Statistical analysis of spectra of single impurity molecules and dynamics of disordered solids: II. Manifestation of interaction of two-level systems with impurity molecules at different distances

Manifestations in the spectra of impurity chromophore molecules in a disordered solid matrix of the interaction of these molecules with two-level systems (TLSs) of the matrix are analyzed. The characteristic distances within the limits of which the interaction between TLSs and an impurity molecule leads, in the main, to either splitting or broadening of the spectrum, as well as the distance beginning with which this interaction is practically undetectable, are determined. Information about the effective value of the minimal distance between impurity molecules and TLSs, which is caused by nonzero sizes of the molecules and the TLSs, is presented. The analysis is performed by a statistical processing of experimental and model spectra of single tetra-tert-butylterrylene molecules in amorphous polyisobutylene at a temperature of 2 K, when the contribution of quasi-local low-frequency vibrational modes of the matrix to these spectra can be neglected.     

Low-temperature dynamics of amorphous polymers and evolution over time of spectra of single impurity molecules: II. Model calculations and analysis of results

The results of a statistical analysis of the spectra of single molecules of tetra-tert-butylterrylene in amorphous polyisobutylene at temperatures of 2, 4.5, and 7 K are presented. Model calculations of such spectra for this system are performed in the context of the stochastic theory of the spectra of single molecules in lowtemperature glasses. Analysis of the multiplet structure of the experimental and model spectra made it possible to obtain data about the minimal distance between impurity chromophore molecules and two-level systems and about the distribution parameters of their coupling constant. The interaction of a chromophore with quasilocal low-frequency vibrational modes of the matrix was found to influence the structure and parameters of the spectra observed. The model calculations performed showed that the specific structure of the spectra of single molecules at low temperatures is determined by the interactions with a small number of nearby two-level systems.     

Statistical analysis of spectra of single impurity molecules and dynamics of disordered solids: I. Distributions of linewidths,moments, and cumulants

A review of recent results of studying the low-temperature dynamics of a disordered solid-state medium that were obtained by the method of single molecule spectroscopy (SMS) is presented. The studies were carried out with the use of the new approach of the statistical analysis of a large number of spectra of single molecules embedded into a medium under study as a microscopic spectral probe. The measurements were performed in the range 2–7 K. The use of SMS allowed us to avoid the information losses connected with the averaging over an ensemble of impurity molecules that is inherent in conventional spectral methods. For the example of the system studied (amorphous polyisobutylene doped with molecules of tetra-tert-butylterrylene), it was shown experimentally that, at low temperatures, the spectra of single impurity molecules in disordered media obey the Levy statistics. New microscopic information on the interaction of two-level systems and quasi-local low-frequency vibrational modes of the matrix with impurity molecules in a disordered medium was obtained.     

Observation of structural relaxations in disordered solid media via spectral histories of single impurity molecules

This paper presents the technique and results of the investigation of the structural relaxation in disordered solid media (polyisobutylene, toluene, ortho-dichlorobenzene) at temperatures below the glass transition point via the spectra and fluorescence images of single impurity fluorescent molecules (terrylene, tetra-tert-butylterrylene). Application of the thermal-cycling method has made it possible to significantly extend the temperature range of investigation (from 4.5 K to the glass transition temperature). The changes observed in individual parameters of low-energy elementary excitations of the tunneling and vibrational types due to structural relaxation processes have been studied. It has been found that there is a spatial inhomogeneity in the distribution of the activation temperatures of local relaxation processes.     

Low-temperature dynamics of amorphous polymers and evolution over time of spectra of single impurity molecules: I. Experiment

The optical dynamics of a doped amorphous system, tetra-tert-butylterrylene in amorphous polyisobutylene, has been experimentally studied by the spectra of single impurity molecules measured at temperatures of 2, 4.5, 7, and 15 K. The study of the temporal evolution of the fluorescence excitation spectra of the molecules under consideration made it possible to unambiguously establish the individual identity of the spectra of particular molecules and to analyze their multiplet structure. Repeated scanning of a selected spectral range with subsequent summation of the data made it possible to considerably reduce the errors that arise upon single scanning of the spectra of single molecules. The majority of the spectral trails detected were in agreement with the model of two-level systems. Jumps of spectral lines due to transitions in such systems were observed at all temperatures.     

Optical phonon spectra of PbF2 single crystals

The spectra of dipole-active optical phonons are measured for the cubic and orthorhombic phases of PbF₂ single crystals. The frequencies and eigenvectors of normal modes in the Pnma orthorhombic phase are calculated. It is found that the spectrum of the cubic phase exhibits excess vibrational modes of the PbF₂ orthorhombic phase.     

Femtosecond dynamics of primary processes in visual pigment rhodopsin

The dynamics of the coherent photoisomerization of the 11-cis-retinal in bovine rhodopsin is studied by femtosecond time-resolved laser absorption spectroscopy with a resolution of 30 fs. Rhodopsin is excited with 500-, 535-, and 560-nm femtosecond pulses to produce different initial Franck-Condon states with different vibrational energies of the molecule in its electronically excited state. The time evolution of the photoinduced differential absorption spectra of rhodopsin is measured upon excitation with a femtosecond pulse in a spectral range from 400 to 720 nm. Oscillations in the time-resolved absorption of the rhodopsin photoproducts, such as photorhodopsin with a vibrationally excited all-trans-retinal and in its initial-state rhodopsin with a vibrationally excited 11-cis-retinal, are examined. It is demonstrated that these oscillations reflect the dynamics of coherent vibrational wavepackets. The Fourier transform of these oscillatory components yields frequencies, amplitudes, and initial phases of various vibrational modes involved in the motion the wavepackets in both photoproducts. The main vibrational modes manifest themselves at frequencies of 62 and 160 cm^?1 for photorhodopsin and 44 and 142 cm^?1 for initial-state rhodopsin. It is shown that these vibrational modes are directly involved in the coherent reaction under the study, with their amplitudes in the power spectrum produced by the Fourier transform of the kinetic curves being dependent on the wavelength of rhodopsin excitation.     

Discrete breather on the edge of the graphene sheet with the armchair orientation

Linear and nonlinear vibrations of a graphene nanoribbon with free armchair edges subjected to tensile deformation have been studied by atomistic simulation methods. It has been shown that the phonon modes are split into two subsets. Atoms in some (XY) modes vibrate in the nanoribbon plane and in other (Z) modes vibrate along the normal to this plane. The possibility of the excitation of a gap discrete breather in an extended nanoribbon in the spectrum of the Z modes, the frequency of which lies in the gap of the spectrum of the XY modes, has been demonstrated. This breather is a large-amplitude vibrational mode in the XY plane localized on the four atoms on the nanoribbon edge. The breather is unstable with respect to small perturbations in the form of displacements of atoms out of the nanoribbon plane. Nevertheless, the discrete breather decays slowly owing to its weak interaction with the Z modes, so that its lifetime can be on the order of 103 vibrational periods.     

Neutron inelastic scattering spectrum and valence force field for neopentane

The neutron inelastic scattering spectrum of neopentane has been measured between 10 and 2000 cm^?1. A partial reassignment of the normal modes of vibration is presented. A vibrational analysis based on the Snyder and Schachtschneider valence force field has been carried out using the frequencies of neopentane and neopentane-d₁₂. The calculated neutron spectrum, using our new force field, is found to be in good agreement with the observed neutron data.     

The phonon densities of states of trigonal,vitreous and red amorphous selenium

For trigonal, vitreous and red amorphous Se the phonon densities of states F(hω) have been determined by inelastic neutron scattering from powder samples. For trigonal Se F(hω) is compared with the phonon dispersion measured by Teuchert[1] and a frequency spectrum derived from a model calculation by Etchepare et al.[2]. This calculation helps interpreting the changes in characteristic vibrational modes when going from the ordered to the disordered phase of Se. It is shown that at present, however, the models for trigonal Se are not good enough to calculate a reliable F(hω). The ω-dependence of F(hω) at low frequencies nicely confirms the predictions of a model which was developed for high polymeric chains by Genensky et al.[3]. For all three modifications the lattice specific heat c_v(T) was deduced from the phonon spectra. The data obtained for the different modifications are compared among each other and also with the measured data of Grosse et al.[4] (c_v(T) for red amorphous Se has not been measured before). From our data as well as from the c_p-data of Grosse the Debye temperatures as a function of temperature have been calculated. For vitreous Se between 10 and 160 K the agreement is excellent, for trigonal Se there are certain deviations which are discussed.     

Vibrational dynamics of Fe in amorphous Fe–Sc and Fe–Al alloy thin films

The atomic vibrational dynamics of ⁵⁷Fe in 800-Å thick amorphous (a-) ⁵⁷Fe_0.25Sc_0.75, a-⁵⁷Fe_0.67Sc_0.33 and a-⁵⁷Fe_0.14Al_0.86 alloy thin films has been investigated at room temperature by nuclear resonant inelastic X-ray scattering (NRIXS) of synchrotron radiation. The amorphous phase has been successfully stabilized by codeposition of Fe and Sc or Al in ultrahigh vacuum onto substrates held at –140 °C during deposition. The amorphous structure of the samples was confirmed by X-ray diffraction and conversion electron Mössbauer spectroscopy. The ⁵⁷Fe-projected partial vibrational density of states, g(E), has been obtained from the measured NRIXS vibrational excitation probability, together with thermodynamic quantities such as the probability of recoilless absorption (f-factor), the average kinetic energy per Fe atom, the average force constant, and the vibrational entropy per Fe atom. A plot of the reduced density of states, g(E)/E², versus excitation energy E proves the existence of non-Debye-like vibrational modes (boson peak) with a peak energy, E _bp , in the range of 3–7 meV. Both, the boson peak height H _bp and E _bp were found to depend on the composition. Above the boson peak, g(E)/E² exhibits an exponential decrease. Our results demonstrates that the features of the boson peak depend on the amount and type of element M (M = Al, Si, Mg, Sc).     

Expansion of monomer units in poly(ethylene terephthalate) molecules under conditions of thermal and zero-point atomic vibrations

The temperature dependence of the expansion ?_C of trans conformers of the carbon skeleton of macromolecules in crystallized and amorphous poly(ethylene terephthalate) (PET) due to zero-point and thermal atomic vibrations is investigated by IR spectroscopy. It is found that the thermal expansion coefficient β_C jumpwise increases at the characteristic temperatures T _t and T _b. This increase is associated with the crossover from the quantum to classical statistics of torsional and bending vibration modes. The quantum and classical contributions to the expansion ?_C are determined for each mode. The quantum and classical contributions of the torsional vibrational mode in the amorphous polymer are approximately 1.5 times larger than those in the crystallized polymer. This effect is caused by an increase in the anharmonicity of torsional vibrations in the amorphous polymer.     

Mössbauer spectroscopical investigation of amorphous Fe–Y alloy ribbons prepared by melt spinning

Fe–Y amorphous alloy ribbons were prepared by the melt spinning method and characterized by X-ray diffraction, Mössbauer spectroscopy and inelastic neutron scattering. X-ray diffraction demonstrates that the Fe_0.7Y_0.3 ribbons are completely amorphous, whereas the Fe_0.3Y_0.7 ribbons contain a small fraction of crystalline Y precipitates in the amorphous Fe–Y matrix. Mössbauer spectroscopy between 4.2 to 300 K reveals the amorphous nature of the Fe–Y matrix and the Fe_0.7Y_0.3 ribbons. The preliminary neutron scattering results S(Q, ω) show excess low energy vibrational modes which gives rise to the so called “boson peak” in this amorphous material.     

Instability of vibrational modes in hexagonal lattice

The phenomenon of modulational instability is investigated for all four delocalized short-wave vibrational modes recently found for the two-dimensional hexagonal lattice with the help of a group-theoretic approach. The polynomial pair potential with hard-type quartic nonlinearity (β-FPU potential with β > 0) is used to describe interactions between atoms. As expected for the hard-type anharmonic interactions, for all four modes the frequency is found to increase with the amplitude. Frequency of the modes I and III bifurcates from the upper edge of the phonon spectrum, while that of the modes II and IV increases from inside the spectrum. It is also shown that the considered model supports spatially localized vibrational mode called discrete breather (DB) or intrinsic localized mode. DB frequency increases with the amplitude above the phonon spectrum. Two different scenarios of the mode decay were revealed. In the first scenario (for modes I and III), development of the modulational instability leads to a formation of long-lived DBs that radiate their energy slowly until thermal equilibrium is reached. In the second scenario (for modes II and IV) a transition to thermal oscillations of atoms is observed with no formation of DBs.     

Cr3+−Cr3+ excited state Raman scattering from molecular vibrations in binuclear Cs3Cr2Cl9 induced by exchange striction

On increasing the temperature, several new bands appear at higher energy from their parent vibrational modes in the Raman spectrum of the molecular complex Cr₂Cl^3?₉. The parent and new bands have intensities that follow the thermal population factors of various ⁴A_2g⁴A_2g Cr³⁺ pair states. This behaviour is attributed to exchange striction which produces a change in vibrational energy with excited state for those normal modes with large net axial Cr³⁺?Cr³⁺ displacements.     

The role of interdiffusion and spatial confinement in the formation of resonant raman spectra of Ge/Si(100) heterostructures with quantum-dot arrays

The phonon modes of self-assembled Ge/Si quantum dots grown by molecular-beam epitaxy in an apparatus integrated with a chamber of the scanning tunneling microscope into a single high-vacuum system are investigated using Raman spectroscopy. It is revealed that the Ge-Ge and Si-Ge vibrational modes are considerably enhanced upon excitation of excitons between the valence band Λ₃ and the conduction band Λ₁ (the E ₁ and E ₁ + Δ₁ transitions). This makes it possible to observe the Raman spectrum of very small amounts of germanium, such as one layer of quantum dots with a germanium layer thickness of ≈10 Å. The enhancement of these modes suggests a strong electron-phonon interaction of the vibrational modes with the E ₁ and E ₁ + Δ₁ excitons in the quantum dot. It is demonstrated that the frequency of the Ge-Ge mode decreases by 10 cm^?1 with a decrease in the thickness of the Ge layer from 10 to 6 Å due to the spatial-confinement effect. The optimum thickness of the Ge layer for which the size dispersion of quantum dots is minimum is determined.     

Atomic vibrational dynamics of amorphous Fe-Mg alloy thin films

The atomic vibrational dynamics of ⁵⁷Fe in 800-Å thick amorphous Fe_xMg_1−x alloy thin films (0.3≤x≤0.7) has been investigated at room temperature by nuclear resonant inelastic X-ray scattering (NRIXS) of 14.4125 keV synchrotron radiation. The amorphous phase has been successfully stabilized by codeposition of Fe and Mg in ultrahigh vacuum onto a substrate held at −140 °C during deposition. The amorphous structure of the samples was confirmed by X-ray diffraction and conversion electron Mössbauer spectroscopy. The ⁵⁷Fe-projected partial vibrational density of states, g(E), has been obtained from the measured NRIXS vibrational excitation probability, together with thermodynamic quantities such as the probability of recoilless absorption (f-factor), the average kinetic energy per Fe atom, the average force constant, and the vibrational entropy per Fe atom. A plot of g(E)/E² versus E proves the existence of non-Debye-like vibrational excitations with a peak at E_bp∼3-5 meV (boson peak). Both the boson peak height and E_bp were found to depend linearly on the composition x. Above the boson peak, g(E)/E² exhibits an exponential decrease.     

Line phosphorescence spectrum of octachlorodibenzo-p-dioxine at 4.2 K

The line phosphorescence spectrum of octachlorodibenzo-p-dioxine (OCDX) is obtained and interpreted. The symmetry of the lowest triplet state of this molecule is established. The vibrational frequencies found from the vibronic phosphorescence spectrum at 4.2 k are assigned to the vibrational modes of certain symmetry related to individual functional atomic groups of the molecule. The relation between contributions from the spin-orbit (SO) and vibronic-spin-orbit (VSO) interactions to the phosphorescence rate constant k _ph of the OCDX molecule is found from the vibronic line intensities. It is found that the increase in the number of Cl atoms in OCDX compared to that in tetrachlorobenzo-p-dioxine results in the increase in the relative contribution of the VSO interaction to k _ph.     

A cellular model for the specific heat of amorphous solids at low temperatures

The wave equation for a non-homogeneous continuum with a statistical mass-density distribution is studied as a model for the vibrational specific heat of amorphous solids. The frequency spectrum is calculated for the simple case of small homogeneous cells separated from each other by hard and soft boundary walls distributed at random. The usual bulk mode density is enhanced by a positive constant term yielding the specific heat AT + BT³. From experimental values of the constants A, an upper limit of about 70 Å is calculated for the average cell diameter in vitreous SiO₂ and GeO₂.     

Terahertz absorption spectrum of D2O vapor

The absorption spectrum of D₂O vapor from 0.2 to 2.0 THz (6.7-67 cm⁻¹) which is associated with rotational modes was measured at one atmosphere using terahertz time-domain spectroscopy (THz-TDS). The linewidth and collisional dephasing times were measured for 26 pure rotational transitions in the ground vibrational state (0 0 0). The temperature dependence of the linewidth (Δν) behaves as Δν ∼ T^−3/4 and the linewidth decrease with increasing temperature is attributed to the 1/r⁶ force of interaction between colliding D₂O molecules.