Partial Phonon Density Of States Research Articles

Partial phonon densities of states ofFe57in Fe-Cr: Analysis by a local-order cluster expansion

Nuclear resonant inelastic x-ray scattering spectra were measured for $^{57}\mathrm{Fe}$ in disordered body-centered-cubic alloys of Fe-Cr. Partial phonon density of states (DOS) curves were obtained from these data. These results, in conjunction with the results of Ruckert et al. [Hyperfine Interact. 126, 363 (2000)] on Fe-Cr thin-film multilayers and alloys, were analyzed with a local-order cluster expansion method. Interaction partial phonon DOS functions for the different short-range correlation functions were obtained from the disordered alloys. These interaction DOS functions were used in reconstructing the $^{57}\mathrm{Fe}$ partial DOS curves measured by Ruckert et al. on a set of thin-film multilayer samples of $^{57}\mathrm{Fe}∕^{56}\mathrm{Fe}∕\mathrm{Cr}$. The method worked well using terms up to a combined first- and second-nearest-neighbor triangle cluster, which were obtained reliably from the disordered alloys. The limitations of a basis set of correlation functions from disordered alloys are discussed but shown to be acceptable for the chemical trends of phonons in the Fe-Cr system.

Ab initiocalculations of magnetic structure and lattice dynamics inFe∕FeSimultilayers

We report the magnetization distribution, the interlayer coupling constants, and lattice dynamics for the $\mathrm{Fe}∕\mathrm{Fe}\mathrm{Si}$ multilayers, investigated with ab initio calculations based on the density functional theory. By considering several different geometries we demonstrate that the magnetic structure depends on the thickness of both FeSi and iron layers. We have identified robust defects in the anti$\ensuremath{-}$feromagnetic order between iron layers found as a common feature of thick multilayer systems---they suggest a possible mechanism of gradual reorientation of the magnetization towards large ferromagnetic domains. Phonon spectra confirm the stability of FeSi layers alternating with Fe layers. Motivated by possible future experiments, we show that partial phonon densities of states projected on iron atoms exhibit a rather strong dependence on the position of iron monolayer in the structure.

151Eu Nuclear Resonant Inelastic Scattering of Eu4As3around Charge Ordering Temperature

151 Eu nuclear resonant inelastic scattering (NRIS) experiments have been performed on the charge ordering Eu 4 As 3 compound from 301 to 406 K and the Eu partial phonon densities of states were extracted from the observed spectra. We derived the thermodynamic parameters from inelastic components in the observed NRIS spectra using the sum rules. The mean recoilless fraction shows the softening in the lattice vibration of the Eu ion around the charge ordering temperature in spite of no anomaly in the temperature dependence of average sound velocity. We present by the temperature dependence of mean force constant that the hybridization between the 4 f states and the conduction or valence bands in Eu 4 As 3 plays a role around the charge ordering temperature and in the valence fluctuating state.

Atomistic simulation for structural and vibrational properties of R2Co7−xMxB3 (R = Y, Gd; M = Ti, V, Cr)

In order to study the effect of M substitution of transition elements on the structural properties of R2Co7−xMxB3 (R = Y, Gd; M = Ti, V, Cr) compounds, the phase stability and site preference are performed by using the pair potentials based on the lattice inversion technique. In R2Co7−xMxB3, M atoms substitute for Co with a strong preference for the 6i1 sites and the order of site preference is 6i1, 2c and 6i2. Calculated lattice parameters are in good agreement with the experimental data. Moreover, the total and partial phonon densities of states are first evaluated for the R2Co7B3 compounds with the hexagonal Ce2Co7B3-type structure.

Shell-model description of lattice dynamical properties ofMgH2

We develop a shell model (SM) for magnesium hydride with interatomic potentialsand anisotropic core–shell interactions. The model is fitted to measuredRaman modes and ab initio results that we obtain for the phonons at theΓ point. We achieve a very good agreement for the Raman and silent phonons,while the infrared-active modes are less accurately described. Using the developedSM, we have computed the phonon dispersion throughout the Brillouin zone(BZ), which turns out to be in very good agreement with previous first-principlesresults. The SM partial phonon density of states due to hydrogen shows verygood agreement with the experimental one. The temperature dependence of thespecific heat is also calculated and shows good accordance with measurements.

Ab initio study of phonons in the rutile structure of TiO2

The local-density approximation is used to find the phonon dispersion relations, total and partial phonon density of states for TiO2 crystal of rutile structure. For that the Hellmann–Feynman forces were computed and direct method applied. Some thermodynamic quantities are also presented. Calculated results are analyzed and compared with the experimental neutron scattering and optic data. Good agreement has been achieved. A giant LO/TO splitting is observed for A2u and Eu modes.

Atomistic simulation on site preference and lattice vibrations of NdMn8T4 (T = Fe, Co, Ni)

We have simulated the structural and vibrational properties of NdMn8T4 compounds (T = Fe, Co, Ni), using the inverted pair potentials ΦMn–Mn(r), ΦNd–Mn(r), ΦNd–R(r), ΦNd–T(r), ΦMn–T(r), and ΦT–T(r). The calculated site preference of the third element, T, is found to be the 8f site. The difference in the lattice parameters between the calculated and the experimental values is less than 3.0%. These results are in agreement with experiments. Moreover, the total and partial phonon densities of states are first evaluated for the NdMn8T4 compounds. A qualitative analysis is carried out with the relevant potentials for the vibrational modes, which makes it possible to predict some properties related to lattice vibration.

Phonon density of states on [formula omitted] determined by 161Dy nuclear resonant inelastic scattering

We have measured the 161Dy nuclear resonant inelastic X-ray scattering on single crystalline DyB 6 sample at low temperatures along [1 0 0] and [1 1 1]. Partial phonon densities of states were extracted from the inelastic component in the observed spectra. These extracted partial phonon densities of states are not strongly modified by the two-phase transitions at 25 and 30 K in spite of the structural change.

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 57Fe 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.

Magnetic transition and sound velocities of Fe3S at high pressure: implications for Earth and planetary cores

Magnetic, elastic, thermodynamic, and vibrational properties of the most iron-rich sulfide, Fe3S, known to date have been studied with synchrotron Mössbauer spectroscopy (SMS) and nuclear resonant inelastic X-ray scattering (NRIXS) up to 57 GPa at room temperature. The magnetic hyperfine fields derived from the time spectra of the synchrotron Mössbauer spectroscopy show that the low-pressure magnetic phase displays two magnetic hyperfine field sites and that a magnetic collapse occurs at 21 GPa. The magnetic to non-magnetic transition significantly affects the elastic, thermodynamic, and vibrational properties of Fe3S. The magnetic collapse of Fe3S may also affect the phase relations in the iron–sulfur system, changing the solubility of sulfur in iron under higher pressures. Determination of the physical properties of the non-magnetic Fe3S phase is important for the interpretation of the amount and properties of sulfur present in the planetary cores. Sound velocities of Fe3S obtained from the measured partial phonon density of states (PDOS) for 57Fe incorporated in the alloy show that Fe3S has higher compressional and shear wave velocity than those of hcp-Fe and hcp-Fe0.92Ni0.08 alloy under high pressures, making sulfur a potential light element in the Earth's core based on geophysical arguments. The VP and VS of the non-magnetic Fe3S follow a Birch's law trend whereas the slopes decrease in the magnetic phase, indicating that the decrease of the magnetic moment significantly affects the sound velocities. If the Martian core is in the solid state containing 14.2 wt.% sulfur, it is likely that the non-magnetic Fe3S phase is a dominant component and that our measured sound velocities of Fe3S can be used to construct the corresponding velocity profile of the Martian core. It is also conceivable that Fe3P and Fe3C undergo similar magnetic phase transitions under high pressures.

Nuclear resonant x‐ray scattering of iron hydride at high pressure

We studied the nuclear resonant x‐ray scattering of iron hydride (FeHx) up to 52 GPa. Coupled with hydrostatic x‐ray diffraction data, the partial phonon density of states measured by nuclear resonant inelastic x‐ray scattering provides information on sound velocities and the Fe contribution to thermodynamic parameters. In particular it constrains the aggregate shear velocity and shear modulus for comparison to seismic observations. We found that VS (km/sec) = 0.023*P (GPa) + 3.2. A loss of magnetism was observed with synchrotron Mössbauer spectroscopy at 22 GPa, lower than theoretically predicted but consistent with the observed anomalous velocity behavior. Results confirm that FeHx could be a major light element bearing phase for explaining the core density deficit relative to pure Fe. Formation of FeHx by reaction with water would be expected to leave a signature in the mantle.

Interplay between structural instability and lattice dynamics inEuRh2(PxAs1−x)2

The interplay between the crystallographic structure, valence state, and lattice dynamics of the series ${\mathrm{EuRh}}_{2}({\mathrm{P}}_{x}{\mathrm{As}}_{1\ensuremath{-}x}{)}_{2}$ $(x=0,$ 0.5, and 1) has been investigated using x-ray diffraction, the ${}^{151}\mathrm{Eu}$ M\"ossbauer effect, and the ${}^{151}\mathrm{Eu}$ nuclear inelastic scattering of synchrotron radiation, respectively. We show that the first-order, isostructural phase transition $(\ensuremath{\alpha}\mathrm{phase}\ensuremath{\rightarrow}\ensuremath{\beta}\mathrm{phase}),$ which occurs at ${x}_{\mathrm{c}}\ensuremath{\approx}0.85,$ is not connected with a change of the ${\mathrm{Eu}}^{2+}$ valence state but is associated with a significant modification of the Eu partial phonon density of states (PDOS). Lattice dynamical calculations on ${\mathrm{EuRh}}_{2}({\mathrm{P}}_{x}{\mathrm{As}}_{1\ensuremath{-}x}{)}_{2}$ show that the observed change in the PDOS can be attributed to the structural change at the phase transition.

Partial Phonon Density of States of Dysprosium and its Compounds Measured Using Inelastic Nuclear Resonance Scattering

Inelastic nuclear resonance scattering measurements, utilizing a submilli eV monochromator, were performed on natural Dy metal, dysprosium oxide, and intermetallic Laves and Chevrel phase dysprosium compounds. The inelastic spectrum directly yields the partial phonon density of states, and thus provides a wealth of information about the modes of vibration occurring in a lattice at the Mossbauer Dy site. The extraction of the partial phonon density of states from a broad range of materials containing dysprosium demonstrates the feasibility of material science studies.

Sound velocities of iron‐nickel and iron‐silicon alloys at high pressures

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 57Fe 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.

Vibrational properties of the rare earth aluminum garnets

In this work we present single crystal infrared (IR) reflectance spectra for the Dy3Al5O12 and Er3Al5O12 compounds, their corresponding optical constants, as well as a discussion concerning the vibrational, dielectric, and elastic properties of various members of the rare earth aluminum garnet family. In the framework of the rigid ion model, the frequencies of the experimentally unresolved infrared active modes, the IR eigenvectors and the partial phonon density of states have been calculated. The role of the different atomic species in the various regions of the IR vibrational spectrum has been elucidated. In particular, it is found that the rare earth ionic mass plays a crucial role in the low frequency IR modes (<200 cm−1), while the high frequency modes are related mainly to the molecular modes of the AlO4 tetrahedral subunit. From the volume dependence of the IR active mode frequencies, their mode Grüneisen parameters are estimated and discussed. Finally, by using a modification of the semiempirical Brout’s formula, the bulk moduli have been determined and are compared to those derived from interatomic potential calculations.

Role of Jahn-Teller disorder in Raman scattering of mixed-valence manganites

The mixed-valence perovskitelike manganites are characterized by unique interrelation of Jahn-Teller distortions, electric and magnetic properties. The Jahn-Teller distortion follows the Mn(3+)->Mn(4+) charge transfer with some delay. Its development depends on the lifetime of Mn in (3+) state, governed by the Mn(4+)/Mn(3+) ratio and magnetic correlation. The non-coherence of Jahn-Teller distortions in orthorhombic mixed-valence manganites and rhombohedral RMnO3 (R = rare earth) results in oxygen disorder. We demonstrate that the Raman spectra in this case are dominated by disorder-induced bands reflecting the oxygen partial phonon density of states (PDOS). The PDOS origin of the main Raman bands in insulating phases of such compounds is evidenced by the similar lineshape of experimental spectra and calculated smeared PDOS and disappearance of the PDOS bands in ordered ferromagnetic metallic phase.

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.

Atomistic simulation of the lattice constants and lattice vibrations in RT 4Al 8 (R=Nd, Sm; T=Cr, Mn, Cu, Fe)

The lattice constants of the rare earth intermetallic compounds RT 4Al 8 (R=Nd, Sm; T=Cr, Mn, Cu, Fe) with ThMn 12-type structure were evaluated. This calculation was based on the interatomic potentials related to the rare earth and transition metals, which were obtained by a lattice inversion method. The results are in agreement with experiments. The total and partial phonon densities of states for these materials are also presented. The analysis for the inverted potentials explains qualitatively the contributions of different atoms to the vibrational modes.

Vibrational dynamics of myoglobin determined by the phonon-assisted Mössbauer effect

The phonon-assisted Mössbauer effect is used to determine the partial phonon density of states of the iron within the active center of deoxymyoglobin, carboxymyoglobin, and dry and wet metmyoglobin between 40 and 300 K. Between 0 and 1 meV the iron density of states increases quadratically with the energy, as in a Debye solid. Mean sound velocities are extracted from this slope. Between 1 and 3 meV a nearly quadratic "Debye-like" increase follows due to the similar strength of intermolecular and intramolecular forces. Above 3 meV, optical vibrations are characteristic for the iron-ligand conformation. The overall mean square displacements of the heme iron atom obtained from the density of states agree well with the values of Mössbauer absorption experiments below 180 K. In the physiological temperature regime the data confirm the existence of harmonic vibrations in addition to the protein specific dynamics measured by Mössbauer absorption. In the Debye energy regime the mean square displacement of the iron is in agreement with that of the hydrogens measured by incoherent neutron scattering demonstrating the global character of these modes. At higher energies the vibration of the heavy iron atom at 33 meV in metmyoglobin is as large as that of the lightweight hydrogens at that energy. A freeze dried, rehydrated (h=0.38 g H2O/g protein) metmyoglobin sample shows an excess of states above the Debye law between 1 and 3 meV, similar to neutron scattering experiments. The room temperature density of states below 3 meV exhibit an increase of the density compared to the low temperature data, which can be interpreted as mode softening.

Source and optics considerations for new generation high-resolution inelastic X-ray spectrometers

The high-resolution inelastic X-ray scattering technique has evolved rapidly at the third-generation synchrotron sources. It is now possible to measure collective excitations with 2 meV resolution. The next level of experiments may require even more stringent conditions in terms of energy resolution, sample size and environment. For example, microscopic single crystals, thin films or multilayers, confined liquids, and samples under high pressure are outside the domain of momentum resolved inelastic X-ray scattering. Inelastic nuclear resonant scattering can measure partial phonon density of states from such samples, provided that the samples contain suitable Mössbauer isotopes. Based on the experience obtained at the high-resolution X-ray scattering beamline (SRI-CAT 3-ID) of the APS, we present some new perspectives for X-ray sources, monochromators and analyzers to improve the performance of the spectrometer by an order of magnitude.