Nonadiabatic effects in the lattice dynamics of compressed rare-gas crystals

Electron-ion contributions to the energy of rare-gas crystals are discussed from first principles in the framework of the Tolpygo model and its variants. The frequencies of phonons in a neon crystal at pressures p ≠ 0 are calculated in terms of models that go beyond the scope of the adiabatic approximation. Analysis of the contributions from different interactions to the lattice dynamics of the crystals demonstrates that the phonon frequencies calculated in the framework of the simplest model (allowing only for the nearest neighbors) and the most complex model (with the inclusion of the nearest neighbors, next-nearest neighbors, nonadiabatic effects, etc.) for small wave vectors are close to each other. The difference between the phonon frequencies calculated within the above models is most pronounced at the Brillouin zone boundary. Under strong compression, the phonon spectrum along the Δ direction is distorted and the longitudinal mode is softened as a result of the electron-phonon interaction. The contribution from terms of higher orders in the overlap integral S at p ≠ 0 to the phonon frequencies is more significant than that obtained in the band-structure calculations of the neon crystal.     

Phonons and electron-phonon interactions in rare-gas crystals at high pressures

The lattice dynamics of compressed rare-gas crystals is theoretically investigated within the ab initio approach in the framework of the Tolpygo model, which explicitly allows for the deformation of electron shells. The deformation of the electron shells is associated with the retardation of the electron response and treated as a nonadiabaticity (the electron-phonon interaction). This approach and the ab initio short-range repulsive potentials are used to construct the dynamic matrix, which makes it possible to calculate the phonon frequencies and the electron-phonon interaction of crystals in the series Ne-Xe at any point of the Brillouin zone. The contributions of the long-range Coulomb and van der Waals forces to the dynamic matrix are the structure sums that depend only on the lattice type. The structure sums for the face-centered cubic lattice are calculated using the Ewald and Emersleben methods, as well as the direct summation over the vectors of the face-centered cubic lattice. The use of 20 spheres in the last case provides an accuracy of no less than four significant figures. An analysis of the role played by the phonon-electron interaction at five points of high symmetry in the Brillouin zone (X, L, U, K, W) at high pressures demonstrates that not only the longitudinal phonon modes (at the points X and L) but also the transverse phonon modes (at the points U, K, and W) are softened. The inclusion of the electron-phonon interaction at the point X improves agreement between the theoretical and experimental phonon frequencies for the argon crystal.     

Lattice dynamics in heavy rare-gas crystals under pressure

The lattice dynamics of compressed rare-gas crystals is theoretically investigated within the ab initio approach in the framework of the Tolpygo model, which explicitly includes the deformation of electron shells in the dipole approximation. The phonon frequencies of compressed rare-gas crystals are calculated with allowance made for the electron-phonon interaction at the mean-value points with the use of the dynamic matrix constructed with the ab initio short-range repulsive potential. The energy of zero-point vibrations and the heat capacity of compressed krypton and xenon face-centered cubic crystals are calculated in the harmonic approximation. The calculated temperature dependences of the specific heat capacity and the Debye temperature are in good agreement with the data available in the literature on the experiment at zero pressure and the results of the calculations within the density-functional theory for all pressures. The quantum effects, in particular, the energies E _zp of zero-point vibrations for krypton and xenon crystals, are investigated at different pressures.     

Lattice dynamics of MF3 crystals (M = Al, Ga, and In)

The phonon spectra, Born effective charges, and dielectric constants ε_∞ for the □AlF₃, □GaF₃, and □InF₃ crystals (where □ is a vacancy) have been calculated in terms of the generalized Gordon-Kim method. The calculated spectra of lattice vibrations contain no imaginary vibrational frequencies. This suggests the stability of the cubic phase of these compounds but contradicts the observable structural transition from cubic to rhombohedral phase. It is assumed that such a transition in the □AlF₃, □GaF₃, and □InF₃ crystals is brought about by structural defects. The calculated spectrum of lattice vibrations of the “completely defective” crystal M□F₃ (M = Al, Ga, and In) indicates a strong instability of the cubic phase. Within the mean crystal approximation, the cubic phase of M _x M _1?x F₃ crystals appears to be unstable at small x≤0.05.     

Longitudinal-phonon relaxation mechanisms in cubic crystals of germanium,silicon, and diamond

The relaxation rates of thermal and high-frequency longitudinal phonons are calculated using an anisotropic-continuum model. Three-phonon scattering mechanisms (L ? L + L, L ? T + L) for the phonon relaxation are considered. Anisotropic anharmonic phonon scattering in cubic crystals is described in terms of the second-and third-order elastic moduli. The parameters determining the longitudinal-phonon relaxation rates are found for germanium, silicon, and diamond crystals. The long-wavelength limit and the transition to the isotropic-medium model are considered, and the dependences of the relaxation rates of thermal and high-frequency phonons on temperature and phonon wave vector are analyzed for these crystals.     

Raman phonon spectra and lattice dynamics of 9,10-dinitroanthracene under pressure

Abstract

Raman phonon spectra of 9, 10-dinitroanthracene have been recorded in the pressure range 0-6GPa. No phase transition is detected up to the maximum pressure studied. Quasi Harmonic Lattice Dynamics calculations, based on an atom-atom potential previously modeled on homologous 9,10-disubstituted anthracenes, have been performed. The optimized potential was used to calculate the equilibrium geometry and the lattice phonon frequencies as a function of pressure. The calculated structure at ambient conditions closely resembles the experimental one. The calculated phonon frequencies show a good agreement with the experimental values at all pressures measured.     

Normal and “Anomalous” isotope shifts of phonon frequencies in mono- and polyisotopic germanium crystals

The shifts of the phonon frequencies in ⁷⁰Ge and ⁷⁴Ge monoisotopic crystals have been studied using inelastic neutron scattering. It has been shown that the frequency shifts for all of the branches are normal, i.e., inversely proportional to √M. At the same time, the gap between acoustic and optical frequencies in monoisotopic crystals appears to be much wider (by about 2 meV in the [111] direction) than that in natural polyisotopic crystals containing “isotopic defects.” In this case, the phonon frequencies undergo “anomalous” shifts; i.e., the oscillation frequency of the heavier isotope is higher than that for the lighter isotope. The effect is in qualitative agreement with old theoretical calculations of the effect of mass defects on the phonon spectra of diatomic lattices.     

Vibrational properties of single-wall BC3 nanotubes

The phonon dispersions of single-wall BC₃ nanotubes with any chirality are calculated within a symmetry-based force constant model of the lattice dynamics. Based on the non-symmorphic symmetry group of the BC₃ tubes, the symmetries and number of the Raman- and infrared-active modes at Γ point of the one-dimensional Brillouin zone are given. The neighbor atom-atomic interaction force constants are recalculated by fitting them to the experimental phonon energy-dispersion curves of honeycomb BC₃ sheet. The frequencies of the optically active modes are presented as the function of diameters and chiralities for BC₃ tubes. The obtained phonon density-of-states spectra, phonon dispersion relations, and vibrational patterns of the zone-center phonons are presented and discussed in detail. The calculated frequencies of infrared-active modes are compared with the experimental values reported in the literature. The results provide comprehensive information about the vibrational properties of the BC₃ tubes and shed light on the interpretation of Raman scattering and infrared spectroscopies.     

Characteristics of F centers in the ground and excited states in alkali halide crystals

The molecular-statics method and the Gourary-Adrian approach are used to calculate the displacements of the lattice ions nearest to the F center in alkali halide crystals with NaCl and CsCl structures (altogether, twenty crystals). The calculations are performed for the 1s and 2p states of the F-center electron with allowance for the angular dependence of the Coulomb potential created by the electron in the 2p state. The absorption and emission energies of the F center are calculated. The calculated energies agree qualitatively with experiment and reproduce the experimentally found tendencies of changes in these energies when going from one crystal to another.     

Indirect electronic transitions in alkali halate crystals-I (sodium and potassium chlorate crystals)

The long wavelength tail of the fundamental absorption in NaClO₃ and KClO₃ crystals has been analysed based on the theory of band to band transitions of Bardeen et al.[8] developed in the case of semi-conducting crystals. Evidence of phonon involvement in the transitions giving an indirect band gap is observed. The energies of the phonons involved in the process are the same for both the crystals, and agree well with combinations of prinicple frequencies of ClO₃^? ion, their overtones and also lattice phonons. The indirect band gap in these crystals varies with temperature more or less linearly and the rate of variation is ?3·8 × 10^?4 eV/K and ?5·0 × 10^?4 eV/K for sodium chlorate and potassium chlorate respectively.     

Structure and lattice dynamics of rare-earth ferroborate crystals: Ab initio calculation

The ab initio calculation of the crystal structure and the phonon spectrum of crystals RFe₃(BO₃)₄ (R = Pr, Nd, Sm) has been performed in the framework of the density functional theory. The ion coordinates in the unit cell, the lattice parameters, the frequencies and the types of fundamental vibrations, and also the intensities of lines in the Raman spectrum and infrared reflection spectra have been found. The elastic constants of the crystals have been calculated. For low-frequency A₂ mode in PrFe₃(BO₃)₄, a “seed” vibration frequency that strongly interacts with the electronic excitation on a praseodymium ion was found. The calculation results satisfactory agree with the experimental data.     

Dispersion properties of two-dimensional phonon crystals with a hexagonal structure

Acoustic and optical properties of two-dimensional phonon crystals with a hexagonal symmetry are described. Differential-difference equations describing plane oscillations of a two-dimensional lattice of material structures are derived in a harmonic approximation, and dispersion dependences of acoustic and optical phonons are calculated. Branches of optical oscillations and intervals of forbidden frequencies are shown to appear when a lattice consists of two types of atoms.     

Lattice dynamics in light rare-gas crystals under pressure

The lattice dynamics of compressed neon and argon crystals has been theoretically investigated within the ab initio approach in the framework of the Tolpygo model, which explicitly includes the deformation of electron shells. The energy of zero-point vibrations, mean-square displacements, and specific heat capacities of compressed neon and argon face-centered cubic crystals have been calculated in the harmonic approximation using the dynamic matrix constructed with the ab initio short-range repulsive potential and integration over the mean-value points in the Brillouin zone. The calculated temperature dependences of the specific heat capacity and the Debye temperature are in good agreement with the data available in the literature on the experiment at zero pressure. The role of zero-point vibrations in the thermodynamics of the entire series of rare-gas crystals and, in particular, in the validity of the Lindemann melting criterion has been analyzed.     

Lattice dynamics of corundum crystals with vacancies in various charge states

The lattice dynamics of an α-Al₂O₃ crystal with vacancies in various charge states is simulated using the recursive method in the shell model. The frequencies of resonant vibrations induced by defects in various directions are calculated. Characteristic features in vibrational spectra of anion-nonstoichiometric α-Al₂O₃ crystals, mostly associated with changes in the effective interaction between vacancies and the nearest neighbor atoms, are analyzed and explained.     

Phonon propagation through photonic crystals—media with spatially modulated acoustic properties

The thermal conductivity κ of photonic crystals differing in degree of optical homogeneity (single crystals of synthetic opals) was measured in the 4.2–300 K temperature range. The thermal conductivity revealed, in addition to the conventional decrease in comparison with solid amorphous SiO₂ characteristic of porous solids, a noticeable decrease for T<20 K, the range wherein the phonon wavelength in amorphous SiO₂ approaches the diameters of the contact areas between the opal spheres. This effect is enhanced in the case of phonon propagation along the SiO₂ sphere chains (six directions in the cubic opal lattice). The propagation of light waves (photons) through a medium with spatially modulated optical properties (photonic crystals) is presently well studied. The propagation of acoustic waves through a medium with spatially modulated acoustic properties (phononic crystals) may also reveal specific effects, which are discussed in this paper; among them are, e.g., the ballistic mode of phonon propagation and waveguide effects.     

Inelastic neutron scattering to very high pressures

Progress in high-pressure and neutron scattering methods has recently allowed measurements of phonon dispersion curves of simple solids at high pressures to 10 GPa. In this technique single crystals of 10–25 mm³ volume are compressed by the Paris-Edinburgh cell and the phonon frequencies are measured on high-flux triple axis spectrometers. Detailed studies of the lattice dynamics of low-compressible systems are feasible, including measurements of mode Grüneisen parameters, elastic constants, and precursor effects of phase transitions. We describe the experimental set-up and illustrate its potential by results on semiconductors (Ge and GaSb) and metals (Fe and Zn) obtained at the LLB (Saclay) and ILL (Grenoble) reactor sources. This revised version was published online in July 2006 with corrections to the Cover Date.     

Far-infrared reflection spectra,TO- and LO-phonon frequencies,coupled and decoupled plasmon-phonon modes,dielectric constants,and effective dynamical charges of manganese,iron, and platinum group pyrite type compounds

The far-infrared reflection spectra of hot-pressed samples of the pyrites MX₂ with M = Mn, Fe, Ru, and Os and X = S, Se, and Te and PtY₂ with Y = P, As, and Sb are presented in the range from 40 to 700 cm^?1. The spectra show five reststrahlen bands and more or less free carrier contributions due to deviation from stoichiometry. The oscillator parameters ω_j, ρ_j, γ_j, ω_p, and γ_o, the transverse optical phonon frequencies ω_TO, and the coupled plasmon-phonon frequencies Ω₊ and Ω_? were calculated. The uncoupled longitudinal optical phonon frequencies ω_LO were determined from ?Im $\text{(}\text{1}\text{}\text{?}\text{ge}\text{)}$ of the plasmon-free phonon spectra calculated from the oscillator parameters, neglecting the free carrier contributions. The obtained effective ionic charges (Szigeti charges) reveal an increasing covalency of the pyrites in the order pnictides > chalcides and Fe > Ru > Os > Mn compounds. The phonon frequencies reflect the increasing bond strengths on going from 3d to 4d and 5d metal compounds, discussed in a former work (Phys. Chem. Miner.9, 109 (1983)). The true intensities of the phonon modes for using them with respect to lattice dynamical calculations are discussed.     

Calculation of the lattice dynamical properties of Ge

The lattice dynamical properties of Ge are studied employing a frozen phonon approach within an ab initio density-functional pseudopotential formalism. Using the atomic number, atomic mass, and crystal structure as the only input information, we calculate phonon frequencies and mode Grüneisen parameters at Γ and X and the third-order anharmonic parameter for the zone center optical mode. The results are in excellent agreement with available experimental data. An analysis of various energy contributions to the TA (X) mode shows that the proper inclusion of the exchange-correlation energy is crucial for accurate microscopic studies of lattice dynamics.     

Comparison of the molecular cluster model with the phonon model for Jahn—Teller active impurities in crystals

For comparing the molecular cluster model with the phonon model in describing the Jahn-Teller interaction for magnetic impurities in crystals, the Jahn-Teller energy and the Ham reduction factors are expressed in terms of the phonon Green's function of the host crystal for an orbital triplet coupled to E_g modes of vibrations. Numerical results for the case of MgO lattice have been obtained using the phonon Green's function derived from the breathing shell model.     

Vibrational spectra and elastic,piezoelectric, and magnetoelectric properties of HoFe3(BO3)4 and HoAl3(BO3)4 crystals

Raman spectra of light are obtained for HoFe₃(BO₃)₄ and HoAl₃(BO₃)₄ crystals at various temperatures and are used for determining the frequencies of crystal lattice vibrations at the center of the Brillouin zone. It is also found that the HoFe₃(BO₃)₄ crystal exhibits a phase transition at T _c ≈ 366 K. The magnetoelectric effect in the paramagnetic phase of these compounds is studied experimentally. The lattice vibration frequencies, elastic and piezoelectric moduli, Born dynamic charges, and the high-frequency permittivity are calculated using the density functional method. A peculiar behavior of the transverse acoustic vibration branch is observed in the Γ → Z direction of the Brillouin zone of the HoFe₃(BO₃)₄ crystal. The electric polarization induced by an external field is estimated using the calculated values of piezoelectric moduli and experimental values of magnetostriction.