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Abstract
We have measured the Brillouin spectrum of LiF at hypersound frequencies in the [100] and [110] planes. In addition to the longitudinal mode we have observed the pure transverse modes in these planes. Both the polarization and the relevant intensities confirm the assignment. The measured elastic constants are compared with ultrasonic data.
Summary This document is part of Subvolume A ‘Second and Higher Order Elastic Constants’ of Volume 29 ‘Low Frequency Properties of Dielectric Crystals’ of Landolt-Börnstein - Group III Condensed Matter.
Raman scattering from LiF nanocluster-assembled films prepared by gas evaporation technique has been investigated. The film with nanoclusters of average diameter 6.2 nm shows fractal structure, and gives Raman peaks at 28, 42, 196, 400, 458, 942, 1044 and 1180 cm−1. Low frequency Raman peaks at 28 and 42 cm−1 stem from the localized acoustic vibration of spherical nanoclusters. The enhanced low frequency Raman scattering is believed to correlate with the fractal structure. The film with nanoclusters of mean diameter 38 nm exhibits homogeneous spatial distribution, and gives Raman peaks at 194, 298, 304, 330 and 944 cm−1. Raman peaks are interpreted in terms of spheroidal and torsional modes, surface optical modes, LO, TO, LA modes and their combination.
The Mandel'shtam-Brillouin and Gross scattering was measured for a series of purified KBr crystals. The ratio , which for a pure, perfect crystal would be the Landau-Placzek ratio, was found to vary with the type of reactive gas treatment used in the final purification. With these crystals both the longitudinal and mixed mode bands were observed with θ and φ equal to 90°. The ratio was in agreement with calculated intensity ratios and the Δμ for these bands gave C11 + C12 = 41.6 GPa and C44 = 5.18 GPa.
Elastic and photoelastic constants of NaCl, KBr and LiF were determined from Brillouin frequency shifts and intensities. Reported differences between the hypersonic and ultrasonic elastic constants for KBr and LiF were not confirmed. For each material the constants were in good agreement with the ultrasonic values. Scattering from longitudinal, transverse and mixed phonon modes was clearly observed for each material.
Single crystals of xenon were grown and Brillouin spectra for various crystal orientations were obtained at a temperature of 156 °K. The spectra exhibited one longitudinal component and either one or two transverse components, depending on crystal orientation. From the observed Brillouin frequency shifts, the adiabatic elastic constants for xenon were evaluated. At 156 °K, c11=2.98±0.05, c12=1.90±0.04, c44=1.48±0.04 in units 1010 dyn/cm2 and the elastic anisotropy was found to be 2.74 ± 0.30. These values were compared with calculated values based on recent theories of lattice dynamics. Good agreement was obtained only with calculations that include all-neighbor interactions. It was also observed that the relative intensities of the Brillouin components were strongly dependent on crystal orientation. An analysis of this variation in intensity gave values of the ratios of the elasto-optic constants for xenon.
The authors discuss the nature of deformation of the electron charge cloud of an ion implied in the deformable shell model and considers an application of the model to the case of LiF crystals. It is found that the properties of the crystal are fairly well reproduced by the present model and certain discrepancies noted by earlier authors are removed. The results of other theoretical investigations are also included for comparison.
It is shown that the bulk modulus of the alkali halides with rocksalt structure follows the simple relation B = b0(1 — b1fc) V where V0 is the unit cell volume, fc the spectroscopically defined covalency of the chemical bond, and b0, b1, and n are constants having the same values for all compounds. This result is compared with the bulk modulus scaling law found for the tetrahedral semiconductors.
Es wird gezeigt, daß der Kompressionsmodul der Alkalihalogenide mit Kochsalzstruktur durch die einfache Beziehung B = b0(1 — b1fc) V beschrieben werden kann, wobei V0 das Volumen der Einheitszelle, fc die spektroskopisch definierte Kovalenz der chemischen Bindung und b0, b1 and n Konstanten sind, die für alle Verbindungen die gleichen Werte haben. Dieses Ergebnis wird mit dem Skalierungsgesetz für den Kompressionsmodul in den tetraedrischen Halbleitern verglichen.
Using a helium-neon laser light source and a high-resolution grating spectrograph we have studied, at room temperature, the Brillouin spectrum of light scattered from three alkali halide crystals: KCl, RbCl, and KI. By suitable orientation of the crystal axes relative to the incident beam we have obtained the frequency and the velocity of thermally excited phonons of ~3000 Å wavelength in longitudinal and "mixed" acoustic phonon branches as a function of the direction of propagation in the [110] plane. From these data we have determined for each crystal, entirely in the absence of acoustic excitation, the elastic constants C11, C12, and C44 for microwave (8-15 kMc/sec) sound waves with an accuracy from 0.25% to 4%. The elastic constants so determined are in very good agreement with investigations made in the ultrasonic region using externally generated sound waves of frequency ~10 Mc/sec. This agreement indicates the absence of dispersion in the sound-wave velocity over three orders of magnitude change in the sound-wave frequency. We also present the theory for the scattering of light from thermally excited sound waves in a cubic crystal. This theory predicts the intensity, polarization, and spectral distribution of the scattered light as a function of the incident and scattered directions in the crystal. By treating the phonons quantum-mechanically at temperatures comparable to the scattering phonon frequency, we have also obtained expressions for the temperatures dependence of the scattering valid at very low temperature. The theory is in quite good agreement with our measurements of the relative intensity of the scattering from phonons in the longitudinal and "mixed" acoustic modes.
DOI:https://doi.org/10.1103/PhysRev.74.229