Phonon Bandwidths Research Articles

Universal disorder-induced broadening of phonon bands: from disordered lattices to glasses

The translational symmetry of solids, either ordered or disordered, gives rise to the existence of low-frequency phonons. In ordered systems, either crystalline solids or isotropic homogeneous continua, some phonons characterized by different wavevectors are degenerate, i.e. they share the exact same frequency ω; in finite-size systems, phonons form a discrete set of bands with nq(ω)-fold degeneracy. Here we focus on understanding how this degeneracy is lifted in the presence of disorder, and its physical implications. Using standard degenerate perturbation theory and simple statistical considerations, we predict the dependence of the disorder-induced frequency width of phonon bands to be , where σ is the strength of disorder and N is the total number of particles. This theoretical prediction is supported by extensive numerical calculations for disordered lattices—characterized by topological, mass, stiffness and positional disorder—and for computer glasses, where disorder is self-generated, thus establishing its universal nature. The predicted scaling of phonon band widths leads to the identification of a crossover frequency in systems of linear size L in dimensions, where the disorder-induced width of phonon bands becomes comparable to the frequency gap between neighboring bands. Consequently, phonons continuously cover the frequency range ω > ω†, where the notion of discrete phonon bands becomes ill-defined. Two basic applications of the theory are presented; first, we show that the phonon scattering lifetime is proportional to (Δω)−1 for ω < ω†. Second, the theory is applied to the basic physics of glasses, allowing us to determine the range of frequencies in which the recently established universal density of states of non-phononic excitations can be directly probed for different system sizes.

A Raman study of multiferroic LuMnO 3

Magnetic and dielectric measurements confirm the multiferroic nature of LuMnO 3. Raman spectra of LuMnO 3 have been recorded in the 77–800 K range covering both the antiferromagnetic transition at 90 K and the ferroelectric–paraelectric transition at 750 K. The changes in the phonon modes frequencies and band-widths indicate the presence of phonon–spin coupling in the antiferromagnetically ordered phase. The ferroelectric–paraelectric transition is accompanied by the broadening and disappearance of many of the phonon modes. Some of the phonon modes also show anomalies at the ferroelectric transition.

Optical properties of Yb-doped Y2SiO5 thin films

Yb-doped Y2SiO5 thin films Raman active phonons and crystal-field (CF) excitations have been studied by Raman spectroscopy and infrared transmission, and compared to the single crystals results. The thin films, grown on Y2SiO5 undoped substrate, have been co-doped with Ge, Gd or La in order to adjust the lattice mismatch. Raman active phonon bandwidths indicate that thin films present less strains and defects than single crystals. Interesting thin films properties, such as Yb3+ site occupancies and Yb3+–Yb3+ pair interaction types, may be adjusted by the co-dopants. Infrared absorption shows notably that La3+ is a good co-doping ion to enhance selectively one of the two Yb sites and pair satellite contributions. Ge and Gd co-dopants may also be used to form independently Yb3+–Yb3+ ion pairs with either ferromagnetic or antiferromagnetic dominant interactions.

Structural and Morphological Properties of 3,4,9,10-PeryleneTetraCarboxylic DiAnhydride Films on Passivated GaAs(100) Substrates

Raman spectroscopy is employed to investigate in situ the structural properties and the morphology of 3,4,9,10-Perylene-TetraCarboxylic DiAnhydride (PTCDA) films deposited onto S-GaAs(100) substrates at various temperatures. Additional two-dimensional Raman mapping measurements are carried out ex situ to extract information at the microscopic level. Complementary atomic force microscopy studies reveal that all the films consist of islands. The crystalline nature of these islands is proven by the observation of libronic phonon-like modes in the Raman spectra characteristic to the molecular crystal. The decrease in the phonon band widths observed at elevated substrate temperatures is related to an increase in the size of the crystalline domains and improvement of crystallinity. The PTCDA films consist of a mixture of two polymorphs α and β having the same symmetry and very similar lattice parameters. An estimation of the α- to β- content at microscopic level is obtained from the deconvolution of an internal Raman mode with C-H deformation character following a previously introduced model.

Structural and morphological properties of N, N′-dimethyl-3,4,9,10-perylenetetracarboxylic diimide films on passivated GaAs(1 0 0) substrates

Molecules of N, N′-dimethylperylene 3,4,9,10-dicarboximide (DiMe-PTCDI) were deposited by organic molecular beam deposition onto passivated GaAs(1 0 0) substrates in ultra high vacuum. Raman spectroscopy was employed to investigate in situ the influence of the substrate temperature during film growth on the structural properties and the morphology of organic films. Complementary scanning electron microscopy studies reveal that all the films consist of islands. The crystalline nature of these islands is proven by the observation of libronic phonon-like modes characteristic of the molecular crystal in the Raman spectra. The decrease in the phonon bandwidths observed at elevated substrate temperatures is related to an increase in the size of the crystalline domains and improved crystallinity.

Study of Raman active phonons in NdMnO 3

A g and B 2g Raman active modes in NdMnO 3 single crystals, grown by flux and floating zone techniques, have been studied in the temperature range from 4.2 to 300 K. Similar to orthorhombic LaMnO 3, the NdMnO 3 structure distorted by a static Jahn–Teller effect is consistent with the D 2h 16 space group. The observed phonon frequencies, intensities and bandwidths are influenced by the temperature evolution of the Mn 3+ magnetic sublattice and, particularly, the most intense B 2g mode (∼601 cm −1) softens below T N∼75 K following the paramagnetic to canted-antiferromagnetic phase transition.

High resolution Raman study of phonon and vibron bandwidths in isotopically pure and natural benzene crystal

The frequency and the bandwidth of the 12 Raman active lattice modes and of more than 45 internal vibrons of natural and C12 isotopically pure benzene have been measured under high resolution with the aid of a tandem interferometer–spectrometer system or alternatively of a two meter focal length grating Sopra spectrometer. For five lattice phonons and for several vibrons the measurements were extended to a sufficient temperature range to study the relaxation processes in terms of anharmonic phonon–phonon and phonon–vibron coupling processes. The effect of the isotopic impurities on the phonon lifetime has been shown to be very important for some vibrons, in particular, for those resonant with the impurity level. The bandwidth evolution with temperature has been interpreted in terms of down- and up- three- and four-phonon as well as of dephasing processes.

Neutron and Raman scattering studies of surface adsorbed molecular vibrations and bulk phonons in ZrO 2 nanoparticles

Inelastic neutron-scattering method (neutron spectroscopy) was applied to the study of the phonon densities of states of zirconia nanoparticles, the OH stretch vibrations of physisorbed water molecules and chemisorbed hydroxyl groups on the surface. Raman scattering was also used to measure the zone-center phonon modes. The observed distinct phonon frequencies and band widths at 10–120 meV reflect the different crystalline symmetries and compositional fluctuations in the small grain and interfacial regions of monoclinic ZrO 2, tetragonal or mixed cubic and tetragonal rare-earth-modified zirconia. The observed neutron spectra for pure ZrO 2, Ce 0.1Zr 0.9O 2 and Nd 0.1Zr 0.9O 1.95 display a band consisting of peaks at 25, 30, and meV and a broad band extending from 50 to 100 meV. The OH bonds in surface hydroxyl groups and water on these zirconias result in the different frequencies of the OH stretch vibrations at 400–600 meV.

Theory of anharmonic processes in crystals with isotopic impurities.

A theory of the influence of isotopic impurities on phonon frequencies and bandwidths, based on the formalism of the retarded Green's functions, is presented. The theory takes into account both harmonic and anharmonic processes in the crystal and yields a proper self-energy that includes impurity-activated contributions depending on the concentration of the impurities and on a parameter \ensuremath{\lambda} defined as the ratio of the mass difference to the mass of the impurity atoms. The theory is developed up to second order in the parameter \ensuremath{\lambda} and in the concentration of impurities. Central to the theory is the technique of averaging the anharmonic-phonon propagators over the ensemble of impurity configurations. This gives rise to a proper self-energy that includes harmonic and anharmonic contributions to both the phonon shift and damping. The most important result is that processes linear in the quartic anharmonicity, that in the pure crystal contribute only to the phonon shift, in the presence of isotopic impurities give rise also to a contribution to the damping.

Anharmonic lattice dynamics and computer simulation for simple model systems.

We have made anharmonic-lattice-dynamics calculations of phonon frequencies and bandwidths up to order ${\ensuremath{\lambda}}^{4}$ for simple model systems consisting of linear chains of diatomic and triatomic molecules, bound by van der Waals intermolecular forces. For each model we discuss the relevant relaxation mechanisms of the optical modes at the \ensuremath{\Gamma} point in terms of the anharmonic phonon-phonon coupling coefficients and of the phonon density of states. Calculated bandwidths and anharmonic shifts are compared to the results of computer simulations for the same models at various temperatures. The comparison shows that bandwidths calculated by the perturbative lattice-dynamics treatment to order ${\ensuremath{\lambda}}^{4}$ agree with those calculated in the computer simulation, thus showing that the imaginary part of the self-energy expansion converges already to this order. The convergence of the imaginary part of the self-energy is further investigated by a calculation of the contribution of some relevant diagrams of order ${\ensuremath{\lambda}}^{6}$ and ${\ensuremath{\lambda}}^{8}$ to the bandwidth of the internal modes. On the contrary, the real part of the self-energy converges much slower and therefore anharmonic shifts calculated by lattice dynamics are different from those obtained by computer simulation.

Raman phonon spectroscopic study of phase transition in o‐aminobenzoic acid crystal (II)

AbstractRaman phonon spectroscopy in the 10–150 cm−1 shift range was used to study the phase transition in an o‐aminobenzoic acid crystal (II). At 77 K, twelve distinct phonon modes are observed whereas at 300 K the spectrum shows ten phonon bands. The temperature dependence of the phonon frequencies and band widths suggests that the crystal goes through a phase transition at ca. 200 K. The temperature dependence of the internal modes predicts that the phase transition is associated with some structural change in the phenyl ring.

Electron-energy-loss spectroscopy of H adsorbed on Rh(100): Interpretation of overtone spectra as two-phonon bound states.

The vibrational properties of H adsorbed in the fourfold-hollow site on Rh(100) have been studied with high-resolution electron-energy-loss spectroscopy. At saturation coverage (one H per Rh atom), proper selection of the incident-electron energy and collection angle of the scattered electrons allow the detection of the symmetric (perpendicular) and asymmetric (degenerate parallel) fundamental transitions and five overtone transitions. The fundamental transitions exhibit significant frequency shifts as the H coverage is changed, establishing that H-H interactions are important in determining the local curvature of the adsorption potential-energy surface. Spectra of isotopically mixed layers (H and D) establish that significant dynamic coupling exists in both the parallel and perpendicular states at 1.0 monolayer coverage. The phonon bandwidths estimated from the isotope dilution experiments are 12--15 meV. The dynamic coupling is comparable to the local anharmonicity of the vibrational potential, and the overtones correspond to two-phonon bound-state excitations. A one-dimensional model of coupled, anharmonic oscillators is used to guide the interpretation of the overtone spectra. A qualitative interpretation of the spectra requires a proper accounting of the dispersion of both the fundamental and overtone excitations and indicates that the predominantly parallel polarized vibrations are extremely anharmonic, and the predominantly vertical polarized vibrations are only mildly anharmonic. Quantitative determination of the local anharmonicity requires a more detailed description of the H-H coupling than is currently available as the dispersion and anharmonicity are comparable.

On the dynamics of the phase transition in phenanthrene

The temperature dependence of the phonon frequencies and bandwidths has been studied using Raman spectroscopy between 293 and 350 K. It can be seen that in the region of the phase transition at≈347 K there is a change in the slope of both curves. We have tried to explain these features by means of reorientation of molecules. Calculations have revealed an additional minimum of the lattice energy where the molecules are rotated by an angle of 180° around their axes relatively to their room temperature position. The stability of this proposed structure has been further tested by the calculation of the dispersion curves. No imaginary frequencies have been detected for the wave vectors chosen. Also, there are no great differences in the phonon frequencies of the two structures for k = 0, as has also been observed in the spectra recorded.

Experimental studies of long life phonons in molecular crystals by high resolution raman spectroscopy

Using an interferometer-spectrometer in tandem with a limiting resolution of 0.005 cm-1 we have measured the band profiles of some low frequency Raman active phonons of monoclinic tetracyanoethylene (TCNE) and α-glycine at low temperature. In this latter case we obtained by deconvolution of the observed profiles residual bandwidths at T = 0 K as small as 0.004 cm-1 for two lattice phonons.The observed bandwiths are interpreted in terms of three-phonon decay processes and the most important relaxation mechanisms are determined. Correlation of the bandwidths with the one-and two-phonon density of states is used to localize the frequency range where decay into two acoustic phonons of the same energy is the dominant relaxation process.The present results are compared with those obtained previously for other molecular crystals such as naphthalene, anthracene and l-alanine. It is shown that at a given frequency the phonon bandwidths of the hydrogen bonded crystals are at least one order of magnitude smaller than those of the normal Van der Waals crystals. This effect is interpreted as due to the different anharmonicity of the intermolecular potential in the two cases.The evolution with temperature of the phonon bandwidths has been followed for α-glycine in the range 5-50 K. An excellent fit of the experimental data is obtained assuming a maximum of two preferential up-conversion decay mechanisms.

General theory of electronic transport in molecular crystals. I. Local linear electron–phonon coupling

An improved general theory of electronic transport in molecular crystals with local linear electron–phonon coupling is presented. It is valid for arbitrary electronic and phonon bandwidths and for arbitrary electron–phonon coupling strength, yielding small-polaron theory for narrow electronic bands and strong coupling, and semiconductor theory for wide electronic bands and weak coupling. Detailed results are derived for electronic excitations fully clothed with phonons and having a bandwidth no larger than the phonon frequency; the electronic and phonon densities of states are taken as Gaussian for simplicity. The dependence of the diffusion coefficient on temperature and on the other parameters is analyzed thoroughly. The calculated behavior provides a rational interpretation of observed trends in the magnitude and temperature dependence of charge-carrier drift mobilities in molecular crystals.

Dipole-dipole interaction and internal vibrations in molecular crystals

The contribution of long-range dipole-dipole forces to the energy of the internal modes in a series of molecular crystals has been evaluated using the Weald-Kornfeld summation method. Comparison with experimental infrared observations such as LO-TO and Davydov splittings, gas to crystal frequency shifts, band shapes, transition dipole moments, phonon bandwidths, is discussed.