Temperature and pressure-independent correlations of olivine/liquid partition coefficients and their application to trace element partitioning

Molar olivine/liquid partition coefficients for Mg, Fe, Mn and Ni are shown to be linearly correlated. These correlations appear to be independent of temperature, pressure and, to some extent, bulk composition and are best explained by the dominance of change-of-state thermodynamics during partitioning. The correlations presented here, when coupled with considerations of olivine stoichiometry, allow (olivine/basalt) partition coeficients of Mg, Fe, Mn and Ni to be predicted if the composition of the basalt is known. Since the correlations hold for major, minor and trace elements and for both compatible and incompatible elements, the inferences drawn from this study appear to have general relevance.     

Stoichiometric control of crystal/liquid single-component partition coefficients

Single-component (e.g., single-element) partition coefficients for silicate melts and the minerals that crystallize from them typically show large variations with temperature and melt composition. It is shown that, in particular cases, these variations can be calculated from two-component distribution coefficients that are practically constants, given the structural formula of the mineral and the melt composition.     

Pressure dependence on partition coefficients for trace elements between olivine and the coexisting melts

Partition coefficients between olivine and melt at upper mantle conditions, 3 to 14 GPa, have been determined for 27 trace elements (Li, Be, B, Na, Mg, Al, Si, P, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Rb, Sr, Y, Zr, Cs, Ba, La and Ce) using secondary-ion mass-spectrometry (SIMS) and electron-probe microanalysis (EPMA). The general pattern of olivine/melt partitioning on Onuma diagrams resembles those reported previously for natural systems. This agreement strongly supports the argument that partitioning is under structural control of olivine even at high pressure. The partition coefficients for mono- and tri-valent cations show significant pressure dependence, both becoming larger with pressure, and are strongly correlated with coupled substitution into cation sites in the olivine structure. The dominant type of trace element substitution for mono- and tri-valent cations into olivine changes gradually from (Si, Mg)↔(Al, Cr) at low pressure to (Si, Mg)↔(Al, Al) and (Mg, Mg)↔(Na, Al) at high pressure. The change in substitution type results in an increase in partition coefficients of Al and Na with pressure. An inverse correlation between the partition coefficients for divalent cations and pressure has been observed, especially for Ni, Co and Fe. The order of decreasing rate of partition coefficient with pressure correlates to strength of crystal field effect of the cation. The pressure dependence of olivine/melt partitioning can be attributed to the compression of cation polyhedra induced by pressure and the compensation of electrostatic valence by cation substitution. Received: March 6, 1997 / Revised, accepted: March 12, 1998     

Some experimentally determined zircon/liquid partition coefficients for the rare earth elements

Partition coefficients for La, Sm, Ho and Lu (REE) between synthetic zircon and felsic, peralkaline liquid were determined at 800°C and 2 kbar water pressure by adding small amounts of REE to experimental charges and analyzing zircons in the quenched runs with an electron microprobe. The preferred zircon/liquid partition coefficients obtained by this method are: La, 1.4–2.1; Sm, 26–40; Ho, 340+; Lu, 72–126. These results confirm the strong heavy rare earth enrichment discovered by Nagasawa (1970) in zircon separates from dacites and granites, but they also introduce a modification to the supposed zircon/liquid partition coefficient pattern. The heavy REE end of the pattern is concave downward, in qualitative resemblance to some garnet/liquid and hornblende/liquid REE partitioning patterns.     

Crystal chemical and energy analysis of partition coefficients of impurities during melt crystallization: The case of olivine

Partition coefficients (K) between forsterite crystal and melt are experimentally determined for many univalent, bivalent, trivalent, and tetravalent trace elements. Using numerical modeling, we calculated the energies of intrinsic and impurity defects in forsterite (E _df) and the energies of dissolution of univalent, bivalent, trivalent, and tetravalent impurities (E _ds). These results are compared with literature data. A linear dependence is established for the energy of defects on the charge of the impurity ion and the relative difference in the radii of the impurity and matrix ions Δr/d, where d is the average interatomic distance in the matrix. Partition coefficients are described by parabolic dependences on Δr/d and charge of the impurity ion using literature data on K of impurity elements in olivines and impurity ion dissolution energies. Linear dependences-RTlnK-(Δr/d)² and E _ds-(Δr/d)² pass through the origin for isovalent substitutions and are well apart from it for heterovalent substitutions. Linear dependence (Δr/d)² has a free term of about 200 kJ/mol, which is approximately equal to a half of the energy of formation of the Frenkel defect in forsterite; this defect maintains electroneutrality. If valency is compensated due to addition into the melt of an ion with another charge (than that of the impurity ion), E _ds-(Δr/d)² and-RTlnK-(Δr/d)² lines at low (Δr/d)² shift to the origin. This means that energy consumption for coupled isomorphism is lower than that for the formation of intrinsic structural defects. Correlation dependences are proposed for the distribution of impurities and the energy of their dissolution. They indicate the increasing contribution of the entropy components of impurity ion dissolution energy during heterovalent isomorphism.     

Partitioning coefficients between olivine and silicate melts

Variation of Nernst partition coefficients (D) between olivine and silicate melts cannot be neglected when modeling partial melting and fractional crystallization. Published natural and experimental ^{olivine/liquid}D data were examined for covariation with pressure, temperature, olivine forsterite content, and melt SiO₂, H₂O, MgO and MgO/MgO + FeO^total. Values of ^{olivine/liquid}D generally increase with decreasing temperature and melt MgO content, and with increasing melt SiO₂ content, but generally show poor correlations with other variables. Multi-element ^{olivine/liquid}D profiles calculated from regressions of D REE–Sc–Y vs. melt MgO content are compared to results of the Lattice Strain Model to link melt MgO and: D₀ (the strain compensated partition coefficient), E_M³⁺ (Young's Modulus), and r₀ (the size of the M site). Ln D₀ varies linearly with Ln MgO in the melt; E_M³⁺ varies linearly with melt MgO, with a dog-leg at ca. 1.5% MgO; and r₀ remains constant at 0.807 Å. These equations are then used to calculate ^{olivine/liquid}D for these elements using the Lattice Strain Model. These empirical parameterizations of ^{olivine/liquid}D variations yield results comparable to experimental or natural partitioning data, and can easily be integrated into existing trace element modeling algorithms. The ^{olivine/liquid}D data suggest that basaltic melts in equilibrium with pure olivine may acquire small negative Ta–Hf–Zr–Ti anomalies, but that negative Nb anomalies are unlikely to develop. Misfits between results of the Lattice Strain Model and most light rare earth and large ion lithophile partitioning data suggest that kinetic effects may limit the lower value of D for extremely incompatible elements in natural situations characterized by high cooling/crystallization rates.     

Experimental measurements of zircon/melt trace-element partition coefficients

Zircon was grown from trace-element doped hydrous peralkaline rhyolite melts with buffered oxygen fugacities in cold-seal experiments at 0.1 and 0.2 GPa and 800 °C and piston-cylinder experiments at 1.5 GPa and 900-1300 °C. Zircon and glass were present in all run products, and small monazite crystals were present in eight of the 12 experiments. Average diameters of zircon crystals ranged from 5 to 20 μm at 800 °C to 30-50 μm at 1300 °C. Zircon crystals have thin rims, and adjacent glass has a narrow (∼1 μm thick) compositional boundary layer. Concentrations obtained through in-situ analysis of cores of run product zircon crystals and melt pools were used to calculate trace-element partition coefficients D^zircon/melt for P, Sc, Ti, V, Y, La, Ce, Pr, Nd, Eu, Gd, Ho, Yb, Lu, Hf, Th, and U. In most cases Lu was the most (D 12-105) and La the least (0.06-0.95) compatible elements. D values from this study fall within the range of previously measured values for Rare Earth Elements (REE). However, D values measured experimentally show less fractionation than those recently measured using natural phenocryst/matrix pairs. For example, D_Lu/D_La measured experimentally in this study range between 27 and 206 compared to a value of 706,522 for a natural zircon/dacite pair [Sano, Y., Terada, K., and Fukuoka, T. 2002 High mass resolution ion microprobe analysis of rare earth elements in silicate glass, apatite and zircon: lack of matrix dependency. Chem. Geol.184, 217-230]. Although D values from this study show good agreement with the lattice strain model, D values from natural phenocryst/matrix pairs combined with measured zircon compositions better reproduce host-rock (magma) compositions of igneous rocks. They also yield more reasonable estimates of magma compositions when combined with compositions of ‘‘out-of-context” zircons. For example, compositions of the Hadean detrital zircons from Jack Hills, Australia yield LREE-enriched magmas when combined with D values from phenocryst/matrix pairs yields, but yield LREE-depleted magmas when experimentally determined D values are used. We infer that experimentally measured D^zircon/melt values represent disequilibrium partitioning resulting from rapid zircon growth during short laboratory timescales. Rapid growth causes development of observed diffusive boundary layers in the melt adjacent to zircon crystals. D values from phenocryst/matrix pairs are therefore recommended for petrogenetic modeling.     

Immiscible silicate liquid partition coefficients: implications for crystal-melt element partitioning and basalt petrogenesis

This study investigates partitioning of elements between immiscible aluminosilicate and borosilicate liquids using three synthetic mixtures doped with 32 trace elements. In order to get a good spatial separation of immiscible liquids, we employed a high-temperature centrifuge. Experiments were performed at 1,050–1,150°C, 1 atm, in sealed Fe and Pt containers. Quenched products were analysed by electron microprobe and LA ICP-MS. Nernst partition coefficients (D’s) between the Fe-rich and Si-rich aluminosilicate immiscible liquids are the highest for Zn (3.3) and Fe (2.6) and the lowest for Rb and K (0.4–0.5). The plots of D values against ionic potential Z/r in all the compositions show a convex upward trend, which is typical also for element partitioning between immiscible silicate and salt melts. The results bear upon the speciation and structural position of elements in multicomponent silicate liquids. The ferrobasalt–rhyolite liquid immiscibility is observed in evolved basaltic magmas, and may play an important role in large gabbroic intrusions, such as Skaergaard, and during the generation of unusual lavas, such as ferropicrites.     

Experimentally determined mineral-melt partition coefficients for Sc,Y and REE for olivine,orthopyroxene, pigeonite,magnetite and ilmenite

Our current lack of understanding of the partitioning behavior of Sc, Y and the REE (rare-earth elements) can be attributed directly to the lack of a sufficiently large or chemically diverse experimental data set. To address this problem, we conducted a series of experiments using several different natural composition lavas, doped with the elements of interest, as starting compositions. Microprobe analyses of orthopyroxene, pigeonite, olivine, magnetite, ilmenite and co-existing glasses in the experimental charges were used to calculate expressions that describe REE partitioning as a function of a variety of system parameters. Using expressions that represent mineral-melt reactions (versus element ratio distribution coefficients) it is possible to calculate terms that express low-Ca pyroxene-melt partitioning behavior and are independent of both pyroxene and melt composition. Compositional variations suggest that Sc substitution in olivine involves either a paired substitution with Al or, more commonly, with vacancies. The partitioning of Sc is dependent both on melt composition and temperature. Our experimentally determined olivine-melt REE Ds (partition coefficients) are similar to, but slightly higher than those reported by McKay (1986) and support their conclusions that olivines are strongly LREE depleted. Y and REE mineral/melt partition coefficients for magnetite range from 0.003 for La to 0.02 for Lu. Ilmenite partition coefficients range from 0.007 for La to 0.029 for Lu. These experimental values are two orders of magnitude lower than many of the published values determined by phenocryst/matrix separation techniques.     

Experimental determination of partition coefficients for Rb,Sr and Ba between alkali feldspar and silicate liquid

Partitioning of Rb, Sr and Ba between alkali feldspar and a synthetic granitic melt has been determined at 8 kb and 720 to 780°C for a single quaternary granite composition. The results suggest that Henry's law is obeyed by Rb up to ~0.8 wt.% Rb₂O in both the liquid and in the alkali feldspar. The measured D values for Rb range from 0.77 to 1.1. For Ba, Henry's Law is obeyed up to ~0.6 wt.% BaO in the liquid and ~5 wt.% BaO in the alkali feldspar. D values for Ba range from 6.4 to 14. For Sr there is only a crude relationship between concentration in the liquid and concentration in the alkali feldspar at concentrations greater than ~0.6 wt.% SrO in the liquid and ~0.4 wt.% SrO in the alkali feldspar. D values for Sr range from 1.2 to 5.0. Partitioning of Sr is apparently sensitive to the concentration of Ba in the system and this partly explains the failure of Sr to obey Henry's Law.Linear least-squares fits to the partitioning data as a function of temperature suggest inverse correlation between temperature and D values. Rb shows only a slight temperature effect whereas Ba and Sr appear to be rather strongly affected by temperature, but the temperature range examined here is small compared to the scatter in the data making these trends relatively uncertain. Other factors that appear to affect partitioning, especially of Sr, are growth rate, development of sector zoning and Or content of the alkali feldspar. These factors severely limit the use of partitioning of these elements in alkali feldspar as geothermometers.The technique for measuring growth rates utilized here combined with measurement of trace element depletion in diffusion boundary layers adjacent to the alkali feldspar crystals makes it possible to estimate diffusivities for Ba and Sr. These estimates suggest a difference of 2 orders of magnitude between diffusivities for Ba and Sr in a vapor-saturated melt and those measured by HOFMANN and MAGARITZ (1976) for a dry obsidian glass.     

Experimental silicate mineral/melt partition coefficients for beryllium and the crustal Be cycle from migmatite to pegmatite

Partition coefficients (D_Be^mineral/melt) for beryllium between hydrous granitic melt and alkali feldspars, plagioclase feldspars, quartz, dark mica, and white mica were determined by experiment at 200 MPa H₂O as a function of temperature (650-900°C), activity of Be in melt (trace levels to beryl saturation), bulk composition, and thermal run direction. At trace levels, Be is compatible in plagioclase of An₃₁ (1.84 at 700°C) and muscovite (1.35 at 700°C) but incompatible in biotite (0.39-0.54 from 650-800°C), alkali feldspar (0.38-0.19 from 680-850°C), quartz (0.24 at 800°C), and albite (0.10 at 750°C). The partition coefficients are different at saturation of the melt in beryl: lower in the case of plagioclase of An₃₁ (0.89 at 700°C), muscovite (0.87 at 700°C), biotite (0.18-0.08 from 675-800°C), alkali feldspar (0.18-0.14 from 680-700°C), and quartz (0.17-0.08 from 750-800°C), but higher in the case of albite (0.37 at 750°C).With other data sources, these new partition coefficients were utilized to track, first, the distribution of Be between aluminous quartzofeldspathic source rocks and their anatectic melts, and second, the dispersion or concentration of Be in melt through igneous crystal fractionation of different magma types (e.g., S-type, I-type) up to beryl-saturated granitic pegmatites and, finally, into their hydrothermal aureoles. Among the rock-forming minerals, cordierite, calcic oligoclase, and muscovite (in this order) control the fate of Be because of the compatibility of Be in these phases. In general, beryl-bearing pegmatites can arise only after extended crystal fractionation of large magma batches (to F, fraction of melt remaining, ≤0.05); granitic magmas that originate from cordierite-bearing protoliths or that contain large modal quantities of calcic oligoclase will not achieve beryl saturation at any point in their evolution.     

Determination of zircon/melt trace element partition coefficients from SIMS analysis of melt inclusions in zircon

Partition coefficients (^zircon/meltD_M) for rare earth elements (REE) (La, Ce, Nd, Sm, Dy, Er and Yb) and other trace elements (Ba, Rb, B, Sr, Ti, Y and Nb) between zircon and melt have been calculated from secondary ion mass spectrometric (SIMS) analyses of zircon/melt inclusion pairs. The melt inclusion-mineral (MIM) technique shows that D_REE increase in compatibility with increasing atomic number, similar to results of previous studies. However, D_REE determined using the MIM technique are, in general, lower than previously reported values. Calculated D_REE indicate that light REE with atomic numbers less than Sm are incompatible in zircon and become more incompatible with decreasing atomic number. This behavior is in contrast to most previously published results which indicate D > 1 and define a flat partitioning pattern for elements from La through Sm. The partition coefficients for the heavy REE determined using the MIM technique are lower than previously published results by factors of ≈15 to 20 but follow a similar trend. These differences are thought to reflect the effects of mineral and/or glass contaminants in samples from earlier studies which employed bulk analysis techniques.D_REE determined using the MIM technique agree well with values predicted using the equations of Brice (1975), which are based on the size and elasticity of crystallographic sites. The presence of Ce⁴⁺ in the melt results in elevated D_Ce compared to neighboring REE due to the similar valence and size of Ce⁴⁺ and Zr⁴⁺. Predicted ^zircon/meltD values for Ce⁴⁺ and Ce³⁺ indicate that the Ce⁴⁺/Ce³⁺ ratios of the melt ranged from about 10⁻³ to 10⁻². Partition coefficients for other trace elements determined in this study increase in compatibility in the order Ba < Rb < B < Sr < Ti < Y < Nb, with Ba, Rb, B and Sr showing incompatible behavior (D_M < 1.0), and Ti, Y and Nb showing compatible behavior (D_M > 1.0).The effect of partition coefficients on melt evolution during petrogenetic modeling was examined using partition coefficients determined in this study and compared to trends obtained using published partition coefficients. The lower D_REE determined in this study result in smaller REE bulk distribution coefficients, for a given mineral assemblage, compared to those calculated using previously reported values. As an example, fractional crystallization of an assemblage composed of 35% hornblende, 64.5% plagioclase and 0.5% zircon produces a melt that becomes increasingly more enriched in Yb using the D_Yb from this study. Using D_Yb from Fujimaki (1986) results in a melt that becomes progressively depleted in Yb during crystallization.     

Two-liquid partition coefficients: Experimental data and geochemical implications

Partition coefficients for Cs, Ba, Sr, Ca, Mg, La, Sm, Lu, Mn, Ti, Cr, Ta, Zr, and P between immiscible basic and acidic liquids in the system K₂O-Al₂O₃-FeO-SiO₂ were experimentally determined at 1,180 °C and 1 atm. Phosphorus is most strongly enriched in the basic melt (by a factor of 10), followed by rare earth elements, Ta, Ca, Cr, Ti, Mn, Zr, Mg, Sr, and Ba (enriched by a factor of 1.5). Of the elements studied, only Cs is enriched in the acidic melt. The two-liquid partition coefficients of Zr, Ta, Sm, and Mn are constant for concentrations ranging from <0.1% to as high as 1 wt.-%, suggesting that Henry's law is applicable in silicate melts (at least for these elements) to concentrations well above typical trace element levels in rocks. The strong relative preference of many elements for the basic melt implies that the structural characteristics of basic melts more readily permit stable coordination of cations by oxygen. Partitioning of elements between crystal and liquid in a magma must therefore be influenced by the composition (and consequent structure) of the liquid.Application of the two-liquid partition coefficients to possible occurrences of liquid immiscibility in magmas reveals that typical basalt-rhyolite associations are probably not generated by two-liquid phase separation. However, liquid immiscibility cannot be discounted as a possible origin for lamprophyric rocks containing felsic segregations.     

Electron microscopy of high-pressure phases synthesized from natural olivine in diamond anvil cell

The products of the transformation of natural (Mg_0.83Fe_0.17)₂SiO₄ olivine have been prepared at various high pressures (between 25 GPa and 90 GPa), and high temperature in a laser-heated diamond-anvil cell (DAC). Studies of the high-pressure phases have been made by transmission electron microscopy (TEM), and X-ray microanalysis. The olivine/spinel boundaries exhibit all the characteristics of a diffusionless shear transition, having a finely sheared structure and a constant orientation relationship between the close-packed planes of the two structures ((100)_ol∥(111)_sp). The TEM observations of zones where olivine (or spinel) transforms into post-spinel phases show that the transformation possesses the features of an eutectoïdal decomposition, leading to a lamellar intergrowth of magnesiowüstite (Mg,Fe)O and perovskite (Mg,Fe)SiO₃. With increasing temperature and/or decreasing pressure, the grain size of the high-pressure phases increases and obeys an Arrhenius law with an activation volume equal to zero. (Mg,Fe)O grains exhibit a very high density of dislocations (higher than 10¹¹cm^?2), whereas (Mg,Fe)SiO₃ grains exhibit no dislocations but systematic twinning. The composition plane of the twins is (112) of the GdFeO₃-type perovskite, corresponding to the {110} plane of the cubic lattice of ideal perovskite.     

Measurement of partition coefficients of phenol and cresols in gas-charged crude oil/water systems

An instrument has been constructed for monitoring the partition coefficients of phenol and cresols between crude oil and water under sub-surface conditions. The device has the capacity for introducing methane gas into crude oil, thereby allowing measurements under live oil (solution gas-containing) conditions. The partition coefficients of phenol and cresols have been measured in crude oil: water substrates under “live” oil and “dead” oil (without solution gas) conditions over a temperature range 25–150 °C. Over the range investigated it is seen that the introduction of gas (crude oil saturated at 100 bar with methane) into the system resulted in an approximate doubling of partition coefficients compared to the equivalent dead oil: brine systems. The partition coefficient data obtained using the device may be employed in a number of petroleum exploration and production activities such as the determination of residual oil saturation of a water-flooded petroleum reservoir. Partition coefficient measurements may help in predicting toxic organic solute loadings in oilfield discharge waters.     

Extension of lattice strain theory to mineral/mineral rare-earth element partitioning: An approach for assessing disequilibrium and developing internally consistent partition coefficients between olivine, orthopyroxene, clinopyroxene and basaltic melt

Olivine/melt and orthopyroxene/melt rare-earth element (REE) partition coefficients consistent with clinopyroxene/melt partition coefficients were determined indirectly from subsolidus partitioning between olivine, orthopyroxene, and clinopyroxene after suitable correction for temperature. Heavy- and middle-REE ratios for olivine/clinopyroxene and orthopyroxene/clinopyroxene pairs correlate negatively with effective cationic radius, whereas those for the light REEs correlate positively with cationic radius, generating a U-shaped pattern in apparent mineral/clinopyroxene partition coefficients versus cationic radius. Lattice strain models of partitioning modified for subsolidus conditions yield negative correlations of olivine/clinopyroxene and orthopyroxene/clinopyroxene with respect to cationic radii, predicting well the measured partitioning behaviors of the heavy and middle REEs but not that of the light REEs. The light-REE systematics cannot be explained with lattice strain theory and, instead, can be explained by disequilibrium enrichment of the light REEs in melt inclusions or on the rims of olivine and orthopyroxene. Realistic light-REE partition coefficients were thus extrapolated from the measured heavy- and middle-REE partition coefficients using the lattice strain model. Light REE olivine/melt and orthopyroxene/melt partition coefficients calculated in this manner are lower than most published values, but agree reasonably well with partitioning experiments using the most recent in situ analytical techniques (secondary-ionization mass spectrometry and laser ablation inductively coupled plasma mass spectrometry). These new olivine/melt and orthopyroxene/melt partition coefficients are useful for accurate modeling of the REE contents of clinopyroxene-poor to -free lithologies, such as harzburgitic residues of melting. Finally, the application of the lattice strain theory to subsolidus conditions represents a framework for assessing the degree of REE disequilibrium in a rock.     

Calculated diffusion coefficients and the growth rate of olivine in a basalt magma

Concentration gradients in glass adjacent to skeletal olivines in a DSDP basalt have been examined by electron probe. The glass is depleted in Mg, Fe, and Cr and enriched in Si, Al, Na, and Ca relative to that far from olivine. Ionic diffusion coefficients for the glass compositions are calculated from temperature, ionic radius and melt viscosity, using the Stokes-Einstein relation. At 1170°C, the diffusion coefficient of Mg²⁺ ions in the basalt is 4·5.10^?9 cm²/s. Comparison with measured diffusion coefficients in a mugearite suggests this value may be 16 times too small. The concentration gradient data and the diffusion coefficients are used to calculate instantaneous olivine growth rates of 2–6.10^?7 cm/s. This is too slow for olivine to have grown in situ during quenching. Growth necessarily preceded emplacement such that the composition of the crystals plus the enclosing glass need not be that of a melt. The computed olivine growth rates are compatible with the rate of crystallization deduced for the Skaegaard intrusion.