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.

Nuclear volume effects in kinetic isotope fractionation:A case study of mercury oxidation by chlorine species

It is well-known that the equilibrium isotope fractionation of mercury(Hg)includes classical massdependent fractionations(MDFs)and nuclear volume effect(NVE)induced mass-independent fractionations(MIFs).However,the effect of the NVE on these kinetic processes is not known.The total fractionations(MDFs+NVEinduced MIFs)of several representative Hg-incorporated substances were selected and calculated with ab initio calculations in this work for both equilibrium and kinetic processes.NVE-induced MIFs were calculated with scaled contact electron densities at the nucleus through systematic evaluations of their accuracy and errors using the Gaussian09 and DIRAC19 packages(named the electron density scaling method).Additionally,the NVE-induced kinetic isotope effect(KIE)of Hg isotopes are also calculated with this method for several representative Hg oxidation reactions by chlorine species.Total KIEs for 202 Hg/^(198)Hg ranging from−2.27‰to 0.96‰are obtained.Three anomalous^(202)Hg-enriched KIEs(δ^(202)Hg/^(198)Hg=0.83‰,0.94‰,and 0.96‰,)caused by the NVE are observed,which are quite different from the classical view(i.e.,light isotopes react faster than the heavy ones).The electron density scaling method we developed in this study can provide an easier way to calculate the NVE-induced KIEs for heavy isotopes and serve to better understand the fractionation mechanisms of mercury isotope systems.

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.

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.

Effects of Feed Fermentation on Chemical Fractionation of Trace Elements in Feed and Pig Manure and Skatole Content in Pig Manure

[Objective] This study aimed to promote the combination of cultivation and livestock farming, and to explore an environment-protecting farming style. [Method]The effects of anaerobically fermented complete compound sow feed, added with Lactobacillus and Bacillus subtilis, on the chemical fractionation of copper, iron, zinc and manganese in feed and pig manure and skatole content in pig manure were investigated. [Result] Compared with those in the non-fermented feed, in the fermented feed and pig manure, the acetic acid-extractable copper, iron, zinc and manganese contents increased significantly（P0.05）, the reduced copper and iron contents increased significantly（P 0.05）, the oxidized copper and iron contents reduced significantly（P0.05）, and the residual copper contents remained unchangeable（P0.05）. The pH value of fermented feed decreased significantly（P0.05）, and that of pig manure increased significantly（P0.05）. The skatole content in pig manure decreased significantly（P 0.01）. The Lactobacillus abundance and amylase and cellulase activity increased significantly（P 0.05）. [Conclusion] The fermentation of feed changed the chemical fractionation of copper, iron, zinc and manganese in feed and pig manure, and reduced the manure odor.

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.

Equilibrium thallium isotope fractionation and its constraint on Earth’s late veneer

Equilibrium isotope fractionation of thallium(Tl) includes the traditional mass-dependent isotope fractionation effect and the nuclear volume effect(NVE). The NVE dominates the overall isotope fractionation, especially at high temperatures. Heavy Tl isotopes tend to be enriched in oxidized Tl^3+-bearing species. Our NVE fractionation results of oxidizing Tl^+ to Tl^3+ can explain the positive enrichments observed in ferromanganese sediments. Experimental results indicate that there could be0.2–0.3 e-unit fractionation between sulfides and silicates at 1650 ℃. It is consistent with our calculation results,which are in the range of 0.17–0.38 e-unit. Importantly,Tl’s concentration in the bulk silicate Earth(BSE) can be used to constrain the amount of materials delivered to Earth during the late veneer accretion stage. Because the Tl concentration in BSE is very low and its Tl isotope composition is similar with that of chondrites, suggesting either no Tl isotope fractionation occurred during numerous evaporation events, or the Tl in current BSE was totally delivered by late veneer. If it is the latter, the Tl-contentbased estimation could challenge the magnitude of late veneer which had been constrained by the amount of highly siderophile elements in BSE. Our results show that the lateaccreted mass is at least five-times larger than the previously suggested magnitude, i.e., 0.5 wt% of current Earth’s mass. The slightly lighter 205 Tl composition of BSE relative to chondrites is probable a sign of occurrence of Tlbearing sulfides, which probably were removed from the mantle in the last accretion stage of the Earth.

Zinc isotope fractionation under vaporization processes and in aqueous solutions

Equilibrium Zn isotope fractionation was inves- tigated using first-principles quantum chemistry methods at the B3LYP/6-311G level. The volume variable cluster model method was used to calculate isotope fractionation factors of sphalerite, smithsonite, calcite, anorthite, for- sterite, and enstatite. The water-droplet method was used to calculate Zn isotope fractionation factors of Zn^2＋-bearing aqueous species; their reduced partition function ratio factors decreased in the order [Zn（H2O）6]^2＋ 〉 [ZnCl（H2O）5]^ ＋ 〉 [ZnCl2（H2O）4] 〉 [ZnCl3（H20）2]^-〉 ZnCl4]^2-. Gas- eous ZnCl2 was also calculated for vaporization processes. Kinetic isotope fractionation of diffusional processes in a vacuum was directly calculated using formulas provided by Richter and co-workers. Our calculations show that in addition to the kinetic isotope effect of diffusional processes, equilibrium isotope fractionation also contributed nontriv- ially to observed Zn isotope fractionation of vaporization processes. The calculated net Zn isotope fractionation of vaporization processes was 7-7.5‰, with ZnCl2 as the gas- eous species. This matches experimental observations of the range of Zn isotope distribution of lunar samples. Therefore, vaporization processes may be the cause of the large distri- bution of Zn isotope signals found on the Moon. However, we cannot further distinguish the origin of such vaporization processes; it might be due either to igneous rock melting inmeteorite bombardments or to a giant impact event. Fur- thermore, isotope fractionation between Zn-bearing aqueous species and minerals that we have provided helps explain Zn isotope data in the fields of ore deposits and petrology.

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)).

Phosphorus fractionation and bio-availability in Taihu Lake(China) sediments

Typical sediments from Taihu Lake, a meso-to-hypereutrophic lake, were collected and examined on the basis of P-fractionation by sequential extraction scheme. Sedimentary inorganic phosphorus were fractioned into four forms and the rank order according to the mean concentration of P-fractions in Taihu Lake was NaOH-P>BD-P>HCl-P>NH_4Cl-P. The concentrations of BD-P were linearly correlated with the content of active Fe(R2=0.96). Also, the linear relationship between the sum of BD-P and NaOH-P and the sum of active Fe and active Al content was observed within the six sediments investigated(R2=0.96). Moreover, the bio-available phosphorus(BAP) content was estimated by the sum of NH_4Cl-P, BD-P, and NaOH-P, viz. BAP=NH_4Cl-P+NaOH-P+BD-P. In Taihu Lake, the BAP contents are ranging from 0.10 mg/g dw to 1.25 mg/g dw, and average 0.40 mg/g dw for all sediment samples. The relative contributions of BAP to total sedimentary phosphorus(TP) and inorganic sedimentary phosphorus(IP) range from 18.67% to 50.79%(33.61% on average) and from 52.82% to 82.09%(67.81% on average), respectively.

Fractionation of heavy metals in shallow marine sediments from Jinzhou Bay,China

This work investigated the distribution and speciation of Cd, Cu, Pb, Fe and Mn in the shallow sediments of Jinzhou Bay, Northeast China, which has been heavily contaminated by nonferrous smelting activities. The concentrations of Cd, Cu and Pb in sediments were found to be 100, 13 and 7 times, respectively, being higher than the national guideline （GB 18668-2002）. Sequential extraction test showed that 39%-61% of Cd were exchangeable fractions, indicating that Cd in the sediments posed a high risk to local environments. While Cu and Pb were at moderate risk levels. According to the relationships between percentage of metal speciation and total metal concentration, it was concluded that the distributions of Cd, Cu and Pb in some geochemical fractions were dynamic in the process of pollutants migration and the stability of metals in sediments of Jinzhou Bay decreased in the order of Pb 〉 Cu 〉 Cd.

Behavior of REE Fractionation during Weathering of Dolomite Regolith Profile in Southwest China

REE fractionation during the weathering of dolomite has been recognized for decades.A regolith profile on dolomite in southwest Yunnan of China was selected to investigate the behaviors of REE during weathering.The weathering of dolomite is divided into two stages：the pedogenesis stage and soil evolution stage,corresponding to the saprolites and soils respectively in the regolith profile. SiO_2,TiO_2,P_2O_5,Zr,Hf,Nb and Ta were immobile components during the weathering by and large, while Al_2O_3,K_2O and Fe_2O_3 were lost during the soil evolution stage in the physical form（clay minerals probably）.REE were fractionated during the whole weathering of dolomite.The field weathering profile and the lab acid-leaching experiments on dolomite indicate that MREE were enriched clearly relative to other REE during the pedogenesis stage in a ＂capillary ascending-adsorption＂ mechanism, but they did not fractionate clearly in the soil evolution stage.REE were lost and accumulated in the weathering front of dolomite during the soil evolution stage in a ＂physical-chemical leaching＂ mechanism.

^(15)N isotope fractionation in an aquatic food chain:Bellamya aeruginosa(Reeve) as an algal control agent

^ 15N isotope tracer techniques and ecological modeling were adopted to investigate the fractionation of nitrogen, its uptake and transformation in algae and snail （Bellamya aeruginosa Reeve）. Different algal species were found to differ in their uptake of nitrogen isotopes. Microcystis aeruginisa Ktitz. demonstrated the greatest ^15N accumulation capacity, with the natural variation in isotopic ratio （δ^15N） and the isotope fractionation factor （ε,‰） being the highest among the species investigated. The transformation and utilization of ^15N by snails differed depending on the specific algae consumed （highest for Chlorella pyrenoidosa Chick., lowest for M. aeruginisa）. When snails was seeded in the experimental pond, the algae population structure changed significantly, and total algal biomass as well as the concentration of all nitrogen species decreased, causing an increase in water transparency. A model, incorporating several chemical and biological parameters, was developed to predict algal biomass in an aquatic system when snails was present. The data collected during this investigation indicated that the gastropods such as snails could significantly impact biological community and water quality of small water bodies, suggesting a role for biological control of noxious algal blooms associated with eutrophication.

Fractionation of Moderately and Highly Stable Organic Phosphorus in Acid Soil *1

The fractionation of moderately and highly organic phosphorus (P o) in acid soil was studied by two me thods. By the first method, after incubation for 40 d, the mineralization rates of eight constituents of stable P o in the soil were determined. By the second method, five constituents of precipitates of stable P o in the soil were separated, then the five precipitates were put back into the original soils and incubated for 40 d and 60 d. Then, mineralization rates of the five precipitates were determined. The same results were obtained by the two methods. When the pH of the alkali solution containing stable P o was adjusted from 3.00 to 3.10, the mineralization rate of moderately stable P o was rapidly raised. Therefore, the pH 3.00 is the critical point between moderately and highly stable P o.

Simulations of Stable Isotopic Fractionation in Mixed Cloud in Middle Latitudes-Taking the Precipitation at Urumqi as an Example

The introduced mathematical model takes into account the role of the kinetic fractionation effect in a supersaturation environment at the ice surface as liquid and solid phases coexist in mixed cloud. Using the model, the temperature effect of stable isotopes in precipitation is simulated under different cooling conditions. The rate of change of δ18O against temperature in the process of wet adiabatic cooling is smaller than in the process of isobaric cooling under the same humidity. The increasing supersaturation ratio at the ice surface, Si, leads to the strengthening of the kinetic fractionation effect. The kinetic fractionation function makes the synthesis fractionation factor decreased and the change of δ18O with temperature flatted, compared with that in the equilibrium state. The simulated results show that the slope parameter b and the intercept d of the meteoric water line (MWL), 6D = bδ18O+d, in wet adiabatic cooling are both greater than those in isobaric cooling. The global MWL lies between the two MWLs simulated under wet adiabatic and isobaric cooling processes, respectively. The magnitudes of 6 and d are directly proportional to Si. The greater the Si, the stronger the kinetic fractionation effect, and thus the greater the 6 and d, and vice versa. However, 6 and d have low sensitivity to the liquid-water contents in the cloud. Using the kinetic fractionation model, the variation of stable isotopes in precipitation at Uriimqi is simulated. The simulated stable isotopic ratio vs temperature and the SD vs δ18O curves are very consistent with the actual regressions and MWL at Uriimqi, respectively.

A review of fractionations of rare earth elements in plants

Studies were carried out on several aspects of rare earth elements （REEs）, such as the theory and practice of their applications in agriculture, their geochemical behaviors in natural and agricultural ecosystems, the mechanisms for the increase of crop yield using REE fertilizer, and their toxicology. However, limited knowledge was available for the transfer processes and the features and mechanisms of distribution and fractionations of REEs inside plants. The characteristics of REE fractionations in plants can be used to ＂trace＂ the pathway of REE transportation from soils （solution） to plants. A better understanding of the mechanisms of REE fractionations was helpful to investigate the controlling factors, including both the internal and the external ones. The characteristics and mechanisms of REE fractionations in plants and their significance were reviewed. Furthermore, the prospect for these fields was discussed, in hope of providing a new way in studying the bioavailability of REEs and heavy metals.

Sequential fractionation of reactive phosphorus in the sediment of a shallow eutrophic lake——Donghu Lake, China

The bioavailability of phosphorus in lake sediment mainly depends on its forms. Therefore, reactive phosphorus (RP) pool of the sediment in a shallow eutrophic lake(Donghu Lake) was determined seasonally and spatially by sequential chemical extraction according to the scheme proposed by Psenner et al. (Psenner, 1985) and its modified version respectively. The ammonium chloride extracted 3%—7% of the total reactive phosphorus (Tot-RP), while the distilled water extracted less(<3%). These two forms of P were significantly higher at the most eutrophic stations(I and IV). The sum of BD-RP(reductant soluble P) and NaOH-RP extracted accounted for 57%—81% of Tot-RP, which could play significant roles in P cycling. The percentages of HCl-extractable RP in the sediments of station III, however, were usually much more than those of other stations, which could reflect the original geochemistrical characteristics and trophic status of the sediments. It was noted that the sediment RP in different fractions varied in different months studied.

Accumulation and Fractionation of Rare Earth Elements in a Soil-Wheat System

Time series bioaccumulation of rare earth elements （REEs） in field-grown wheat with and without a dressing of extraneous REE fertilizer at different growth stages and fractionation of REEs during their transport in a soil-wheat system were determined. Time-dependent accumulation of extraneous REEs was found in different parts of wheat. An upward transport of extraneous REEs from roots to shoots under a soil dressing and a downward transport from leaves to roots with a foliar dressing were also observed. Moreover, fractionation of REEs occurred in the soil-wheat system. Compared to the host soil a positive Eu anomaly in the stems and grains as well as heavy REE enrichment in the grains were found. The ability of the different wheat organs to fractionate Eu from the REE series was ranked in the order of sterns 〉 grains 〉 leaves 〉 roots.

RELATIONSHIPS BETWEEN FRACTIONATIONS OF Pb, Cd, Cu, Zn AND Ni AND SOIL PROPERTIES IN URBAN SOILS OF CHANGCHUN, CHINA

An extensive soil investigation was conducted in different domains of Changchun to disclose the fractionations of Pb, Cu, Cd, Zn and Ni in urban soils. Meanwhile correlation analysis and multiple stepwise regressions were used to define relationships between soil properties and metal fractions and the chief factors influencing the fractionation of heavy metals in the soils. The results showed that Pb, Ni and Cu were mainly associated with the residual and organic forms; most of Cd was concentrated in the residual and exchangeable fractions. Zn in residual and carbonate fraction was the highest. The activities of the heavy metals probably declined in the following order: Cd, Zn, Pb, Cu and Ni. The chemical fractions of heavy metals in different domains in Changchun City were of significantly spatial heterogeneity. Soil properties had different influences on the chemical fractions of heavy metals to some extent and the main factors influencing Cd, Zn, Pb, Cu and Ni fractionation and transformation were apparently different.

Deep Fractionation of Clinopyroxene in the East Pacific Rise 13°N:Evidence from High MgO MORB and Melt Inclusions

Mid-ocean ridge basalts （MORBs） from East Pacific Rise （EPR） 13°N are analysed for major and trace elements, both of which show a continuous evolving trend. Positive MgO-Al2O3 and negative MgO-Sc relationships manifest the cotectic crystallization of plagioclase and olivine, which exist with the presence of plagioclase and olivine phenocrysts and the absence of clinopyroxene phenoerysts. However, the fractionation of clinopyroxene is proven by the positive correlation of MgO and CaO. Thus, MORB samples are believed to show a “clinopyroxene paradox”. The highest magnesium-bearing MORB sample E13-3B （MGO=9.52%） is modelled for isobaric crystallization with COMAGMAT at different pressures. Observed CaO/Al2O3 ratios can be derived from E13-3B only by fractional crystallization at pressure 〉4±1 kbar, which necessitates clinopyroxene crystallization and is not consistent with cotectic crystallization of olivine plus plagioclase in the magma chamber （at pressure -1 kbar）. The initial compositions of the melt inclusions, which could represent potential parental magmas, are reconstructed by correcting for post-entrapment crystallization （PEC）. The simulated crystallization of initial melt inclusions also produce observed CaO/Al2O3 ratios only at 〉4±1 kbar, in which clinopyroxene takes part in crystallization. It is suggested that MORB magmas have experienced clinopyroxene fractionation in the lower crust, in and below the Moho transition zone. The MORB magmas have experienced transition from clinopyroxene＋plagioclase＋olivine crystallization at 〉4±1 kbar to mainly olivine＋plagioclase crystallization at 〈1 kbar, which contributes to the explanation of the “clinopyroxene paradox”.