High-temperature neutron diffraction study of deuterated brucite

To study the structural behavior of brucite at high temperature, we conducted in situ neutron diffraction experiments of a deuterated brucite powder sample, Mg(OD)₂, in the temperature range 313–583 K. The sample was stable up to 553 K, above which it started to decompose into periclase (MgO) and D₂O vapor. Rietveld analyses of the obtained data were performed using both single-site and three-site split-atom hydrogen models. Our results show that with increasing temperature, unit-cell parameter c increases at a rate ~7.7 times more rapidly than a. This large anisotropy of thermal expansion is primarily due to rapid increase in the interlayer thickness along the c-axis on heating. The amplitudes of thermal vibration for Mg, O, and D increase linearly with increasing temperature; however, the rate of the increase for the lighter D is much larger. In addition, D vibrates anisotropically with a higher magnitude within the (001) plane, as confirmed by our first-principles phonon calculations. On heating, the interatomic distances between a given D and its associated O and D from the adjacent [MgO₆] layer increase, whereas the O–D bond length decreases. This behavior suggests weakened D···O and D···D interlayer interactions but strengthened O–D bonding with increasing temperature.     

Thermal expansion and decomposition of jarosite: a high-temperature neutron diffraction study

The structure of deuterated jarosite, KFe₃(SO₄)₂(OD)₆, was investigated using time-of-flight neutron diffraction up to its dehydroxylation temperature. Rietveld analysis reveals that with increasing temperature, its c dimension expands at a rate ~10 times greater than that for a. This anisotropy of thermal expansion is due to rapid increase in the thickness of the (001) sheet of [Fe(O,OH)₆] octahedra and [SO₄] tetrahedra with increasing temperature. Fitting of the measured cell volumes yields a coefficient of thermal expansion, α = α₀ + α₁ T, where α₀ = 1.01 × 10⁻⁴ K⁻¹ and α₁ = −1.15 × 10⁻⁷ K⁻². On heating, the hydrogen bonds, O1···D–O3, through which the (001) octahedral–tetrahedral sheets are held together, become weakened, as reflected by an increase in the D···O1 distance and a concomitant decrease in the O3–D distance with increasing temperature. On further heating to 575 K, jarosite starts to decompose into nanocrystalline yavapaiite and hematite (as well as water vapor), a direct result of the breaking of the hydrogen bonds that hold the jarosite structure together.     

Computer modelling of a pressure induced phase change in clinoenstatite pyroxenes

 Using lattice dynamic modelling of pure MgSiO₃ clinopyroxenes, we have be able to simulate the properties of both the low-clino (P2₁/c) and a high-density-clino (C2/c) phases and our results are comparable with the high pressure (HP) X-ray study of these phases (Angel et al. 1992). The transition between the two phases is predicted to occur at 6GPa. The volume variation with pressure for both phases is described by a third-order Birch-Murnaghan equation of state with the parameters V _{0  low}=31.122 cm³·mol⁻¹, K _{T0  low}= 107.42 GPa, K′ _{T0  low}=5.96, V _{0  high}=30.142 cm³·mol^–1, K _{T0  high}102.54 GPa and K′ _{T0  high}=8.21. The change in entropy between the two modelled phases at 6GPa is ΔS _{6 Gpa}=−1.335 J·mol⁻¹·K⁻¹ and the equivalent change in volume is ΔV _{6 GPa}=−0.92 cm³·mol⁻¹, from which the gradient of the phase boundary δP/δT is 0.0014 GPa·K⁻¹. The variation of the bulk modulus with pressure was also determined from the modelled elastic constants and compares very well with the EOS data. The reported Lehmann discontinuity, ∼220 km depth and pressure of 7.11Gpa, has an increase in the seismic compressional wave velocity, v _p , of 7.14% using the data given for PREM (Anderson 1989). At a pressure of 7GPa any phase transition of MgSiO₃ pyroxene would be between ortho (Pbca) and high-clino. We find the value of v _p at 7GPa, for modelled orthoenstatite (Pbca), is 8.41 km·sec⁻¹ and that for the modelled high-clino phase at 7GPa is 8.93 km·sec⁻¹, giving a dv _p /v _p of 6.18%. Received: July 26, 1996 / Revised, accepted: September 27, 1996     

Solubility of water in the α, β and γ phases of (Mg,Fe)2SiO4

 The solubility of hydroxyl in the α, β and γ phases of (Mg,Fe)₂SiO₄ was investigated by hydrothermally annealing single crystals of San Carlos olivine. Experiments were performed at a temperature of 1000° or 1100 °C under a confining pressure of 2.5 to 19.5 GPa in a multianvil apparatus with the oxygen fugacity buffered by the Ni:NiO solid-state reaction. Hydroxyl solubilities were determined from infrared spectra obtained of polished thin sections in crack-free regions ≤100 μm in diameter. In the α-stability field, hydroxyl solubility increases systematically with increasing confining pressure, reaching a value of ∼20,000 H/10⁶Si (1200 wt ppm H₂O) at the α-β phase boundary near 13 GPa and 1100 °C. In the β field, the hydroxyl content is ∼400,000 H/10⁶Si (24,000 wt ppm H₂O) at 14–15 GPa and 1100 °C. In the γ field, the solubility is ∼450,000 H/10⁶Si (27,000 wt ppm H₂O) at 19.5 GPa and 1100 °C. The observed dependence of hydroxyl solubility with increasing confining pressure in the α phase reflects an increase in water fugacity with increasing pressure moderated by a molar volume term associated with the incorporation of hydroxyl ions into the olivine structure. Combined with published results on the dependence of hydroxyl solubility on water fugacity, the present results for the α phase can be summarized by the relation C _OH = A(T)f nH₂Oexp(−PΔV/RT), where A(T) = 1.1 H/10⁶Si/MPa at 1100 °C, n = 1, and ΔV = 10.6×10^–6 m³/mol. These data demonstrate that the entire present-day water content of the upper mantle could be incorporated in the mineral olivine alone; therefore, a free hydrous fluid phase cannot be stable in those regions of the upper mantle with a normal concentration of hydrogen. Free hydrous fluids are restricted to special tectonic environments, such as the mantle wedge above a subduction zone. Received: 10 February 1995 / Accepted: 23 October 1995     

Do carbonate liquids become denser than silicate liquids at pressure? Constraints from the fusion curve of K<Subscript>2</Subscript>CO<Subscript>3</Subscript> to 3.2 GPa

Brackets on the melting temperature of K₂CO₃ were experimentally determined at 1.86 ± 0.02 GPa (1,163–1,167°C), 2.79 ± 0.03 GPa (1,187–1,195°C), and 3.16 ± 0.04 GPa (1,183–1,189°C) in a piston-cylinder apparatus. These new data, in combination with published experiments at low pressure (<0.5 GPa), establish the K₂CO₃ fusion curve to 3.2 GPa. On the basis of these experiments and published thermodynamic data for crystalline and liquid K₂CO₃, the high-pressure density and compressibility of K₂CO₃ liquid were derived from the fusion curve. The pressure dependence of the liquid compressibility (K′₀ = dK ₀/dP, where K ₀ = 1/β₀) is between 16.2 and 11.6, with a best estimate of 13.7, in a third-order Birch–Murnaghan equation of state (EOS). This liquid K′₀ leads to a density of 2,175 ± 36 kg/m³ at 4 GPa and 1,500°C, which is ∼30% lower than that reported in the literature on the basis of the falling-sphere method at the same conditions. The uncertainty in the liquid K′₀ leads to an error in melt density of ± 2% at 4 GPa; the error decreases with decreasing pressure. With a K′₀ of 13.7, the compressibility of K₂CO₃ at 1,500°C and 1 bar (K ₀ = 3.8 GPa) drops rapidly with increasing pressure ( ), which prevents a density crossover with silicate melts, such as CaAlSi₂O₈ and CaMgSi₂O₆, at upper mantle depths.     

Hydrogen sites in the dense hydrous magnesian silicate phase E: a pulsed neutron powder diffraction study

Hydrogen site positions and occupancy in the crystal structure of dense hydrous magnesium silicate (DHMS) phase E were determined for the first time by pulsed neutron powder diffraction. A fully deuterated pure phase E powder sample, which had space group \(R\overline{3} m\) and lattice parameters of a = 2.97065(8) Å and c = 13.9033(4) Å, was synthesized at 15 GPa and 1100 °C. Through quantitative evaluation of refined structure parameters obtained with sufficient spatial resolution and very high signal-to-background ratio, we conclude that the O–D dipoles in the refined phase E structure are tilted by 24° from the direction normal to the layers of edge-shared MgO₆ octahedra (octahedral layers). The tilted dipole structure of phase E is in remarkable contrast to that of brucite, Mg(OH)₂, which has dipoles exactly normal to the octahedral layer. This contrast exists because the O–Si–O bonding unique in the phase E structure connects two adjacent octahedral layers and thereby reduces the interlayer O···O distance. This shrinkage of the interlayer distance induces the tilting of the O–D dipole and also generates unique O–D···O hydrogen bonding connecting all the layers in the phase E structure.     

A study of phase transformation in hedenbergite to 40 GPa at ∼1200° C

Phase transformations in a natural sample of hedenbergite ((Ca_0.93Fe_0.61Mn_0.34Mg_0.08Na_0.01Zn_0.02Al_0.003)Si₂O₆) have been studied by X-ray diffraction up to 40 GPa at ∼ 1200°C in a diamond anvil cell interfaced with a laser heating system. The starting hedenbergite phase decomposed into a garnet plus γ-spinel and stishovite at ∼ 14 GPa; then into garnet plus stishovite and wüstite at ∼ 18 GPa; and finally into perovskite plus stishovite and wüstite at pressures higher than ∼ 24 GPa. On decompression to 0.1 MPa, all the high pressure phases are retained except for the cubic perovskite, which reverts back into the ɛ-CaSiO₃ phase, in accordance with previous reports. Energy-dispersive SEM analyses show that the garnet is present as a calcium-rich ABO ₃-type phase. As no garnet phase has been previously observed either in pure CaSiO₃ or in pure CaMgSi₂O₆, it appears that the observed calcium-rich garnet phase has been stabilized by the presence of other cations such as the Na⁺, Zn²⁺, Mn²⁺, Fe²⁺, Mn³⁺, Fe³⁺ and Al³⁺.     

Melting of iron–silicon alloy up to the core–mantle boundary pressure: implications to the thermal structure of the Earth’s core

The melting temperature of Fe–18 wt% Si alloy was determined up to 119 GPa based on a change of laser heating efficiency and the texture of the recovered samples in the laser-heated diamond anvil cell experiments. We have also investigated the subsolidus phase relations of Fe–18 wt% Si alloy by the in-situ X-ray diffraction method and confirmed that the bcc phase is stable at least up to 57 GPa and high temperature. The melting curve of the alloy was fitted by the Simon’s equation, P(GPa)/a = (T _m(K)/T ₀) ^c , with parameters, T ₀ = 1,473 K, a = 3.5 ± 1.1 GPa, and c = 4.5 ± 0.4. The melting temperature of bcc Fe–18 wt% Si alloy is comparable with that of pure iron in the pressure range of this work. The melting temperature of Fe–18 wt% Si alloy is estimated to be 3,300–3,500 K at 135 GPa, and 4,000–4,200 K at around 330 GPa, which may provide the lower bound of the temperatures at the core–mantle boundary and the inner core–outer core boundary if the light element in the core is silicon.     

High pressure behaviour of lead feldspar (PbAl2Si2O8)

An in situ high pressure powder diffraction study, using high-brilliance synchrotron radiation, on lead feldspar (PbAl₂Si₂O₈) was performed. Two samples, with Q _od=0.68 and 0.76, were loaded in a diamond anvil cell and were compressed up to 11 GPa. Up to P=7.1 GPa the only phase present is lead feldspar. In the range 7.1–9.4 GPa sudden changes in the position of the reflections suggest the transformation of lead feldspar to a new phase (probably feldspar-like). The absence of split that would be compatible with triclinic symmetry rules out the monoclinic-triclinic transition, that was reported for the structurally similar strontium feldspar. At P>9.4 GPa some new extra reflections not indexable in the feldspar cell are present as well. During decompression the lead feldspar was the only phase present at P<6 GPa. Peak enlargement was observed with pressure, probably preliminary to amorphization. However almost complete amorphization was observed only after fortuitous shock compression at ∼18 GPa; the crystallinity was recovered at room pressure after decompression. The bulk modulus for lead feldspar was K=71.0(9) and 67.6(1.2) GPa for the two samples, in the range reported for feldspars. The cell parameters show a compression pattern which is similar to that observed in anorthite, with Δa/a ₀>Δc/c ₀>Δb/b ₀; comparison with the high temperature behaviour shows that for lead feldspar the strain tensor with pressure is more isotropic and the deformation along a is less prominent. A turnover in the behaviour of the β angle with pressure suggests a change in the compression behaviour at P∼2 GPa. Rietveld refinement of the Pb coordinates was performed in a series of spectra with pressure ranging from 0.6 to 6.5 GPa. The combined analysis of cell parameters and Pb coordinates with pressure showed that the compression of the structure is mainly achieved by an approach of Pb atoms along a *. Received: 21 July 1998 / Revised, accepted: 13 October 1998     

Hydrogen bonding interactions in phase A [Mg7Si2O8(OH)6] at ambient and high pressure

Neutron powder diffraction data of phase A (Mg₇Si₂O₈(OH)₆) were collected at ambient pressure and 3.2?GPa (calculated from the compressibility of phase A) from the deuterated compound, and the structure was refined using the Rietveld method. The derived crystal structure implies that hydrogen atoms occupy two distinct sites in phase A, both forming hydrogen bonds of different lengths with the same oxygen atom. This picture is supported by IR spectra, which exhibit two absorption bands at 3400 and 3513?cm^?1 corresponding to OH stretching vibrations, and proton NMR spectra, which display two peaks with equal intensities and isotropic chemical shifts of 3.7 and 5?ppm. The D-D distance [D(1)-D(2) distance] at ambient pressure was found to be 2.09?±?0.02?Å from the neutron diffraction data and 2.09?±?0.05?Å from the NMR spectra. At 3.2?GPa, there is no statistically significant increase in the O-D interatomic distance while the hydrogen bonding interaction D···O appears to increase for one of the hydrogen sites, D(1), which has the stronger hydrogen bonding interaction compared with the other hydrogen, D(2), at ambient pressure. The O-D bond valences, determined indirectly from the D···O distances were 0.86 and 0.91 at ambient pressure, and 0.83 and 0.90?at 3.2?GPa, for D(1) and D(2), respectively.     

Synchrotron X-ray powder diffraction study of natural P2 /n-omphacites at high-pressure conditions

 Synchrotron X-ray powder diffraction experiments at high pressure conditions (0.0001–13 GPa) were performed at ESRF (Grenoble-F), on the beamline ID9, to investigate the bulk elastic properties of natural P2/n-omphacites, with quasi-ideal composition. The monoclinic cell parameters a, b, c and β were determined as a function of pressure, and their compressibility coefficients are 0.00277(7), 0.00313(8), 0.00292(5) and 0.00116(4) GPa⁻¹, respectively. The third-order Birch-Murnaghan equation of state was used to interpolate the experimental P−V data, obtaining K ₀=116.6(±2.5) GPa and K′₀=6.03(±0.60). K ₀ was also determined by means of the axial and angular compressibilities [122.5(±1.7) GPa], and of the finite Lagrangian strain theory [121.5(±1.0) GPa]. The discrepancies on K ₀ are discussed in the light of a comparison between techniques to determine the bulk modulus of crystalline materials from static compression diffraction data. Received: 22 February 2000 / Accepted: 10 July 2000     

H<Subscript>2</Subscript>O storage capacity of MgSiO<Subscript>3</Subscript> clinoenstatite at 8–13 GPa, 1,100–1,400°C

We present H₂O analyses of MgSiO₃ pyroxene crystals quenched from hydrous conditions in the presence of olivine or wadsleyite at 8–13.4 GPa and 1,100–1,400°C. Raman spectroscopy shows that all pyroxenes have low clinoenstatite structure, which we infer to indicate that the crystals were high clinoenstatite (C2/c) during conditions of synthesis. H₂O analyses were performed by secondary ion mass spectrometry and confirmed by unpolarized Fourier transform infrared spectroscopy on randomly oriented crystals. Measured H₂O concentrations increase with pressure and range from 0.08 wt.% H₂O at 8 GPa and 1,300°C up to 0.67 wt.% at 13.4 GPa and 1,300°C. At fixed pressure, H₂O storage capacity diminishes with increasing temperature and the magnitude of this effect increases with pressure. This trend, which we attribute to diminishing activity of H₂O in coexisting fluids as the proportion of dissolved silicate increases, is opposite to that observed previously at low pressure. We observe clinoenstatite 1.4 GPa below the pressure stability of clinoenstatite under nominally dry conditions. This stabilization of clinoenstatite relative to orthoenstatite under hydrous conditions is likely owing to preferential substitution of H₂O into the high clinoenstatite polymorph. At 8–11 GPa and 1,200–1,400°C, observed H₂O partitioning between olivine and clinoenstatite gives values of D ^ol/CEn between 0.65 and 0.87. At 13 GPa and 1,300°C, partitioning between wadsleyite and clinoenstatite, D ^wd/CEn, gives a value of 2.8 ± 0.4.     

P-V equation of state of portlandite, Ca(OH)2, from powder neutron diffraction data

 A high pressure neutron powder diffraction study of portlandite [Ca(OH)₂] has been performed at ISIS facility (U.K.); nine spectra have been collected increasing the pressure by steps, up to 10.9 GPa, by means of a Paris-Edinburgh cell installed on the POLARIS diffractometer. The tensorial formalism of the lagrangian finite strain theory and the Birch-Murnaghan equation of state have been used to determine, independently, two values of the bulk modulus of portlandite, obtaining K ₀=38.3(±1.1) GPa [linear incompressibilities: K _0a=188.4(±9.9), K _0c=64.5(±2.5) GPa] and K ₀=34.2(±1.4) GPa, respectively. The present results comply with values from previous measurements by X-ray diffraction [K ₀=37.8(±1.8) GPa] and Brillouin spectroscopy [K ₀=31.7(±2.5) GPa]. Reasonably, Ca(OH)₂ has revealed to be bulkly softer than Mg(OH)₂ [K ₀=41(±2), K _0a=313, K _0c=57 GPa]. The Ca(OH)₂ linear incompressibility values reflect the nature of forces acting to stabilize the (001) layer structure and, further, prove that the replacement Ca/Mg mainly affects the elastic properties in the (001) plane, rather than along the [001] direction. Data from a full refinement of the structure at room pressure are reported. Received January 12, 1996/Revised, accepted June 15, 1996     

Displacive phase transitions in C-centred clinopyroxenes: spodumene, LiScSi2O6 and ZnSiO3

The clinopyroxenes spodumene (LiAlSi₂O₆), LiScSi₂O₆ and ZnSiO₃, all with space group C2/c at ambient conditions, were studied under high pressures by single-crystal X-ray diffraction in a diamond-anvil cell. Changes in the evolution of the unit-cell parameters, optical properties and the appearance of h + k odd reflections characteristic of a primitive lattice, indicate that all three pyroxenes undergo phase transitions. The transitions are mostly displacive in character, and are non-quenchable. Transition pressures are 3.19 GPa in spodumene, ∼0.6 GPa in LiScSi₂O₆ and 1.92 GPa in ZnSiO₃. The space group of all three high-pressure phases was determined to be P2₁/c by structure refinement to single-crystal X-ray intensity data collected in the DAC. In the ZnSiO₃ clinopyroxene the intermediate P2₁/c phase further transforms to a second C2/c phase (HP-C2/c) at 4.9 GPa (confirmed by structure refinement). The volume change at this transition is about 2.6%, three times larger than in the first phase transition, and typical of the P2₁/c→ HP-C2/c phase transitions found previously in MgSiO₃, FeSiO₃, etc. These results therefore provide the first direct evidence that the HP-C2/c and the HT-C2/c structures of pyroxenes are distinct polymorphs with the same space group. The phase transition from C2/c to P2₁/c symmetry in spodumene and LiScSi₂O₆ therefore occurs because the polymorphs stable at ambient conditions are isotypic to the high-temperature C2/c phases of clinopyroxenes such as pigeonite and clinoenstatite. Received: 22 December 1999 / Accepted: 7 June 2000     

Sequential high-pressure transformations of FeGeO3 high-P clinopyroxene (C 2 /c) at temperatures up to 365 ¯C

 In order to elucidate high-pressure transformations of high-P clinopyroxene (C2/c) at kinetically low temperature where atoms are not thermally activated, the transformation processes of FeGeO₃ clinopyroxene (C2/c) have been investigated at pressures up to 20 GPa and 365 °C by powder X-ray diffraction using a synchrotron radiation source and TEM observation. With increasing pressure up to 20 GPa at room temperature, FeGeO₃ high-P clinopyroxene (C2/c) reversibly transforms into a new high-pressure phase, FeGeO₃(II). On increasing the temperature up to 365 °C, this phase rapidly transforms into FeGeO₃ ilmenite within about 2 h. Intensity analysis of the X-ray diffraction pattern reveals that the high-pressure phase of FeGeO₃(II) has an intermediate structure between clinopyroxene and ilmenite: the cation arrangement is similar to that of clinopyroxene and the oxygen arrangement is similar to that of ilmenite. The comparison of the crystal structures of these polymorphs suggests that clinopyroxene to FeGeO₃(II) and FeGeO₃(II) to ilmenite transformations are performed by the slight deformation of the oxygen packing and the short-range movement of cations, respectively. It is shown that this high-P clinopyroxene transforms into ilmenite through a low-activation energy path under the low-temperature condition. Received: 30 August 2000 / Accepted: 10 February 2001     

The Thermodynamics of Ordered Perovskites on the CaTiO3-FeTiO3 Join

The enthalpies of formation from ilmenite, FeTiO₃, and perovskite, CaTiO₃, of two intermediate ordered perovskite phases, CaFeTi₂O₆ and CaFe₃Ti₄O₁₂, have been measured at 801°C using oxide melt solution calorimetry. These data, in combination with experiments at high pressure and temperature, indicate that below 1518±50°C CaFe₃Ti₄O₁₂ is stable at lower pressures (∼7 GPa at 1200°C) than CaFeTi₂O₆ (∼13 GPa at 1200°C). This relationship should be reversed, and CaFeTi₂O₆ should become stable at lower pressures than CaFe₃Ti₄O₁₂, at temperatures above 1518±50°C. These intermediate phases are of petrological interest because they form as a reaction between two minerals, ilmenite and perovskite, which are commonly associated in kimberlites, and because their pressure-temperature range of formation overlaps that of origin of kimberlites. Received: 10 November 1997 / Revised; accepted: 15 January 1998     

The nonlinear anomalous lattice elasticity associated with the high-pressure phase transition in spodumene: a high-precision static compression study

The high-pressure behavior of the lattice elasticity of spodumene, LiAlSi₂O₆, was studied by static compression in a diamond-anvil cell up to 9.3 GPa. Investigations by means of single-crystal XRD and Raman spectroscopy within the hydrostatic limits of the pressure medium focus on the pressure ranges around ~3.2 and ~7.7 GPa, which have been reported previously to comprise two independent structural phase transitions. While our measurements confirm the well-established first-order C2/c–P2₁/c transformation at 3.19 GPa (with 1.2% volume discontinuity and a hysteresis between 0.02 and 0.06 GPa), both unit-cell dimensions and the spectral changes observed in high-pressure Raman spectra give no evidence for structural changes related to a second phase transition. Monoclinic lattice parameters and unit-cell volumes at in total 59 different pressure points have been used to re-calculate the lattice-related properties of spontaneous strain, volume strain, and the bulk moduli as a function of pressure across the transition. A modified Landau free energy expansion in terms of a one component order parameter has been developed and tested against these experimentally determined data. The Landau solution provides a much better reproduction of the observed anomalies than any equation-of-state fit to data sets truncated below and above P _tr, thus giving Landau parameters of K ₀ = 138.3(2) GPa, K′ = 7.46(5), λ _V  = 33.6(2) GPa, a = 0.486(3), b = −29.4(6) GPa and c = 551(11) GPa.     

Phase relations and formation of sodium-rich majoritic garnet in the system Mg3Al2Si3O12–Na2MgSi5O12 at 7.0 and 8.5 GPa

The pseudo-binary system Mg₃Al₂Si₃O₁₂–Na₂MgSi₅O₁₂ modelling the sodium-bearing garnet solid solutions has been studied at 7 and 8.5 GPa and 1,500–1,950°C. The Na-bearing garnet is a liquidus phase of the system up to 60 mol% Na₂MgSi₅O₁₂ (NaGrt). At higher content of NaGrt in the system, enstatite (up to ∼80 mol%) and then coesite are observed as liquidus phases. Our experiments provided evidence for a stable sodium incorporation in garnet (0.3–0.6 wt% Na₂O) and its control by temperature and pressure. The highest sodium contents were obtained in experiments at P = 8.5 GPa. Near the liquidus (T = 1,840°C), the equilibrium concentration of Na₂O in garnet is 0.7–0.8 wt% (∼6 mol% Na₂MgSi₅O₁₂). With the temperature decrease, Na concentration in Grt increases, and the maximal Na₂MgSi₅O₁₂ content of ∼12 mol% (1.52 wt% Na₂O) is gained at the solidus of the system (T = 1,760°С). The data obtained show that most of natural diamonds, with inclusions of Na-bearing garnets usually containing <0.4 wt% Na₂O, could be formed from sodium-rich melts at pressures lower than 7 GPa. Majoritic garnets with higher sodium concentrations (>1 wt% Na₂O) may crystallize at a pressure range of 7.0–8.5 GPa. However the upper pressure limit for the formation of naturally occurring Na-bearing garnets is restricted by the eclogite/garnetite bulk composition.     

Trace element partitioning between orthopyroxene and anhydrous silicate melt on the lherzolite solidus from 1.1 to 3.2 GPa and 1,230 to 1,535°C in the model system Na<Subscript>2</Subscript>O–CaO–MgO–Al<Subscript>2</Subscript>O<Subscript>3</Subscript>–SiO<Subscript>2</Subscript>

We determined experimentally the Nernst distribution coefficient between orthopyroxene and anhydrous silicate melt for trace elements i in the system Na₂O–CaO–MgO–Al₂O₃–SiO₂ (NCMAS) along the dry model lherzolite solidus from 1.1 GPa/1,230°C up to 3.2 GPa/1,535°C in a piston cylinder apparatus. Major and trace element composition of melt and orthopyroxene were determined with a combination of electron microprobe and ion probe analyses. We provide partitioning data for trace elements Li, Be, B, K, Sc, Ti, V, Cr, Co, Ni, Rb, Sr, Y, Zr, Nb, Cs, Ba, La, Ce, Sm, Nd, Yb, Lu, Hf, Ta, Pb, U, and Th. The melts were chosen to be boninitic at 1.1 and 2.0 GPa, picritic at 2.3 GPa and komatiitic at 2.7 and 3.2 GPa. Orthopyroxene is Tschermakitic with 8 mol% Mg-Tschermaks MgAl[AlSiO₆] at 1.1 GPa while at higher pressure it has 18–20 mol%. The rare earth elements show a continuous, significant increase in compatibility with decreasing ionic radius from D _La^opx−melt ∼ 0.0008 to D _Lu^opx−melt ∼ 0.15. For the high-field-strength elements compatibility increases from D _Th^opx−melt ∼ 0.001 through D _Nb^opx−melt ∼ 0.0015, D _U^opx−melt ∼ 0.002, D _Ta^opx−melt ∼ 0.005, D _Zr^opx−melt ∼ 0.02 and D _Hf^opx−melt ∼ 0.04 to D _Ti^opx−melt ∼ 0.14. From mathematical and graphical fits we determined best-fit values for D ₀^M1, D ₀^M2, r ₀^M1, r ₀^M2, E ₀^M1, and E ₀^M2 for the two different M sites in orthopyroxene according to the lattice strain model and calculated the intracrystalline distribution between M1 and M2. Our data indicate extreme intracrystalline fractionation for most elements in orthopyroxene; for the divalent cations D _i ^M2−M1 varies by three orders of magnitude between D _Co^M2−M1 = 0.00098–0.00919 and D _Ba^M2−M1 = 2.3–28. Trivalent cations Al and Cr almost exclusively substitute on M1 while the other trivalent cations substitute on M2; D _La^M2−M1 reaches extreme values between 6.5 × 10⁷ and 1.4 × 10¹⁶. Tetravalent cations Ti, Hf, and Zr almost exclusively substitute on M1 while U and Th exclusively substitute on M2. Our new comprehensive data set can be used for polybaric-polythermal melting models along the Earth’s mantle solidus. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A modified iterative sandwich method for determination of near-solidus partial melt compositions. II. Application to determination of near-solidus melt compositions of carbonated peridotite

We performed modified iterative sandwich experiments (MISE) to determine the composition of carbonatitic melt generated near the solidus of natural, fertile peridotite + CO₂ at 1,200–1,245°C and 6.6 GPa. Six iterations were performed with natural peridotite (MixKLB-1: Mg# = 89.7) and ∼10 wt% added carbonate to achieve the equilibrium carbonatite composition. Compositions of melts and coexisting minerals converged to a constant composition after the fourth iteration, with the silicate mineral compositions matching those expected at the solidus of carbonated peridotite at 6.6 GPa and 1,230°C, as determined from a sub-solidus experiment with MixKLB-1 peridotite. Partial melts expected from a carbonated lherzolite at a melt fraction of 0.01–0.05% at 6.6 GPa have the composition of sodic iron-bearing dolomitic carbonatite, with molar Ca/(Ca + Mg) of 0.413 ± 0.001, Ca# [100 × molar Ca/(Ca + Mg + Fe*)] of 37.1 ± 0.1, and Mg# of 83.7 ± 0.6. SiO₂, TiO₂ and Al₂O₃ concentrations are 4.1 ± 0.1, 1.0 ± 0.1, and 0.30 ± 0.02 wt%, whereas the Na₂O concentration is 4.0 ± 0.2 wt%. Comparison of our results with other iterative sandwich experiments at lower pressures indicate that near-solidus carbonatite derived from mantle lherzolite become less calcic with increasing pressure. Thus carbonatitic melt percolating through the deep mantle must dissolve cpx from surrounding peridotite and precipitate opx. Significant FeO* and Na₂O concentrations in near solidus carbonatitic partial melt likely account for the ∼150°C lower solidus temperature of natural carbonated peridotite compared to the solidus of synthetic peridotite in the system CMAS + CO₂. The experiments demonstrate that the MISE method can determine the composition of partial melts at very low melt fraction after a small number of iterations.