Synchrotron x-ray diffraction (XRD) measurements, nuclear forward scattering (NFS) measurements, and density functional theory (DFT) calculations were performed on L1_{2}-ordered Pd3Fe. Measurements were performed at 300 K at pressures up to 33 GPa, and at 7 GPa at temperatures up to 650 K. The NFS revealed a collapse of the 57Fe magnetic moment between 8.9 and 12.3 GPa at 300 K, coinciding with a transition in bulk modulus found by XRD. Heating the sample under a pressure of 7 GPa showed negligible thermal expansion from 300 to 523 K, demonstrating Invar behavior. Zero-temperature DFT calculations identified a ferromagnetic ground state and showed several antiferromagnetic states had comparable energies at pressures above 20 GPa.

X-ray diffraction measurements were performed on nanocrystalline iron up to 46 GPa. For nanocrystalline ε-Fe, analysis of lattice parameter data provides a bulk modulus, K, of 179±8 GPa and a pressure derivative of the bulk modulus, K′, of 3.6±0.7, similar to the large-grained control sample. The extrapolated zero-pressure unit cell volume of nanocrystalline ε-Fe is 22.9±0.2 Å3, compared to 22.3±0.2 Å3 for large-grained ε-Fe. No significant grain growth was observed to occur under pressure.

Abstractions which occupy the tetrahedral (8a) sites in normal spinel move to the octahedral (16d) sites in inverse spinel while half of the smaller Al 3+ ions move in the opposite direction. The extent of this move is measured by the disorder or inversion parameter, I (the fraction of tetrahedral sites occupied by the Al ions; I = 0 for normal spinel and I = 1 for inverse spinel). Previous studies suggest that the lattice constant of spinel can decrease as the disorder parameter increases to better accommodate the Ni ions. In situ neutron diffraction studies performed by us indicate that this process is also occurring during the reduction of NiAl 2 O 4 to Ni and Al 2 O 3 . It is possible that the compressive residual stresses generated during reduction play a role in the structural evolution of NiAl 2 O 4 .To systematically investigate the effect of pressure on the structure of NiAl 2 O 4 , x-ray diffraction studies at the X17 beamline of the National Synchrotron Light Source were performed. The pressure (up to 35 GPa) was applied via a diamond anvil cell and the experiments were conducted using a polychromatic x-ray beam. By comparing the relative intensities of certain spinel reflections that are sensitive to cationic disorder, a trend toward inverse spinel as a function of pressure was observed. The results are presented in comparison to previous studies on this material.

The phonon density of states ͑DOS͒ of nanocrystalline 57 Fe was measured using nuclear resonant inelastic x-ray scattering ͑NRIXS͒ 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 AE n , 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.

The phonon density of states of nanocrystalline bcc Fe and nanocrystalline fcc Ni 3 Fe were measured by inelastic neutron scattering in two different ranges of energy. As has been reported previously, the nanocrystalline materials showed enhancements in their phonon density of states at energies from 2 to 15 meV, compared to control samples composed of large crystals. The present measurements were extended to energies in the micro-eV range, and showed significant, but smaller, enhancements in the number of modes in the energy range from 5 to 18 eV. These modes of micro-eV energies provide a long-wavelength limit that bounds the fraction of modes at milli-eV energies originating with the cooperative dynamics of the nanocrystalline microstructure. DOI: 10.1103/PhysRevLett.93.205501 PACS numbers: 63.22.+m, 61.46.+w, 81.07.-b The vibrational spectra of nanocrystalline materials differ from those of materials composed of larger crystals. Earlier measurements of Debye-Waller factors and Lamb-Mössbauer factors showed large mean-squared atomic displacements in nanocrystalline materials [1][2][3][4]. More recently, neutron and x-ray inelastic scattering measurements revealed that nanocrystalline materials have an increased number of vibrational modes at the highest and lowest energies of their measured spectra, compared to materials with crystals of conventional sizes [5][6][7][8][9][10][11][12]. Enhanced intensity above the high-energy cutoff of the bulk material has been attributed to phonon lifetime broadening caused by phonon interactions with grain boundaries [9][10][11] and recent measurements on iron have isolated a contribution from surface oxides [12]. The increased number of phonon modes at low energies [5][6][7][8][9][10][11] is less well understood. The phonon density of states (DOS) at low energies is up to a factor of 5 times larger than the DOS of control samples of material composed of larger crystals [10]. The number of these low-energy modes was found to increase with the inverse of the crystallite size, implying a scaling with the number of grain boundaries. Surface vibrational modes could be responsible for such behavior because grain boundaries have elastic constants differing from the crystal interiors. There are some experimental and computational reports that the low-energy phonon DOS in nanocrystalline materials scales linearly with energy, indicative of twodimensional vibrations [13,14]. Other theoretical models include the idea of a nonintegral spatial dimension of the low-energy modes [15][16][17][18].Surface modes on individual, isolated crystallites have a maximum wavelength comparable to the crystallite size, and therefore a lower bound on their energy. For a wave velocity of 2 km=s and a particle of 10 nm dimension, the characteristic energy is 1 meV. Energies of a milli-electron volt have been approximately the lower limit of the inelastic spectra measured to date. Surface modes around nanoparticles should not extend to energies much below 100 eV, however. The present experiment was d...