from the preferential sequestration of 235U to Fe (oxyhydr)oxide minerals elsewhere in the Hamersley basin. The supracrustal δ238U signatures are associated with some of the highest Mo and Re enrichments in the Mt. McRae Shale as well as distinctive Mo, S and N isotope signatures that are indicative of mild environmental oxygenation. Hence, our findings suggest that small amounts of U were oxidatively mobilized from the upper crust at 2.50 Ga. Unlike Mo and Re, however, U oxidation may not have occurred on land. Instead, we hypothesize that oxidative U mobilization occurred by submarine weathering in an oxygen oasis.

Experimental determination of carbon isotope equilibrium fractionation between dissolved carbonate and carbon dioxide

By mixing aliquots of pure Na 2CO 3 and CO 2, solutions with precisely known molal fractions of CO 3 =, HCO 3 −, and dissolved CO 2 were prepared. The apparent fractionation factor between gaseous CO 2 and total carbon in the solution was determined mass spectrometrically from which the CO 3 = − CO 2 fractionation factor was calculated taking into account the known fraction of HCO 3 − and respective isotope fractionation. Although the measurements have been made for a rather narrow temperature range, from 4 to 80°C, a theoretical curve was fitted through the experimental points, and thereby, tge isotopic partition function ratio of 13CO 3 = and 12CO 3 = molecules has been obtained for an extended temperature range. The results obtained for CO 3 =−CO 2 isotope fractionation are significantly lower than those for HCO 3 −−CO 2 exchange (with 10 3(α − 1) = 5.0 ± 0.2 at 25°C and cross-over point at about 63°C).

Microbial influence on the oxygen isotopic composition of diagenetic siderite

Numerous early diagenetic siderite concretions previously described have been interpreted as the results of microbially mediated reactions. Interpretation of oxygen isotope data for such material requires an understanding of the effect of temperature on fractionation processes. However, whilst equilibrium fractionation of oxygen isotopes between siderite and water has been measured down to 33°C, extrapolation to lower temperatures may be invalid. Furthermore, inorganic measurements may not be applicable to microbial systems. The specific iron-reducing microorganism, Geobacter metallireducens, has been cultured anaerobically in the laboratory using acetate as an organic substrate and amorphous FeOOH as an electron acceptor. The acetate is oxidised to CO 2, with concurrent iron reduction and extracellular siderite precipitation. Rhombohedral siderite crystals up to 25 μm in size have been precipitated over a range of temperatures (18–40°C). Stable isotopic analysis of these crystals and the solutions from which they precipitate shows that this microbial precipitation of siderite has an associated isotopic fractionation different from the published equilibrium, and which is not simply a function of temperature. In all cases, δ 18O values of siderite are lower than predicted by inorganic equilibrium fractionation data. This may explain the numerous anomalously-low δ 18O values reported for early diagenetic marine siderites and previously attributed to mechanisms such as mixing with meteoric water, sediment-water interaction, recrystallisation, or variable isotopic fractionation, despite a lack of supporting evidence.

Temperature dependence of the isotope chemistry of the heavy elements.

The temperature coefficient of equilibrium isotope fractionation in the heavy elements is shown to be larger at high temperatures than that expected from the well-studied vibrational isotope effects. The difference in the isotopic behavior of the heavy elements as compared with the light elements is due to the large nuclear isotope field shifts in the heavy elements. The field shifts introduce new mechanisms for maxima, minima, crossovers, and large mass-independent isotope effects in the isotope chemistry of the heavy elements. The generalizations are illustrated by the temperature dependence of the isotopic fractionation in the redox reaction between U(VI) and U(IV) ions.

Isotopic composition of water used for triple point of water cells

Measurements of the isotopic composition of water used in the production of triple point of water cells show that state-of-the-art triple point realizations must consider corrections and uncertainties due to variations in the isotopic composition of water. Triple point cell production processes yield cells with triple point temperatures 60 µK below that implied by the definition, with a similar sized uncertainty in the value. The use of isotopically impure water for the triple point leads to a fundamental uncertainty in the definition of the kelvin of around 14 µK because of the equilibrium isotope fractionation between the ice and liquid water in the triple point cell.

The use of heat capacity data to calculate carbon isotope fractionation between graphite, diamond, and carbon dioxide: a new approach

A new approach for calculating the β-factors of elements (substances consisting of single-element atoms) from calorimetric data on the specific heat capacities has been established. The approach is based on first order thermodynamic perturbation theory and harmonic approximation. It has been applied to calculate the β-factors of graphite and diamond. The polynomial expansions for them have been evaluated: ▪ A comparison with values of the β-factors obtained by Bottinga (1969b) has shown a disagreement that seems to be essential for carbon isotope geothermometry. The carbon dioxide β-factors have been calculated in the harmonic approximation from spectroscopic data on fundamental frequencies. The method of calculation is based on the group theory technique. The calculated equilibrium isotope fractionation factors between carbon dioxide and graphite are significantly lower than those obtained from partial exchange experiments by Scheele and Hoefs (1992). Combining the Chacko (1991) data on the calcite β-factors with the present data on the β-factors of graphite, the isotope equilibrium fractionation curve between calcite and graphite has been evaluated. This curve shows somewhat better coincidence with the Valley and O'Neil (1981) empirical fractionation curve than the curve obtained by Chacko (1991). The excellent agreement between the theoretical and the empirical calibrated isotope fractionation curves has been achieved by taking into account a pressure effect on the calcite-graphite equilibrium isotope fractionation factor. Nevertheless, significant disagreement with appropriate data of Scheele and Hoefs (1992) is observed.