Fundamental Lattice Absorption Research Articles

Analysis of SCS-6 silicon carbide fibers by Fourier transform infrared spectroscopy

Fourier transform infrared (FTIR) spectroscopy analysis of SCS-6 silicon carbide fibers was performed to detect the presence of oxygen in the form of SiO2. The results showed infrared peaks corresponding to SiC fundamental lattice absorption as well as reflection. No absorption peak due to SiO2 was observed. These results are in agreement with previously reported data indicating low levels of oxygen in this fiber.

Dielectric susceptibility and infrared absorption in an imperfect anharmonic crystal

Using the technique of thermodynamic double-time Green's function and Kubo formalism an expression is obtained for the dielectric susceptibility of an imperfect anharmonic crystal taking into account the second-order terms in the dipole moment expansion and third- and fourth-order anharmonic terms in the crystal potential energy. The crystal contains randomly distributed substitutional impurities. Mass changes as well as force constants changes between the impurity atoms and host-lattice atoms are explicitly included. The polarization operators of the Green's functions are obtained in the lowest-order approximation using renormalized Hamiltonian. The results are used to obtain an expression for the frequency and temperature dependence of the infrared absorption coefficient. It is observed that in the temperature region above the Debye temperature, the width of the fundamental lattice absorption peak is proportional to the first and second powers of the absolute temperature which is in agreement with the experimental observations and the absorption at high frequencies is caused due to the fourth- and higher-order anharmonicity. It is also observed that at sufficiently high temperature, the damping constant associated with the fundamental lattice vibration absorption will vary as T 2 in agreement with experimental observations.

Dielectric Susceptibility and Infrared Absorption in an Anharmonic Crystal

Using the method of temperature-dependent double-time Green's function, an expression is obtained for the dielectric susceptibility of an anharmonic crystal considering second-order terms in the dipole moment expansion and third- and fourth-order anharmonic terms in the crystal potential energy. The polarization operator and the phonon Green's function are evaluated in two successive approximations by means of equivalent renormalized Hamiltonian using Dyson's equation for the phonon spectrum. The results are used to obtain an expres­ sion for the frequency and temperature dependence of the coefficient of infrared optical absorption. It is shown that in the high temperature region, the width of the fundamental lattice absorption peak is the sum of two terms proportional to the first and second powers of the absolute temperature in conformity with experiments. The results obtained are general and are applicable to the ionic crystals as well as to covalent crystals, where the linear dipole moment is zero. § I. Introduction It is well known that the lattice optical absorption properties of ionic and covalent crystals in the infrared region are not adequately described by the classical theory.1l' 2l In the simplest approach based on first-order approximation, it is assumed that during the course of lattice vibrations, the ions are displaced rigidly without any deformation of the electron shells. Under this approximation, the dipole moment is a linear function of the ionic displacements and the potential energy due to internal forces is harmonic, which means that the electric field interacts independently with each lattice wave. Under these conditions, in the case of diatomic cubic crystal, the infrared absorption should have a single and narrow absorption band. On the other hand, the experimental measurements on infrared spectra of ionic and covalent crystals show broad absorption band consisting of a central maximum and several side maxima on the short wave­ length side· of the central absorption peaks. Recent advances in the solid state theory indicate that these discrepancies between theory and experiment are attributable to the neglect of two higher-order effects, namely, anharmonic terms in the expansion of the potential energy and the nonlinear terms in the expansion of the dipole moment. During the last few years, there have been a number of theoretical studies of infrared lattice vibra­ tion absorption in crystals by many workers using different models and approxi­ mations.3l-15l The basic point has been how to take into account anharmonic effects and terms in the expansion of dipole moment operators. The first ex

Theory of Infrared Absorption by Crystals in the High-Frequency Wing of Their Fundamental Lattice Absorption

We have calculated the frequency dependence of infrared absorption in the classical limit for an exactly soluble model of a lattice of noninteracting diatomic molecules, each bound internally by a potential for which the classical equation of motion can be solved in closed form. Four potentials have been used: a Morse potential, a potential of the form $V(x)=\frac{a}{{x}^{2}}+b{x}^{2}$, an infinite-square-well potential, and a triangular-well potential. The analytic results we obtain show that the absorption coefficient for large frequencies associated with potentials which admit an harmonic approximation decreases nearly exponentially over the frequency region covered by recent experiments, with significant deviations from exponential behavior at higher frequencies. For the square- and triangular-well potentials, the absorption decreases as ${\ensuremath{\omega}}^{\ensuremath{-}2}$ for frequencies large compared to a characteristic frequency.

Infrared Active Two?Phonon Processes in Cubic ZnS

Results are presented of a study of the infrared transmission spectrum of cubic ZnS at room temperature. Besides the fundamental lattice absorption, a number of subsidiary bands due to the interaction of infrared radiation with more than one lattice phonon in the frequency range 250-800 cm - 1 have been observed. These multiphonon bands are explained using inelastic neutron scattering data for the four characteristic phonon frequencies at various critical points and applying selection rules.

Infrared Absorption in Small Ionic Crystals

AbstractThe infrared transmission of 0.1 μm crystals of MgO has been measured in the region of fundamental lattice absorption. In particular, the effects of anharmonicity and particle density on the transmission have been observed. These effects have also been calculated using a continuum model applicable to spheres very much smaller than the wavelength of light. In agreement with these calculations, the frequency of the fundamental infrared absorption of small particles was found to decrease with increasing particle density. In addition, it was observed that the frequency dependent damping function of massive MgO must be increased by a factor of about eight in small crystals in order to fit the experimental data.

Infrared lattice vibrational spectrum of CaF2

The infrared transmission spectrum of calcium fluoride in the region of fundamental lattice absorption has been recorded on a perkin-elmer 521 model double beam grating spectrophotometer. The accuracy of the measured frequency is discussed.

Effect of anharmonicity on the K ≈ 0 modes of MgO and ZnS

AbstractExperimental investigations are made of the infrared transmission spectra of MgO and ZnS in the region of the fundamental lattice absorption at room temperature. The magnitude of the effect of anharmonicity has been calculated and discussed in the light of symmetry of spectra at the resonance frequencies. The effective ionic charge and compressibility of Szigeti's relations are calculated and the significance of these results is discussed from the point of view of various models of dielectric behaviour.

Lattice vibrational spectra and grüneisen parameter of some metal oxides

The infrared transmission spectra of CoO, NiO and CaO have been recorded at room temperature in the region of fundamental lattice absorption. These spectra are correlated with the earlier measured spectra of MgO and ZnS and the ratio of β */β m estimated. The Grüneisen parameters of these crystals are also evaluated and dependence of the vibrational frequency on temperature discussed.

The temperature dependence of the fundamental lattice vibration absorption by localized modes

A calculation of the fundamental lattice absorption by localized vibration modes associated with impurity ions in crystals, with particular reference to U-centers in alkali-halide crystals of the rocksalt structure, is carried out utilizing two different approaches to this problem. The first method of calculation of the localized mode contribution to the absorption coefficient of an impure crystal is based on an adiabatic theory of the localized modes, in which the localized modes and the band modes are regarded as two systems which interact through the anharmonic terms in the crystal potential energy. The second approach to the calculation is through many body perturbation theory and proceeds from the Kubo expression for the imaginary part of the dielectric function. The results of both of these calculations show that the strength of the absorption by localized modes has a temperature dependence which is described by a factor exp(−2 M( T)), where T is the absolute temperature, and a microscopic theory for the function 2 M( T) is presented.

Impurity-Induced Second-Harmonic Infrared Absorption and Raman Scattering byU-Center Localized Modes in Alkali-Halide Crystals

The addition of cation impurities to alkali-halide crystals containing $U$ centers substitutionally in the anion sublattice removes the center of inversion from a certain fraction of the $U$-center sites. The potential energy of such $U$ centers consequently acquires nonzero cubic anharmonic terms which are absent in the absence of the additive cation impurities. The cubic anharmonic terms allow electric dipole transitions to occur between the ground state and the second excited state of the localized modes associated with the $U$ center. These transitions can be observed as second harmonics of the fundamental lattice absorption by the $U$-center localized vibration modes. The strength of such impurity-induced second-harmonic absorption has been calculated for the system NaCl: K. In addition, the removal of the center of inversion from certain $U$-center sites by the addition of cation impurities has the consequence that the localized vibration modes associated with $U$ centers at such sites, which in the absence of the additive cation impurities do not give rise to a first-order Raman scattering of light, therefore become Raman-active in first order. The Raman scattering efficiency for the first-order scattering by $U$-center localized modes induced by additive cation impurities in a typical alkali-halide crystal is calculated. In the particular case of NaCl: ${\mathrm{H}}^{\ensuremath{-}}$ containing 5% KCl, the scattering efficiency is estimated to be 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}12}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ sec ${\mathrm{sr}}^{\ensuremath{-}1}$.

Elastic constants of HgTe

Using the ultrasonic pulse technique, the room temperature elastic constants of HgTe were found to be, in units of 10 11 dynes/cm 2: c 11 = 5.08, c 12 = 3.58, and c 44 = 2.05. From these values, a fundamental lattice absorption frequency ω o = 1.87 × 10 13 and a Debye characteristic temperature at absolute zero, ϑ o = 105° K have been calculated.

Restrahlen reflection in HgTe

We have observed the restrahlen reflection at λ = 85 μ. By fitting the experimental points with a classical Lorentz oscillator, it is found that the fundamental lattice absorption frequency ν 0 = 3.45 × 10 12, the optical dielectric constant ϵ 0 = 14 and the effective charge q ∗ = 0.6 e .

Microwave Absorption in Cubic Strontium Titanate

An analysis of the temperature dependence of the microwave loss in SrTiO/ sub 3/ is presented using the linear chain model of a ferroelectric, It is shown that a plausible explanation of the temperature dependence of the microwave loss tangent above liquid air temperature is possible if the loss due to the damping of a virtual excitation in the wing of a fundamental lattice absorption is considered. The fundamental lattice absorption is associated with a lowfrequency ferroelectric'' transverse optical mode of the material. The microwave loss tangent can be expressed by tan delta = (T - T/aub c/)- (A + BT + DT/sub 2/). The parameter A is a measure of the damping due to the presence of imperfections in the lattice. The parameters B and D arise from damping due to three- and four- phonon processes whose origin is attributed to the anharmonic interactions of the lattice. (auth)

Temperature Dependence of the Infrared Reflection Spectrum of Sodium Chloride

Experimental studies of the reflection spectrum of NaCl from 300\ifmmode^\circ\else\textdegree\fi{}K to 985\ifmmode^\circ\else\textdegree\fi{}K were carried out in the region of the fundamental lattice absorption. This reflection spectrum was analyzed using a simple dispersion formula. The damping constant deduced in this manner varied approximately with the square of the temperature. The relation of these results to various theories of lattice absorption in solids is discussed.

Infrared absorption of free carriers produced in semiconductors by photoeffect

IN the following paper will be found the results of the infrared absorption of free carriers produced in semiconductors by the inner photoelectric effect in the range of the fundamental lattice absorption. The number of electrons and holes is equal because of the electrical neutrality of the crystal. The carrier absorption is modulated by the use of chopped light and detected by a tuned amplifier. Absorption measurements on injected carriers have been carried out in the case of germanium but with contradictory resu1ts.o~3) The following investigation with photoelectricallyproduced excess carriers tries to clear up these results for germanium and gives the absorption cross-section for electron-hole pairs in silicon.* Because the investigation method is independent of the macroscopic structure of the sample and is independent of an electrical contact or barrier layer it is hoped to extend the measurements to other polycrystalline semiconductors or photoconductors. The following questions are connected with the production of carriers by photons: (1) If the energy of the photon is greater than the energy gap, the carriers may have a large kinetic energy. The question of the decay of this energy is connected with the dependence of the effective mass on the kinetic energy. On the other hand, it is possible that the relative population of overlapping bands is changed. (2) If one has a sufficiently high trap density one might have an optical regeneration of the carriers out of these traps and find the corresponding absorption band. In this case the trap level is given by the wavelength of the absorption maximum.