Experimental Phonon Spectra Research Articles

Nonharmonic phonons in MgB2at elevated temperatures

Inelastic neutron scattering was used to measure phonon spectra in MgB_2 and Mg_(0.75)Al_(0.25)B_2 from 7 to 750 K to investigate anharmonicity and adiabatic electron-phonon coupling. First-principles calculations of phonons with a linear response method were performed at multiple unit cell volumes, and the Helmholtz free energy was minimized to obtain the lattice parameters and phonon dynamics at elevated temperature in the quasiharmonic approximation. Most of the temperature dependence of the phonon density of states could be understood with the quasiharmonic approximation, although there was also significant thermal broadening of the phonon spectra. In comparison to Mg_(0.75)Al_(0.25)B_2, in the energy range of 60 to 80 meV the experimental phonon spectra from MgB_2 showed a nonmonotonic change with temperature around 500 K. This may originate from a change with temperature of the adiabatic electron-phonon coupling.

Inelastic neutron scattering, lattice dynamics, and high-pressure phase stability of zircon-structured lanthanide orthophosphates

Inelastic neutron-scattering experiments and lattice-dynamical calculations are reported on a series of rare-earth orthophosphates $R{\text{PO}}_{4}$ ($R=\text{Tm}$, Er, Ho, and Tb). The experimental phonon spectra for the compounds are in good agreement with our model calculations. The lattice-dynamical model is found useful for the calculation of various thermodynamic properties such as the lattice specific heat, thermal expansion, and equation of state of these compounds. The $R{\text{PO}}_{4}$ compounds are known to transform to the scheelite (body-centered tetragonal, $I{4}_{1}/a$) or monoclinic phase $(P{2}_{1}/n)$ at high pressures. Our calculations show that while the scheelite phase stabilizes at high pressure due to its lower volume, the monoclinic phase may occur as an intermediate phase depending on the ionic size of the $R$ atom. The latter phase is stabilized at higher temperature (at high pressure) due to its high vibrational entropy. A pressure-temperature phase diagram is proposed.

Inelastic neutron scattering and lattice-dynamical calculations ofBaFe2As2

We report here extensive measurements of the temperature dependence of phonon density of states of ${\text{BaFe}}_{2}{\text{As}}_{2}$, the parent compound of the FeAs-based superconductors, using inelastic neutron scattering. The experiments were carried out on the thermal time-of-flight neutron spectrometer IN4 at the Institut Laue Langevin on a polycrystalline sample. There is no appreciable change in the spectra between $T=10$ and 200 K, although the sample undergoes a magnetic as well as a tetragonal-to-orthorhombic structural phase transition at 140 K. This indicates a rather harmonic phonon system. Shell-model lattice-dynamical calculations based on interatomic potentials are carried out to characterize the phonon data. The calculations predict a shift of the Ba phonons to higher energies at 4 GPa. The average energy of the phonons of the Ba sublattice is also predicted to increase on partial substitution of Ba by K to ${\text{Ba}}_{0.6}{\text{K}}_{0.4}$. The calculations show good agreement with the experimental phonon spectra and also with the specific-heat data from the literature.

Construction of a dynamical matrix for an HCP crystal using phonon data at the symmetry points of the Brillouin zone and elastic constants

General analytical expressions are obtained for the dynamical matrix D(k) and the elastic constants C ik in an HCP crystal in terms of the Born-von Karman (BvK) parameters. An analytical method is proposed for constructing D(k) on the basis of data about the phonon frequencies ω i (N) at the symmetry points of the Brillouin zone and the elastic constants C ik . A number of relations between the values of ω i (N) and C ik are presented for conventional interaction models. It is shown that the standard method for determining BvK parameters by fitting them to experimental phonon spectra in HCP lattices is, as a rule, ambiguous, whereas the analytical method proposed allows one to find all the solutions of the problem. The methods developed are illustrated by the construction of dynamical matrices for Tb, Sc, Ti, and Co.

Gold Nanostructures on TiOx/Mo(112) Thin Films

The structure and composition of Au nanostructures deposited on TiOx/Mo(112) films has been investigated based on first principles DFT calculations. The aim of the calculations is to identify plausible candidates for the structures generated under experimental conditions in the growth of Au/TiOx/Mo(112) films. To this end, both static and molecular dynamics (MD) calculations have been performed. Various Au coverages have been considered, low (below monolayer), medium (monolayer), and high (bilayer) coverages. An ab initio thermodynamic analysis shows that, at the experimental temperature and oxygen partial pressure, the Au monolayer forms a (1 × 1) Au/TiO3/Mo(112) structure. On the basis of the comparison of the computed and experimental valence bands, phonon spectra, and STM images, we propose a tentative assignment to a structure where Au chains are formed at the interface between the Mo support and the TiO3 film. The additional deposition of Au results in the formation of a bilayer (1 × 3) Au/TiO3/Mo(112) structure. Here, we observe the tendency for gold to aggregate and form nanowires with half of the Au atoms in contact with the TiO3/Mo(112) support and the rest forming a second layer. The top and bottom Au layers of the nanowire exhibit a different chemical nature.

Lattice vibrations of para-hydrogen impurities in a solid deuterium matrix: An inelastic neutron scattering study

In the present study, we report inelastic neutron scattering measurements from para-hydrogen defects in solid normal deuterium at three different concentrations (between 3% and 11%) using the time-of-flight spectrometer TOSCA-II. The measured double-differential cross sections give access to the self-inelastic structure factors for the ${\mathrm{H}}_{2}$ centers of mass. Corrected experimental data, analyzed through the Young-Koppel model and the Gaussian approximation, are transformed into defect densities of phonon states, which come out to be broad, structured, and nearly concentration independent. Two experimentally determined Bose-corrected spectral moments are found to be in agreement with independent estimates, providing a strong validation of our data reduction procedure. Subsequently, experimental phonon spectra are compared to three calculations, namely, a simple harmonic model at infinite dilution, a more advanced harmonic model with concentration effects, and finally a lattice dynamics simulation based on self-consistent phonon and coherent potential approximations. However, while the first part of the defect spectral density, attributed to the propagating modes, turns out to be roughly explained, the localized part is properly described by none of these models, except for its mean frequency position. The large overall width appears so far impossible to be reproduced, representing a challenge for the physicists involved in quantum dynamics simulations.

Inelastic neutron scattering and lattice dynamical calculation of negative thermal expansion compoundsCu2OandAg2O

Negative thermal expansion (NTE) is known in ${\mathrm{Cu}}_{2}\mathrm{O}$ below $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and in ${\mathrm{Ag}}_{2}\mathrm{O}$ up to its decomposition temperature of about $500\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Inelastic neutron scattering measurements in ${\mathrm{Cu}}_{2}\mathrm{O}$ and lattice dynamics calculations of NTE in both ${\mathrm{Cu}}_{2}\mathrm{O}$ and ${\mathrm{Ag}}_{2}\mathrm{O}$ are reported. The phonon density of states from a polycrystalline sample of ${\mathrm{Cu}}_{2}\mathrm{O}$ is measured using the triple-axis spectrometer at Trombay. A lattice dynamical model is used for the calculations of phonon frequencies and their pressure dependence in the entire Brillouin zone. The experimental phonon spectrum is in fair agreement with calculations. The calculated Gr\uneisen parameters for ${\mathrm{Cu}}_{2}\mathrm{O}$ have lower negative values in comparison with ${\mathrm{Ag}}_{2}\mathrm{O}$. This results in a smaller value of negative thermal expansion coefficient in ${\mathrm{Cu}}_{2}\mathrm{O}$, in fair agreement with the experimental data from the literature. An important librational mode is identified that is related to NTE. Variance of bond lengths $(⟨{u}_{\mathit{\text{bond}}}^{2}⟩)$ and their temperature dependence have been calculated and compared with extended x-ray absorption fine structure data that illustrates the nature of the $M\text{\ensuremath{-}}\mathrm{O}$ and $M\text{\ensuremath{-}}M$ $(M=\mathrm{Cu},\mathrm{Ag})$ bonds in these compounds.

Phonons in a one-dimensional Yukawa chain: Dusty plasma experiment and model

Phonons in a one-dimensional chain of charged microspheres suspended in a plasma were studied in an experiment. The phonons correspond to random particle motion in the chain; no external manipulation was applied to excite the phonons. Two modes were observed, longitudinal and transverse. The velocity fluctuations in the experiment are analyzed using current autocorrelation functions and a phonon spectrum. The phonon energy was found to be unequally partitioned among phonon modes in the dusty plasma experiment. The experimental phonon spectrum was characterized by a dispersion relation that was found to differ from the dispersion relation for externally excited phonons. This difference is attributed to the presence of frictional damping due to gas, which affects the propagation of externally excited phonons differently from phonons that correspond to random particle motion. A model is developed and fit to the experiment to explain the features of the autocorrelation function, phonon spectrum, and the dispersion relation.

Phonons in suspensions of hard sphere colloids: volume fraction dependence.

The propagation of sound waves in suspensions of hard sphere colloids is studied as a function of their volume fraction up to random close packing using Brillouin light scattering. The rich experimental phonon spectra of up to five phonon modes are successfully described by theoretical calculations based on the multiple scattering method. Two main types of phonon modes are revealed: Type A modes are acoustic excitations which set up deformations in both the solid (particles) and the liquid (solvent) phases; for type B modes the stress and strain are predominantly localized near the interface between the solid particles and the surrounding liquid (interface waves). While the former become harder (increase their effective sound velocity) as the particle volume fraction increases the latter become softer (the corresponding sound velocity decreases).

Temperature-dependent electron mobility and large polaron interpretation inBi12SiO20

The electron band mobility in ${\mathrm{Bi}}_{12}{\mathrm{SiO}}_{20}$ is determined down to 100 K by the holographic time of flight method. Data are presented for different crystals of different origins in the temperature range between 100 and 500 K. The observed mobility rises from $\ensuremath{\sim}1.7{\mathrm{cm}}^{2}{\mathrm{V}}^{\ensuremath{-}1}{\mathrm{s}}^{\ensuremath{-}1}$ at 500 K to $\ensuremath{\sim}10{\mathrm{cm}}^{2}{\mathrm{V}}^{\ensuremath{-}1}{\mathrm{s}}^{\ensuremath{-}1}$ at 190 K, and decreases again at lower temperature. We show that the data correspond to an intrinsic band mobility between 190 and 500 K. The temperature dependence of the mobility can be reproduced in this temperature range with a large polaron model that derives all its parameters from the experimental phonon spectrum of the material. A deviation from the large polaron prediction that takes place between 250 and 190 K, depending on the sample, can be ascribed to the influence of defects or impurities.

Lattice dynamics of the fullerenesMxC60

Lattice dynamical calculations of the phonon density of states of external modes are reported for ${\mathrm{K}}_{3}{\mathrm{C}}_{60},$ ${\mathrm{Rb}}_{3}{\mathrm{C}}_{60},$ and ${\mathrm{Rb}}_{6}{\mathrm{C}}_{60}$ using three different models of transferable interatomic potentials. On comparison with the experimental reported data, an interatomic potential consisting of Coulomb and short range interactions has been found most suitable to explain the phonon density of states of the systems studied. Calculations using the rigid molecular ion model have enabled assignment of various important features in the experimental phonon spectra in terms of the vibrations of different species.

原子間力第１及び第２微係数と弾性定数

Using the first-and second-derivatives of the effective interatomic potential in the microscopic electronic theory, the interatomic force constants are calculated for practical material Al with low density and for alkali metal K with high density. The interatomic force constants so obtained are in good agreement with those derived from fitting the experimental phonon spectra and give a set of important data for the binding forces of solids. Dynamical elastic constants are also calculated using the long-wave phonon method and are also compared with observed data from ultrasonic pulse method. The compressibility problem, proposed by Brovman and Kagan, is that the lattice dynamical method in terms of second-order perturbation based on the pseudopotential does not give the self-consistent results for calculation of the elastic constants accompanied by a volume change. This problem is studied quantitatively and is shown to be important for Al and K. Consecluently, the obtained data of the elastic constants C11, C12 and bulk modulus B related to volume change are in good agreement with the observed data in spite of introducing no adjustable parameter. Then, in quasi-harmonic approximation considering temperatureand pressure-dependence of the lattice constant, the temperature and pressure effect on the elastic constants are calculated. The obtained data are consistent with the qualitative tendency of observed data and are useful in studying the mechanical and thermal properties of theses materials.

Lattice dynamics of YBa2Cu3O7.

The lattice vibration of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ is investigated based on a distributed-multipole model. In this model, the interatomic potential is expressed by means of a multipole-multipole interaction. The dipole and quadrupole moments are taken into account as higher-order multipole moments in order to include structural anisotropy in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$. The quadrupole moments, as compared with the dipole moments, play an important role in the structural stability of this material. The phonon-dispersion relation and the density of states are calculated. The obtained neutron-weighted density of states gives good agreement with the experimental phonon spectrum. The relation between the vibrational properties of the oxygen atoms and the structural a-b anisotropy is discussed.

Effect of charge fluctuations on the phonon dispersion and electron-phonon interaction in La2CuO4.

In this paper we propose a formulation of the electronic density response that is well suited to investigate the influence of localization and delocalization properties of the electrons on the phonon dispersion and the electron-phonon interaction. The formalism is applied to study nonlocal, long-range, electron-phonon-interaction effects of the charge-fluctuation type in high-temperature superconductors, using ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ as an example. Some important features in the experimental phonon spectrum can be understood within such an approach. We discuss the modification of the usual picture of electron pairing, taking into account these nonlocal effects. In this context the symmetric apical oxygen breathing mode at the Z point is of special importance. In this vibration, nonlocal electron-phonon-interaction effects of the charge-fluctuation type are shown to generate in the metallic phase of ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ an interplane charge transfer that is blocked completely in the insulating phase if a strictly two-dimensional electronic structure is assumed. Very recently we became aware of unpublished experimental results where this previously undetected mode appears, unusually broad, as the highest ${\mathrm{\ensuremath{\Lambda}}}_{1}$ mode at the Z point, in agreement with our theoretical predictions for the insulating phase. Finally, our considerations point towards a simple structure that could be very effective for high-temperature superconductivity.

Lattice-mediated interaction of Cu2+ Jahn-Teller ions in insulating cuprates.

The interaction of the copper d orbitals with the lattice is investigated with the goal of finding the lattice and orbital ground state in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. Due to the considerable tetragonality of the crystal, the Kanamori interaction is strongly anisotropic. This results in a tendency to a lattice instability with rhombic distortion of the oxygen squares around the Cu ions. In the present approach, the experimentally observed partial occupation of ${\mathit{d}}_{3\mathit{z}}^{2}$-${\mathit{r}}^{2}$ orbitals can be accounted for by the Jahn-Teller effect. The renormalization of the phonon spectrum due to virtual ${\mathrm{Cu}}^{2+}$ d-d orbital transitions is calculated using appropriate electronic and phononic model parameters. A qualitative agreement with some features in the experimental phonon spectra is obtained.

Deformable shell description for the phonon spectra of semiconductors with unstable valency

The theory of interaction between charge-density distortions (CDD) and phonons is proposed for insulating crystals with soft intra-atomic modes. A general classification of the possible types of phonon renormalisation is given for cubic crystals with NaCl and CsCl structures. A novel excitonic mechanism of CDD is offered and additional dispersion of the phonon renormalisation due to non-locality of such excitons is discussed in comparison with the standard theory of CDD. The theory is applied to the special case of rare-earth semiconductors with unstable valency. In these systems the sources of such CDD modes are the dipole excitations of the f shells and the very soft monopole excitons corresponding to valency fluctuations. The theory is compared with the experimental phonon spectra of SmS.

Thermodynamic properties of anharmonic noble metals in terms of interatomic potentials from experimental phonon spectra

A new model interatomic pair potential derived from the experimental phonon spectra is applied to the investigation of the thermodynamical properties of anharmonic noble metals.

First-principles phonon spectra in Ca and Sr

Experimental phonon spectra for the fcc alkaline-earth metals Ca and Sr have only recently been obtained. First-principles, generalized-pseudopotential-theory predictions of these spectra, including the full effects of $d$-state hybridization, are reported and compared with these results. The overall agreement between theory and experiment is found to be quite good (within about 10%). In addition, anomalous behavior observed in the ${\mathrm{T}}_{1}$[110] branch for single-crystal Ca is also found theoretically.

Stochastic Trajectory Studies of Chemical Processes at Surfaces

AbstractClassical trajectory studies have been carried out of the dynamics of simple chemical processes at surfaces. Empirical potential energy hyper‐surfaces were employed. The motion of only a few (5 or 6) atoms in the immediate vicinity of the reactive event was followed explicitly. The effects of the remaining surface and bulk atoms were replaced by friction and random forces (with memory), constructed from experimental phonon spectra. Among the systems studied are inelastic scattering of N2 from Ag(111), and recombination of O with C on Pt(111). Particular attention was paid to the mechanisms of energy transfer and to the specificity of energy disposal in surface reactions.

Pseudopotential calculation of the vacancy formation energy in polyvalent metals

Values of the vacancy formation energy have been calculated in polyvalent metals Be, Mg, Zn, Tl, and Sc, without taking into account lattice relaxation energy. Parameters of the model pseudopotential used in the calculations were determined from experimental phonon spectra. Sensitivity of the quantities calculated to the choice of the approximation for exchange-correlation corrections in the dieletric function has been studied.