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

The spin state of iron in minerals of Earth's lower mantle

The spin state of Fe(II) and Fe(III) at temperatures and pressures typical for the Earth's lower mantle is discussed. We predict an extended high-spin to low-spin crossover region along the geotherm for Fe-dilute systems depending on crystal-field splitting, pairing energy, and cooperative interactions. In particular, spin transitions in ferromagnesium silicate perovskite and ferropericlase, the dominant lower mantle components, should occur in a wide temperature-pressure range. We also derive a gradual volume change associated with such transitions in the lower mantle. The gradual density changes and the wide spin crossover regions seem incompatible with lower mantle stratification resulting from a spin transition

Enhanced convection and fast plumes in the lower mantle induced by the spin transition in ferropericlase

Using a numerical model we explore the consequences of the intrinsic density change (Δρ/ρ ≈ 2–4%) caused by the Fe^(2+) spin transition in ferropericlase on the style and vigor of mantle convection. The effective Clapeyron slope of the transition from high to low spin is strongly positive in pressure-temperature space and broadens with high temperature. This introduces a net spin-state driving density difference for both upwellings and downwellings. In 2-D cylindrical geometry spin-buoyancy dominantly enhances the positive thermal buoyancy of plumes. Although the additional buoyancy does not fundamentally alter large-scale dynamics, the Nusselt number increases by 5–10%, and vertical velocities by 10–40% in the lower mantle. Advective heat transport is more effective and temperatures in the core-mantle boundary region are reduced by up to 12%. Our findings are relevant to the stability of lowermost mantle structures

Sound velocity and density of magnesiowüstites: Implications for ultralow-velocity zone topography

We explore the effect of Mg/Fe substitution on the sound velocities of iron-rich (Mg_(1 – x)Fe_x)O, where x = 0.84, 0.94, and 1.0. Sound velocities were determined using nuclear resonance inelastic X-ray scattering as a function of pressure, approaching those of the lowermost mantle. The systematics of cation substitution in the Fe-rich limit has the potential to play an important role in the interpretation of seismic observations of the core-mantle boundary. By determining a relationship between sound velocity, density, and composition of (Mg,Fe)O, this study explores the potential constraints on ultralow-velocity zones at the core-mantle boundary

Behavior of iron in (Mg,Fe)SiO_3 post-perovskite assemblages at Mbar pressures

The electronic environment of the iron sites in post-perovskite (PPv) structured (^(57)Fe,Mg)SiO_3 has been measured in-situ at 1.12 and 1.19 Mbar at room temperature using ^(57)Fe synchrotron Mössbauer spectroscopy. Evaluation of the time spectra reveals two distinct iron sites, which are well distinguished by their hyperfine fields. The dominant site is consistent with an Fe^(3+)-like site in a high spin state. The second site is characterized by a small negative isomer shift with respect to α-iron and no quadrupole splitting, consistent with a metallic iron phase. Combined with SEM/EDS analyses of the quenched assemblage, our results are consistent with the presence of a metallic iron phase co-existing with a ferric-rich PPv. Such a reaction pathway may aid in our understanding of the chemical evolution of Earth's core-mantle-boundary region

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

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

Electronic environments of ferrous iron in rhyolitic and basaltic glasses at high pressure

The physical properties of silicate melts within Earth's mantle affect the chemical and thermal evolution of its interior. Chemistry and coordination environments affect such properties. We have measured the hyperfine parameters of iron-bearing rhyolitic and basaltic glasses up to ~120 GPa and ~100 GPa, respectively, in a neon pressure medium using time domain synchrotron Mössbauer spectroscopy. The spectra for rhyolitic and basaltic glasses are well explained by three high-spin Fe^(2+)-like sites with distinct quadrupole splittings. Absence of detectable ferric iron was confirmed with optical absorption spectroscopy. The sites with relatively high and intermediate quadrupole splittings are likely a result of fivefold and sixfold coordination environments of ferrous iron that transition to higher coordination with increasing pressure. The ferrous site with a relatively low quadrupole splitting and isomer shift at low pressures may be related to a fourfold or a second fivefold ferrous iron site, which transitions to higher coordination in basaltic glass, but likely remains in low coordination in rhyolitic glass. These results indicate that iron experiences changes in its coordination environment with increasing pressure without undergoing a high-spin to low-spin transition. We compare our results to the hyperfine parameters of silicate glasses of different compositions. With the assumption that coordination environments in silicate glasses may serve as a good indicator for those in a melt, this study suggests that ferrous iron in chemically complex silicate melts likely exists in a high-spin state throughout most of Earth's mantle

Experimental constraints on the thermodynamics and sound velocities of hcp-Fe to core pressures

We report the high-pressure thermoelastic and vibrational thermodynamic parameters for hexagonal close-packed iron (ε-Fe), based on nuclear resonant inelastic X-ray scattering and in situ X-ray diffraction experiments at 300 K. Long data collection times, high-energy resolution, and quasi-hydrostatic sample conditions produced a high-statistical quality data set that comprises the volume-dependent phonon density of states (DOS) of ε-Fe at eleven compression points. From the integrated phonon DOS, we determine the Lamb-Mössbauer factor (f_(LM)), average force constant (Φ), and vibrational entropy (S_(vib)) of ε-Fe to pressures relevant to Earth's outer core. We find f_(LM) = 0.923 ± 0.001 at 171 GPa, suggesting restricted thermal atomic motion at large compressions. We use Φ to approximate ε-Fe's pressure- and temperature-dependent reduced isotopic partition function ratios (β-factors), which provide information about the partitioning behavior of iron isotopes in equilibrium processes involving solid ε-Fe. In addition, we use the volume dependence of S_(vib) to determine the product of ε-Fe's vibrational thermal expansion coefficient and isothermal bulk modulus, which we find to be pressure-independent and equal to 5.70 ± 0.05 MPa/K at 300 K. Finally, from the low-energy region of each phonon DOS, we determine the Debye sound velocity (v_D), from which we derive the compressional (v_P) and shear (v_S) sound velocities of ε-Fe. We find v_D = 5.60 ± 0.06, v_P = 10.11 ± 0.12, and v_S = 4.99 ± 0.06 km/s at 171 GPa, thus providing a new tight constraint on the density dependence of ε-Fe's sound velocities to outer core pressures

Measuring velocity of sound with nuclear resonant inelastic x-ray scattering

Nuclear resonant inelastic x-ray scattering is used to measure the projected partial phonon density of states of materials. A relationship is derived between the low-energy part of this frequency distribution function and the sound velocity of materials. Our derivation is valid for harmonic solids with Debye-like low-frequency dynamics. This method of sound velocity determination is applied to elemental, composite, and impurity samples which are representative of a wide variety of both crystalline and noncrystalline materials. Advantages and limitations of this method are elucidated