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.

[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.

The elastic properties of compressed Fe and FeO are examined using density of states measured by nuclear resonant inelastic X-ray scattering. We analyze the data both from non-hydrostatic and nearly hydrostatic experiments. The effects of preferred orientation in non-hydrostatic experiments could be substantial. We present also evidence in favor of strong softening of the Debye sound velocity due to the magnetoelastic coupling in iron oxide near the Neel transition. The geophysical implications resulting from the elastic and magnetoelastic properties of these and related materials under compression are discussed.

The elastic properties of compressed Fe and FeO are examined using density of states measured by nuclear resonant inelastic X-ray scattering. We analyze the data both from non-hydrostatic and nearly hydrostatic experiments. The effects of preferred orientation in non-hydrostatic experiments could be substantial. We present also evidence in favor of strong softening of the Debye sound velocity due to the magnetoelastic coupling in iron oxide near the Neel transition. The geophysical implications resulting from the elastic and magnetoelastic properties of these and related materials under compression are discussed.

Attributed to their specific atomic bonding, the soft, graphite-like, hexagonal boron nitride (h-BN) and its superhard, diamond-like, cubic polymorph (c-BN) are important technological materials with a wide range of applications(1). At high pressure and temperature, h-BN can directly transform to a hexagonal close-packed polymorph (w-BN)(2) that can be partially quenched after releasing pressure. Previous theoretical calculations(3-5) and experimental measurements (primarily on quenched samples)(6-9) provided substantial information on the transition, but left unsettled questions due to the lack of in situ characterization at high pressures. Using inelastic X-ray scattering to probe the boron and nitrogen near K-edge spectroscopy, here we report the first observation of the conversion process of boron and nitrogen sp(2)- and p-bonding to sp(3) and the directional nature of the sp(3) bonding. In combination with in situ X-ray diffraction probe, we have further clarified the structure transformation mechanism. The present archetypal example opens two enormous, element-specific, research areas on high-pressure bonding evolutions of boron and nitrogen; each of the two elements and their respective compounds have displayed a wealth of intriguing pressure-induced phenomena(10) that result from bonding changes, including metallization(11,12), superconductivity(13,14), semiconductivity(15), polymerization(16) and superhardness(2,17,18).

Attributed to their specific atomic bonding, the soft, graphite-like, hexagonal boron nitride (h-BN) and its superhard, diamond-like, cubic polymorph (c-BN) are important technological materials with a wide range of applications(1). At high pressure and temperature, h-BN can directly transform to a hexagonal close-packed polymorph (w-BN)(2) that can be partially quenched after releasing pressure. Previous theoretical calculations(3-5) and experimental measurements (primarily on quenched samples)(6-9) provided substantial information on the transition, but left unsettled questions due to the lack of in situ characterization at high pressures. Using inelastic X-ray scattering to probe the boron and nitrogen near K-edge spectroscopy, here we report the first observation of the conversion process of boron and nitrogen sp(2)- and p-bonding to sp(3) and the directional nature of the sp(3) bonding. In combination with in situ X-ray diffraction probe, we have further clarified the structure transformation mechanism. The present archetypal example opens two enormous, element-specific, research areas on high-pressure bonding evolutions of boron and nitrogen; each of the two elements and their respective compounds have displayed a wealth of intriguing pressure-induced phenomena(10) that result from bonding changes, including metallization(11,12), superconductivity(13,14), semiconductivity(15), polymerization(16) and superhardness(2,17,18).

The magnetic properties of iron in cementite (Fe3C) have been measured by x-ray emission spectroscopy in a diamond cell up to 45 GPa. The Fe-K-beta fluorescence peaks reveal that Fe3C undergoes a magnetic collapse at approximately 25 GPa, consistent with theoretical predictions. This transition is likely to be a second-order phase transition without a major structural change. The magnetic collapse transition is expected to affect the elastic and thermodynamic properties of Fe3C; the nonmagnetic phase predicted theoretically has a higher incompressibility and density than the magnetic state. Our results support recent theoretical and thermodynamic calculations indicating that Fe3C is unlikely to be the major component in the Earth's inner core.

The magnetic properties of iron in cementite (Fe3C) have been measured by x-ray emission spectroscopy in a diamond cell up to 45 GPa. The Fe-K-beta fluorescence peaks reveal that Fe3C undergoes a magnetic collapse at approximately 25 GPa, consistent with theoretical predictions. This transition is likely to be a second-order phase transition without a major structural change. The magnetic collapse transition is expected to affect the elastic and thermodynamic properties of Fe3C; the nonmagnetic phase predicted theoretically has a higher incompressibility and density than the magnetic state. Our results support recent theoretical and thermodynamic calculations indicating that Fe3C is unlikely to be the major component in the Earth's inner core.