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Temperature profiles of the lower mantle
We can obtain more direct information on temperature in the mantle by associating phase transformations with seismic discontinuities, if the phase boundaries of selected transformations are reliably defined (Ito and Katsura, 1989; Hernlund et al., 2005; Ono and Oganov, 2005; Katsura et al., 2010). In order to obtain a better description of the Earth’s composition and thermal structure, seismic data must be compared with mineralogical data and thermodynamic models (Wang, 1972; Brown and Shankland, 1981; Anderson, 1982; Ito and Kastura, 1989; Stacey, 1992). Moreover, because of uncertainties and limitations in previously used models, there are considerable discrepancies between the various proposed descriptions of the Earth’s thermal and compositional structure (da Silva, 2000).
The agreement between body wave and normal data suggest that the lower mantle is likely to be nearly adiabatic (Masters, 1979; Dziewonski and Anderson, 1981; Bunge et al., 2001) and modeled geotherms have been found in good agreement with the adiabat (Shankland and Brown, 1985). Therefore, an adiabatic geotherm is used as a reference mantle temperature profile (Dziewonski and Anderson, 1981; Matas et al., 2007), which assumes that the convective mantle is homogeneous and adiabatic. Then, geotherms are derived by comparison with the PREM model (da Silva, 2000). A constraint of the Earth density profile is given by the observation of the Bullen parameter (Bullen, 1963), 2 d dP 1 V (1.3) dr dr.
Liquidus and solidus phase relations in the lower mantle
In order to understand the details of the early melting and crystallization history of the Earth, melting phase relations of the mantle at very high pressures must be known.
The system MgO-MgSiO3 is the most fundamental starting point for development of an understanding of these phase relations (Presnall et al., 1998; Liebske et al., 2005). In Figure 1.20 is reported the eutectic melting curve for this system at pressures between 10 and 22 GPa, obtained using a multi-anvil press (Presnall et al., 1998 (P-98 in Fig. 1.20)). Melting of (Mg,Fe)SiO4 olivine was determined using shock-wave experiments (Ahrens and Holland, 1997; Luo et al., 2004 (L-04 in Fig. 1.20)) and was reported at 4300 K and 130 GPa. Regarding to the classic pyrolite model for the lower mantle, many information are available for pressures up to ~60 GPa (Litasov and Ohtani, 2002; Trønnes and Frost, 2002; Zerr et al., 1998 (LO-02, TF-02, and Z-98 respectively in Fig. 1.20)).
Recently, have been determined liquidus and solidus melting curves for peridotite compositions between 36 and 140 GPa, using laser-heated diamond anvil cell (LH-DAC) (Fiquet et al., 2010 (F-10l and F-10s in Fig. 1.20)). In particular, it has been shown that for peridotite compositions, olivine is the liquidus phase up to 13-16 GPa (Takahashi and Scarfe, 1985; Walter, 1998), but is replaced at higher pressures by majorite (Mj) garnet (Ito and Takahashi, 1987; Herzberg et al., 1990; Zhang and Herzberg, 1994). At 22-23 GPa, the liquidus phase is ferropericlase (Fp) (Zhang and Herzberg, 1994; Trønnes and Frost, 2002; Fiquet et al., 2010). At higher pressures, P>30 GPa, ferropericlase is replaced by MgSiO3 perovskite (Mg-Pv) as liquidus phase (Ito et al., 2004; Fiquet et al., 2010). The melting curve of end-member phases is relatively well determined using the LH-DAC technique (Boehler, 2000 (B-00 in Fig. 1.20)) or shock-wave experiments (Luo et al., 2004 (L-04 in Fig. 1.20)). However, for phase relations of chondritic compositions, at pressure higher than ~30 GPa, not much information is available. Anyway, it is well known that olivine is the liquidus phase up to ~10-15 GPa (Herzberg et al., 1990; Ohtani et al., 1986), majorite replaces it up to approximately 24-25 GPa (Ohtani et al., 1986) and Mg-perovskite is observed to replace majorite at 25 GPa (Ito et al., 2004).
The European Synchrotron Radiation Facility (ESRF)
ESRF was the first third generation synchrotron source, starting its user operation in 1995. Located in Grenoble, France, it is one of the three high energy 3rd generation SR sources operational worldwide (Fig. 2.2).
The source is optimized to produce hard X-rays in the 1 to 100 KeV range. The ID27 beamline uses an insertion device (ID) as a source point which generates high fluxes and brilliance in the 20 to 90 KeV range of photon energy.
Figure 2.2 and 2.3 show different parts of ESRF. Electrons are produced with an electron canon and accelerated with a linear accelerator (LINAC). The booster accelerates particles up to a relativistic speed and energy of 6 GeV. Once accelerated, electrons are injected into the ring storage with a circumference of 844 m.
The ESRF consists of 40 beamlines. Beamlines placed on the bending magnets (BM) are intercalated between the beamlines that work with undulators (ID).
The ID27 beamline
ID27 is specialized in high-pressure applications employing diamond-anvil and large-volume cells. ID27 is fully optimized for monochromatic high-resolution XRD under extreme pressure and temperature for diamond anvil cell experiments. The monochromatic beam is selected using a nitrogen-cooled Si(111) monochromator and focused on the sample using multilayers mirrors in the Kirkpatrick-Baez (KB) geometry (Fig. 2.4). These mirrors possess a very board energy band pass from 6 KeV to 80 KeV with a maximum of 80% reflectivity at 30 KeV.
High pressure and high temperature experiments
When a material is pressurized using two opposed anvils, a uniaxial force is applied on the sample. Pressure undergone by material is dependent on applied force and the sample contact with the surface. Fortunately, the Re or W gasket helps to transform this uniaxial pressure into a hydrostatic pressure.
The best material for the anvils is the diamond because of: its extreme hardness (10 in the hardness scale) and it is transparent over a large range of wavelengths (from the ultraviolet up to the far infrared). The diamond transparency allows us to do spectrometric analyses and in-situ observations. Diamond anvil cells are generally made of tungsten carbide (WC) or steel. Physical properties of diamond and WC allow big conical opening of the seat for diamond cells. Thanks to conical opening and transparency of diamond, laser heating of sample and X-ray diffraction are possible for high pressure and high temperature conditions. The main inconvenient for the DAC is the little size of the sample, ~50-100 μm in diameter.
Le Toullec and Chervin refined the concept of “membrane” diamond anvil cell (Le Toullec et al., 1988; Chervin et al., 1995). These DACs allow performing X-ray diffraction at high pressure and high temperature with a large diffraction cone. These cells have been optimized to obtain an opening at the bottom of diamond very large. The pressurization system is separated from the body of the cell. Pressure is transmitted to the diamond by a steel membrane blown up with helium gas. It is injected onto the membrane with an external pump. During my thesis I used both Le Toullec and Chervin cell (Fig. 2.9 and 2.10-2.11 respectively).
Pressure transmitting medium
In order to obtain correct information about structure, elastic and lattice parameters for phases present in the sample at high pressure, it is required to limit constraints deviations that move pressure from hydrostaticity. To keep hydrostaticity, uniaxial and radial constraint could not be sufficient; it is preferable to add a liquid pressure transmitting medium. However, any material rest in liquid phase for pressure higher than 12 GPa and ambient temperature. For this reason, at very high pressure it is necessary the use of solid pressure transmitting medium. We can choose among several materials in function of sample and pressure. The more a solid is compressible (“soft”) the more its shear modulus is weak, the more the medium can be considered hydrostatic. Moreover, it is preferable do not have chemical reactions between transmitting medium and sample. For this, rare gases in the solid state are considered the best materials (e.g. He, Ar, N). We can also use salts or oxides as MgO, Al2O3 or SiO2; during my experiments I used MgO (chapter 3), NaCl or KCl (chapters 4-5). Briefly, we have to choose materials in function of experiments. We used the pressure transmitting medium as an internal pressure standard mixing standard and sample.
High temperature and temperature gradient
We can use two types of laser, CO2 or YAG laser in function of the sample characteristics. Wavelengths are 10.6 and 1.06 μm for CO2 and YAG laser, respectively. They produce different size of heating laser spot. I will present briefly the YAG laser, because it was used during the experiments. It works by interaction with valence electrons of metals or transition elements, e.g. Fe in (Mg,Fe)SiO3. The YAG laser is focused on the sample surface with a diameter lower than 10 μm and then it produces very high gradient of temperature. The YAG laser does not heat white oxides, and for this is ideal for pressure transmitting medium as NaCl, KCl, MgO or Al2O3. This type of laser is particularly appropriate for extreme pressure, and then for this study. The YAG laser can cause elemental migration under chemical gradient (Soret diffusion), even if the segregation is very limited when the sample is heated between the NaCl insulation layers without additional laser absorber (Sinmyo and Hirose, 2010).
The temperature distribution within the laser-heated sample can be modeled based on the thermal diffusion equation (Li et al., 1996): C T k T A (2.1) t.
Where T, , C and k are temperature, density, specific heat and thermal conductivity of the sample. The absorbed power density is described by A.
The accuracy and precision of temperature measurement in the laser heated diamond anvil cell have been much improved in the past with the use of spectral radiometry (Boehler, 1986). This method is adopted in this study. Temperatures are determined by fitting the thermal radiation to the Planck radiation formula, assuming constant emissivity with respect to wavelength: I = c1 -5 / [exp (c2 / (2.2).
Table of contents :
1 Introduction
1.1 The structure of the Earth’s mantle
1.2 Early Earth differentiation
1.2.1 Core formation
1.3 Differentiation of Earth’s mantle and floatability of silicate melts
1.4 The composition of the Earth
1.5 Magma ocean hypothesis
1.6 The magma ocean models
1.6.1 Tonks and Melosh , 1990
1.6.2 Abe, 1997
1.6.3 Solomatov, 2000
1.6.4 Liebske et alii, 2005
1.6.5 Wood et alii, 2006
1.6.6 Labrosse et alii, 2007
1.6.7 Elkins-Tanton, 2008
1.6.8 Nomura et alii, 2011
1.6.9 Summary of different magma ocean models
1.7 Temperature profiles of the lower mantle
1.8 Liquidus and solidus phase relations in the lower mantle
1.9 Partition coefficient
2 Experimental and analytical methods
2.1 Starting materials and sample assembly
2.1.1 Chondritic composition
2.1.2 Forsterite
2.1.3 Sample assembly
2.2 ESRF and the ID27 beamlin
2.2.1 The European Synchrotron Radiation Facility (ESRF)
2.2.2 The ID27 beamline
2.2.3 Mirrors
2.3 High pressure and high temperature experiments
2.3.1 Diamond anvil cell
2.3.2 Diamonds and sample loading
2.3.3 Pressure transmitting medium
2.3.4 High temperature and temperature gradient
2.4 X-ray diffraction (XRD)
2.4.1 Principle
2.4.2 Treatment of data
2.5 X-ray diffraction (XRD) procedure
2.5.1 XRD procedure: study of forsterite melting curve (chapter 3)
2.5.2 XRD procedure: study of chondrite melting curves (chapter 4)
2.5.3 XRD procedure: study of chondrite (chapter 5)
2.6 X-ray fluorescence
2.6.1 Principle of absorption
2.6.2 Photoelectric effect
2.6.3 Fluorescence yield
2.6.4 Anisotropic fluorescence emission
2.6.5 Processing of X-ray fluorescence data
2.6.6 Quantification methods
2.6.6.1 Semi-quantitative elemental analysis
2.6.6.2 External standardization
2.6.6.3 Internal standardization
2.6.6.4 Fundamental parameter (FP) methods
2.6.6.5 Monte Carlo methods
2.6.6.6 Standardless quantifiation
2.6.7 Mapping
2.7 X-ray fluorescence (XRF) procedure: study of chondrite
2.8 Scanning electron microscope
2.9 Inductively coupled plasma atomic emission spectroscopy (ICP-AES)
2.10 Electron microprobe (EMP)
3 Melting in the MgO-MgSiO3 system: A simplified chemical model for the lower mantle
3.1Abstract
3.2 Introduction
3.3 Technical details
3.4 Experimental methodology
3.5 Results and Discussions
3.5.1 Silicate melting
3.5.2 Platinum melting
3.6 Conclusions
4 Solidus and liquidus profiles of chondritic mantle: Implication for melting of the Earth across its history
4.1Abstract
4.2 Introduction
4.3Methods
4.4Results
4.4.1 Melting criteria
4.4.2 Determination of solidus temperature
4.4.3 Determination of liquidus temperature
4.4.4 Melting curves
4.5Discussions
4.5.1 Thermal structure of the D » layer
4.5.2 Melting in the D » region of the ULVZ
4.5.3 Depth extension of the early magma ocean
4.5.4 Formation of a basal magma ocean?
4.6 Conclusions
5 Phase relations in partially molten lower mantle: A X-ray fluorescence study at very high-pressures
5.1Abstract
5.2 Introduction
5.2.1 Mantle melting in the past and at present time?
5.2.2 Liquid floatability in the Earth mantle
5.2.3 Atomic packing of liquid structure
5.2.4 Melt composition
5.3 Experimental methods
5.3.1 Laser heating in the diamond anvil cell
5.3.2 X-ray methods
5.4Results
5.4.1 Diffraction results
5.4.2 Fluorescence results
5.5Discussions
5.5.1 Sample heterogeneity
5.5.2 Fe partition coefficient
5.5.3 Geophysical consequences
Conclusions and outlooks
Bibliography
