Lattice Strain Theory Research Articles

Revealing the role of crystal chemistry in REE fractionation in skarn garnets: insights from lattice-strain theory

Revealing the role of crystal chemistry in REE fractionation in skarn garnets: insights from lattice-strain theory

Application of Onuma and lattice strain derived methods to calculate missing REE and Ce and Eu anomalies in magmatic zircons

The shape of chondrite normalized zircon rare earth element (REE) patterns, including the magnitude of the Cerium (Ce) and Europium (Eu) anomalies, provide valuable insights into the magmatic conditions under which a zircon formed. However, lanthanum (La) and praseodymium (Pr), which are essential for the calculation of Ce anomalies, are often present at concentrations close to or below the detection limit of most analytical methods. We propose two new methods to calculate missing REE, based on Onuma diagrams (Chondrite-Onuma) and the lattice strain theory (Chondrite-Lattice), but using chondrite normalized values instead of partition coefficients. We compiled a dataset of ~ 1500 zircons with known REE + Y concentrations and used it to test and calibrate these methods and demonstrate that they are more accurate than other previously published models, with the Chondrite-Onuma method performing better than the Chondrite-Lattice method. These methods require analyses of as few as five REEs to impute the missing REE data or to estimate La and Pr concentrations or Ce anomalies in magmatic zircons, which allows a reduction in the number of REE analysed, where desirable, or to impute missing REEs in legacy data. The imputeREE package for the R programming language was written with a set of tools to apply these methods. A companion app is available to calculate missing REE and Ce and Eu anomalies.

Sectoral and growth rate control on elemental uptake by individual calcite crystals

Heterogeneous distribution of trace elements (impurities) within individual calcite crystals is a phenomenon commonly observed in natural and laboratory systems. Changes in thermodynamic intensive parameters (mostly chemical potential and temperature) cannot always explain the inhomogeneous impurity patterns in calcite crystals and it has been suggested that growth rate and crystallographic orientation may exert strong effects on elemental incorporation into calcite. In addition, there are a number of experimental studies on micro-scale element (E) distribution between non-equivalent pairs of calcite vicinal faces (known as sectoral zoning); however, the variability of partition coefficients (e.g., KE = (E/Ca)calcite/(E/Ca)fluid) within individual crystals remains undetermined.In this study, we have extended the work on elemental distribution between crystal sectors to evaluation of partition coefficients of trace and minor elements (Li, B, Mg, and Sr) in calcite crystal faces (10–14) and (01−12), whose growth rates were assessed. Growth entrapment model (GEM) and lattice strain theory were applied to explain KE heterogeneity by varying near-surface diffusivity of Mg and Sr and by varying surface enrichment factor for Li, B, Mg, and Sr. Decoupling of sectoral and growth rate effects reveals that sectoral zoning plays a key role in elemental distribution. More specifically, KLi and KB vary by more than one order of magnitude and KMg varies by a factor of two within individual crystal faces. Strontium sectoral distribution is different from those of Li, B, and Mg and KSr varies by up to a factor of two. These behaviors likely reflect different mechanisms of incorporation of Li, B, Mg, and Sr into calcite.

Strength, deformation, and equation of state of tungsten carbide to 66 GPa

Strength, texture, and equation of state of hexagonal tungsten monocarbide (WC) have been determined under quasi-hydrostatic and non-hydrostatic compression to 66 GPa using angle-dispersive X-ray diffraction in the diamond anvil cell. Quasi-hydrostatic compression in a Ne pressure medium demonstrates that nanocrystalline WC is slightly less incompressible than bulk-scale WC, with respective bulk moduli of K0 = 377 ± 7 and 397 ± 7 GPa and pressure derivatives K0’ = 3.8 ± 0.3 and 3.7 ± 0.3. This decrease in incompressibility with grain size is similar to behavior observed in other ceramics. Under nonhydrostatic compression, WC supports a mean differential stress of ∼12-15 GPa at plastic yielding, which occurs at ∼30 GPa. Strength in WC is anisotropic, with the (001) plane supporting 29-42% higher stress than stresses calculated from mean strain. Simulations using an Elasto-ViscoPlastic Self-Consistent model indicate that strength inferred from lattice strain theory may be overestimated due to effects of plastic deformation. Plastic deformation generates a texture maximum near 〈2¯110〉 in the compression orientation, initially through prismatic slip on the {101¯0}〈1¯21¯0〉 and {101¯0}〈0001〉 slip systems, followed by activation of pyramidal slip on {101¯1}〈2¯113〉 at ∼40-50 GPa.

Effect of fO2 on Eu partitioning between clinopyroxene, orthopyroxene and basaltic melt: Development of a Eu3+/Eu2+ oxybarometer

We present partition coefficients for Cs, Li, Sr, Ba, Zn, Mn, Co, Ni, Sc, Ga, Y, La, Nd, Sm, Eu, Tb, Yb, Lu, Ti, Zr, Hf, Ta, Nb and P for synthetic clinopyroxene and orthopyroxene crystallized from a Fe-free basalt at 1.5 GPa and four different oxygen fugacities (fO2) ranging from 6 log units above the quartz-fayalite-magnetite oxygen buffer (QFM + 6) to QFM-5 at temperatures of 1275–1300 °C. Partition coefficients for the rare earth elements (REE) vary as a function of their ionic radii, in agreement with lattice strain theory. We use the lattice strain model to evaluate partition coefficients for Eu2+ and Eu3+. Our results suggest that fO2 exerts a primary and important control on Eu, Ni and Co partitioning in clinopyroxene whereas fO2 seemingly has no recognizable effect on the partitioning behavior of these elements in orthopyroxene. However Eu anomalies in orthopyroxene, orthopyroxene Onuma diagrams and calculated proportions of Eu2+ in melts all show evidence that fO2 influence Eu partitioning also in orthopyroxene. We combined our results, available experimental data and predictive models for divalent and trivalent Eu clinopyroxene-melt and orthopyroxene-melt partitioning to parameterize fO2-dependent Eu partitioning models. The reported models reproduce measured Eu partition coefficients within a factor of two. Our model can be applied as clinopyroxene-melt and orthopyroxene-melt oxybarometers if Eu equilibrium partitioning between melt and pyroxene can be demonstrated.

Negative differential stresses in niobium: Analysis of x-ray measured pressure–volume data

The macro-stresses that develop in a sample under nonhydrostatic compression in a diamond anvil cell (DAC) are axially symmetric about the load axis, the axial stress component being larger than the radial stress component. The difference between the two, termed differential stress t, is a positive quantity. The lattice strain theory (LST) suggests that the measured unit cell volume using conventional x-ray diffraction geometry of the DAC is overestimated in the presence of a positive t. In an earlier study on niobium, one set of x-ray measured compression data was found to yield negative t. It is suggested that the inward collapse of the gasket leads to negative t. It is shown that the volume-effect produced by negative t is also in accordance with the existing LST.

Modelling garnet-fluid partitioning in H2O-bearing systems: a preliminary statistical attempt to extend the crystal lattice-strain theory to hydrous systems

Accurate geochemical models of magmatic processes require an understanding of crystal-melt partitioning of trace elements. Many major igneous processes at different tectonic environments in Earth occur in the presence of garnet as a residual phase. Since the pioneering crystal lattice-strain model, several attempts have been made to quantify garnet-melt partitioning coefficients over a wide range of conditions. However, high pressure high-temperature experimental data demonstrate distinct differences in partitioning determined at anhydrous conditions and partitioning determined in the presence of H2O. In this study, we present for the first time a constraint on the partitioning of REE, Y, and Sc between garnet and hydrous fluids as a function of the water content in the fluid phase. We analysed published hydrous experimental partitioning data using different statistical methods and modelled key parameters in the crystal lattice strain model (r0, D0, and E). We show a robust correlation between r0, temperature and garnet-fluid partitioning of Mg. We further show that D0 can be predicted using the garnet-fluid partitioning of Fe and that E can be predicted using various parameters describing the fluid phase. We validate and illustrate the ability to predict partitioning of REE in H2O-bearing systems using major element analysis of garnet and fluid only. Consequently, our statistical model paves the way to integrate thermodynamic models based on major element chemical equilibria with trace element studies on hydrous magmatic systems, allowing a description of the transfer of key trace elements in more realistic conditions.

Experimental determinations of trace element partitioning between plagioclase, pigeonite, olivine, and lunar basaltic melts and an fO2 dependent model for plagioclase-melt Eu partitioning

We report partition coefficients for Sr, Sc, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Y, and Th for plagioclase, pigeonite, and olivine experimentally grown from a lunar basaltic liquid at 1 bar and two different oxygen fugacities (fO2; fayalite-magnetite-quartz (FMQ) and the iron-wüstite (IW) oxygen buffers) at temperatures (Ts) of 1100–1125 °C. These results expand the partitioning database for plagioclase-silicate melt partitioning at lunar relevant conditions and compositions. Variations of partition coefficients for rare earth elements (REEs) are highly systematic with respect to ionic radii, in agreement with lattice strain theory. We use the lattice strain model to evaluate partition coefficients for highly incompatible elements such as the light (or in the case of plagioclase, heavy) REEs, for which direct determinations are experimentally and analytically difficult. Our experiments suggest that within analytical and experimental uncertainty, over the range of explored fO2 (FMQ to IW), T (1100–1125 °C) and An# conditions (An# >94.5, where An#=Ca/(Ca + Na) × 100, in moles), fO2 exerts an important but secondary control on Eu partitioning in anorthitic plagioclase. In contrast, the global plagioclase-melt partitioning dataset highlights the first-order role of fO2 in determining plagioclase-melt Eu partition coefficients over a wide range of An#s. Using experimental results and predictive models for divalent and trivalent element plagioclase-melt partitioning in the plagioclase ring site, we parameterized an fO2-dependent plagioclase-melt Eu partitioning model. Within a factor of two, the model reproduces measured Eu partition coefficients for a wide range of experimental conditions (750–1400 °C) and compositional systems (basalts to dacites) over > 15 orders of magnitude variation in fO2. When equilibrium partitioning of Eu between plagioclase and melt can be established, the model may be applied as a plagioclase-melt oxybarometer. Preliminary application to plagioclase-hosted melt inclusions in mid-ocean ridge basalts suggests they equilibrated near the FMQ buffer. We used the new Eu partitioning model to evaluate the petrogenesis of a lunar anorthositic impactite that hosts plagioclase with both positive and negative Eu anomalies. Our investigation suggests the distribution of REEs and Eu in this sample is consistent with subsolidus reequilibration after impact-induced heating.

Mineral–melt partition coefficients and the problem of multiple substitution mechanisms: insights from the rare earths in forsterite and protoenstatite

A trace element may substitute into a mineral by more than one substitution mechanism, complicating the thermodynamic description of its partition coefficients. In order to understand this phenomenon better, the mineral/melt partition coefficients for all 14 rare earth elements (REE) plus Y and Sc were measured experimentally for coexisting forsterite and protoenstatite in the system CaO–MgO–SiO2 ± Al2O3 ± TiO2 at 1406 °C and atmospheric pressure. For both phases, the results show these large trivalent cations (REE3+) replace Mg2+ on octahedral sites, but with charge-balance achieved by two different mechanisms: (1) cation vacancies (2 REE3+ + vacancy = 3 Mg2+); and (2) substitution of Al for Si (REE3+ + Al3+ = Mg2+ + Si4+). The overall REE partition coefficient is the sum of the partition coefficients for each substitution mechanism. Because the stoichiometric control is different for each mechanism, the relative importance of the mechanism varies with melt composition, including the activities of both silica and alumina in the melt ($${{a}}_{{{\text{SiO}}_{ 2} }}^{\text{melt}}$$ and $${{a}}_{{{\text{AlO}}_{ 1. 5} }}^{\text{melt}}$$). The coexistence of forsterite and protoenstatite fixes the silica activity, allowing the effect of $${{a}}_{{{\text{AlO}}_{ 1. 5} }}^{\text{melt}}$$ to be separated from that of $${{a}}_{{{\text{SiO}}_{ 2} }}^{\text{melt}}$$. The relative importance of the two mechanisms depends strongly on the identity of the REE for forsterite, but not for protoenstatite. The results are used to test the lattice strain model: the two substitution mechanisms in forsterite imply different values for the Young’s modulus in the Brice equation, despite the fact that the REE3+ cations likely occupy the same crystallographic site in both mechanisms, casting doubt on the physical basis of the lattice strain theory. Comparison with literature data confirms earlier observations that the activity coefficients of REE2O3 in silicate melts decrease with increasing SiO2 content of the melt, but the effect decreases with increasing atomic number, from La to Lu, and is almost negligible for Sc. The influence of melt composition should apply to the mineral/melt REE partition coefficients of all other minerals. Recognizing that observed mineral/melt partition coefficients are often the sums of contributions from multiple substitution mechanisms, each with its own dependence on both crystal composition and the stoichiometric control from the melt composition, will improve parameterizations of the mineral/melt partition coefficients of other rock-forming minerals. Partition coefficients for Na, Al, Ca, Ti, and Zr are also reported.

Structural state of rare earth elements in eudialyte-group minerals

AbstractEudialyte-group minerals (EGM) attract global interest as potential resources for high-field-strength elements (e.g. Zr, Nb, Ta, and rare-earth elements), i.e. critical materials for modern technologies. They are particularly valued for their relative enrichment in the most critical lanthanides, i.e. Nd and heavy rare earth elements (Gd–Lu). However, rare earth element (REE) substitution mechanisms into the EGM structure are still poorly understood. Light and heavyREEmay occupy different sites and there may be ordering and/or defect clustering in the structure. This study uses X-ray absorption spectroscopy to determine the structural state ofREEin EGM from prospective eudialyte-bearing complexes. YttriumK-edge and NdL3-edge spectra were collected as proxies for heavy and lightREE, respectively, and compared to natural and syntheticREE-bearing standards. Extended X-ray absorption fine structure data yield best fits for Y in six-fold coordination with Y–O distances of 2.24–2.32 Å, and a second coordination sphere comprising Fe, Na, Ca, Si and O at radial distances of 3.6–3.8 Å. These findings are consistent with dominant Y3+substitution for Ca2+on the octahedralM1 site in all the samples studied, and exclude preferential substitution of Y3+onto the smaller octahedralZsite or the large low-symmetryN4 site.Using lattice strain theory, we constructed relative partitioning models to predict site preferences of lanthanides we have not measured directly. The models predict that allREEare favoured on the Ca-dominantM1 site and that preferential partitioning of heavy over lightREEincreases in EGM containing significant Mn in theM1-octahedral rings (oneillite subgroup). Thus, the flatREEprofiles that make EGM such attractive exploration targets are not due to preferential partitioning of light and heavyREEonto different sites. Instead, local ordering of Mn- and Ca-occupiedM1 sites may influence the capacity of EGM to accommodate heavyREE.

Tracing the evolution of a fertile REE granite by modelling amphibole-melt partitioning, the Strange Lake story

In principle, potentially economic (fertile) granites can be distinguished from uneconomic (barren) granites based on the composition of their magmas. Ideally, this composition would be evaluated by analysing melt inclusions, but such inclusions are rarely preserved and difficult to analyse. Information on the composition of magmas can also be obtained from the composition of the minerals crystallising from these magmas, if the mineral-melt partition coefficients are known. In some cases, where these partition coefficients are not known, they have been calculated from lattice strain theory. Here we report arfvedsonite-melt partition coefficients for the rare earth elements (REE) calculated from the results of analyses of arfvedsonite, bulk rock and melt inclusions in granites and pegmatites in the Strange Lake peralkaline rare metal pluton. These coefficients were fitted to the lattice strain model from which values of the ideal partition coefficient (D0), the ideal radius (r0) and the elastic response (EM) were determined. The light REE were shown to partition preferentially into the M4 site and the heavy REE into the M2 site, requiring that partition coefficients be calculated for each site. The partition coefficients for both sites were shown to decrease systematically with increasing evolution of the magma, i.e., from the early hypersolvus granite to the late pegmatites. In the case of the M4 site, D0, r0 and EM vary linearly with the Ca content of the arfvedsonite. By contrast, these parameters for the M2 site vary linearly with temperature. The two relationships form the basis of a predictive model, in which the arfvedsonite-melt REE partition coefficients for other peralkaline granites can be estimated, provided that the Ca content of the amphibole and its crystallisation temperature are known. This model was applied to a peralkaline granitic pegmatite from the Amis complex (Namibia) for which data on the composition of the amphibole and corresponding magma (melt inclusions) have been reported. The model successfully predicts the concentrations of the various REE in this magma, thereby providing confidence that it can be used to discriminate between granites that are potentially fertile and those that are barren in respect to the REE.

Modeling the Crystallization and Emplacement Conditions of a Basaltic Trachyandesitic Sill at Mt. Etna Volcano

This study documents the compositional variations of phenocrysts from a basaltic trachyandesitic sill emplaced in the Valle del Bove at Mt. Etna volcano (Sicily, Italy). The physicochemical conditions driving the crystallization and emplacement of the sill magma have been reconstructed by barometers, oxygen barometers, thermometers and hygrometers based on clinopyroxene, feldspar (plagioclase + K-feldspar) and titanomagnetite. Clinopyroxene is the liquidus phase, recording decompression and cooling paths decreasing from 200 to 0.1 MPa and from 1050 to 940 °C, respectively. Plagioclase and K-feldspar cosaturate the melt in a lower temperature interval of ~1000–870 °C. Cation exchanges in clinopyroxene (Mg-Fe) and feldspar (Ca-Na) indicate that magma ascent is accompanied by progressive H2O exsolution (up to ~2.2 wt. %) under more oxidizing conditions (up to ΔNNO + 0.5). Geospeedometric constraints provided by Ti–Al–Mg cation redistributions in titanomagnetite indicate that the travel time (up to 23 h) and ascent velocity of magma (up to 0.78 m/s) are consistent with those inferred for other eruptions at Mt. Etna. These kinetic effects are ascribed to a degassing-induced undercooling path caused principally by H2O loss at shallow crustal conditions. Rare earth element (REE) modeling based on the lattice strain theory supports the hypothesis that the sill magma formed from primitive basaltic compositions after clinopyroxene (≤41%) and plagioclase (≤12%) fractionation. Early formation of clinopyroxene at depth is the main controlling factor for the REE signature, whereas subsequent degassing at low pressure conditions enlarges the stability field of plagioclase causing trace element enrichments during eruption towards the surface.

The effect of CaO on the partitioning behavior of REE, Y and Sc between olivine and melt: Implications for basalt-carbonate interaction processes

The partitioning of REE,Y and Sc (R3+) between olivine and melt has been investigated experimentally during basalt-carbonate interaction. Three synthetic basalts (meltMg#72, meltMg#75 and meltMg#78) were doped with 0, 10 and 20 wt% CaCO3 and then equilibrated for 72 h at 1 atm, 1,150, 1,200 and 1,250 °C, and the QFM oxygen buffer. The thermal decomposition of CaCO3 produced CaO contents in the melt up to ~22 wt%. Regular relationships are found between the ionic radius and the partition coefficient (DR3+), showing typical near-parabolic patterns. DR3+ is weakly dependent on temperature, but decreases with increasing CaCO3 in the starting material (e.g., DSc decreases from 0.20 to 0.13). From the point of view of the lattice strain theory, DR3+ is described in terms of the radius of the crystal site (r0), the Young Modulus (E) due to the elastic response of that site to lattice strain caused by cation insertion, and the strain-free partition coefficient (D03+). The value of r0 decreases as Ca cations are accommodated into the more distorted M2 site of olivine via progressive CaFe substitutions. This mechanism is accompanied by a higher proportion of Mg cations entering into the smaller M1 site, making the optimum ionic radius smaller and favoring the crystallization of more forsteritic olivines from decarbonated melts. The enrichment of Ca in the crystal lattice is also proportional to the number of Si and Ca cations available in the melt. This causes E to be anticorrelated either with Ca in olivine or the activity of CaO in the melt. R3+ cations behave as network modifiers and, during basalt-carbonate interaction, the increasing abundance of non-bridging oxygens enhances the solubility of REE, Y and Sc in the melt. As a consequence, D03+ is negatively correlated with the degree of melt depolymerization. Additionally, the strain of the crystal lattice dominates the DR3+ parabolic patterns and D03+ is strongly controlled by forsterite and aluminium concentrations in olivine. The accommodation of REE, Y and Sc in the crystal lattice requires maintenance of local charge-balance by the generation of vacancies, in accord with a paired substitution of R3+ and a vacancy for Mg in octahedral sites.

Understanding How Bonding Controls Strength Anisotropy in Hard Materials by Comparing the High-Pressure Behavior of Orthorhombic and Tetragonal Tungsten Monoboride

In this work, we investigate the high-pressure behavior of the stabilized high-temperature (HT) orthorhombic phase of WB using radial X-ray diffraction in a diamond-anvil cell at room temperature. The experiments were performed under nonhydrostatic compression up to 52 GPa. For comparison, the low-temperature (LT) tetragonal phase of WB was also compressed nonhydrostatically to 36 GPa to explore structurally induced changes to its mechanical properties. Although our microindentation hardness tests indicate that the HT WB possesses slightly higher hardness, synchrotron-based high-pressure compression data yield significant distinct incompressibilities. The ambient pressure bulk modulus of the HT phase of WB is 341 ± 5 GPa obtained by using the second-order Birch–Murnaghan equation of state, while for the LT phase of WB the incompressibility increased to 381 ± 3 GPa. The elastically supported differential stress was measured in a lattice-specific manner and analyzed by using lattice strain theory. Greater s...

Zircon/fluid trace element partition coefficients measured by recrystallization of Mud Tank zircon at 1.5 GPa and 800–1000 °C

Hydrothermal zircon grains have trace element characteristics such as low Th/U, high U, and high rare earth element (REE) concentrations that distinguish them from magmatic, metamorphic, and altered zircon grains, but it is unclear whether these characteristics result from distinctive fluid compositions or zircon/fluid fractionation effects. New experiments aimed at measuring zircon/fluid trace element partition coefficients Dz/f involved recrystallizing natural Mud Tank zircon with low trace element concentrations in the presence of H2O, 1 m NaOH, or 1 m HCl doped with ∼1000 ppm of rare earth elements (REE), Y, U and Th and ∼500 ppm of Li, B, P, Nb, Ba, Hf, and Ta. Experiments were run for 168 h at 1.5 GPa, 800–1000 °C, and fO2 = NNO in a piston cylinder apparatus using the double capsule method. LA-ICP-MS analysis shows that run product zircon crystals have much higher trace element concentrations than in Mud Tank zircon starting material. Dz/f values were estimated from run product zircon analyses and bulk composition using mass balance.Most elements behave incompatibly, with median Dz/f being highest for Hf = 8 and lowest for B = 0.02. Addition of NaOH or HCl had little influence on Dz/f values. Dz/f for LREE are anomalously high, likely due to contamination of run product zircon with quenched solutes enriched in incompatible elements, so DLREE were estimated using lattice strain theory. Brice curves for +3 ions yield zircon/fluid DLu/DLa of ∼800–5000. A Brice curve fit to +4 ions yielded DCe4+ values. Estimated concentrations of Ce3+ and Ce4+ show that the average Ce4+/Ce3+ in zircon of 27 is much higher than in fluid of 0.02. Th and U show little fractionation, with median DTh/DU = 0.7, indicating that the low Th/U in natural hydrothermal zircon is inherited from the fluid. Natural fluid compositions estimated from measured Dz/f and published compositions of hydrothermal zircon grains from aplite and eclogite reflect the mineralogy of the host rock, e.g., fluid in equilibrium with eclogite garnet is depleted in heavy REE relative to middle REE, and has low Th/U.

Radial X-ray diffraction study of the static strength and texture of tungsten to 96 GPa

Investigations of equation of state, strength and texture of tungsten (W) have been performed under nonhydrostatic compression up to 96 GPa using an angle-dispersive radial X-ray diffraction (RXRD) techniques together with the lattice strain theory in a 2-fold paranomic diamond anvil cell (DAC) at ambient temperature. The ratio of t/G is found to remain constant above ∼35 GPa, indicating that the W started to experience macro yield with plastic deformation at this pressure. Combined with independent constraints on the high-pressure shear modulus, we found that W sample could support a differential stress of ∼4.57 GPa when it started to yield with plastic deformation at ∼35 GPa under uniaxial compression. The differential stress in W ranges from 0.01 GPa to 1.46 GPa with pressure increasing from 6 GPa to 35 GPa and can be described as t = −0.904(136) + 0.154(6)P, where P is the pressure in GPa. A maximum differential stress, as high as ∼6.46 GPa can be supported by W at the highest pressure of ∼96 GPa. In addition, we have investigated the texture of W under nonhydrostatic compression up to the highest pressure of 96 GPa using the software package MAUD (Material Analysis Using Diffraction). It is convinced that the plastic deformation due to stress under high pressures is responsible for the development of texture.

Rare earth element partitioning and subsolidus exchange behaviour in olivine

The systematics of the rare earth element (REE) abundances in olivine are poorly understood and this undermines their usefulness in deciphering petrogenetic processes. Here we report a novel REE dataset for olivine spanning a wide range in Mg number (Mg# 1–59) from the Skaergaard Layered Intrusion.Olivine La and Lu concentrations vary from 0.68 to 56ppb and 66 to 571ppb, respectively. Apparent olivine/melt partition coefficients for the heavy to middle REE define near-symmetrical parabolas, consistent with lattice strain theory, indicating that these elements are structurally bound within the olivine lattice. The parabolas define peaks with variable optimal radii (ro). This suggests that the Fe-content of olivine exerts a strong influence on REE partitioning, as fayalitic olivines display more open parabolas (higher apparent Young's modulus, E) than forsteritic olivines. The greater site elasticity is manifest as higher REE concentrations in the fayalitic samples. The observation that E and ro are not constant accross a range of Mg# has implications for predictive models for olivine REE.The CI chondrite-normalised olivine REE patterns show smooth trends from the heavy to the middle REE, with greater variation amongst the light REE (LREE). Variation and enrichment of the LREE are ubiquitous within published data for natural olivine, yet are not predicted by experimental results. This study also presents two-dimensional REE maps illustrating the behaviour of the REE in olivine in unprecedented detail. Mapping of magnesian olivine shows core to rim increase in Al, LREE, and Eu and the development of a positive Eu anomaly in olivine, resulting from solid-state, likely diffusive re-equilibration with adjacent plagioclase. We propose that secondary redistribution is the principal cause of elevated LREE patterns in natural olivine.The results from the present investigation show that from a petrological point of view, MREE to HREE systematics of olivine hold promise for study of olivine petrogenesis and that the LREE in olivine may be further developed to understand diffusion time scales and cooling rates in magmatic systems.

Radial X-Ray Diffraction Study of Static Strength of Tantalum to 80 GPa**Supported by the National Natural Science Foundation of China under Grant Nos 10875142 and 11079040, and the Chinese Academy of Sciences under Grant Nos KJCX2-SW-N03 and KJCX2-SW-N20.

We study the strength and texture of tantalum (Ta) under uniaxial compression up to 80 GPa using an angle-dispersive radial x-ray diffraction technique together with the lattice strain theory in a diamond anvil cell at ambient temperature. The ratio of differential stress to shear modulus (t/G) is found to remain constant above ∼60 GPa, indicating that the Ta starts to experience macro yield with plastic deformation at this pressure. Combined with independent constraints on the high-pressure shear modulus, we find that the Ta sample could support a differential stress of ∼4.67 GPa when it starts to yield with plastic deformation at ∼60 GPa under uniaxial compression. The differential stress in Ta ranges from 0.216 GPa to 4.67 GPa with pressure increasing from 1 GPa to 60 GPa and can be expressed as t = 0.199(33) + 0.075(1)P, where P is the pressure in GPa. A maximum differential stress as high as ∼5.37 GPa can be supported by Ta at the high pressure of ∼80 GPa. In addition, we investigate the texture of Ta under nonhydrostatic compression to 80 GPa using the software package material analysis using diffraction. It is proven that the plastic deformation due to stress under high pressures is responsible for the development of texture.

Clinopyroxene-melt element partitioning during interaction between trachybasaltic magma and siliceous crust: Clues from quartzite enclaves at Mt. Etna volcano

A peculiar characteristic of the paroxysmal sequence that occurred on March 16, 2013 at the New South East Crater of Mt. Etna volcano (eastern Sicily, Italy) was the eruption of siliceous crustal xenoliths representative of the sedimentary basement beneath the volcanic edifice. These xenoliths are quartzites that occur as subspherical bombs enclosed in a thin trachybasaltic lava envelope. At the quartzite-magma interface a reaction corona develops due to the interaction between the Etnean trachybasaltic magma and the partially melted quartzite. Three distinct domains are observed: (i) the trachybasaltic lava itself (Zone 1), including Al-rich clinopyroxene phenocrysts dispersed in a matrix glass, (ii) the hybrid melt (Zone 2), developing at the quartzite-magma interface and feeding the growth of newly-formed Al-poor clinopyroxenes, and (iii) the partially melted quartzite (Zone 3), producing abundant siliceous melt. These features makes it possible to quantify the effect of magma contamination by siliceous crust in terms of clinopyroxene-melt element partitioning. Major and trace element partition coefficients have been calculated using the compositions of clinopyroxene rims and glasses next to the crystal surface. Zone 1 and Zone 2 partition coefficients correspond to, respectively, the chemical analyses of Al-rich phenocrysts and matrix glasses, and the chemical analyses of newly-formed Al-poor crystals and hybrid glasses. For clinopyroxenes from both the hybrid layer and the lava flow expected relationships are observed between the partition coefficient, the valence of the element, and the ionic radius. However, with respect to Zone 1 partition coefficients, values of Zone 2 partition coefficients show a net decrease for transition metals (TE), high-field strength elements (HFSE) and rare earth elements including yttrium (REE+Y), and an increase for large ion lithophile elements (LILE). This variation is associated with coupled substitutions on the M1, M2 and T sites of the type M1(Al, Fe3+)+TAl=M2(Mg, Fe2+)+TSi. The different incorporation of trace elements into clinopyroxenes of hybrid origin is controlled by cation substitution reactions reflecting local charge-balance requirements. According to the lattice strain theory, simultaneous cation exchanges across the M1, M2, and T sites have profound effects on REE+Y and HFSE partitioning. Conversely, both temperature and melt composition have only a minor effect when the thermal path of magma is restricted to ~70°C and the value of non-bridging oxygens per tetrahedral cations (NBO/T) shifts moderately from 0.31 to 0.43. As a consequence, Zone 2 partition coefficients for REE+Y and HFSE diverge significantly from those derived for Zone 1, accounting for limited cation incorporation into the newly-formed clinopyroxenes at the quartzite-magma interface.

Trace element partitioning between clinopyroxene and trachy-phonolitic melts: A case study from the Campanian Ignimbrite (Campi Flegrei, Italy)

The partitioning of trace elements between crystals and melts provides an important petrogenetic tool for understanding magmatic processes. We present trace element partition coefficients measured between clinopyroxene phenocrysts and trachy-phonolitic magmas at the Campi Flegrei (Italy), whose late Quaternary volcanism has been characterized by two major caldera-forming events (Campanian Ignimbrite at ~39ka, and Neapolitan Yellow Tuff at ~15ka). Our data indicate that the increase of trivalent rare earth elements and yttrium into the crystal lattice M2 site is facilitated by the charge-balancing substitution of Si4+ with Al3+ on the tetrahedral site. Higher concentrations of tetravalent and pentavalent high field strength elements on the M1 site are also measured when the average charge on this site is increased by the substitution of divalent cations by Alvi. In contrast, due to these charge balance requirements, divalent transitional elements become less compatible within the crystal lattice. On the basis of the lattice strain theory, we document that the incorporation of rare earth elements and yttrium in clinopyroxene is influenced by both compositional and physical parameters. Data from this study allow to update existing partitioning equations for rare earth elements in order to construct a self-consistent model for trachy-phonolitic magmas based on the lattice strain theory. The application of this model to natural products from the Campanian Ignimbrite, the largest caldera-forming eruption at the Campi Flegrei, reveals that the complex rare earth element pattern recorded by the eruptive products can be successfully described by the stepwise fractional crystallization of clinopyroxene and feldspar where the clinopyroxene–melt partition coefficient changes progressively as a function of the physicochemical conditions of the system.