Results and Discussion
3.4 Single-Crystal Elasticity of Wadsleyite at High Pres- Pres-sures and High Temperatures
Brillouin spectroscopy experiments on wadsleyite were also performed at combined high pressures and high temperatures. As explained in section 2.3.2, we used a resistive heater placed around the diamond anvils to heat the high-pressure chamber of the DAC. As with room temperature experiments, sound wave velocities were measured on two crystals that were loaded together inside the high-pressure chamber of the same DAC. The orientations of the crystals were chosen to complement each other so as to provide sufficient propaga-tion direcpropaga-tions of sound waves to constrain the full elastic stiffness tensor. At combined high pressures and high temperatures, this is of great advantage as all sound wave veloci-ties can be determined at the same conditions. Otherwise, identical conditions of pressure and temperature would have to be inferred for separated experiments indirectly based on measurements that might be biased, for instance, by thermal gradients. Pressure and tem-perature were determined from fluorescence spectra of standard materials that were placed next to the crystals inside the high-pressure chamber of the DAC (see section 2.3.3). Den-sities of the crystals were calculated from unit cell volumes determined by X-ray diffraction
Figure 3.3: Sound wave velocities of wadsleyite single crystals with propagation directions within the (120) and (243) crystallographic planes. Solid circles show sound wave velocities determined by Brillouin spectroscopy at 11.8(3) GPa and 640(25) K as a function of rotation angle. Lines show fitted angular dispersion curves.
at the same pressures and temperatures were Brillouin spectra were recorded. While the approach used here allows deriving complete elastic stiffness tensors at individual combina-tions of pressure and temperature, sound wave velocities collected at various pressures and temperatures and for different propagation directions can also be analyzed using the global inversion procedure outlined in chapter 5. Isolated sound wave velocity measurements may result from failure of components of the DAC during high-pressure high-temperature exper-iments. By applying the global inversion procedure, their information can still contribute to the description of elastic properties even though it may not be possible to derive the complete elastic stiffness tensor directly from the sound wave velocities determined at the respective conditions.
Figure 3.3 illustrates the analysis of sound wave velocities collected at 11.8(3) GPa and 640(25) K. Elastic stiffness tensors of iron-bearing wadsleyite determined at combined high pressures and high temperatures are compiled in Table 3.2. Following the lines in the pre-vious section, I calculated bulk and shear moduli of isotropic wadsleyite aggregates. Figure 3.4 compares the corresponding P and S wave velocities with velocities predicted based on the results of chapter 6 (Buchen et al., 2018b) and tabulated thermoelastic parameters (Stixrude and Lithgow-Bertelloni, 2011; see also Table 6.2 on page 145). While the direct experimental results at pressures around 12 GPa indicate a reduction of sound wave veloci-ties with increasing temperature, more measurements at combined high pressures and high temperatures are needed to refine tabulated thermoelastic parameters. In view of the uncer-tainties as indicated by the experimental scatter of results at room temperature, I conclude that tabulated thermoelastic parameters are consistent with the here-presented
measure-3.4 HP–HT Single-Crystal Elasticity of Wadsleyite
Figure 3.4:P wave (a) and S wave (b) velocities for isotropic aggregates of iron-bearing wadsleyite as a function of pressure at different temperatures. Solid circles show experimental results at ambient temperature (blue) and at high temperatures (Table 3.2). Lines were calculated based on finite-strain parameters reported in Buchen et al. (2018b) (Table 6.1) and tabulated thermoelastic parameters (Stixrude and Lithgow-Bertelloni, 2011).
ments at combined high pressures and high temperatures. This finding also justifies the use of tabulated thermoelastic parameters in modeling sound wave velocities of wadsleyite at conditions of the transition zone in chapter 6.
In addition to P and S wave velocities of isotropic aggregates, the acoustic anisotropy of wadsleyite single crystals can be computed from elastic stiffness tensors using the solu-tions to equation (5.10) as derived in section 5.2.2. Figure 3.5 displays the variation in propagation velocities of quasi-longitudinal (P) waves and quasi-transverse waves (S1 and S2) with propagation direction for a wadsleyite single crystal at ambient conditions and at 11.8(3) GPa and 640(25) K. For all three types of waves, the anisotropy of their propaga-tion velocity decreases from ambient condipropaga-tions to 11.8 GPa and 640 K as can be read from the range of velocities covered at each set of conditions. For quasi-transverse waves, the anisotropy can be expressed in terms of the relative difference in propagation velocities of perpendicularly polarized waves propagating in the same direction (Mainprice, 2015) (in
%):
AS = vS2−vS1
vS1+vS2×200 (3.1)
with the velocities vS1 and vS2of S1 and S2 waves, respectively. The maximum anisotropy AS decreases from about 18 % at ambient conditions to about 12 % at 11.8 GPa and 640 K.
This reduction is accompanied by a shift of the propagation direction with maximalAS from a direction that makes nearly equal angles to all three crystallographic axes to a direction in thea-bplane with nearly equal angles to these two crystallographic axes. These changes in the pattern of acoustic anisotropy are similar to pressure-induced changes observed for Mg2SiO4 wadsleyite (Zha et al., 1997).
Information on the acoustic anisotropy of single crystals can be integrated with mi-crostructural observations on natural rocks or on synthetic polycrystalline aggregates
de-Figure 3.5: Equal-area projections showing the sound wave velocities and acoustic anisotropy of a wadsleyite single crystal at ambient conditions (upper row) and at 11.8(3) GPa and 640(25) K (lower row) for quasi-longitudinal (P) waves and quasi-transverse waves (S1 and S2). The shear wave anisotropyASis defined in equation (3.1).
formed at high pressures and high temperatures to predict the anisotropic seismic prop-erties of deformed rocks (Mainprice, 2015; Almqvist and Mainprice, 2017). Viscoplastic self-consistent modeling and deformation experiments on polycrystalline wadsleyite aggre-gates suggest that wadsleyite grains tend to align in a crystallographic preferred orientation under shear deformation (Tommasi et al., 2004; Kawazoe et al., 2013; Ohuchi et al., 2014;
Farla et al., 2015). The orientation distribution function describing the crystallographic pre-ferred orientation can be combined with the elastic stiffness tensor of a wadsleyite single crystal to calculate the elastic stiffness tensor and the acoustic anisotropy of a polycrystalline wadsleyite aggregate (Mainprice et al., 2000; Tommasi et al., 2004; Kawazoe et al., 2013;
Ohuchi et al., 2014; Mainprice, 2015).
Evidence for azimuthal and radial seismic anisotropy within the transition zone comes from the analysis of higher mode surface waves (Trampert and van Heijst, 2002; Visser et al., 2008). Seismic anisotropy at depths relevant to wadsleyite has also been inferred from observations of shear wave splitting (Fouch and Fischer, 1996; Foley and Long, 2011; Long, 2013). In comparison to other transition zone minerals, wadsleyite shows the strongest acoustic anisotropy (Mainprice, 2015) and can therefore be expected to contribute most to seismic anisotropy in the transition zone if the observed anisotropy reflects crystallographic preferred orientation of minerals. Since deformation and plastic flow of rock leads to the development of crystallographic preferred orientation (Karato, 2008), seismic anisotropy may contain information about material flow patterns in the transition zone. To translate seismically observed anisotropy to flow patterns, however, more information about the de-formation behavior and the elastic properties of wadsleyite at realistic pressures, temper-atures, and time scales is needed. The elastic stiffness tensors of wadsleyite compiled in Table 3.2 are the first ones determined at combined high pressures and high temperatures