Lattice Strain Model Research Articles

Parameterized lattice strain models for REE partitioning between amphibole and silicate melt

The distribution of rare earth elements (REEs) between amphibole and silicate melt is important for understanding a wide variety of igneous and metamorphic processes in the lithosphere. In this study, we used published experimental REE and Y partitioning data between amphibole and silicate melt, the lattice strain model, and nonlinear least-squares regression method to parameterize key partitioning parameters in the lattice strain model ( D 0 , r 0 , and E ) as a function of pressure, temperature, and both amphibole and melt compositions. Two models, which give nearly identical results, are obtained in this study. In the first model, D 0 depends on temperature and amphibole composition: it positively correlates with Ti content and negative correlates with temperature and Mg, Na, and K contents in the amphibole. In the second model, D 0 depends solely on the melt composition: it positively correlates with Si content and negatively correlates with Ti and Ca contents in the melt. In both the mineral and melt composition models, r 0 negatively correlates with the ferromagnesian content in the M4 site of the amphibole, and E is a constant. The very similar coefficients in the equations for r 0 and best-fit values for E in the two models allow us to connect the two models through amphibole-melt phase equilibria. An application of our model to amphiboles in mantle xenoliths shows that observed major element compositional variations in amphibole alone can give rise to order of magnitude variations in amphibole-melt REE partition coefficients. Together with experimental data simulating fractional crystallization of arc magmas, out models suggest that: (1) REE partition coefficients between amphibole and melt can vary by an order of magnitude during arc magma crystallization due to variation in the temperature and composition of the amphibole and melt, and that (2) amphibole fractional crystallization plays a key role in depleting the middle REEs relative to heavy REEs and light REEs in arc magmas.

Ab initio crystal structure and elasticity of tuite, γ-Ca3(PO4)2, with implications for trace element partitioning in the lower mantle

Tuite forms by the breakdown of apatite at high pressure and is thus expected to play a role in extending the phosphorus cycle beyond the stability field of apatite and into the lower mantle. With its large, high-coordination cation sites, tuite is thought to be able to dissolve large quantities of incompatible elements such as rare earth elements, Sr, Th, and U, and is potentially an important mantle reservoir for these elements. In this paper, ab initio calculations of the structure and elasticity of tuite to lower mantle pressure are presented and used to probe trace element incorporation. The calculated zero-pressure volumes of the M1 and M2 cation sites were 50.23 and 36.61 A3, while the corresponding bulk moduli K 0 are 116.1 and 94.2 GPa, significantly lower than the 234.1 GPa calculated for the M site of CaSiO3 perovskite (cpv), another likely host for incompatible elements in the mantle. The partitioning of impurities between tuite and cpv is investigated using a lattice strain model, parameterized by the ab initio calculations, to calculate isovalent substitution energies across a range of pressures and impurity sizes. Additionally, energies of strontium and barium defects in tuite are compared with those of equivalent defects in cpv, and it is found that both elements will partition strongly from cpv into tuite.

Competing effects of crystal chemistry and silicate melt composition on trace element behavior in magmatic systems: insights from crystal/silicate melt partitioning of the REE, HFSE, Sn, In, Ga, Ba, Pt and Rh

We present new partition coefficients for the REE, HFSE, Sn, In, Ga, Ba, Pt and Rh between clinopyroxene, olivine and basaltic melt as a function of crystal chemistry and melt composition at temperatures of 1190–1300 °C and 1-bar pressure. Two components, namely $$\mathrm {Al_2O_3}$$ and $$\mathrm {Na_2O}$$ , were chosen to be investigated since they are known to affect the structure of silicate melts and especially clinopyroxene crystal chemistry. The amount of $$^{[4]}\mathrm{Al}$$ in clinopyroxene will result in an increase of $$D_i^\mathrm{{cpx/melt}}$$ even after applying a correction factor to account for the effect of melt polymerization. Moreover, the positive correlation between $$^{[4]}\mathrm{Al}$$ and $$D_i^\mathrm{{cpx/melt}}$$ is not restricted to the REE, but also applies for Sn, Ga, In, and Ba. The addition of up to 2.6 wt% $$\mathrm {Na_2O}$$ to the silicate melt universally increases the $$D_i^\mathrm{{cpx/melt}}$$ without any concomitant change in crystal chemistry or a significant effect in melt polymerization. This compositional effect is likely due to the ability of Na to break REE–Al complexes in the melt. Our results emphasize the importance of considering all variables that affect the behavior of trace elements in magmatic systems before applying the lattice strain model and derive meaningful results for the changes in the parameters of the crystallographic sites.

The experimental determination of REE partition coefficients in the water-calcite system

To better quantify the behaviour of rare earth elements (REE) in low temperature natural systems, calcite was precipitated from NaCl-bearing aqueous solutions in the presence of La and Yb using a constant addition technique at pH ~6 and 25°C under steady-state conditions. The presence of REE in the fluid significantly slows calcite growth rates. Partition coefficients (DREE), determined from analysis of the aqueous solution compositions, range from 102.8 at the lowest aqueous La concentration to 101.4 at the highest aqueous concentration of Yb. DREE was found to correlate with aqueous REE concentrations, as well as with the calcite saturation state. Experimental results, together with previous spectroscopic evidence, suggest the incorporation of REE3+ into the Ca2+ site of calcite while maintaining charge balance by the concurrent incorporation of Na+. The value of the equilibrium constants for the corresponding exchange reaction was determined for La, Eu and Yb by combining our results with previously published experimental data. Subsequently, these constants were used together with a lattice strain model to estimate corresponding values for the other REE. Application of this exchange model suggests that DREE vary significantly with the composition of natural waters including seawater. Such variations are likely the origin for the large differences of DREE values reported in the literature based on experimental and field evidence.

A REE-in-plagioclase–clinopyroxene thermometer for crustal rocks

A REE-in-plagioclase-clinopyroxene thermometer has been developed on the basis of the temperature- and composition-dependent rare-earth element (REE) partitioning between coexisting plagioclase and clinopyroxene. This two-mineral exchange thermobarometer is constructed using parameters from lattice strain models for REE + Y partitioning in plagioclase and in clinopyroxene that were independently calibrated against experimentally determined mineral-melt partitioning data. An important advantage of this REE-based thermometer is that it can provide accurate temperatures through linear least-squares analysis of REE + Y as a group. Applications of the REE-in-plagioclase-clinopyroxene thermometer to volcanic and cumulate rocks show that temperatures derived from the new thermometer agree well with independently constrained magma crystallization temperatures, which adds confidence to applications of the REE-exchange thermometer to natural rocks with a wide spectrum of composition (i.e., from basalt to rhyolite). However, systematic temperature differences appear between the REE- and Mg-exchange thermometers for the volcanic and cumulate rocks. Through numerical simulations of diffusion in plagioclase-clinopyroxene systems, we demonstrate that (1) due to their slower diffusion rates, REE in minerals preferentially records crystallization or near-crystallization temperatures of the rock, and that (2) Mg is readily rest to lower temperatures for rocks from intermediately or slowly cooled magma bodies but records the initial crystallization temperatures of rocks from rapidly cooled magmas. Given their distinct diffusive responses to temperature changes, REE and Mg closure temperatures recorded by the two thermometers can be used in concert to study thermal and magmatic histories of plagioclase- and clinopyroxene-bearing rocks.

Trace element partitioning between plagioclase and silicate melt: The importance of temperature and plagioclase composition, with implications for terrestrial and lunar magmatism

Trace element partition coefficients between anorthitic plagioclase and basaltic melts (D) have been determined experimentally at 0.6GPa and 1350–1400°C in a lunar high-Ti picritic glass and a mid-ocean ridge basalt (MORB). Plagioclases with 98mol% and 86mol% anorthite were produced in the lunar picritic melt and MORB melt, respectively. Based on the new experimental partitioning data and those selected from the literature, we developed parameterized lattice strain models for the partitioning of monovalent (Na, K, Li), divalent (Ca, Mg, Ba, Sr, Ra) and trivalent (REE and Y) cations between plagioclase and silicate melt. Through the new models we showed that the partitioning of these trace elements in plagioclase depends on temperature, pressure, and the abundances of Ca and Na in plagioclase. Particularly, Na content in plagioclase primarily controls divalent element partitioning, while temperature and Ca content in plagioclase are the dominant factors for REE partitioning in plagioclase. From these models, we also derived a new expression for DRa/DBa that can be used for Ra-Th dating on volcanic plagioclase phenocrysts, and a new model for plagioclase-melt noble gas partitioning. Applications of these partitioning models to fractional crystallization of MORB and lunar magma ocean (LMO) indicate that (1) the competing effect of temperature and plagioclase composition leads to small variations of plagioclase-melt DREE during MORB differentiation, but (2) the temperature effect is especially significant and can vary anorthite-melt DREE by over one order of magnitude during LMO solidification. Temperature and plagioclase composition have to be considered when modeling the chemical differentiation of mafic to felsic magmas involving plagioclase.

Trace element partitioning between silicate melts – A molecular dynamics approach

Knowledge of trace element partition coefficients is crucial for our understanding of global element cycles. While a great number of experimental studies on mineral-melt partitioning have been performed in the past, the influence of melt structure on partitioning has mostly been considered empirically. This is mainly due to the lack of reliable structure models for typical melts at the relevant pressure and temperature conditions. Molecular dynamics simulations on the other hand may open a new window into this problem as they provide a unique approach to both structural and thermodynamic properties of minerals and melts. In this contribution, we employ first-principles and classical molecular dynamics simulations to (1) explore further a new approach to predict trace element partitioning between several silicate melts and (2) simultaneously investigate the structural controls of the observed partitioning. Specifically, we use a thermodynamic integration scheme to investigate the partitioning behavior of various trace elements (Y, La, As) in a granitic and gabbroic as well as two Ti-bearing melts and compare our data to experimental findings. Our results indicate that, similar to the lattice strain model, partitioning in melts as well seems to depend on an ideal coordination environment for each trace element and on how well this environment can be accommodated in a specific melt.

Crystal-melt elemental partitioning in silicic magmatic systems: An example from the Peach Spring Tuff high-silica rhyolite, Southwest USA

Partition coefficients (Kd) are critical for the quantitative modeling of the evolution of magmatic systems. High-silica rhyolites (HSR) are characterized by saturation in numerous phases, such that a comprehensive Kd database is necessary. While there exists a large body of published Kd values, various methods have been used by different authors over time, focusing on different compositions and conditions, and most investigations are limited to small suites of elements (e.g. rare earth elements - REE), typically in few (2–3) mineral phases. In this study, we present Kd values for a suite of 45 elements in 8 mineral phases from a HSR pumice clast from the Peach Spring Tuff (PST): sanidine, plagioclase, biotite, amphibole, titanite, apatite, zircon, and chevkinite.We determine Kd by measuring crystal rim compositions and unaltered glass from a single volcanic sample, which reflect equilibration between crystals and melt in the system at or near the time of eruption. We measure compositions using a combination of SEM-EDS and LA-ICPMS analysis.We show that titanite strongly partitions REE from the melt, with a significant preference for middle (MREE) over light (LREE) and heavy-REE (HREE). Apatite and amphibole share a similar MREE-enriched pattern, though with absolute Kd values more than an order of magnitude lower than titanite; while apatite displays a slight preference for LREE over HREE, amphibole shows a higher affinity for HREE than LREE. Zircon strongly partitions HREE, Hf, and U, with little affinity for LREE. Chevkinite concentrates LREE and Th significantly more than any other phase we analyzed. Biotite Kd are generally low (<10), with the highest values for transition metals and Ba. Sanidine and plagioclase display a strong preference for Sr, Ba, and Eu.Our dataset is largely consistent with published studies that use similar (in-situ) techniques in samples of similar composition (HSR). We observe a large variation in other studies that we attribute in part to contamination from inclusions in crystals, particularly when measuring compositions by whole-crystal methods.Our dataset suggests that accessory minerals play a dominant role in the partitioning of trace elements. They collectively control the distribution of REE and high field strength elements (HFSE) in the system. On the other hand, large ion lithophile elements (LILE) are most dominantly influenced by feldspars, but, if abundant, phases such as biotite and apatite may also influence the partitioning of LILE from the melt.We analyze our Kd values in light of the theoretical crystal lattice strain model (LSM), by fitting our data to curves that have the expected form in ln(Kd) versus ionic radius space (Onuma diagrams). The fact that we are successful in finding good fits for our Kd values, especially the REE, reinforces the idea that mineral-melt equilibrium was attained and analytical data are of appropriate quality. Additionally, we use the fitted curves to estimate Ce3+/Ce and Eu2+/Eu ratios in the melt, which are controlled by the oxidation state of the magma. We estimate that >97% of all Ce in the PST melt existed as Ce3+. The proportion of Eu2+ in the melt is not as well constrained; we estimate Eu2+ ranges mainly from ~10 to ~50% of the total Eu.

Trace element thermometry of garnet-clinopyroxene pairs

We present major and trace element data on coexisting garnet and clinopyroxene from experiments carried out between 1.3 and 10 GPa and 970 and 1400 °C. We demonstrate that the lattice strain model, which was developed for applications to mineral-melt partitioning, can be adapted to garnet-clinopyroxene partitioning. Using new and published experimental data we develop a geothermometer for coexisting garnet and clinopyroxene using the concentration of rare earth elements (REE). The thermometer, which is based on an extension of the lattice strain model, exploits the tendency of minerals at elevated temperatures to be less discriminating against cations that are too large or too small for lattice sites. The extent of discrimination against misfit cations is also related to the apparent elasticity of the lattice site on which substitution occurs, in this case the greater stiffness of the dodecahedral X-site in garnet compared with the eightfold M2-site in clinopyroxene. We demonstrate that the ratio of REE in clinopyroxene to that in coexisting garnet is particularly sensitive to temperature. We present a method whereby knowledge of the major and REE chemistry of garnet and clinopyroxene can be used to solve for the equilibrium temperature. The method is applicable to any scenario in which the two minerals are in equilibrium, both above and below the solidus, and where the mole fraction of grossular in garnet is less than 0.4. Our method, which can be widely applied to both peridotitic and eclogitic paragenesis with particular potential for diamond exploration studies, has the advantage over commonly used Fe-Mg exchange thermometers in having a higher closure temperature because of slow interdiffusion of REE. The uncertainty in the calculated temperatures, based on the experimental data set, is less than ±80 °C.

Distribution of halogens between fluid and apatite during fluid-mediated replacement processes

Apatite (Ca5(PO4)3(OH, F, Cl)) is one of the main host of halogens in magmatic and metamorphic rocks and plays a unique role during fluid–rock interaction as it incorporates halogens (i.e. F, Cl, Br, I) and OH from hydrothermal fluids to form a ternary solid solution of the endmembers F-apatite, Cl-apatite and OH-apatite. Here, we present an experimental study to investigate the processes during interaction of Cl-apatite with different aqueous solutions (KOH, NaCl, NaF of different concentration also doped with NaBr, NaI) at crustal conditions (400–700°C and 0.2GPa) leading to the formation of new apatite. We use the experimental results to calculate partition coefficients of halogens between apatite and fluid. Due to a coupled dissolution–reprecipitation mechanism new apatite is always formed as a pseudomorphic replacement of Cl-apatite. Additionally, some experiments produce new apatite also as an epitaxial overgrowth. The composition of new apatite is mainly governed by complex characteristics of the fluid phase from which it is precipitating and depends on composition of the fluid, temperature and fluid to mineral ratio. Furthermore, replaced apatite shows a compositional zonation, which is attributed to a compositional evolution of the coexisting fluid in local equilibrium with the newly formed apatite. Apatite/fluid partition coefficients for F depend on the concentration of F in the fluid and increase from 75 at high concentrations (460μg/g F) to 300 at low concentrations (46μg/g F) indicating a high compatibility of F in apatite. A correlation of Cl-concentration in apatite with Cl− concentration of fluid is not observed for experiments with highly saline solutions, composition of new apatite is rather governed by OH− concentration of the hydrothermal fluid. Low partition coefficients were measured for the larger halogens Br and I and vary between 0.7*10−3–152*10−3 for Br and 0.3*10−3–17*10−3 for I, respectively. Br seems to have D values of about one order of magnitude higher than I. These data allow an estimation of the D values for the other halogens based on a lattice strain model which displays a sequence with DF of ∼120, DOH of ∼100, DCl of ∼2.3 DBr ∼0.045, and DI ∼0.0025. Results from this experimental study help to better understand fluid–rock interaction of an evolving fluid, as it enables the composition of hydrothermally derived apatite to be used as a fluid probe for halogens at crustal conditions. It further shows the importance of mineral replacement as one of the key reactions to generate apatite of different composition.

The behaviour of incompatible elements during hydrous melting of metasomatized peridotite at 4–6 GPa and 1000 °C–1200 °C

Trace element behavior during hydrous melting of a metasomatized garnet–peridotite was examined at pressures of 4–6GPa and temperatures of 1000°C–1200°C, conditions appropriate for fluid penetrating the mantle wedge atop the subducting slab. Experiments were performed in a rocking multi-anvil apparatus using a diamond-trap setup. The compositions of the fluid and melt phases were measured using the cryogenic LA-ICP-MS technique. The water-saturated solidus of the K-lherzolite composition is located between 900°C and 1000°C at 4GPa and between 1000°C and 1100°C at 5 and 6GPa. The partition coefficients between fluid or melt and clinopyroxene reveal an asymmetric MREE trough with a minimum at Dy. The clinopyroxene in equilibrium with aqueous fluids is characterized by DUfluid–cpx>DThfluid–cpx while DUmelt–cpx tends to be similar to DThmelt–cpx. The partition coefficients between fluid or melt and garnet reveal very strong light to heavy REE fractionation, DLa/DLu from 95 (hydrous melt) to 1600 (aqueous fluid). The LILE are highly incompatible with partition coefficients >50. The behavior of HFSE are decoupled, with DZr,Hf close to 1 while DNb,Ta>10. Garnet is characterized by DUmelt/fluid–garnet<DThmelt/fluid–garnet.A comparison of our experimental partitioning results for trivalent cations as well as the results from the literature and the calculations carried out using the lattice strain model adapted to the presence of water in the bulk system indicates that H2O in the fluid or melt phase has a prominent effect on trace element partitioning. Garnet in mantle rocks in equilibrium with an aqueous fluid is characterized by significantly higher Do(3+) for REE in the X site of the garnet compared with the partitioning values of the optimal cation in garnet in equilibrium with hydrous melts. Our data show for the first time that the change in the nature of the mobile phase (fluid vs. melt) does affect the affinities of trace elements into the garnet crystal at conditions below the second critical endpoint of the system. The same also applies for clinopyroxene, although this is less clear. Consequently, our new data allow for refinements in predictive modeling of element transfer from the slab to the mantle wedge and of possible compositions of metasomatized mantle that sources OIB magmatism.

A protracted timeline for lunar bombardment from mineral chemistry, Ti thermometry and U–Pb geochronology of Apollo 14 melt breccia zircons

New zircon U–Pb and trace element investigations from Apollo 14 lunar impact breccia sample #14311 reveal at least three distinct (Concordia, 2σ) age populations at 4334 ± 10, 4245 ± 10 and 3953 ± 10 Ma. Titanium-in-zircon thermometry (Tixln) results correlated with U–Pb ages range from ~800–1200 oC. Lattice strain models used to infer zircon versus whole-rock rare earth element contents, and partitioning calculations against lunar impact breccia component compositions, quantitatively constrain formation conditions for the different age populations. A compilation of new data with published work shows that Apollo 14 zircons older than ca. 4300 Ma formed by igneous processes associated with lunar crust formation. Compositional variability in the ca. 4240 Ma zircon age population is interpretable, however, via a mixture of inherited and melt-generated components from one or more large impacts perhaps related to a marked increase in bombardment flux. Ages from the youngest zircon group at ca. 3950 Ma coincide with the classical “late heavy bombardment” (LHB) as documented from previous lunar geochronologies. These results lend support to the idea that instead of a simple unimodal LHB scenario, or a monotonic decline in impacts, the Moon was battered by multiple cataclysms since ca. 4240 Ma. Such a “Picket fence”-like bombardment to the Moon best describes the mode and tempo of impacts that accompanied the late stages of solar system formation and giant planet migration.

A predictive thermodynamic model for element partitioning between plagioclase and melt as a function of pressure, temperature and composition

One-atmosphere experiments in the system diopside-albite-anorthite (Di-Ab-An) have been used to explore the controls on plagioclase-melt partitioning of trace elements (Li, K, Rb, Cs, Mg, Zn, Sr, Ba, La, Sm, Y). By performing experiments along isotherms it was possible to isolate compositional controls from those of temperature. The lattice strain model accounts for variations in partition coefficients (<i>K</i>_<i>p</i>(i)) for isovalent series of cations (<i>i</i>^<i>n</i>+) and the experimental data are used to optimize the lattice strain parameters so that partition coefficients for <i>n</i> = 1 to 3 can be derived from <i>K</i>_<i>p</i>(Na), <i>K</i>_<i>p</i>(Ca), and <i>K</i>_<i>p</i>(La), respectively, at the conditions of interest. The optimized lattice strain parameters have magnitudes and compositional and thermal dependences that are consistent with elastic data for plagioclases. <i>K</i>_<i>p</i>(La) is parameterized via an exchange reaction involving CaAl₂Si₂O₈ and the La-feldspar component La_0.5Na_0.5Al₂Si₂O₈. The free energy change of this reaction is small, but well constrained by the data, such that for a given <i>P-T-X K</i>_<i>p</i>(La) can be derived from a combination of <i>K</i>_<i>p</i>(Na) and <i>K</i>_<i>p</i>(Ca). In the case where <i>K</i>_<i>p</i>(Na) and <i>K</i>_<i>p</i>(Ca) are independently constrained, the models reproduce the experimental values of 749 <i>K_p</i>s for Li, Mg, K, Rb, Sr, Y, Cs, Ba, and REE (obtained from 91 individual experiments varying over five orders of magnitude) within a factor of 1.5 for 53 percent of the data and a factor of 2 for 74 percent of the data. The isothermal experimental data reveal that additional compositional effects, arising from non-ideal mixing in plagioclase and in melt, also influence <i>K</i>_{<i>p</i>(<i>i</i>)}. A thermodynamic model based on the free energy of fusion of albite (NaAlSi₃O₈) and anorthite (CaAl₂Si₂O₈), and taking into account plagioclase and melt non-ideality in Di-Ab-An, is developed to express <i>K</i>_<i>p</i>(Na), <i>K</i>_<i>p</i>(Ca) as functions of pressure (<i>P</i>), temperature (<i>T</i>) and composition (<i>X</i>). The thermodynamic models are extended to a wider compositional range by means of an empirical parameterization of 919 <i>K</i>_<i>p</i>(Na) and 920 <i>K</i>_<i>p</i>(Ca) from a database of 991 published experiments. These models are able to reproduce 919 measured partitioning values for Li, Na, Mg, Ca, K, Rb, Sr, Y, Cs, Ba, and REE (from 91 experiments) with 47 percent of the model values within a factor of 1.5 of the measured values and 69 percent within a factor of 2 for any <i>P-T-X</i> condition. The models can also be used to constrain the dependence of the chemical potential of trace cations in plagioclase solid solutions (μ_i^pl) for use in diffusion chronometry where the fully equilibrated trace element concentration profile must be known in order to calculate timescales. It is shown that μ_i^pl is not adequately described by existing empirical models used to predict <i>K_p</i> as a function of anorthite because of the conflating effects of <i>T</i> and <i>X</i> in the polythermal experimental datasets from which those models were derived.

Trace element mass balance in hydrous adiabatic mantle melting: The Hydrous Adiabatic Mantle Melting Simulator version 1 (HAMMS1)

AbstractA numerical mass balance calculation model for the adiabatic melting of a dry to hydrous peridotite has been programmed in order to simulate the trace element compositions of basalts from mid‐ocean ridges, back‐arc basins, ocean islands, and large igneous provinces. The Excel spreadsheet‐based calculator, Hydrous Adiabatic Mantle Melting Simulator version 1 (HAMMS1) uses (1) a thermodynamic model of fractional adiabatic melting of mantle peridotite, with (2) the parameterized experimental melting relationships of primitive to depleted mantle sources in terms of pressure, temperature, water content, and degree of partial melting. The trace element composition of the model basalt is calculated from the accumulated incremental melts within the adiabatic melting regime, with consideration for source depletion. The mineralogic mode in the primitive to depleted source mantle in adiabat is calculated using parameterized experimental results. Partition coefficients of the trace elements of mantle minerals are parameterized to melt temperature mostly from a lattice strain model and are tested using the latest compilations of experimental results. The parameters that control the composition of trace elements in the model are as follows: (1) mantle potential temperature, (2) water content in the source mantle, (3) depth of termination of adiabatic melting, and (4) source mantle depletion. HAMMS1 enables us to obtain the above controlling parameters using Monte Carlo fitting calculations and by comparing the calculated basalt compositions to primary basalt compositions. Additionally, HAMMS1 compares melting parameters with a major element model, which uses petrogenetic grids formulated from experimental results, thus providing better constraints on the source conditions.

Magma oxygen fugacities of granitoids in the Xiaoqinling area, central China: implications for regional tectonic setting

The trace element compositions of zircons from four granitoids/metagranitoids in the Xiaoqinling area in the TransNorth China Orogen of the North China Craton were determined by in-situ laser ablation (LA) ICP-MS. The results were used to compute the zircon Ce anomaly, Ti-in-zircon temperature, and the magma oxygen fugacity. Generally, the Ce anomalies determined with La-Pr interpolation are prone to be underestimated due to the influence of tiny inclusions or analytical errors. This underestimation can markedly influence the data processing and generate unrealistically low oxygen fugacity values. In contrast, the lattice strain model yields more reliable results, and offers a robust tool in determining the magma oxidation state. The calculated magma oxygen fugacities are in the range of FMQ-1.41 to +3.21, FMQ-3.25 to +3.74, FMQ +3.66 to +5.27, and FMQ +2.51 to +4.67, respectively. The high average oxygen fugacities of FMQ +4.51 and FMQ +3.46 for a 1881 Ma old pegmatitic granite and 1866 Ma old granitic veins suggest these rocks were probably formed in arc setting, which further supports the ~1.8 Ga collision between the Western and Eastern Blocks of the North China Craton.

The role of natural solidification paths on REE partitioning between clinopyroxene and melt

We document for the first time the role played by natural solidification paths on the partitioning of rare earth elements (REE) between clinopyroxene and melt. To do this, we investigated the compositional variation of clinopyroxenes formed under increasing cooling rate conditions from core to rim of a dike at Mt. Etna volcano. As the rate of cooling increases, clinopyroxenes are progressively depleted in Si + Ca + Mg counter-balanced by enrichments in Al + Na + Ti. Consequently, the concentration of REE in clinopyroxene increases due to an increased ease of locally balancing the excess charge at the M2 site as the number of surrounding tetrahedral aluminium atoms increases. Since Aliv in clinopyroxene is a charge-balancing cation for REE, the partition coefficients (DREE) measured at the dike chilled margin are distinctly higher than those from the dike interior. We conclude that, in naturally solidifying magmas, kinetically controlled cation substitution reactions can be treated in terms of the energetics of the various charge-imbalanced configurations. This finding is corroborated by the near-parabolic dependence of DREE on cation radius due to charge-balance mechanisms described by the lattice strain model.

An assessment of subsolidus re-equilibration on REE distribution among mantle minerals olivine, orthopyroxene, clinopyroxene, and garnet in peridotites

The distribution of rare earth elements (REEs) in mantle minerals depends on temperature, pressure, and mineral composition. We developed parameterized lattice strain models for rare earth element partitioning among mantle minerals (olivine, orthopyroxene, clinopyroxene, and garnet) using mineral–melt partitioning models that were calibrated against experimentally determined high quality mineral–melt REE partition coefficients. The validity of the mineral–mineral REE partitioning models were independently tested using measured REE abundances in minerals from well-equilibrated mantle peridotites and eclogites reported in the literature. Using the new partitioning models, we critically assessed the extent of subsolidus re-equilibration on REE distribution among major rock-forming minerals in spinel and garnet peridotites. During subsolidus re-equilibration, REEs are preferentially partitioned into clinopyroxene in peridotites. The extent of REE redistribution in clinopyroxene depends on the modal abundance of clinopyroxene in the peridotite. Subsolidus exchange with orthopyroxene and olivine can increase heavy REE abundances in clinopyroxene from spinel harzburgite and middle REE abundances in clinopyroxene from garnet harzburgite by a factor of three. The higher than expected heavy REE abundances in clinopyroxene from spinel harzburgite may give rise to a false garnet signature in residual peridotites. The extents of melting for abyssal peridotites based on REE abundances in clinopyroxene can be significantly over-estimated without proper correction for subsolidus re-equilibration. REE abundances in both clinopyroxene and orthopyroxene are needed to assess the melting processes from residual peridotites.

An experimental study of trace element partitioning between augite and Fe-rich basalts

Aluminous titanium-rich hedenbergite and Fe-rich augite were experimentally produced at 1050–1220°C and 0.8–2.2GPa. Major element compositions are analogous to clinopyroxene from layered intrusions, angrites, nakhlites, and late-stage lunar magma ocean cumulates. Trace element concentrations in pyroxene and coexisting melt were measured by laser ablation inductively coupled plasma mass spectrometry for rare earth elements (REE), high field strength elements (HFSE), transition metals, and large-ion lithophile elements. REE, HFSE, and transition metal partition coefficients (Ds) are tightly correlated with the cation abundance of Fe on the pyroxene M1 site (XFeM1), and also correlated with Al on the tetrahedral site (XAlT). Parameterized lattice-strain models were developed to predict REE and HFSE partition coefficients as functions of temperature and pyroxene composition (XAlT or XFeM1). The parameterized models can be used to calculate REE and HFSE partition coefficients for Fe-rich high-Ca pyroxene. We calculated partition coefficients for clinopyroxene derived from modeled end-stage lunar magma ocean cumulate compositions and observe a factor of 3 variation in clinopyroxene-melt REE partition coefficients. Using representative nakhlite clinopyroxene core and rim compositions we calculated partition coefficients and observed a factor of 4 variability in clinopyroxene-melt REE partition coefficients. HFSE partition coefficients are even more sensitive to composition, showing variations of a factor of 4 for lunar late cumulates and an order of magnitude for nakhlites. The strong dependence of REE and HFSE partitioning on composition necessitates careful selection of appropriate partition coefficients for Fe-rich systems.

Parameterizations of calcic clinopyroxene—Melt trace element partition coefficients

Semiempirical parameterizations of the values and trends of variation of Nernst trace element partition coefficient data for Ca‐rich clinopyroxene (cpx/liquidD) are provided, applicable mainly to common terrestrial magmatic suites. cpx/liquidD data for most trace elements show significant variability which cannot be neglected when modeling melting and crystallization. The influence of pressure on cpx/liquidD is strong for many elements, particularly Na and Sr, which increase as pressure rises, and most high‐field strength elements, which decrease with increasing pressure. Most cpx/liquidD values increase as temperature decreases, as wt % melt MgO, MgO# (MgO/MgO+FeOtotal), CaO, and FeO contents drop, as cpx molar Mg# (Mg/Mg+Fetotal) decreases, and as wt % melt SiO2 and Na2O+K2O increase. No clear trends are seen for variations of cpx/liquidD against melt H2O. For mafic melts, many elements show well‐defined trends of cpx/liquidD increase as the clinopyroxene tetrahedral Al content (cpx Aliv) increases. Many cpx/liquidD are well correlated against cpx/liquidDTi, and many “near‐neighbor” elements show good cpx/liquidD intercorrelations (e.g., Zr‐Hf, U‐Th, Nb‐Ta, La‐Ce, Yb‐Lu). Cpx/liquidD profiles calculated from these parameterizations can constrain changes of D values during melting or crystallization. Cpx/liquidD for the rare earth elements were fit to the lattice strain model to derive fits that can reproduce the cpx/liquidDREE profile shapes (REE = rare earth elements). These fits indicate that cpx/liquidDREE for melts more evolved than picritic basalts cannot be modeled assuming that all REE are in octahedral coordination in a single M2 site, but also require sixfold partitioning into an M1 site for Lu‐Yb‐Tm‐Er.

Experimental study of trace element partitioning between enstatite and melt in enstatite chondrites at low oxygen fugacities and 5 GPa

In order to investigate the influence of very reducing conditions, we report enstatite-melt trace element partition coefficients (D) obtained on enstatite chondrite material at 5GPa and under oxygen fugacities (fO2) ranging between 0.8 and 8.2log units below the iron–wustite (IW) buffer. Experiments were conducted in a multianvil apparatus between 1580 and 1850°C, using doped (Sc, V, REE, HFSE, U, Th) starting materials. We used a two-site lattice strain model and a Monte-Carlo-type approach to model experimentally determined partition coefficient data. The model can fit our partitioning data, i.e. trace elements repartition in enstatite, which provides evidence for the attainment of equilibrium in our experiments. The precision on the lattice strain model parameters obtained from modelling does not enable determination of the influence of intensive parameters on crystal chemical partitioning, within our range of conditions (fO2, P, T, composition). We document the effect of variable oxygen fugacity on the partitioning of multivalent elements. Cr and V, which are trivalent in the pyroxene at around IW−1 are reduced to 2+ state with increasingly reducing conditions, thus affecting their partition coefficients. In our range of redox conditions Ti is always present as a mixture between 4+ and 3+ states. However the Ti3+-Ti4+ ratio increases strongly with increasingly reducing conditions. Moreover in highly reducing conditions, Nb and Ta, that usually are pentavalent in magmatic systems, appear to be reduced to lower valence species, which may be Nb2+ and Ta3+. We propose a new proxy for fO2 based on D(Cr)/D(V). Our new data extend the redox range covered by previous studies and allows this proxy to be used in the whole range of redox conditions of the solar system objects. We selected trace-element literature data of six chondrules on the criterion of their equilibrium. Applying the proxy to opx-matrix systems, we estimated that three type I chondrules have equilibrated at IW−7±1, one type I chondrule at IW−4±1, and two type II chondrules at IW+3±1. This first accurate estimation of enstatite-melt fO2 for type I chondrules is very close to CAI values.