Implications of a low solidus melting-temperature for the history of the Earth’s upper mantle

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Multi Anvil Experiments

During the last 50 years, a number of different MAAs have been used in high pressure and high temperature experiments. From the Bridgman anvil (developed in 1952 and used by Ringwood to observe the olivine-spinel transformation (Ringwood, 1970) to the 6/8 Kawai-type multi anvil (Kawai and Endo, 1970), the evolution of such devices passed through many stages. We can distinguish between three main MAAs, i.e. tetrahedral, cubic and octahedral types, corresponding to the geometry of the system. Each type has a precise number of anvils (4, 6 and 8, respectively) and a different polyhedral pressure medium (cubic, tetrahedral and octahedral, respectively). In the so-called Hall’s tetrahedral apparatus (Hall, 1958), four tungsten carbide anvils compress simultaneously four faces of the tetrahedral pressure medium (usually pyrophyllite), and, at room temperature, a maximum pressure of ~12 GPa can be reached (Ito, 2007). Today, the most used large volume apparatuses are the DIA-type multi anvil and the 6/8 Kawai-type multi anvil. In the DIA-type MAA (cubic geometry) six so-called primary-stage anvil (made of either hardened steel or tungsten carbide) are driven along three opposite directions perpendicular to each other, compressing a cubic high pressure medium. Since pressure generation in the DIA-type MAA is usually limited to approximately 10 GPa, a second stage anvil system can be implemented to achieve higher pressure (see later). A modified version of the cubic geometry large volume press is the D-DIA (deformation-DIA) MAA, which allows us to drive independently two of the six primary anvils, in order to create a non-hydrostatic stress and to apply a controlled strain rate to the sample. In the Kawai-type MAA (also known as split cylinder-type), the force is applied simultaneously to 8 inner cubic anvils (tungsten carbide, synthered diamond, polycrystalline diamond) by 6 outer anvils, usually made of hardened steel or tungsten carbide. When implementing a secondary stage system, a corner of each cube has been truncated in order to create a triangular face with a precise edge length (TEL, truncation edge length). The cavity generated by the eight truncations is the vessel of the pressure medium. The pressure medium is usually made of semi-sintered MgO-5%Cr2O3 ceramic, although other ceramic material, such as zirconia or pyrophyllite, are sometimes used. During compression, the pressure medium edges are extruded into the space between the anvils. This determines non-hydrostatic conditions inside the pressure chamber. In order to prevent such problem, a lateral supports for the pressure medium is used. The support, called gasket, should be made of a softer material than the pressure medium (e.g. pyrophyllite).

Electrical conductivity experiments

High-pressure assembly

Electrical conductivity measurements were performed using the 1500-Tons 6-8 split cylinder Kawai-type multi anvil apparatus operating at the Laboratoire Magmas et Volcans (Clermont-Ferrand, France). Quasi-hydrostatic pressures of 5, 10 and 20 GPa were provided by compressing octahedral pressure medium with edge length of 18, 14 or 10 mm between 8 tungsten carbide cubic anvils which edges truncated to 11, 8 or 4 mm, respectively. The sample pressure estimations were was based on room temperature pressure calibration of Bi (2.55, 7.7 GPa), ZnS (15.6 GPa), GaAs (18.3 GPa) and GaS (22 GPa) (Bean et al., 1986) and at high temperature using the phase transformation of quartz to coesite (Bose and Ganguly, 1995), CaGeO3 garnet to perovskite (Susaki et al., 1985), coesite to stishovite (Zhang et al., 1996), forsterite to wadsleyite (Katsura et al., 2004), wadsleyite to ringwoodite (Suzuki et al., 2000) and majorite to perovskite (Hirose et al., 2001). The error in pressure determination at high temperature is of about 0.5-1 GPa.
A schematic view of our sample assembly is shown in Figure 2.2. We used octahedra made of semi-sintered MgO with 5% Cr2O3, which encompasses the interesting properties of low thermal conductivity, low electrical conductivity and high melting point. A ZrO2 cylindrical sleeve was placed around the heater to enhance thermal insulation. The heater was made of a 50 μm thick rhenium foil folded into a cylindric shape and inserted within the ZrO2 sleeve. Re provides very stable heating for temperatures up to more than 2273K. We kept sample length to less than 1mm, in order to reduce the effect of temperature gradient during heating.. A cylindrical sleeve of MgO is inserted between the heater and the sample to (i) prevent chemical reactions with the Re heater, (ii) insure the electrical insulation of the sample and (iii) contain the sample upon melting.
The sample temperature was measured using type C thermocouple (W5%Re-W26%Re). Diameter of thermocouple wires were adapted the size of the octahedra (50 μm for 18/11 and 14/8, and 30 μm for 10/4 assemblies). The thermocouple was positioned on one side of the assembly. We added a third W5%Re wire on the other side of the cylindrical sample to allow measurements of the sample impedance. The Re disks placed either side of the sample facilitate the electrical connection between the sample and the electrode wires.

Temperature gradient

Because the temperature determination is major in this study, it is crucial to estimate the thermal gradient in our sample. We modelled the cell assembly used for electrical conductivity measurements based on the finite element method (Hernlund et al., 2006). The schematic cut of ¼ of the high pressure assembly was modelled for thermocouple temperatures between 1473 and 2273 K (Figure 2.3).
As expected, the hottest part is found at the centre of the sample (extreme top-left position). The limited distance between sample and thermocouple (TC, blue dot) is achieved thanks to the penetration of thermocouple wires at the centre of the cylindrical Re-furnace (See figure 2.2). Each temperature contour (thin black lines) represents a temperature interval of 50 K. In all simulations, the temperature difference (TSimul) between the sample centre and the thermocouple does not exceed 100 K. In this work, we apply a temperature correctionTSimul to all our temperature measurements (see Table 2.2).

In situ impedance spectroscopy method

Impedance spectroscopy (IS) is a very well-known method of characterizing many of the electrical properties of materials, and it is an ideal technique in experimental petrology to monitor the evolution of a sample during experiments, since it can be used to investigate the changes in the conductance of solids (due to e.g. chemical reactions, defects, compositional changes). Generally, impedance spectroscopy is used to measure the total opposition that a material presents to a current flow when applying alternating (AC) signals of varying frequency.
Impedance data are plotted in the complex impedance plane (Z’, Z”) as semi-circular arcs and the sample’s resistance can be ideally given by the intersection between the real impedance Z’ and the arc itself. Impedance arcs are characterized by a relaxation time ( = × ), and they are related to one or more distinct conduction processes taking place at a specific frequency range. Generally, a basic impedance arc is generated by an electrical circuit where a resistor is in parallel with a capacitor (RC circuit). In the case of a polycrystalline material, the single impedance arc is characteristic of conduction through the grain interior (Figure 2.4). In many cases however, since transport properties in polycrystalline solids are strongly affected by microstructure, and impedance spectra usually contain features that can be directly related to microstructure, a more complicated pattern can be observed when data are plotted in the complex impedance plane. A perfect example is given by the asymmetry of the arc in complex plane, which is ideally centered on the real axis, but can be frequently displaced below it. This can be due to the presence of microstructures in the sample, which generally can result in the presence of multiple arcs at higher frequencies. Such complex datasets can be solved using the equivalent circuit model by replacing simple capacitor with a constant-phase-element (CPE). Equivalent circuits are electrical circuits made of resistors and capacitors in arrangement, which respond with frequency in the same manner as the sample. Each part of the circuit represents different processes taking place either in the sample. In their work, (Roberts and Tyburczy, 1991) provided an ideal example of a simple equivalent circuit, composed by three resistor-capacitor (RC) circuits. This RC circuit translate to the complex plane as three impedance arcs, corresponding to three distinct conductions media in the sample: conduction through grain interior (first arc), conduction through grain boundary (second arc), and reactions taking place at the sample-electrode interface (third arc), from the highest to the lowest frequency, respectively.

Electrical conductivity measurements

Electrical conductivity was determined using impedance sp ectroscopy method in the frequency range of 10 6 -101 Hz (F igure 2.6). Insulation resi stance (detection limit) of the assembly at sim ilar pressure-temperature conditions was determined prior to the actua l experiments. Polycrystalline samples are characterized by a combination of resister- / constant phase element (R-C/CPE) circuits and the resistance can be obtained by fitting the impedance spectra to appropriate equivalent circuits . Once the sam ple resistance is determ ined, conductivity can be calculated using the sam ple diameter and length m easured after each experiment, assuming the sample geometry remained unchanged during the experiment using, where l and A are sample length and area of the cross-section, respectively.
The activation enthalpy ( H) of each conduction mechanism can be obtained by fitting the data to Arrhenius equation, where is the e lectrical conductivity (S/m), T the absolute temperature, 0 the pre-exponential factor (S/m), and k the Boltzmann constant (J/K):
For each experiment, we performed a series of heating and cooling cycles, similar to previous works (e.g. (Manthilake et al., 2009), see figure 3.1.a). The low activation enthalpy observed in the first heating cycle below 573 K is likely to result from an extrinsic mechanism such as the presen ce of free pro tons. The ad sorbed moisture in the assem bly poses overestimation of the electrical conductivity due to current leakages through the surrounding ceramic components. We m inimized such e ffects during our experim ents by keeping the assembly at 500 K at desired pressure for more than 12 hours. While maintaining a temperature of 500 K, electrical resistance of the sample was measured at regular intervals until the sample resistance reached a steady value, often 1-2 or ders of magnitude higher than the res istance measured at the beginning of the heating cycle. Sample resistance was usually m easured in several heating-cooling cycles at temperature steps of 50-100 K until the heating and cooling paths were fully reproducible. Upon heating to higher temperatures, we observed a clear drop in the sample conductivity at around 1100 K, due tothe glass transition in the sample. It induces the sample crystallization that was clearly observed during the in situ X-ray diffraction experiments (see below, figure 2.10). The samples were kept between 1370 and 1570 K for ~3h, allowing the complete crystallization of initial glass, which is confirmed by the textural analysis of quenched experiments. Sample resistance was usually measured in several heating-cooling cycles at temperature steps of 50-100 K until the heating and cooling paths were reproducible. This minimizes the uncertainty of electrical conductivity measurements. Below the melting temperature of our sample impedance appears to vary exponentially with temperature with an activation energy of 1.02 eV (Figure 3.1.b, green line). This is typical of electron hole hopping between Fe2+ and Fe3+ conduction mechanism by small polarons (Yoshino, 2010).
For a nominal pressure of 5 GPa, we observed a clear change of slope in the conductivity profile at a temperature of ~1700 K, It can be interpreted as the onset of partial melting in the sample. At small melt fractions, the melt is likely found within grain boundaries and/or in isolated melt pockets and the total conductivity is weekly affected by their contribution. Thus, reaching the solidus temperature is not expected to produce a first order change in the overall sample conductivity. However, when temperature is further increased, progressive increase of the melt fraction induces more interconnection between the melt pockets. The conductivity is observed to increase up to ~102 S/m. At this temperature, the melt becomes the dominant conductive phase, interconnected between the two electrodes, with an ionic conduction mechanism (Gaillard et al., 2008). Similar evolutions of sample conductivity were already interpreted previously by the occurrence of an interconnected network of melt (Maumus et al., 2005; Partzsch et al., 2000; Sato and Ida, 1984).
As long as the sample is below solidus temperature, conduction will mostly happen through the grain interior (simple RC circuit, figure 2.4). At the onset of melting, however, isolated melt pockets will start to form within grain boundaries, and the sample electrical behaviour can be modelled by two RC circuit in series, one for conduction through grain interior and one for the contribution of the isolated melt pockets at the grain boundaries (Figure 2.5.a). The total resistance of the sample will therefore be equal to the sum of the individual resistances of the two circuits. With a melt fraction sufficiently high, melt pockets will interconnect within the sample, becoming the preferable medium for conduction. The sample can be modelled by two RC circuit in parallel (Figure 2.5.b), and total resistance is equal to the sum of the two resistances divided by their products.
(a) Low temperature conduction through grain interior modelled by simple RC circuit. (b) At solidus temperature, isolated melt pockets at the grain boundaries contribute to the total conduction in the sample, which can be schematized by RC circuits in series. (c) Once melt interconnect, very low resistances can be observed, and sample conduction can be modelled by a parallel circuit between the solid and molten sample fractions.
A typical impedance profiles obtained for chondritic samples during melting experiments is shown in figure 2.6. After compression, electrical conduction in our samples occurs through the grains interior, which can be modelled by as a simple RC circuit (Figure 2.6.a). Then, impedance appears to vary exponentially with temperature. Upon melting, electrical conduction also occurs through the melt pockets located at the grain boundaries. Insulated melt pockets could corresponds to a second RC circuit in series with that of grains interior (Figure 2.6.b). However, by further increasing the melt fraction, melt pockets eventually connect with each other, making the melt the predominant conductive phase (Figure 2.6.c). It yields the very low resistances observed at high temperatures. This behaviour can be modelled by a parallel circuit between the solid and molten sample fractions. During the measurement of impedance, these high-frequency low real Z arcs remain partial because of instrumentation limitations at high frequency.

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Synchrotron X-ray diffraction experiments

In the interaction of an incident X-ray beam with the analysed material, some of the X-ray photon will be deflected from their original trajectory upon collision with electrons within the atoms. These scattered X-rays, carrying the information relative to the electronic distribution in the material, are what we study during diffraction experiments. Interaction between different diffraction waves can results in a constructive interference, where the intensity varies depending on the atomic arrangement. In the case of a crystal for example, where atoms are arranged in a periodic lattice, the intensity of the diffraction waves will reach maxima (so called “diffraction peaks”) in correspondence to the location of the atoms in the crystalline structure. By collecting diffraction patterns of a material, one can therefore infer the atomic distribution in a material. The peaks in an X-ray diffraction pattern are directly related to the atomic distances, according to Bragg´s law where n is the order of reflection, λ is the X-ray wavelength, d is the interplanar distance and the angle θ is the half of the so-called diffraction angle which represents the total deviation of the X-ray beam due to the diffraction process. The Bragg’s law provides information on the inter-planar distances (dhkl) and the relative positions of the planes. Such information permit to extrapolate the structure of the primitive cell. They, however, do not allow us to determine the position of the atoms in the cell, which can be extrapolated from the relative intensities of the peaks. The d-spacing of different lattice planes can be determined by angular dispersive X-ray diffraction (ADXD), which uses monochromatic X-radiation with a fixed λ, and records the diffraction rings on two-dimensional detectors from which different θ are measured. Energy dispersive X-ray diffraction (EDXD) an also be used to determine the interplanar distance, using a polychromatic (white) beam at a fixed angle, using a germanium detector to record patterns at different energies.
Powder X-ray Diffraction (XRD) is likely the most commonly used X-ray diffraction method used in the characterization of materials, which is generally in a powder form. This technique is based on the concept that the crystalline domain in the substance being analysed is randomly oriented. The recorded diffraction patterns will display the peaks corresponding to the dhkl in the crystal structure. By analysing the position and the intensity of the peaks, one can then proceed to identify the phases in the material.

High-pressure assembly used for X-ray diffraction

In situ X-ray diffraction experiments were performed using the 1200 tonnes multi anvil press operating at PSICHÉ beamline in the SOLEIL synchrotron facility (Gif-sur-Yvette, France). To generate pressures up to 30 GPa, we used the DIA-geometry with secondary cubic anvils of 14 mm edges (Figure 2.7). High pressure assemblies consisted of cubes with 3mm truncation and 7 mm octahedron. We used similar assemblies than for electrical conductivity measurements, with octahedra made of semi-sintered MgO with 5% Cr2O3, a ZrO2 cylindrical sleeve placed around the heater, itself made of a 50 μm thick rhenium foil. However, in this case, the Re furnace is horizontal (Figure 2.8), which allows an X-ray path parallel to the Re-tube. In order to supply current to the heater, two Re electrodes were place in contact with it. These donut-like electrodes are kept in position after folding several 500 μm long segments at the extremities of the heater, as shown in the drawing in figure 2.8. The glass sample was embedded into an MgO capsule, and its pressure during the experiments was determined based on the P-V-T equation of state of MgO, with an accuracy of about ~0.5 GPa at all P-T conditions.
Figure 2.7. Close-up of the 6-8 DIA set-up used for in-situ X-ray diffraction measurements in the Soleil synchrotron. The finger shows the X-ray path. The red wire is the thermocouple.
Electrical power to heat the Re-furnace was alternative current at 100 Hz frequency. Temperature was measured using a W/Re thermocouple touching the Re-furnace. The thermocouple signal was filtered to remove the common vibrating mode at 100 Hz. Consequently, the thermocouple emf could be measured up to the maximum temperature of 1700 K. We used gasket alternatively made of pyrophilite or a mixture of boron and epoxy.

X-ray diffraction method

At the PSICHE beamline, an X-ray beam with energy range from 20 to ~100 keV is produced by an ondulator located on the synchrotron ring operating at 2.75 GeV. The whole X-ray flux is focussed vertically between the anvil gap of the MAA using a horizontal mirror located at 18.5 meters from the source and 4 meters from the sample. The resulting vertical FWHM of the beam at the sample position is approximately 20 µm, which corresponds to almost one order of magnitude flux gain compared to the unfocussed beam. The beam is collimated horizontally.
Figure 2.9. A typical X-ray radiography of our assembly after compression to ~15 GPa. The white circle at the center of the image corresponds to the tubular Re-furnace in which our sample is located. Further away from the sample after the Re-furnace (i.e. the darkest ring), the two wires of the W-Re thermocouple are clearly visible.
Two different modes where used: (i) samples were first aligned in the X-ray beam using X-ray radiography. For this, the press is scanned vertically in the X-ray beam, with the horizontal slits widely opened. The image is reconstructed numerically (Figure 2.9); (ii) Diffraction was performed in energy dispersive mode using a Caesar-type diffractometer (Wang et al., 2004). A typical diffraction 2-theta angle of 8.0 degrees is convenient to register the major diffraction lines of our silicate samples. The best compromise between X-ray flux and resolution in dhkl is achieved after the X-ray beam is collimated horizontally to a typical width of 50 µm, thanks to a system of slits located after and before the sample.

Table of contents :

1.1. CI Chondrite: a primitive Earth proxy
1.2. Structure of the Earth
1.3. Mantle Heterogeneities
1.3.1. Seismic anomalies in the upper mantle
a. Melting curves of the upper mantle/transition zone
b. Effect of volatiles on melting curves
c. Melting in the early Earth’s mantle
d. Aim of this study
1.3.2. Ultra-low velocity zones at the CMB
2.1. Sample preparation
2.2. Multi Anvil Experiments
2.2.1. Electrical conductivity experiments
a. High-pressure assembly
b. Temperature gradient
c. In situ impedance spectroscopy method
d. Electrical conductivity measurements
2.2.2. Synchrotron X-ray diffraction experiments
a. High-pressure assembly used for X-ray diffraction
b. X-ray diffraction method
c. Crystallization in subsolidus conditions
2.3. Diamond anvil cell (DAC)
2.3.1. High temperature in the DAC
2.3.2. In situ synchrotron X-Ray diffraction
2.4. Analytical techniques
2.4.1. Scanning Electron Microscopy
a. Textural and semi-quantitative analysis
2.4.2. Determination of the water contents
2.5. Cryoscopic relation
3.1. Implications of a low solidus melting-temperature for the history of the Earth’s upper mantle
3.1.1. Electrical conductivity measurements
3.1.2. X-ray diffraction measurements
3.1.3. The revisited solidus temperature: comparison with previous studies
3.1.4. Determination of the degree of partial melting in previous experiments
3.1.5. Implications for the presence of water in the upper mantle today
3.1.6. Implications for state and dynamics of the early upper mantle
3.1.7. Implications for Magma Ocean crystallization
3.2. Melting of subducted basalt at the core-mantle boundary (CMB)


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