Grüneisen parameter of hcp‐Fe to 171 GPa

We measured the phonon density of states (DOS) of hexagonal close-packed iron (ɛ-Fe) with high statistical quality using nuclear resonant inelastic X-ray scattering and in situ X-ray diffraction experiments between pressures of 30 GPa and 171 GPa and at 300 K, with a neon pressure medium up to 69 GPa. The shape of the phonon DOS remained similar at all compression points, while the maximum (cutoff) energy increased regularly with decreasing volume. As a result, we present a generalized scaling law to describe the volume dependence of ɛ-Fe's total phonon DOS which, in turn, is directly related to the ambient temperature vibrational Grüneisen parameter (γ_(vib)). Fitting our individual γ_(vib) data points with γ_(vib) = γ_(vib),0(V/V0)^q, a common parameterization, we found an ambient pressure γ_(vib,0) = 2.0 ± 0.1 for the range q = 0.8 to 1.2. We also determined the Debye sound velocity (v_D) from the low-energy region of the phonon DOS and our in situ measured volumes, and used the volume dependence of v_D to determine the commonly discussed Debye Grüneisen parameter (γ_D). Comparing our γ_(vib)(V) and γ_D(V), we found γ_(vib) to be ∼10% larger than γ_D at any given volume. Finally, applying our γ_(vib)(V) to a Mie-Grüneisen type relationship and an approximate form of the empirical Lindemann melting criterion, we predict the vibrational thermal pressure and estimate the high-pressure melting behavior of ɛ-Fe at Earth's core pressures

Very low sound velocities in iron-rich (Mg,Fe)O: Implications for the core-mantle boundary region

The sound velocities of (Mg_(.16)Fe_(.84))O have been measured to 121 GPa at ambient temperature using nuclear resonant inelastic x-ray scattering. The effect of electronic environment of the iron sites on the sound velocities were tracked in situ using synchrotron Mössbauer spectroscopy. We found the sound velocities of (Mg_(.16)Fe_(.84))O to be much lower than those in other presumed mantle phases at similar conditions, most notably at very high pressures. Conservative estimates of the effect of temperature and dilution on aggregate sound velocities show that only a small amount of iron-rich (Mg,Fe)O can greatly reduce the average sound velocity of an assemblage. We propose that iron-rich (Mg,Fe)O be a source of ultra-low velocity zones. Other properties of this phase, such as enhanced density and dynamic stability, strongly support the presence of iron-rich (Mg,Fe)O in localized patches above the core-mantle boundary

Phonons in Nanocrystalline 57Fe

We measured the phonon density of states (DOS) of nanocrystalline Fe by resonant inelastic nuclear γ-ray scattering. The nanophase material shows large distortions in its phonon DOS. We attribute the high energy distortion to lifetime broadening. A damped harmonic oscillator model for the phonons provides a low quality factor, Qu, averaging about 5, but the longitudinal modes may have been broadened most. The nanocrystalline Fe also shows an enhancement in its phonon DOS at energies below 15 meV. The difference in vibrational entropy of the bulk and nanocrystalline Fe was small, owing to competing changes in the nanocrystalline phonon DOS at low and high energies

Vibrational properties of alpha- and sigma-phase Fe-Cr alloy

Experimental investigation as well as theoretical calculations, of the Fe-partial phonon density-of-states (DOS) for nominally Fe_52.5Cr_47.5 alloy having (a) alpha- and (b) sigma-phase structure were carried out. The former at sector 3-ID of the Advanced Photon Source, using the method of nuclear resonant inelastic X-ray scattering, and the latter with the direct method [K. Parlinski et al., Phys. Rev. Lett. {78, 4063 (1997)]. The characteristic features of phonon DOS, which differentiate one phase from the other, were revealed and successfully reproduced by the theory. Various data pertinent to the dynamics such as Lamb-Mossbauer factor, f, kinetic energy per atom, E_k, and the mean force constant, D, were directly derived from the experiment and the theoretical calculations, while vibrational specific heat at constant volume, C_V, and vibrational entropy, S were calculated using the Fe-partial DOS. Using the values of f and C_V, we determined values for Debye temperatures, T_D. An excellent agreement for some quantities derived from experiment and first-principles theory, like C_V and quite good one for others like D and S was obtained.Comment: 4 pages, 3 figure

Phonon density of states and compression behavior in iron sulfide under pressure

We report the partial phonon densities of states (DOS) of iron sulfide, a possible component of the rocky planet's core, measured by the Fe-57 nuclear resonant inelastic x-ray scattering and calculate the total phonon DOS under pressure. From the phonon DOS, we drive thermodynamic parameters. A comparison of the observed and estimated compressibilities makes it clear that there is a large pure electronic contribution in the observed compressibility in the metallic state. Our results present the observation of thermodynamic parameters of iron sulfide with the low-spin state of an Fe2+ ion at the high density, which is similar to the condition of the Martian core

Synchrotron Mössbauer spectroscopic study of ferropericlase at high pressures and temperatures

The electronic spin state of Fe^(2+) in ferropericlase, (Mg_(0.75)Fe_(0.25))O, transitions from a high-spin (spin unpaired) to low-spin (spin paired) state within the Earth’s mid-lower mantle region. To better understand the local electronic environment of high-spin Fe^(2+) ions in ferropericlase near the transition, we obtained synchrotron Mössbauer spectra (SMS) of (Mg_(0.75),Fe_(0.25))O in externally heated and laser-heated diamond anvil cells at relevant high pressures and temperatures. Results show that the quadrupole splitting (QS) of the dominant high-spin Fe^(2+) site decreases with increasing temperature at static high pressure. The QS values at constant pressure are fitted to a temperature-dependent Boltzmann distribution model, which permits estimation of the crystal-field splitting energy (Δ_3) between the d_(xy_ and d_(xz) or d_(zy) orbitals of the t_(2g) states in a distorted octahedral Fe^(2+) site. The derived Δ_3 increases from approximately 36 meV at 1 GPa to 95 meV at 40 GPa, revealing that both high pressure and high temperature have significant effects on the 3d electronic shells of Fe^(2+) in ferropericlase. The SMS spectra collected from the laser-heated diamond cells within the time window of 146 ns also indicate that QS significantly decreases at very high temperatures. A larger splitting of the energy levels at high temperatures and pressures should broaden the spin crossover in ferropericlase because the degeneracy of energy levels is partially lifted. Our results provide information on the hyperfine parameters and crystal-field splitting energy of high-spin Fe^(2+) in ferropericlase at high pressures and temperatures, relevant to the electronic structure of iron in oxides in the deep lower mantle

High-energy-resolution X-ray monochromator calibration using the detailed-balance principle

A new method is presented to calibrate an X-ray energy scale with sub-meV relative accuracy by using the detailed-balance principle of the phonon creation and annihilation. This method is conveniently used to define or verify the energy scale of high-energy-resolution monochromators that are used in inelastic X-ray scattering and nuclear resonant inelastic X-ray scattering instruments at synchrotron radiation facilities. This method does not rely on sample properties and its precision only depends on the statistical data quality. Well calibrated instruments are essential for reliable comparison of data sets obtained at different synchrotron radiation beamlines, of data with theoretical predictions, and of data from other techniques such as neutron or light scattering. The principle of the detailed-balance method is described in this paper and demonstrated experimentally

Atom clusters and vibrational excitations in chemically-disordered Pt357Fe

Inelastic nuclear resonant scattering spectra of Fe-57 atoms were measured on crystalline alloys of Pt3Fe-57 that were chemically disordered, partially ordered, and L1(2) ordered. Phonon partial density of states curves for Fe-57 were obtained from these spectra. Upon disordering, about 10% of the spectral intensity underwent a distinct shift from 25 to 19 meV. This change in optical modes accounted for most of the change of the vibrational entropy of disordering contributed by Fe atoms, which was (+0.10 +/- 0.03) k(B) (Fe atom)(-1). Prospects for parametrizing the vibrational entropy with low-order cluster variables were assessed. To calculate the difference in vibrational entropy of the disordered and ordered alloys, the clusters must be large enough to account for the abundances of several of the atom configurations of the first-nearest-neighbor shell about the Fe-57 atoms

Vibrational modes in nanocrystalline iron under high pressure

The phonon density of states (DOS) of nanocrystalline 57Fe was measured using nuclear resonant inelastic x-ray scattering (NRIXS) at pressures up to 28 GPa in a diamond anvil cell. The nanocrystalline material exhibited an enhancement in its DOS at low energies by a factor of 2.2. This enhancement persisted throughout the entire pressure range, although it was reduced to about 1.7 after decompression. The low-energy regions of the spectra were fitted to the function AEn, giving values of n close to 2 for both the bulk control sample and the nanocrystalline material, indicative of nearly three-dimensional vibrational dynamics. At higher energies, the van Hove singularities observed in both samples were coincident in energy and remained so at all pressures, indicating that the forces conjugate to the normal coordinates of the nanocrystalline materials are similar to the interatomic potentials of bulk crystals

Local Chemical Environments and the Phonon Partial Densities of States of 57Fe in 57Fe3Al

Inelastic nuclear resonant scattering spectra were measured on alloys of Fe3Al that were chemically disordered, partially ordered, and D03 ordered. The features in the phonon partial density of states of 57Fe were found to change systematically with chemical short-range order in the alloy. Changes in the phonon partial density of states were modeled successfully by assigning vibrational spectra to 57Fe atoms in different first-nearest-neighbor chemical environments