Lattice Strain Model Research Articles

Effect of redox on Fe\u2013Mg\u2013Mn exchange between olivine and melt and an oxybarometer for basalts

The Fe–Mg exchange coefficient between olivine (ol) and melt (m), defined as {text{Kd}}_{{{text{Fe}}^{T} {-} {text{Mg}}}} = (Feol/Fem)·(Mgm/Mgol), with all FeT expressed as Fe2+, is one of the most widely used parameters in petrology. We explore the effect of redox conditions on {text{Kd}}_{{{text{Fe}}^{T} {-} {text{Mg}}}} using experimental, olivine-saturated basaltic glasses with variable H2O (≤ 7 wt%) over a wide range of fO2 (iron-wüstite buffer to air), pressure (≤ 1.7 GPa), temperature (1025–1425 °C) and melt composition. The ratio of Fe3+ to total Fe (Fe3+/∑Fe), as determined by Fe K-edge µXANES and/or Synchrotron Mössbauer Source (SMS) spectroscopy, lies in the range 0–0.84. Measured Fe3+/∑Fe is consistent (± 0.05) with published algorithms and appears insensitive to dissolved H2O. Combining our new data with published experimental data having measured glass Fe3+/∑Fe, we show that for Fo65–98 olivine in equilibrium with basaltic and basaltic andesite melts, {text{Kd}}_{{{text{Fe}}^{T} {-} {text{Mg}}}} decreases linearly with Fe3+/∑Fe with a slope and intercept of 0.3135 ± 0.0011. After accounting for non-ideal mixing of forsterite and fayalite in olivine, using a symmetrical regular solution model, the slope and intercept become 0.3642 ± 0.0011. This is the value at Fo50 olivine; at higher and lower Fo the value will be reduced by an amount related to olivine non-ideality. Our approach provides a straightforward means to determine Fe3+/∑Fe in olivine-bearing experimental melts, from which fO2 can be calculated. In contrast to {text{Kd}}_{{{text{Fe}}^{T} {-} {text{Mg}}}}, the Mn–Mg exchange coefficient, {text{Kd}}_{{{text{Mn}} {-} {text{Mg}}}}, is relatively constant over a wide range of P–T–fO2 conditions. We present an expression for {text{Kd}}_{{{text{Mn}} {-} {text{Mg}}}} that incorporates the effects of temperature and olivine composition using the lattice strain model. By applying our experimentally-calibrated expressions for {text{Kd}}_{{{text{Fe}}^{T} {-} {text{Mg}}}} and {text{Kd}}_{{{text{Mn}} {-} {text{Mg}}}} to olivine-hosted melt inclusions analysed by electron microprobe it is possible to correct simultaneously for post-entrapment crystallisation (or dissolution) and calculate melt Fe3+/∑Fe to a precision of ≤ 0.04.

Textures and compositions of clinopyroxene in an Fe skarn with implications for ore-fluid evolution and mineral-fluid REE partitioning

Clinopyroxene is a common phase in a variety of hydrothermal ore deposits, notably in skarn deposits where it typically occurs as a major constituent. It commonly displays variations in texture and composition due to changing physicochemical conditions and contains relatively high concentrations of rare earth elements (REEs), making it an important petrogenetic indicator. In this study, we integrate textural and geochemical investigations of clinopyroxene from the Baijian Fe skarn deposit (eastern China) to constrain the evolution of ore-forming fluids and provide significant new insights into partitioning of REEs between the clinopyroxene and hydrothermal fluids.In the Baijian Fe skarn, endoskarn clinopyroxene is typically zoned with homogeneous Fe-poor cores and oscillatory zoned Fe-rich rims. The rims are also enriched in Na, Co, Ni, and V and contain primary fluid inclusions with high salinities of 57.7–61.2 wt.% NaCl equiv. The compositional differences between the cores and rims reflect a transition from dilute, Fe-poor fluids to saline, Fe-rich components, likely a result of fluid boiling. In the exoskarn, early formed Fe-poor clinopyroxene is commonly replaced with Fe-rich clinopyroxene through fluid-assisted, coupled dissolution-reprecipitation processes. Overall, the textural features and compositional variations of clinopyroxene reflect a transition from early diffusive metasomatism by low-salinity fluids under low water/rock ratios to later advective metasomatism by high-salinity fluids under high water/rock ratios.When normalized to the modeled composition of the melt-equilibrated fluid, the log light REE and middle REE abundances in the clinopyroxene fit a linear function of the radius parameter (expressed as r0/2 × (ri − r0)2 + 1/3×(ri − r0)3) of the lattice strain model, indicating that crystal lattice strain has exerted a major control on REE clinopyroxene-fluid partitioning. Cores of zoned endoskarn clinopyroxenes show an upward increase in heavy REE (HREE) from Ho to Lu, likely caused by incorporation of those elements both into the eightfold M2 site and the sixfold M1 site of clinopyroxene. The increasing HREE compatibility coincides with elevated Mn contents in the cores of the clinopyroxene grains, implying that Mn has a significant effect on the accommodation of HREE into the sixfold M1 site of clinopyroxene, presumably due to the similar ionic radius between Mn2+ in sixfold coordination (Mn2+ = 0.83 Å) and the HREE (e.g., Lu3+ = 0.861 Å).

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.

Hydrothermal calcite-fluid REE partitioning experiments at 200 °C and saturated water vapor pressure

Calcite is a common vein mineral associated to ore deposits and alteration zones geothermal systems. The concentration of rare earth elements (REE) in calcite can potentially be used to fingerprint the changing physicochemical conditions during mineralization from hydrothermal fluids. Previous calcite-fluid partitioning experiments have been carried out at ambient temperature but models aiming at predicting the behavior of REE at elevated temperature have not yet been developed. This study aims at determining the controls on REE incorporation into calcite mineralized from hydrothermal aqueous fluids above 100 °C. Here, we present a series of hydrothermal batch-type REE partitioning experiments at 200 °C and saturated water vapor pressure (15.5 bar). The experiments were designed to synthesize REE-doped calcite from fluid mixing with varying initial REE concentrations (250 ppb to 1000 ppb) and permit in situ sampling of the aqueous fluids. Calcite-fluid partition coefficients (KD) were observed to depend on the ionic radius of the REE and vary as a function of initial REE concentrations: logKD of 0.86–1.67 at 250 ppb REE; logKD of 1.05–1.70 at 500 ppb REE; logKD of 0.47–1.07 at 1000 ppb REE. These data fit a parabola according to the lattice strain model from which calculated Young’s modulus (ES) values range between 21.6 and 63.2 GPa. The fits indicate that the partitioning of the light REE is controlled by the strain-induced Ca2+ substitution in the calcite structure, whereas the heavy REE deviate from these trends. The development of a binary REE(OH)3 - CaCO3 solid solution model based on the dual-thermodynamic (DualTh) approach suggests that the REE partitioning is controlled by the following possible coupled substitutions at pH of 6:Eu3++3OH-⇔Ca2++CO32-Eu3++O2-+OH-⇔Ca2++CO32-The lattice strain fits are useful to interpret deviations of the experimental data from the solid solution model and possible non-ideal mixing behavior. Application of this model to natural systems yields some limitations because of the variability of experimental mineral-fluid KD values with REE concentrations in the aqueous fluids. The DualTh approach considers the aqueous speciation and activity-concentration relationships of the aqueous fluids, and therefore, provides an efficient method to evaluate the partitioning of REE between mineral and aqueous fluids. This research is a first step in building an experimental database of calcite-fluid partitioning data at hydrothermal conditions and aims at developing more accurate models for predicting the behavior of the REE in natural mineral-fluid systems.

Petrologic Reconstruction of the Tieshan Magma Plumbing System: Implications for the Genesis of Magmatic-Hydrothermal Ore Deposits within Originally Water-Poor Magmatic Systems

Abstract Most genetic models for magmatic-hydrothermal ore deposits are based on the prerequisite that the parental magmas associated with mineralization are enriched in water (> ∼4 wt %). However, it has been recognized that a number of magmatic-hydrothermal ore deposits also formed within tectono-magmatic settings that produce initially water-poor magmas such as Climax-type porphyry deposits. Here, we present a detailed reconstruction of the Tieshan magma plumbing system related to skarn-porphyry Cu–Fe–Au mineralization in the Edong district, in which primitive magmas typically show water-poor features. Applications of multiple thermodynamic calibrations on various magmatic units from the Tieshan and Tonglushan deposits provide a wealth of information regarding the structure and evolution of the transcrustal magmatic system. Petrographic observations and clinopyroxene-liquid thermobarometry calculations indicate that the Tieshan magmatic-hydrothermal system was fed by a deep crustal magma reservoir. An accurate picture of the evolution of H2O within the magma plumbing system is presented using the plagioclase-liquid hygrometer in combination with the amphibole hygrometer. Three critical stages during the evolution of water within the plumbing system have been recognized, associated with H2O contents of 0·8–1·7 wt %, 2·1–2·8 wt % and 3·2–4·6 wt %, respectively. The first enrichment of water in the magmas can be attributed to the separation and transfer of evolved melts from the deep magma reservoir to the shallow crust. Continuous cooling and solidification of the shallow magma body gave rise to the second enrichment of H2O in residual melts, leading to magmas that were fertile for the formation of ore deposits. The detailed chemical evolution of the magma plumbing system was investigated using mineral trace element compositions in combination with the partition coefficients predicted by the lattice strain model. The earliest equilibrium melts are characterized by high Sr contents (the average = 658 ± 64 ppm), suggesting that high Sr/Y signatures were likely derived from their magma sources or fractionation at deeper levels in initially water-poor environments. Variations of some particular geochemical fingerprints in equilibrium melts such as, Dy/Dy* and Eu/Eu*, also provide fundamental information on the evolution of the magma plumbing system. Our study confirms the critical role of a deep crustal magma reservoir on the formation of magmatic-hydrothermal ore deposits. The fertility of magmas with respect to ore deposit formation was enhanced by the extraction and transfer of evolved magmas from the deep reservoir to shallower levels, particularly due to the enrichment of magmatic water contents. In addition, the presence of a deep magma reservoir also sustains the incremental growth of shallow magma chambers, which provide ore-forming fluids.

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.

Amphibole-rich cumulate xenoliths in the Zhazhalong intrusive suite, Gangdese arc: Implications for the role of amphibole fractionation during magma evolution

Abstract Amphibole fractionation during the early evolution of arc magmas has been widely inferred on the basis of distinctive geochemical fingerprints of the evolved melts, although amphibole is rarely found as a major mineral phase in arc volcanic rocks, so-called cryptic amphibole fractionation. Here, we present a detailed case study of xenoliths of amphibole-rich cumulate from the Zhazhalong intrusive suite, Gangdese arc, which enables an investigation of this differentiation process using a combination of petrological observations and in situ geochemical constraints. Evidence that the xenoliths represent fragments of igneous cumulates includes: (1) the presence of an amphibole-dominated crystal framework; (2) mineral and whole-rock Fe–Mg exchange coefficients; (3) rare-earth element patterns that are similar in the amphiboles and the xenoliths; (4) the compositions of basaltic to andesitic liquids in equilibrium with amphiboles; and (5) enrichment of the xenoliths in compatible elements and depletion in incompatible elements. The amount of trapped liquid based on La, Ce, and Dy abundances varies from ~12 to ~20%. Actinolitic cores within amphibole grains likely represent reaction between olivine precursor and hydrous melt, as evidenced by their high Cr and Ni contents. Amphibole thermometry and oxybarometry calculations indicate that crystal accumulation occurred over temperatures of 857–1014 °C, at mid-crustal pressures of 312 to 692 MPa and oxygen fugacity between 0.4 and 1.9 log units above the nickel–nickel oxide buffer. Quantification of the major-element compositions of the parent liquids indicates that the Zhazhalong amphibole cumulates crystallized from basaltic to andesitic magmas, probably with a shoshonitic affinity, and with SiO2 contents of 46.4–66.4 wt%. Appropriate partition coefficients, calculated using a parameterized lattice strain model and an empirical partitioning scheme, were employed to calculate the trace-element compositions of the liquids in equilibrium with amphibole. Our results confirm that Dy/Yb and Dy/Dy* ratios, which decrease with increasing degrees of differentiation, can be used as robust signatures of amphibole fractionation. This work presents a direct snapshot of the process of amphibole fractionation and provides a natural example of the hidden amphibole “sponge” in arc crust. In particular, this study also suggests that some appinites likely represent amphibole-rich cumulates, which may help to explain the genesis of other unusual but petrologically significant rocks.

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.

Characterization of the zircon Ce anomaly for estimation of oxidation state of magmas: a revised Ce/Ce* method

As a proxy of magmatic oxidation state, the accurate characterization of the Ce anomaly of zircon is of great significance since it can give important information for provenance studies of rocks as well as for exploration of intrusion-related mineral deposits. The magnitude of the zircon Ce anomaly has been traditionally described by Ce/Ce*, where Ce* is the theoretical Ce value derived from a chondrite-normalized rare earth element (REE) pattern. More recently, the Ce4+/Ce3+ method based on the lattice strain model has been proposed, since the latter method does not need La and Pr contents for zircon, both of which are commonly below the limit of detection and susceptible to contamination from melt/mineral inclusions. In this contribution we show that the Ce4+/Ce3+ method is confronted with some problems in practice and should be further improved. In contrast, by re-examining chondrite-normalized REE patterns of zircon, we find that Ce* can be estimated according to a logarithmic function curve without involvement of La and Pr contents. Application of this new method to zircon data from 11 giant to supergiant porphyry Cu deposits suggests this revised method as a more valid measure in evaluating magmatic oxidation state. The revised Ce/Ce* method is of particular importance for analyses where the provenance of the analyzed zircon is unknown or in question, since the method does not require knowledge of the melt composition.

Effect of substitutional impurities on vibrational properties of zircon: a first-principles study

Density-functional theory was used to investigate the effect of atomic impurities on the structural and vibrational properties of zircon (tetragonal ZrSiO4). Atomic impurities considered include radioactive elements U and Th, as well as Hf, Sn, and Ti, substituted on the Zr-site. Using the supercell approach to model a range of substitutional concentrations, impurities were found to cause changes in the volume of the host lattice. This effect was shown to be partially equivalent to the application of a lattice strain. This quantum-based finding is in excellent agreement with the heuristic lattice-strain model traditionally employed in the geosciences to account for the compatibility of impurities in host lattices. Vibrational properties of substituted zircon were also investigated in order to provide a quantum mechanical understanding of Raman spectroscopy measurements on natural zircon. The computational analysis reproduces existing experimental data reported for uranium-substituted zircon and provides general predictive trends for other impurities including Th, Hf, Sn, and Ti. The insights gained by this study regarding the Raman signature of the presence of substitutional impurities set the groundwork for future study of the more substantial lattice disruptions that characterize radiation damage due to alpha decay in zircon.

Trace element partitioning between wollastonite and alkaline silicate magmas

The partitioning of trace elements between wollastonite and melt provides a choice tool for understanding differentiation processes and trace element fractionation in alkaline-rich and silica-undersaturated magmatic systems at crustal conditions, but very few data are currently available. Here we provide the first partition coefficients and associated lattice strain parameters between wollastonite and silicate magmas of Oldoinyo Lengai (Tanzania). Trace element partitioning of isovalent cations shows a parabolic dependence between the partition coefficients and ionic radii explained by the lattice strain model with the site radius (r0) decreasing with increasing charge from r01+ = 1.2 Å to r05+ = 0.6 Å. Bivalent cations are moderately incompatible (DMg = 0.12 and DSr = 0.5) to compatible (DMn = 1). High field strength elements such as Zr and Nb are strongly incompatible in wollastonite (D < 0.01), and rare earth element (REE) partition coefficients increase with decreasing ionic radius from DLa = 0.19 to DLu = 2.8. The crystallization of wollastonite could eventually strongly influence REE fractionation (and more specifically the light-heavy REE ratios) during magmatic differentiation of alkali-rich foiditic melts and should therefore be considered to fully understand trace element evolution and partitioning in alkaline and silica-undersaturated magmas.

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.

Trace element partitioning between amphibole and hydrous silicate glasses at 0.6–2.6 GPa

Partitioning behavior between amphibole and silicate glass of thirty-three minor and trace elements (Sc, Ti, V, Cr, Co, Rb, Sr, P, Y, Zr, Nb, Cs, Ba, K, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta, Pb, Th, and U) have been determined experimentally. Products of crystallization of hydrous basalt melts from 0.6 GPa/860 °C up to 2.6 GPa/970 °C were obtained in a multi-anvil apparatus. Major and trace element compositions of amphibole and glass were determined with a combination of electron microprobe and laser ablation inductively coupled plasma mass spectrometry. The main mineral phase is calcic amphibole, and the coexisting glass compositions are tonalite, granodiorite, and granite. The compatibility of rare earth elements increase at 915 °C and then decrease at 970 °C, but the compatibility of most of these elements shows a continued, significant increase with increasing pressure. For high-field strength elements, large ion lithophile elements, actinide compatibility decrease with increasing temperature or pressure, but transition metals show a continued increase in compatibility within the temperature–pressure conditions. From mathematical and graphical fitting, we determined best-fit values for the ideal ionic radius (r0, 1.01–1.04 A), the strain-free partition coefficient (D0, 1.18–1.58), and apparent Young’s modulus (E, 142–370 GPa) for the M4 site in amphibole according to the lattice strain model. The $$D_{0}^{M4}$$ for rare earth elements rises at 915 °C and then drops at 970 °C at 0.6 GPa. However, the $$D_{0}^{M4}$$ values are positively proportional to the pressure for rare earth elements in the amphibole-glass pairs at 0.6–2.6 GPa and 970 °C. Furthermore, the derived best-fit values for $$r_{0}^{M4}$$ and $$E^{M4}$$ are almost constant and trend to increase with rising temperature and pressure, respectively. The partition coefficient is distinctly different for different melt compositions. The rare earth elements become more enriched in amphibole if the quenched glass is granodiorite or granite compared to the tonalitic glasses.

Ra/Th ages of sanidine in young trachytes erupted at Changbaishan Volcano, China

Accurately dating Holocene volcanic rocks poses many challenges but is critical to assessing the magmatic evolution and hazard risks of highly active volcanoes. Here, Ra/Th isotopes are used to determine crystallization ages of sanidine from trachytes recently erupted at Changbaishan volcano, best known for its destructive “Millennium Eruption” at 946 CE. To determine Ra/Th crystallization ages, the partition coefficient of radium (DRa) in sanidine has to be known or accurately estimated. We employ the lattice strain model (Blundy and Wood, 1994) to predict DRa and DRa/DBa that yields ages that are consistent with historical eruption dates at Changbaishan and that allow for ~100–500 years of crystal residence prior to eruption. Deduced 226Ra/230Th sanidine ages are progressively younger in trachytes erupted at 946, 1668, and 1903 CE. These ages confirm young sanidine-hosting eruptions that post-date Millennium Eruption activity at 946 CE and indicate the likely continued presence of explosive trachytic magma residing under the edifice.

Insight into zircon REE oxy-barometers: A lattice strain model perspective

Zircon rare earth element (REE) oxy-barometers have been widely used to calculate magma oxygen fugacity. However, sometimes confusing results are obtained, such as extremely reduced oxygen fugacity in Hadean magmas (e.g. ΔFMQ−8), extremely oxidized oxygen fugacity in post-Hadean magmas (e.g. ΔFMQ+10) and contradictory oxygen fugacities recorded in ore-related porphyry magmas (ΔNNO+5 vs ΔNNO+1). To address these issues, this work reviews the underlying assumption of zircon REE oxy-barometers, the lattice strain model. By introducing a geochemical filter to identify clean, inclusion-free zircon and a new parameter δK to constrain the Dzircon/wholerock deviation from the lattice strain model, we systematically re-evaluate the common zircon REE oxy-barometers, address the issues noted in Hadean, post-Hadean and ore-related magmas, and provide an alternate approach to using zircon REE in studies of magmatic processes.

DOUBLE FIT: Optimization procedure applied to lattice strain model

Modeling trace element partition coefficients using the lattice strain model is a powerful tool for understanding the effects of P-T conditions and mineral and melt compositions on partition coefficients, thus significantly advancing the geochemical studies of trace element distributions in nature. In this model, partition coefficients describe the strain caused by a volume change upon cation substitution in the crystal lattice. In some mantle minerals, divalent, trivalent, and tetravalent trace element cations are mainly substituted in one specific site. Lattice strain model parameters, for instance in olivine and plagioclase, are thus fit for one crystal site. However, trace element cations can be substituted in two sites in the cases of pyroxenes, garnets, amphiboles, micas, or epidote-group minerals.To thoroughly study element partitioning in those minerals, one must consider the lattice strain parameters of the two sites. In this paper, we present a user-friendly executable program, working on PC, Linux, and Macintosh, to fit a lattice strain model by an error-weighted differential-evolution-constrained algorithm (Storn, R., and Price, K. 1997. Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11, 341–359). This optimization procedure is called DOUBLE FIT and is available for download on http://celiadalou.wixsite.com/website/double-fit-program. DOUBLE FIT generates single or double parabolas fitting experimentally determined trace element partition coefficients using a very limited amount of data (at minimum six experimental data points) and accounting for data uncertainties. It is the fastest calculation available to obtain the best-fit lattice strain parameters while accounting for the elastic response of two different sites to trace element substitution in various minerals.

Physicochemical Control of the Early Permian Xiangshan Fe-Ti Oxide Deposit in Eastern Tianshan (Xinjiang), NW China

The Xiangshan mafic-ultramafic complex is one of the major Early Permian mafic-ultramafic intrusions in eastern Tianshan (Xinjiang, NW China), and consists of two major intrusive phases. The first intrusive phase is mainly gabbroic rocks hosting ilmenite mineralization, while the second intrusive phase is mainly lherzoilite associated with Ni-Cu sulfide mineralization. The Xiangshan ilmenite orebodies hosted in the Fe-Ti oxide-bearing gabbro occur along the contact between hornblende gabbros and leucogabbros. The hornblende gabbros and Fe-Ti oxide rich gabbros at Xiangshan are newly dated to be Early Permian (280.1 and 279.2 Ma, respectively). Major and trace element compositions of zircons and whole rocks from Xiangshan hornblende gabbro and Fe-Ti oxide gabbro have been measured by in situ excimer laser ablation ICP-MS. Zircon Ce4+/Ce3+ ratios based on lattice-strain model and Ti-in-zircon temperatures of hornblende gabbro and Fe-Ti oxide gabbro of the Xiangshan complex are calculated to evaluate the physicochemical variations during the ilmenite mineralization. Whole-rock geochemistry and zircon trace element geochemistry suggest that Fe-Ti oxide gabbros were formed from a basaltic parent magma which had undergone a transfromation from being H2O-rich to H2O-poor. During the magmatic evolution, primitive, H2O-poor basaltic melts may have been replenished into the system, increasing its solidus temperature and decreasing its oxygen fugacity and H2O contents. This may have supperessed the Ti-rich poikilitic hornblende fractionation and promoted the plagioclase fractionation, which consequently concentrated the ore-forming components in the residual melts and generated the ilmenite mineralization.

Controls on Trace Element Distribution in Oxides and Silicates

Understanding and quantifying the partitioning of elements at low concentrations is important for petrology, as minor and trace elements are used as tracers of many geological processes. The lattice strain model has consequently been found to be very useful, as it links mineral/melt partition coefficients to the elastic properties of the mineral and to the difference in ionic radius between the trace element and the cation it replaces. However, this model has limitations, particularly in terms of describing crystal strain, due to the form of the equation and from the choice of a hard-sphere model. After a review of the thermodynamics of trace element incorporation into crystal sites and equilibrium between mineral phases, we present classical atomistic modelling using transferable empirical potentials. Following incorporation of one (or more) mismatching element(s), crystal strain appears strongly related to the environment of the site of exchange, with anisotropic, vacancy-rich minerals deforming more than densely-packed minerals, due to anisotropic deformation, rotation and tilting of the surrounding polyhedra. As shown by the computed cation–oxygen length in strained crystal sites, bond strain is smaller than the difference in cation radii, and varies between structures, with densely-packed minerals being less strained. Consequently, computed relaxation energies are smaller in less compressible minerals. This has implications for modelling the partitioning of trace elements, and highlights the limits of using continuum mechanics below crystal cell scale. Neither oxides nor silicates have isotropic elastic properties, and at nanoscale they do not deform like continuous material. Predictions of partitioning between mineral and melt (or fluid) remain hampered by several factors, amongst which are (i) knowledge of the thermodynamics properties of the dissolved species (in melts and fluids); (ii) the precision of estimated defect and strain energies; and (iii) the presence of solid solution in natural systems, even when limited to a few percent. The latter may have orders-of-magnitude effects on the calculated partition coefficients due to interactions between strain fields around minor cations, leading to a chemical mixing regime at low concentration different from solid solutions where phase components are found in high proportions. Partitioning between mineral phases in an assemblage is described with similar equations as for mineral/liquid equilibria. In cases where terms linked to fluid species disappear, such as incorporation with similar substitutions in two minerals, the assumption that crystal strain energy is the preponderant term during cation exchange becomes unnecessary and it is preferable to use defect energies rather than strain energies. Application and discussion of these concepts are presented for mineral/melt partitioning and for partitioning between minerals, using garnet/clinopyroxene equilibria. The advantage of atomistic modelling is that it does not rely on fitting. Agreement with experimental data shows predictive accuracy within an order of magnitude, which is poorer than what may be achieved by fitting the lattice strain model to experimental data, but validating the theoretical approach and sufficient for application to some petrology problems. Improvements of the modelling for better application to minerals like augite involve systematic work on the effect of solid solutions on the strain field around defects and imply solving ordering problems.

Effect of Swift Heavy Ion Irradiation on Dielectric Properties of Manganite Based Thin Films

In this communication, we report the results of the investigations on the structural, microstructural and electrical properties of Y0.95Sr0.05MnO3 (YSMO) thin films with 100 nm thickness grown on (100) single crystalline SrNb0.002Ti0.998O3 (SNTO) substrates using pulsed laser deposition (PLD) technique. YSMO films were irradiated using 100 MeV O+7 swift heavy ions (SHI) with different fluence using 15 UD Tandem Accelerator, IUAC, New Delhi facility. Structural investigations using θ – 2θ X – ray diffraction (XRD) reveal that all the films crystallize in single phasic nature. With increase in ion fluence, structural strain is found to increase upon the irradiation using lower fluence of 1 × 1011 ions/cm2 which can be ascribed to the irradiation induced creation of defects at the interface. Further increase in ion fluence up to 1×1012 ions/cm2 can create more defects resulting in the degradation in lattice structure and hence strain gets enhanced. For the higher ion fluence of 1×1013 ions/cm2, local annealing takes place at the interface which in turn results in the improved structural strain and recrystallization process. To study the surface morphology of the pristine and irradiated films, atomic force microscopy (AFM) measurement was performed. To understand the electrical properties of presently studied YSMO / SNTO pristine and irradiated films, frequency dependent dielectric behavior was studied. It is seen that dielectric constant increases upon irradiation using the fluence of 1 × 1011 ions/cm2 and 1 × 1012 ions/cm2 while gets suppressed for 1 × 1013 ions/cm2 fluence. Variation in dielectric behavior with different ion fluence has been discussed on the basic of lattice strain and universal dielectric response (UDR) model.

Constraints on the uptake of REE by scheelite in the Baoshan tungsten skarn deposit, South China

Scheelite is the main ore mineral in skarn-type tungsten deposits, and a common accessory mineral in a variety of rock-types. The Baoshan deposit in South China is one of the most important polymetallic scheelite skarn deposits in China, hosting 40,000t of WO3 with economic concentrations of Zn, Cu, and Ag. It is hosted by a calcic skarn that is zoned outwards mineralogically from garnet-clinopyroxene, through clinopyroxene-garnet, to wollastonite, and overprinted by retrograde minerals. Scheelite occurs in both the prograde and retrograde skarns, and is complexly zoned. On the basis of its textures, the scheelite was classified into three types. Scheelite I and II belong to the early and late prograde stages, respectively, and Scheelite III precipitated during the retrograde stage. The molybdenum (Mo) content of these scheelite types ranges from 54ppm to 24wt%, and the total rare earth element content ranges from 12 to 321ppm. Rare earth element (REE) concentrations and chondrite-normalized REE profiles vary with the distribution of major elements. The profiles indicate variable degrees of REE enrichment, which correlates negatively with the Mo content. Molybdenum-rich scheelite displays a negative Eu anomaly, and Mo-poor scheelite a positive Eu anomaly. Crystal structure provided the first-order control on the minor and trace element composition of the scheelite. Incorporation of REE3+ into scheelite was controlled partly by a coupled substitution involving Mo. The lattice strain model was used to estimate scheelite-fluid partition coefficients for the REE from the contents of these elements in the scheelite and to predict the relative distributions of the REE in the ore-forming fluids. It is proposed that conditions were initially oxidizing, leading to strong incorporation of Mo in Scheelite I, that they became more reducing with the crystallization of Scheelite II containing lesser Mo, and that during retrograde skarn formation there was a return to oxidizing conditions due to an influx of meteoric waters, which altered Scheelite II giving rise to the formation of Scheelite III. The study shows that the composition of scheelite recorded the history of the Baoshan hydrothermal system, and that the behaviour of the REE could be used to quantitatively reconstruct the changing physicochemical conditions during ore formation.