We report phonon densities of states (DOS) of iron measured by nuclear resonant inelastic x-ray scattering to 153 gigapascals and calculated from ab initio theory. Qualitatively, they are in agreement, but the theory predicts density at higher energies. From the DOS, we derive elastic and thermodynamic parameters of iron, including shear modulus, compressional and shear velocities, heat capacity, entropy, kinetic energy, zero-point energy, and Debye temperature. In comparison to the compressional and shear velocities from the preliminary reference Earth model (PREM) seismic model, our results suggest that Earth's inner core has a mean atomic number equal to or higher than pure iron, which is consistent with an iron-nickel alloy.

The partial density of vibrational states has been measured for Fe in compressed FeO (wustite) using nuclear resonant inelastic x-ray scattering. Substantial changes have been observed in the overall shape of the density of states close to the magnetic transition around 20 GPa from the paramagnetic (low pressure) to the antiferromagnetic (high pressure) state. The results indicate that strong magnetoelastic coupling in FeO is the driving force behind the changes in the phonon spectrum of FeO. The paper presents the first observation of changes in the density of terahertz acoustic phonon states under magnetic transition at high pressure.

The partial density of vibrational states has been measured for Fe in compressed FeO (wustite) using nuclear resonant inelastic x-ray scattering. Substantial changes have been observed in the overall shape of the density of states close to the magnetic transition around 20 GPa from the paramagnetic (low pressure) to the antiferromagnetic (high pressure) state. The results indicate that strong magnetoelastic coupling in FeO is the driving force behind the changes in the phonon spectrum of FeO. The paper presents the first observation of changes in the density of terahertz acoustic phonon states under magnetic transition at high pressure.

Nuclear resonant inelastic X-ray scattering of synchrotron radiation is being applied to ever widening areas ranging from geophysics to biophysics and materials science. Since its first demonstration in 1995 using the Fe-57 resonance, the technique has now been applied to materials containing Kr-83, Eu-151, Sn-119, and Dy-161 isotopes. The energy resolution has been reduced to under a millielectronvolt. This, in turn, has enabled new types of measurements like Debye velocity of sound, as well as the study of origins of non-Debye behavior in presence of other low-energy excitations. The effect of atomic disorder on phonon density of states has been studied in detail. The flux increase due to the improved X-ray sources, crystal monochromators, and time-resolved detectors has been exploited for reducing sample sizes to nano-gram levels, or using samples with dilute resonant nuclei like myoglobin, or even monolayers. Incorporation of micro-focusing optics to the existing experimental setup enables experiments under high pressure using diamond-anvil cells. In this article, we will review these developments.

Nuclear resonant inelastic X-ray scattering of synchrotron radiation is being applied to ever widening areas ranging from geophysics to biophysics and materials science. Since its first demonstration in 1995 using the Fe-57 resonance, the technique has now been applied to materials containing Kr-83, Eu-151, Sn-119, and Dy-161 isotopes. The energy resolution has been reduced to under a millielectronvolt. This, in turn, has enabled new types of measurements like Debye velocity of sound, as well as the study of origins of non-Debye behavior in presence of other low-energy excitations. The effect of atomic disorder on phonon density of states has been studied in detail. The flux increase due to the improved X-ray sources, crystal monochromators, and time-resolved detectors has been exploited for reducing sample sizes to nano-gram levels, or using samples with dilute resonant nuclei like myoglobin, or even monolayers. Incorporation of micro-focusing optics to the existing experimental setup enables experiments under high pressure using diamond-anvil cells. In this article, we will review these developments.

We have built a high-energy-resolution monochromator for nuclear resonant scattering from the 9.4 keV nuclear transition of Kr-83. The monochromator consists of two highly asymmetric silicon single crystals arranged in a dispersive geometry and produces an energy bandwidth of 2.3 meV. This monochromator has been successfully used for a study of nuclear forward scattering and nuclear resonant inelastic scattering from a Kr-83 sample that was solidified in a diamond anvil cell at 2.15 GPa and room temperature. (C) 2002 American Institute of Physics.

We have built a high-energy-resolution monochromator for nuclear resonant scattering from the 9.4 keV nuclear transition of Kr-83. The monochromator consists of two highly asymmetric silicon single crystals arranged in a dispersive geometry and produces an energy bandwidth of 2.3 meV. This monochromator has been successfully used for a study of nuclear forward scattering and nuclear resonant inelastic scattering from a Kr-83 sample that was solidified in a diamond anvil cell at 2.15 GPa and room temperature. (C) 2002 American Institute of Physics.

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.

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.

[1] Understanding the alloying effects of nickel and light element(s) on the physical properties of iron under core conditions is crucial for interpreting and constraining geophysical and geochemical models. We have studied two alloys, Fe0.92Ni0.08 and Fe0.85Si0.15, with nuclear resonant inelastic x-ray scattering up to 106 GPa and 70 GPa, respectively. The sound velocities of the alloys are obtained from the measured partial phonon density of states for Fe-57 incorporated in the alloys. Addition of Ni slightly decreases the compression wave velocity and shear wave velocity of Fe under high pressures. Silicon alloyed with Fe increases the compressional wave velocity and shear wave velocity under high pressures, which provides a better match to seismological data of the Earth's core.