Aggregate sound velocities and acoustic Grüneisen parameter of iron up to 300 GPa and 1,200 K

Abstract

Successful interpretation of available geophysical data requires experimental and theoretical information on the elasticity of solids under physical conditions of Earth's interior. Because iron is considered as major component in Earth's core, elastic properties of iron at high pressures and temperatures are very important for modeling its composition and dynamics. We use in situ x-ray diffraction data on -iron at static pressures up to 300 GPa and temperatures to 1,200 K to determine the Debye-Waller temperature factors and calculate aggregate sound velocities and Grü neisen parameter of -iron by using an approach that is based on Rietveld refinement at high pressures and temperatures.T he data on static compression of iron at ambient and elevated temperatures (1-4) provides important information on compressibility at the conditions present in Earth's deep interior. However, information on shear modulus, which is crucial for calculating sound velocities, is very limited. Mao et al. (5) published results of a study of elasticity of iron to a pressure of 220 GPa based on a novel method of determination of elastic moduli with diamond anvil cells (DAC) (6). This method utilizes the fact that in opposite anvil devices (like DAC) compression is not hydrostatic. As a result, positions of the reflections on the powder diffraction patterns depend not only on bulk modulus of the compressed material, but also on all of the elastic moduli and a value of deviatoric stress. The method cannot be used at high temperatures because deviatoric stress in DAC practically vanishes above Ϸ800 K (4). The mean sound velocities of hcp iron were extracted from phonon density measurements at pressures up to 153 GPa and ambient temperature (7,8). Raman spectroscopy (9) of -Fe at pressures up to 150 GPa gave additional input to elastic properties of iron at high pressures. However, so far there are no experimental information on sound velocities of iron at pressure range of 300 GPa and high temperaturesconditions that are relevant to Earth's inner core.The vibrations of individual atoms, as applied to intensities of x-ray diffraction peaks, control the Debye-Waller temperature factor B. This includes all wavelengths of phonons. As a result, the information on temperature factors has been used over years to determine Debye temperatures and Gruneisen parameters of different materials (10-15). The Debye temperature depends on aggregate elastic properties of a crystal-the adiabatic bulk modulus K S and shear modulus G (16). Moreover, it was demonstrated by Anderson (16) that the Debye temperature is primarily dependent on the shear modulus, and this opens the way, as we are going to show in the present study, to extract aggregate shear and compressional sound velocities from data on temperature factors. Following Grimvall's (12) consideration and using dispersion relation (10, 11)where is the circular frequency, V sound is the sound velocities, q is the wave number of a lattice mode, and q D is the Debye cut-off wave number. We found for the ...

Sound velocity of hcp-Fe at high pressure: experimental constraints, extrapolations and comparison with seismic models

“…Application of classic pulse-echo ultrasonic techniques in multi-anvil presses is feasible but challenging, and only a single measurement has been obtained on hcp-Fe, at the relatively low pressure of 16.5 GPa (Mao et al, 1998). As already mentioned, V P derived from XRD-based techniques suffers from model dependence, but data have been obtained up to pressures close to 300 GPa (Mao et al, 1998;Dubrovinski et al, 2001), supporting a linear dependence of V P with density. NRIXS measurements may provide the most accurate determination of V S (Murphy et al, 2013;Gleason et al, 2013), while V P values are more dependent on the choice of the EOS used in the data analysis.…”

“…Alternatively, Rietveld refinement has been exploited to estimate the Debye-Waller factor and then to calculate the aggregate velocities starting from X-ray diffraction measurements on hcp-Fe up to 300 GPa and 1,200 K (Dubrovinski et al, 2001). Although such studies provide very valuable information, they only probe the sound velocities indirectly, relying heavily on interpretative schemes and assumptions in data analysis.…”

“…Although such studies provide very valuable information, they only probe the sound velocities indirectly, relying heavily on interpretative schemes and assumptions in data analysis. Specifically, stress inhomogeneities resulting from grain-to-grain interaction in combination with effects of plastic deformation undermine the validity of the continuum elasticity theory used by Mao et al (1998) to invert the singlecrystalline elastic moduli from the measured lattice strain (Merkel et al, 2006;, while the results of Dubrovinski et al (2001) explicitly depend on the assumed relation between the Debye-Waller temperature factor and the aggregate elastic properties.…”

“…Estimations of V P starting from XRD measurements are one of the most indirect and model-dependent approach, but with the advantage of providing the largest coverage in pressure (and hence density) range (up to approximately 200 GPa in Mao et al (1998) and up to approximately 275 GPa in Dubrovinski et al (2001), once rescaling reported values to the Matsui P scale). V P obtained as a function of density is illustrated in Figure 1.…”

“…This sub-linear relation is also at odds with the V P -ρ trend derived by the analysis of XRD Figure 1 XRD-derived compressional sound velocity as a function of density. Grey right-pointing triangles (Mao et al, 1998); dark cyan left-pointing triangles (Dubrovinski et al, 2001). Lines are linear fit to the distinct experimental data sets.…”