Lyddane-Sachs-Teller Relation Research Articles

Generalized Lyddane-Sachs-Teller relation and disordered solids.

The realization that the Lyddane-Sachs-Teller (LST) relation can be presented in a particular second-moment representation with the use of only sum rules and causality provides a new way to characterize the electrodynamic response of disordered solids. In this paper we extend this idea in three different directions. (1) The individual second moments of the frequency-dependent transverse and longitudinal dielectric response functions are obtained for the case of multiple dispersion oscillators in high-symmetry crystals, and the generalized LST relation is recovered. (2) The fluctuation-dissipation theorem is used to show the connection between the second moments in ordered or disordered solids and the corresponding mean-square fluctuating polarization densities, thus relating these fluctuations with the generalized LST relation. (3) The moment representation is used to construct a wave-vector-dependent LST relation, applicable when the length scale of the disorder in an isotropic medium is smaller than that of the probing wavelength.

Generalization of the Lyddane-Sachs-Teller relation to disordered dielectrics.

Generalization of the Lyddane-Sachs-Teller relation to disordered dielectrics.

SURFACE MODE ABSORPTION AND INFRARED OPTICAL PROPERTIES OF SMALL SPHERICAL α-Fe2O3 PARTICLES

The small spherical α-Fe2O3 particles with uniform size and regular shape were prepared by improved hydrolysis method. The infrared transmisson spectra of this two kinds of particles different in dimension were measured, and all surface modes of small spherical α-Fe2O3 particles were obtained. The effect of aggregation on absorption were discussed, and the two absorption bands in spectra were explained with the approximation of chain aggregation by cylindrical microcrystals. Surface mode theory of multi-atomic cubic particles was generalized and applied to α-Fe2O3 particles in monoaxial crystal structure. The theoretical results of surface mode frequency of α-Fe2O3 particles were presented, which agreed well with those of experiments. The existence of generalized modified LST relation was verified.

Dispersive effects on the Brewster angle in moving isotropic dielectrics

A general method to study dispersive effects on the Brewster angle in moving isotropic semi-infinite dielectrics is discussed. In particular, the Brewster angle and the index of refraction of NaCl are calculated as functions of its velocity. A law of dispersion without absorption, which is used in ionic crystals and contains the Lyddane–Sachs–Teller relation, is assumed. Two cases are considered: direction of motion parallel to the dielectric–vacuum interface and direction of motion perpendicular to the same interface.

An improved analysis of the OH stretching region of the vibrational spectrum of ice Ih

We report the results of an analysis of the OH stretching region of the vibrational spectrum of ice Ih. The model of ice Ih discussed in an earlier paper [J. Chem. Phys. 69, 3483 (1978)] is considerably improved in that a larger section of the proton disordered lattice is included in the dynamical description, the shift in the OH stretching force constant on hydrogen bonding is calculated from molecular properties, the interaction force constants are re-evaluated using newer and more extensive data, and Fermi resonance and internal field effects on the lattice dynamics are accounted for. We show the following: (i) Strong coupling between OH oscillators on different molecules is responsible for the major features of the vibrational spectrum, namely, its breadth and gross distribution of intensity. (ii) Internal field effects, which lead to wave vector dependent polar mode mixing in a proton ordered model of ice I, do not influence the distribution of intensity in the Raman spectrum of proton disordered ice Ih, despite the fact that the internal field does play an important role in altering the states of the system. Our calculations provide no support for the suggestion that structure in the Raman spectrum of ice Ih can be assigned using the Lyddane–Sachs–Teller relation, i.e., that structure in the Raman spectrum can be related to system modes arising under the influence of the longitudinal field. (iii) Fermi resonance between the OH stretching mode and the overtone of the bending mode has more influence on the vibrational spectrum of D2O ice Ih than on that of H2O ice Ih. The inclusion of Fermi resonance in the description of the OD stretching dynamics materially improves the agreement between the predicted and observed vibrational spectra. However, the redistribution of spectral intensity attributable to Fermi resonance is a second order effect relative to the distribution of intensity determined by the interaction between OH oscillators on different molecules. (iv) The change in OH stretching frequency when a water molecule is incorporated in ice Ih can be accounted for self-consistently using only the known free molecule anharmonic potential energy coefficients and a parametric description of the dependence of the harmonic force constants on the strength of hydrogen bonding. This finding validates and provides an interpretation of the quasiharmonic representation of OH stretching motions used in our earlier work.

High-temperature optical modes of vibration in LiF thin films (thermal emission spectra)

The thermal emission of a metal-backed thin film of LiF is observed at the emission angle of 20 degrees . The observed spectra measured at elevated temperatures are analysed by using the response function based on the virtual-mode theory for the ionic film in order to derive the temperature dependence of the lattice dynamical quantities, such as phonon frequency and damping. The dielectric function derived from a theory based on the thermodynamic Green function technique is considered in the spectrum analysis. The estimated temperature dependence is discussed in terms of the phonon anharmonicity. The LST relation including the phonon anharmonicity is derived from the virtual-mode theory.

Polaritons in β-AgI

The room temperature polariton data of β-AgI fits to dispersion curves of three oscillators rather than a single oscillator. This is also true for the LST relation. These results are not compatible with the various explanations suggested earlier for the extra modes observed in β-AgI. Another explanation assuming Ag + at off center positions is suggested.

Dielectric properties of SbSI

Abstract It is a fascinating problem whether the LST relation is obeyed in ferroelectric materials with overdamped ferroelectric soft TO modes. Resolution of this point has been desired for SbSI. One can determine whether the LST relation is obeyed in SbSI by comparing the magnitude of the static constant experimentally obtained with that calculated from the LST relation.

Soft mode and Debye relaxations in Thiourea

AbstractThe infrared reflection spectra of a single crystal of thiourea polarized along the ferroelectric axis [100], are extended up to very low frequencies with the help of ε data obtained by some authors. The whole reflectivity spectrum is fitted with a generalized dielectric constant model at several temperatures. So for the first time all the dispersion parameters of the soft mode (a comparison with Raman data is made) are obtained and the existence of two Debye relaxations is shown. One is attributed to domain wall motion and the other to reorientation of molecules. With the help of a generalized LST relation, it is proved that the discontinuity of ε(0) at 169 K is due to a relaxation process.

Soft mode in thiourea by Raman measurements

AbstractRaman measurements have been carried out on the soft mode of thiourea and the wave vector and temperature dependence of the soft mode frequency (ωS) are observed. The longitudinal (ωSL) and transverse (ωST) frequencies are used to derive a comparison between the dielectric constant obtained from the LST relation and that obtained from standard measurements of the capacitance.

On the energy band structure and the phase transitions in a cuprous chloride crystal

AbstractTo explain the break‐down of the Lyddane‐Sachs‐Teller (LST) relation and the compressibility anomaly for CuCl a new energy band model is proposed to include a small indirect gap comparable to the binding energy of direct excitons. It is found for such a model that the condensation of excitons can result in the break‐down of the LST relation as well as a number of other anomalies of properties, i.e. CuCl is a high‐temperature excitonic dielectric with an effective mass ratio mh/mc ≈ 102 of electrons and holes. It is also shown that high pressure can induce a possible excitonic dielectric‐superconductor phase transition.

Generalized dielectric function and the plasmon-phonon coupling in GaAs and CdTe

Far infrared (12–235 cm -1 reflectivity data for GaAs and CdTe have been fitted equally well with the usual two-oscillator dielectric function and Kukharskii's generalized form ϵ K . Kukharskii's extended Lyddane—Sachs—Teller relation was confirmed and the quantities appearing in ϵ K agreed fairly well with other determinations. ϵ K was used to analyze the damped plasmon-phonon modes.

Effect of a Brownian Sublattice on Polariton Dispersion

AbstractA set of coupled equations describing the effect of a disorder mechanism on polariton dispersion is given. The treatment differs from that one finds in the literature because the disorder mechanism is not taken as a second‐order perturbation. A particular solution of these coupled equations shows that all originally undamped polaritons become damped waves. They all shift in frequency. Physical properties of different wave types in an order‐disorder crystal are discussed. For the complex frequencies of the coupled waves a modified Kurosawa relation and a modified LST relation is valid. Numerical evaluations of this model shall be given in a forthcoming paper.

Reststrahlen of Alkali Halides in the Far-Infrared Region

The assumption in deriving the Lyddane–Sachs–Teller relation and the simple harmonic oscillator model do not hold well in the understanding of the optical properties of alkali halides in the far-infrared region.

Permittivity of Strontium Titanate

The permittivity of single-crystal single-domain strontium titanate has been measured in detail in the [001], [011], and [111] directions, as a function of temperature (from 4.2 to 300 °K), electric field (from −23 000 to +23 000 V/cm, and frequency (from 1 kHz to 50 MHz). The free energy of the crystal is determined as a function of polarization with temperature as a parameter. The Curie-Weiss law is satisfied in the temperature range 60–300 °K, giving a Curie temperature of 30 ± 2 °K for the three crystal orientations. The Lyddane-Sachs-Teller (LST) relation is satisfied for temperatures between 30 and 300 °K and for electric fields between 0 and 12 000 V/cm. A generalized LST relation is used to calculate the permittivity of strontium titanate from zero to optic frequencies. Two active optic modes are important. The lower-frequency mode is attributed mainly to motion of the strontium ions with respect to the rest of the lattice, while the higher-frequency active mode is attributed to motion of the titanium ions with respect to the oxygen lattice. The restoring forces that act on the Ti ions begin to ``harden'' when these ions are displaced approximately 0.002 Å from their equilibrium positions.

Raman scattering by polaritons in tetragonal BaTiO 3

Raman scattering spectra by polaritons of A 1 symmetry in tetragonal BaTiO 3 at room temperature are used to establish the q ≈ 0 TO phonon frequencies and to estimate the dielectric constant along the ferroelectric axis ϵ cs. Values of ϵ cs = 37 ± 5 and ϵ cs = 38 ± 6 are found from the LST relation and the polariton dispersion curves respectively. It is also found that the two broad bands centered at 270 cm -1 and 520 cm -1 correspond to TO phonons. Their widths are explained by large anharmonic couplings and a frequency dependent damping constant.

Raman Spectrum of Single-Domain BaTiO3

Room-temperature Raman spectra of high-quality single-domain BaTi${\mathrm{O}}_{3}$ crystals are reported. The frequencies of the Raman-active long-wavelength optical phonons are determined and shown to be in reasonable agreement with the Lyddane-Sachs-Teller (LST) relation as well as infrared reflectivity data. The effects of mode damping on the Raman line shape are discussed using a classical lattice-polarization-fluctuation model for the Raman scattering process. Based on this model, it is shown that the soft $E$ mode is overdamped, and at 25\ifmmode^\circ\else\textdegree\fi{}C has an undamped mode frequency ${\ensuremath{\omega}}_{\mathrm{TO}}$ of 36\ifmmode\pm\else\textpm\fi{}3 ${\mathrm{cm}}^{\ensuremath{-}1}$ and a damping constant $\ensuremath{\Gamma}$ of 1.1\ifmmode\pm\else\textpm\fi{}0.1. The temperature dependence of ${\ensuremath{\omega}}_{\mathrm{TO}}$ is given and found to be consistent with the LST relation. The soft ${A}_{1}$ mode is not observed, but is estimated from the LST relation and infrared reflectivity data to be heavily damped ($\ensuremath{\Gamma}\ensuremath{\approx}0.5$) and to have an undamped mode frequency of 180\ifmmode\pm\else\textpm\fi{}10 ${\mathrm{cm}}^{\ensuremath{-}1}$.

On the validity of the lyddane-sachs-teller relation at long wavelengths

Among the polarization modes of an ionic crystal there exists no Lyddane-Sachs-Teller relation for very long wavelengths. The implication in certain recent experiments that the LST relation is valid at k = 0 is shown to be due to misinterpretation of the theory and the experimental data.

Longitudinal Optical Phonons in CaF2, SrF2, and BaF2

Off-normal reflection spectra of thin films of CaF2, SrF2, and BaF2 deposited on a silver substrate have been obtained. They exhibit decreased reflectivity at the long wave limit of the longitudinal optical branch. The values so obtained are in agreement with the predictions by the Lyddane—Sachs—Teller relation. They are also in agreement with vibrational levels obtained from vibronic data for SrF2:Sm2+ and BaF2:Sm2+. The observed longitudinal optical phonons are at 466 cm—1 in CaF2, 366 cm—1 in SrF2, and 319 cm—1 in BaF2. The close agreement between vibronic data and direct observation of these vibrations is considered further evidence that a good model for these vibronic transitions must consider vibrations of a relatively large segment of crystal and not merely nearest neighbors.

On the validity of the Lyddane-Sachs-Teller relation at long wavelengths

On the validity of the Lyddane-Sachs-Teller relation at long wavelengths