Aluminum-dependent trace element partitioning in clinopyroxene

As technical advances have dramatically increased our ability to analyze trace elements, the need for more reliable data on the compositional dependence of trace element partitioning between minerals and melt has become increasingly important. The late-Cretaceous Carmacks Group of south central Yukon comprises a succession of primitive high-Mg ankaramitic lavas characterized by shoshonitic chemical affinities and containing large complexly zoned clinopyroxene phenocrysts. The compositional zonation of the clinopyroxene phenocrysts is characterized by relatively Fe-rich (Mg^# = Mg/(Mg + Fe) = 0.85), but mottled, cores surrounded by mantles of cyclically-zoned clinopyroxene whose Mg^# varies repeatedly between 0.9 and 0.80. These cyclically zoned clinopyroxene mantles appear to record the repeated influx and mixing of batches of primitive with more evolved magma in a deep sub-crustal (∼1.2 GPa) magma chamber(s). Laser ablation ICP-MS was used to analyze the trace element variation in these zoned clinopyroxenes. The results indicate more than a threefold variation in the absolute concentrations of Th, Zr, rare earth elements (REE), and Y within individual clinopyroxene phenocrysts, with no apparent change in the degree of REE or high field strength element (HFSE) fractionation. The variation in absolute abundances of trace elements correlates closely with the major element composition of the clinopyroxene, with the most enriched clinopyroxene having the lowest Mg^# and highest Al contents. The problem is that the amount of crystal fractionation required to explain the major element variation (∼20%) in these clinopyroxene phenocrysts cannot explain the increase in the abundance of the incompatible trace elements, which would require more than 70% crystal fractionation, if constant partition coefficients are assumed. The anomalous increase in incompatible trace elements appears to reflect an increase in their partition coefficients with increasing Al^IV in the clinopyroxene; with an increase in Al₂O₃ from 1.5 to 4.0 wt.% during ∼20% crystal fractionation over a temperature decrease of ∼100°C being associated with more that a threefold increase in the partition coefficients of Th, Zr, REE, and Y. The magnitude of these increases may indicate that the substitution of these trace elements into clinopyroxene is better modeled in some natural systems by a local charge balance model, rather than the distributed charge model that better replicates the results of annealed experiments. These findings indicate that the effect of Al on the partition coefficients of incompatible trace elements in clinopyroxene may be under appreciated in natural magmatic systems and that the application of experimentally determined clinopyroxene partition coefficients to natural systems must be done with caution.     

The partitioning of trace elements between clinopyroxene and trachybasaltic melt during rapid cooling and crystal growth

We present the variation in trace element partition coefficients measured at the interface between rapidly cooled clinopyroxene crystals and co-existing melts. Results indicate that, as the cooling rate is increased, clinopyroxene crystals are progressively depleted in Si, Ca and Mg counterbalanced by enrichments in Al (mainly tetrahedral Al^iv), Na and Ti. Partition coefficients (Ds) for rare earth elements (REE), high field strength elements (HFSE) and transition elements (TE) increase with increasing cooling rate, in response to clinopyroxene compositional variations. The entry of REE into the M2 site is facilitated by a coupled substitution where either Na substitutes for Ca on the M2 site or Al^iv substitutes for Si in the tetrahedral site. The latter substitution reflects an increased ease of locally balancing the excess charge at M2 as the number of surrounding Al^iv atoms increases. Due to the lower concentration of Ca in rapidly cooled clinopyroxenes, divalent large ion lithophile elements (LILE) on M2 decrease at the expense of monovalent cations. Conversely, higher concentrations of HFSE and TE on the M1 site are facilitated as the average charge on this site increases with the replacement of divalent-charged cations by Al^vi. Although crystallization kinetics modify clinopyroxene composition, deviations from equilibrium partitioning are insufficient to change the tendency of a trace element to be compatible or incompatible. Consequently, there are regular relationships between ionic radius, valence of the trace element and D. At both equilibrium and cooling rate conditions, Ds for isovalent cations define parabola-like curves when plotted against ionic radius, consistent with the lattice strain model, demonstrating that the partitioning of trace elements is driven by charge balance mechanisms; cation substitution reactions can be treated in terms of the energetics of the various charge-imbalanced configurations.     

The partitioning of Zr and Nb between diopside and melts in the system diopside-albite-anorthite

The crystal liquid partitioning of Zr and Nb has been measured experimentally between diopsidic clinopyroxene and melts in the system Di-Ab-An. Nb was found to be excluded from diopside (D(Nb) is always less than 0.02). D(Zr) is quite variable, ranging from 0.05 to 0.45. D(Zr) is positively correlated with the Al content of both the melt and the pyroxene and is negatively correlated with temperature. Both D(Zr) and D(Nb) were found to be independent of oxygen fugacity. This implies that neither Zr or Nb suffer valence changes over a range of oxygen fugacities spanning both lunar and terrestrial conditions.     

The effect of Ca-Tschermaks component on trace element partitioning between clinopyroxene and silicate melt

We have studied the influence of Ca-Tschermaks (Calcium Tschermaks or CaTs) content of clinopyroxene on the partitioning of trace elements between this phase and silicate melt at fixed temperature and pressure. Ion probe analyses of experiments carried out in the system Na₂O–CaO–MgO–Al₂O₃–SiO₂, at 0.1 MPa and 1218°C, produced crystal-melt partition coefficients (D) of 36 trace elements (Li, Cl, Sc, Ti, V, Cr, Fe, Co, Ge, Sr, Y, Zr, Nb, Mo, Ru, Rh, In, Sn, Sb, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta and W), for clinopyroxene compositions between 10 and 32 mol% CaTs. Partition coefficients for 2+ to 5+ cations show, for each charge, a near parabolic dependence of log D on ionic radius of the substituting cation, for partitioning into both the M1 and M2 sites of clinopyroxene. Fitting the results to the elastic strain model of Blundy and Wood [Blundy, J.D., Wood, B.J., 1994. Prediction of crystal-melt partition coefficients from elastic moduli. Nature 372, 452–454] we obtain results for the strain-free partition coefficients of theoretical cations (D₀), with site radius r₀, and for the site's Young's Modulus (E).

In agreement with earlier data our results show that increasing ^ivAl concentration in cpx is matched by increasing D, E_M1, E_M2 and D₀ for tri-, tetra- and pentavalent cations. The degree of fractionation between chemically similar elements (i.e. Ta/Nb, Zr/Hf) also increases. In contrast, D values for mono-, di- and hexavalent cations decrease with increasing ^ivAl in the cpx. The large suite of trace elements used has allowed us to study the effects of cation charge on D₀, r₀ and E. We have found that D₀ and r₀ decrease with increasing cation charge, e.g. r₀=0.66 Å for 4+ cations and 0.59 Å for 5+ cations substituting into M1. Values of E_M1 and E_M2 increase with cation charge as well as with increasing ^ivAl content. The increase in E_M2 is linear and close to the trend set by Hazen and Finger [Hazen, R.M., Finger, L.W., 1979. Bulk modulus-volume relationship for cation–anion polyhedra. J. Geophys. Res. 84 (10) 6723–6728] for oxides. E_M1 values are much higher and do not fit the trend predicted by the Hazen and Finger relationship.     

An experimental study of the partitioning of K,Rb, Cs,Sr and Ba between clinopyroxene and liquid at high pressures

The partition coefficients of K, Rb, Cs, Sr and Ba between clinopyroxene and liquid were experimentally determined in the system diopside-albite-anorthite-water at 15–30 kb and 1100–1200°C. Clinopyroxene and liquid (glass) were separated by a new technique (differential dissolution technique—DDT) and analyzed by isotope dilution. The partition coefficients lie in the range 0.054–0.081 for Sr, 0.0014–0.0026 for K, 0.00078–0.0023 for Ba, 0.0010–0.0041 for Rb, 0.00035–0.0036 for Cs. Variations of the partition coefficients with pressure, temperature and composition of the phases are relatively small, though no systematic study of these parameters was attempted.     

Rare earth element partitioning between clinopyroxene and silicate liquid at moderate to high pressure

Experimental determination of over seventy sets of clinopyroxene/silicate liquid (glass) partitition coefficients (D) for four rare earth elements (REE — La, Sm, Ho, Lu) in a range of REE-enriched natural rock compositions (basalt, basaltic andesite, andesite and rhyodacite) demonstrate a convex upward pattern, favouring the heavy REE (Ho, Lu) and markedly discriminating against the light REE (La). These patterns are consistent with previously documented clinopyroxene D values reported from natural phenocryst/matrix pairs and from experimental work using either REE-enriched compositions and electron microprobe analytical techniques (as in the present study) or natural or synthetic undoped compositions and mass spectrometric, ion probe or X-ray autoradiographic analytical techniques. However, the large data base in the present study allows evaluation of the effect of compositional and physical parameters on REE partitioning relationships. Considering D_Ho, it is shown that (1) D increases 6-fold with increasing SiO₂ content of the coexisting liquid from 50 to 70 wt% SiO₂ (2) D increases 4-fold with decreasing temperature from 1,120°C to 900° C (3) D increases 2-fold with increasing pressure from 2.5 to 20 kb. (4) D increases 2-fold fO₂ increases from approximately that of the MW buffer to the HM buffer (5) D remains unchanged within experimental error as the water content of the melt changes from 0.3 to 10% by weight H₂O.The absolute REE content of the clinopyroxene shows no consistent trend with temperature, but decreases slightly with increasing pressure, paralleling an increase in the jadeite component of the pyroxene. Thus the increase in D with increasing pressure is attributed to changes in the silicate liquid structure, which discriminate against accommodation of REE with increasing pressure. The clinopyroxene REE content increases with increasing fO₂, and in this case the increase in D with increasing fO₂ may be attributed mainly to this change in the clinopyroxene composition. Application of the present results to geochemical modelling allows a more appropriate choice of D values, according to the liquid composition and physical conditions applicable in the modelled system. They may also be used to evaluate cognate or xenocrystic relationships between clinopyroxene megacrysts and their host matrix.     

Experimental determination of the partitioning of gallium between solid iron metal and synthetic basaltic melt: Electron and ion microprobe study

The distribution of Ga between solid Fe metal and synthetic basaltic melt has been investigated experimentally at two temperatures over a limited range of oxygen fugacities. Reversal experiments were conducted, indicating a close approach to equilibrium. Analysis of run products was performed using an electron and an ion microprobe. At 1 bar total pressure, the solid metal/silicate melt partition coefficient. D(Ga), is given by: 1190°C: logD(Ga) = ?0.92 logfO₂ ? 11.91330°C: logD(Ga) = ?0.77 logfO₂ ? 8.8. For the common assumption of a valence state for Ga of 3 in silicates and assuming ideal solution of Ga in both phases, a slope of ?0.75 is predicted. The slope obtained at 1300°C (?0.77) is indistinguishable from this value, while the slope at 1190°C (?0.92) is somewhat higher. Henry's law is obeyed over the concentration range 0.007 wt.% to 0.15 wt.% Ga in metal, a factor of 20 in concentration. These partition coefficients may be utilized to evaluate metal/silicate fractionation processes in the Earth, Moon and Eucrite Parent Body. The lunar mantle appears to be depleted in Ga by a factor of 20–40 relative to CI abundances. This depletion is consistent with extraction of Ga into a geophysically plausible lunar core if Ga was initially present at a subchondritic concentration. A similar explanation probably accounts for the depletion of Ga in the Eucrite Parent Body. The upper mantle of the Earth appears to be depleted in Ga by a factor of 4– 7 relative to CI abundances. This depletion is far smaller than would be expected as a result of core formation, but is consistent with two quite different hypotheses: (i) a small amount of solid metal and sulfur-bearing metallic liquid was retained in the mantle after core formation; or (ii) addition of a late-stage chondritic component involving 5% to 10% of the upper mantle following core formation.     

Effect of melt composition on the partitioning of trace elements between titanite and silicate melt

Isobaric and isothermal experiments were performed to investigate the effect of melt composition on the partitioning of trace elements between titanite (CaTiSiO₅) and a range of different silicate melts. Titanite-melt partition coefficients for 18 trace elements were determined by secondary ion mass spectrometry (SIMS) analyses of experimental run products. The partition coefficients for the rare earth elements and for Th, Nb, and Ta reveal a strong influence of melt composition on partition coefficients, whereas partition coefficients for other studied monovalent, divalent and most quadrivalent (i.e., Zr, Hf) cations are not significantly affected by melt composition. The present data show that the influence of melt composition may not be neglected when modelling trace element partitioning.It is argued that it is mainly the change of coordination number and the regularity of the coordination space of trace elements in the melt structure that controls partition coefficients in our experiments. Furthermore, our data also show that the substitution mechanism by which trace elements are incorporated into titanite crystals may be of additional importance in this context.     

Experimental comparison of trace element partitioning between clinopyroxene and melt in carbonate and silicate systems, and implications for mantle metasomatism

Experiments in the systems diopside-albite (Di-Ab) and diopside-albite-dolomite (Di-Ab-Dmt), doped with a wide range of trace elements, have been used to characterise the difference between clinopyroxene-silicate melt and clinopyroxene-carbonate melt partitioning. Experiments in Di-Ab-Dmt yielded clinopyroxene and olivine in equilibrium with CO₂-saturated dolomitic carbonate melt at 3 GPa, 1375 °C. The experiments in Di-Ab were designed to bracket those conditions (3 GPa, 1640 °C and 0.8 GPa, 1375 °C), and so minimise the contribution of differential temperature and pressure to partitioning. Partition coefficients, determined by SIMS analysis of run products, differ markedly for some elements between Di-Ab and Di-Ab-Dmt systems. Notably, in the carbonate system clinopyroxene-melt partition coefficients for Si, Al, Ga, heavy REE, Ti and Zr are higher by factors of 5 to 200 than in the silicate system. Conversely, partition coefficients for Nb, light REE, alkali metals and alkaline earths show much less fractionation (<3). The observed differences compare quantitatively with experimental data on partitioning between immiscible carbonate and silicate melts, indicating that changes in melt chemistry provide the dominant control on variation in partition coefficients in this case. The importance of melt chemistry in controlling several aspects of element partitioning is discussed in light of the energetics of the partitioning process. The compositions of clinopyroxene and carbonate melt in our experiments closely match those of near-solidus melts and crystals in CMAS-CO₂ at 3 GPa, suggesting that our partition coefficients have direct relevance to melting of carbonated mantle lherzolite. Melts so produced will be characterised by elevated incompatible trace element concentrations, due to the low degrees of melting involved, but marked depletions of Ti and Zr, and fractionated REE patterns. These are common features of natural carbonatites. The different behaviour of trace elements in carbonate and silicate systems will lead to contrasted styles of trace element metasomatism in the mantle. Received: 15 July 1999 / Accepted: 18 February 2000     

Determination of rare earth and refractory trace element abundances in early solar system objects by ion microprobe

Experimental and analytical procedures devised for measurement of rare earth element (REE) abundances using a secondary ion mass spectrometer (ion microprobe) are described. This approach is more versatile than the conventional techniques such as neutron activation analysis and isotope dilution mass spectrometry by virtue of its high spatial resolution that allows determination of REE abundances in small domains (10-20 micron) within individual mineral phases. The ion microprobe measurements are performed at a low mass-resolving power adopting the energy-filtering technique (Zinner and Crozaz 1986) for removal and suppression of unresolved complex molecular interferences in the REE masses of interest. Synthetic standards are used for determining various instrument specific parameters needed in the data deconvolution procedure adopted for obtaining REE abundances. Results obtained from analysis of standards show that our ion microprobe may be used for determining REE abundances down to ppm range with uncertainties of ∼ 10 to 15%. Abundances of rare earth and several other refractory trace elements in a set of early solar system objects isolated from two primitive carbonaceous chondrites were determined using the procedures devised by us. The results suggest that some of these objects could be high temperature nebular condensates, while others are products of melting and recrystallization of precursor nebular solids in a high temperature environment.     

Matrix isolation technique for the study of some factors affecting the partitioning of trace elements

Some of the factors that affect the preferred positions of cations in ionic-solid solutions were investigated utilizing vibrational spectroscopy. Solid solutions of the sulfate and chromate ions codoped with La³⁺ and Ca²⁺ in a KBr host lattice were examined as a function of the polyvalent-cation concentration. The cation—anion pairing process was found to be random for Ca²⁺ whereas the formation of La³⁺SO₄^2? ion-pairs with a C_2v bonding geometry is highly preferential to any type of La³⁺CrO₄^2? ion-pair formation. The relative populations of ion-pair site configurations are discussed in terms of an energy—entropy competition which can be applied to the partition of trace elements during magmatic processes.     

汉诺坝幔源单斜辉石巨晶氢同位素组成的离子探针分析：微尺度不均一性

运用离子探针技术测定了河北汉诺坝新生代玄武岩中3个单斜辉石巨晶的氢同位素组成，结果显示同一颗粒内部表现出微尺度的不均一性，2mm范围内δD的变化达到60‰。δD和氢含量之间不存在同步的变化，巨晶内部的化学成分均一，因此我们认为巨晶的氢同位素不均一性继续自母岩浆。母岩浆的氢同位素变化可能是去气过程中气相与熔体之间的分馏引起的。单斜辉石巨晶形成后很短的时间内即被寄主岩浆带至地表并经历了快速淬火。     

The importance of adsorption in igneous partitioning of trace elements

For accurate mathematical modeling of trace-element partitioning during igneous fractionation, adsorption should be considered. Because of adsorption, the partitioning of elements between liquid and a surface layer of a crystal is often not the same as the partitioning between liquid and the solid crystal at true equilibrium. In some minerals e.g. high-calcium pyroxene, the effect of adsorption during crystal growth may be very important; this is suggested by the frequent occurrence of sector zoning in augite, and the wide range in measured partition coefficients for such elements as rare earths. The ions which are enriched by adsorption are usually those which are favored substituents according to Goldschmidt's rules. In other minerals, uptake of trace elements may be closer to equilibrium partitioning, rather than being determined by kinetic factors. For example, the relative partitioning of REE, U, Th and Pb into feldspars is qualitatively predicted by Pauling's rules for complex ionic crystals, rather than by Goldschmidt's rules.     

Experimental determination of partition coefficients of ten rare earth elements and barium between clinopyroxene and liquid in the synthetic silicate system at 20 kilobar pressure

Two experiments were carried out at 20 kb pressure for the measurement of partition coefficients of ten lanthanides and barium between diopside clinopyroxene and liquid in the synthetic system diopside-enstatite-silica-H₂O. Starting materials are glass of two different compositions CaMgSi₂O₆ 56, MgSiO₃ 14, SiO₂ 30 weight % and CaMgSi₂O₆ 80, MgSiO₃ 20 weight %.In the experiment on the former composition, the partition coefficient increases regularly with decrease of ionic radii from La to Dy and decreases also regularly from Dy to Lu. In the experiment on the latter composition, stepwise shift of partition coefficient was observed between Dy and Er.The results suggest that the lanthanide cations occupy the site of 8-fold coordination in the clinopyroxene and that the partition coefficients depend on the ionic radii of lanthanide elements and also on the chemical composition of the starting material or heating process during the run.     

Experimental cpx/melt partitioning of 24 trace elements

Cpx/melt partition coefficients have been determined by ion probe for 24 trace elements at natural levels in an alkali basalt experimentally equilibrated at 1,380°C and 3 GPa. One goal was to intercompare Ds for both high-field-strength elements and rare earth elements (REE) in a single experiment. Relative to the REE spidergram, Hf and Ti show virtually no anomaly, whereas Zr exhibits a major negative anomaly. Other incompatible elements (Ba, K, Nb) fall in the range of published values, as do elements such as Sr, Y, Sc, Cr and V. Pb shows a value intermediate between La and Ce. Values for Be, Li and Ga are reported for the first time, and show that Be is as incompatible as the light REEs whereas Li and Ga are somewhat more compatible than the heavy REE.     

Ar and K partitioning between clinopyroxene and silicate melt to 8 GPa

The relative incompatibility of Ar and K are fundamental parameters in understanding the degassing history of the mantle. Clinopyroxene is the main host for K in most of the upper mantle, playing an important role in controlling the K/Ar ratio of residual mantle and the subsequent time-integrated evolution of ⁴⁰Ar/³⁶Ar ratios. Clinopyroxene also contributes to the bulk Ar partition coefficient that controls the Ar degassing rate during mantle melting. The partitioning of Ar and K between clinopyroxene and quenched silicate melt has been experimentally determined from 1 to 8 GPa for the bulk compositions Ab₈₀Di₂₀ (80 mol% albite-20 mol% diopside) and Ab₂₀Di₈₀ with an ultraviolet laser ablation microprobe (UVLAMP) technique for Ar analysis and the ion microprobe for K. Data for Kr (UVLAMP) and Rb (ion probe) have also been determined to evaluate the role of crystal lattice sites in controlling partitioning. By excluding crystal analyses that show evidence of glass contamination, we find relatively constant Ar partition coefficients (D_Ar) of 2.6 × 10⁻⁴ to 3.9 × 10⁻⁴ for the Ab₈₀Di₂₀ system at pressures from 2 to 8 GPa. In the Ab₂₀Di₈₀ system, D_Ar shows similar low values of 7.0 × 10⁻⁵ and 3.0 × 10⁻⁴ at 1 to 3 GPa. All these values are several orders of magnitude lower than previous measurements on separated crystal-glass pairs.D_K is 10 to 50 times greater than D_Rb for all experiments, and both elements follow parallel trends with increasing pressure, although these trends are significantly different in each system studied. The D_K values for clinopyroxene are at least an order of magnitude greater than D_Ar under all conditions investigated here, but D_Ar appears to show more consistent behavior between the two systems than K or Rb. The partitioning behavior of K and Rb can be explained in terms of combined pressure, temperature, and crystal chemistry effects that result in changes for the size of the clinopyroxene M2 site. In the Ab₂₀Di₈₀ system, where clinopyroxene is diopside rich at all pressures, D_K and D_Rb increase with pressure (and temperature) in an analogous fashion to the well-documented behavior of Na. For the Ab₈₀Di₂₀ system, the jadeite content of the clinopyroxene increases from 22 to 75 mol% with pressure resulting in a contraction of the M2 site. This has the effect of discriminating against the large K⁺ and Rb⁺ ions, thereby countering the effect of increasing pressure. As a consequence D_K and D_Rb do not increase with pressure in this system.In contrast to the alkalis (Na, K, and Rb), D_Kr values are similar to D_Ar despite a large difference in atomic radius. This lack of discrimination (and the constant D_Ar over a range of crystal compositions) is also consistent with incorporation of these heavier noble gases at crystal lattice sites and a predicted consequence of their neutrality or “zero charge.” Combined with published D_Ar values for olivine, our results confirm that magma generation is an efficient mechanism for the removal of Ar from the uppermost 200 km of the mantle, and that K/Ar ratios in the residuum are controlled by the amount of clinopyroxene. Generally, Ar is more compatible than K during mantle melting because D_Ar for olivine is similar to D_K for clinopyroxene. As a result, residual mantle that has experienced variable amounts of melt extraction may show considerable variability in time-integrated ³⁶Ar/⁴⁰Ar.     

Ni partitioning between diopside and silicate melt: A redetermination by ion microprobe and recognition of an experimental complication

The ion probe is uniquely suited for measurement of element partitioning between phases in experimental and natural systems. A redetermination of the partitioning of Ni between diopside and quenched silicate melt using samples previously measured by β-track mapping gives 1.87 (weight ratio of ⁶²Ni in diopside/melt), slightly lower than the β-track value of 2.05. Critical to the accurate determination of distribution coefficients are: (1) a secondary ion signal that is linear with concentration in the range measured, and (2) a calibration using known concentrations to correct for differential secondary ion yields from different phases. In the present case the secondary ion signal is linear with Ni concentrations below ~ 1 wt% in both diopside and glass, but nonlinear above. Differential yields were corrected by calibrating the secondary ion signal against compositions determined by electron microprobe.Partition coefficients measured using ⁵⁸Ni and ⁶⁰Ni, in contrast to ⁶²Ni, are not constant with concentration in these samples probably due to Ni migration during crystallization. Measurements using these isotopes (or bulk Ni) show a change of partition coefficient with Ni concentration.     

汉诺坝幔源单斜辉石巨晶氢同位素组成的离子探针分析:微尺度不均一性

运用离子探针技术测定了河北汉诺坝新生代玄武岩中3个单斜辉石巨晶的氢同位素组成,结果显示同一颗粒内部表现出微尺度的不均一性,2mm范围内δD的变化达到60‰。δD和氢含量之间不存在同步的变化,巨晶内部的化学成分均一,因此我们认为巨晶的氢同位素不均一性继承自母岩浆。母岩浆的氢同位素变化可能是去气过程中气相与熔体之间的分馏引起的。单斜辉石巨晶形成后很短的时间内即被寄主岩浆带至地表并经历了快速淬火。     

Isovalent trace element partitioning between minerals and melts: A computer simulation study

We present a new approach for the rationalisation of trace element partitioning between silicate melts and minerals, which is not based on the empirical, parameterised continuum models in common use. We calculate the energetics of ion substitution using atomistic simulation techniques, which include an explicit evaluation of the relaxation energy (strain energy) contribution to this process. Solution energies are estimated for isovalent impurities in CaO, diopside, orthoenstatite, and forsterite. These show a parabolic dependence on ionic radius, similar to the variation of mineral-melt partition coefficients with ionic radius. The success of the empirical models, which often include only the strain energy, appear to have been due to the partial cancellation of energy terms, and to the empirical fitting of the parameters included in these models. Our approach can be readily extended to aliovalent substitution.