Microscopic theory of second-order and third-order elastic constants for an NaCl crystal

Relations between the second-order and third-order symmetry-independent elastic constants and the energy of interatomic interactions dependent on the mutual arrangement of pairs and triplets of atoms are obtained for crystals belonging to the crystal class O _h. The derived relations and experimental data on the elastic constants are used to calculate four third-order elastic constants and the temperature dependence of the elastic anisotropy factor a(T) for an NaCl crystal. The calculated dependence a(T) is in qualitative agreement with the experimental dependence a _exp(T).     

Pressure dependence of phonon energies at critical points in the Brillouin zone in KTaO3 measured with differential second order raman scattering

Wavelength modulated Raman scattering was used to study the effects of pressure on the second order spectrum of KTaO₃. The pressure results lend support to previous identifications of structures in the second order differential Raman spectrum in terms of pairs of phonons from critical points in the Brillouin zone. Using these identification mode Grüneisen parameters are obtained for several vibrational modes. Strong anharmonic behavior of of the TA(X) mode is observed when we correlate the results from pressure measurements with previous studies of the effects of temperature.     

Determination of elastic, piezoelectric, and dielectric constants of an R:BaTiO3 single crystal by Brillouin scattering

From the sound velocity measured using the Brillouin scattering technique, the elastic, piezoelectric, and dielectric constants of a high-quality monodomain tetragonal Rh：BaTiO3 single crystal are determined at room temperature. The elastic constants are in fairly good agreement with those of the BaTiO3 single crystal, measured previously by Brillouin scattering and the low-frequency equivalent circuit methods. However, their electromeehanical properties are significantly different. Based on the sound propagation equations and these results, the directional dependence of the compressional modulus and the shear modulus of Rh：BaTiO3 in the （010） plane is investigated. Some properties of sound propagation and electromechanical coupling in the crystal are discussed.     

Brillouin and ultrasonic study of the temperature dependence of the elastic constants in NaCN

The temperature dependence of the elastic constants of NaCN has been studied by propagation of ultrasonic waves at 15 MHz and by Brillouin scattering at 3 GHz over the temperature range from 287K to 355K. c₄₄ is observed to soften linearly with temperature as the order-disorder phase transition at 284K is approached from above. The other elastic constants also soften, except for c₁₂ which stiffens. Considerable dispersion is seen in the values of c₄₄ obtained ultrasonically and by Brillouin scattering. Measurements of the temperature dependence of the density are also reported.     

Irreducible multiplier representations for some points in the Brillouin zone of D 6h 4

The irreducible multiplier representations (ray representation) for the pointsΓ and A of the Brillouin zone of the space group D _6h ⁴ are constructed using the method given in the previous paper.

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Zusammenfassung Die irreduziblen Multiplikatordarstellungen (Strahldarstellungen) für die PunkteΓ und A der Brillouinzone der Raumgruppe D _6h ⁴ werden mit der Methode der vorangehenden Arbeit konstruiert.

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Résumé Les représentations multiplicatrices irréductibles pour les pointsΓ et A de la zone Brillouin qui appertiennent au groupe d’espace D _6h ⁴ sont contruites en utilisant la méthode décrite dans un article précédent.

     

Linear wave-vector dependence of an optical phonon frequency in Bi12GeO20 in the vicinity of the Brillouin zone center

A Raman spectroscopic study of a zone center optical phonon of Bi₁₂GeO₂₀ which exhibits simultaneously a LO-TO and a linear wave-vector dependent splitting is presented. These are separated experimentally by studying the Raman line with a piezoelectrically scanned Fabry-Perot interferometer and the sample with and without an applied uniaxial stress.     

Determination of elastic,piezoelectric,and dielectric constants of an R:BaTiO₃ single crystal by Brillouin scattering

From the sound velocity measured using the Brillouin scattering technique,the elastic,piezoelectric,and dielectric constants of a high-quality monodomain tetragonal Rh:BaTiO3 single crystal are determined at room temperature.The elastic constants are in fairly good agreement with those of the BaTiO3 single crystal,measured previously by Brillouin scattering and the low-frequency equivalent circuit methods.However,their electromechanical properties are significantly different.Based on the sound propagation equations and these results,the directional dependence of the compressional modulus and the shear modulus of Rh:BaTiO3 in the(010) plane is investigated.Some properties of sound propagation and electromechanical coupling in the crystal are discussed.     

二维单斜点阵光子晶体的第一布里渊区及带隙计算

二维单斜点阵光子晶体在光学聚焦器件及光子晶体波导中有重要的应用价值，详细讨论了二维单斜点阵光子晶体的第一布里渊区及带隙计算，并与常规方法计算得出的二维正三角形晶格光子晶体的带隙结构进行了比较.最后讨论了临界条件下二维单斜点阵光子晶体的带隙结构，证明了本方法的有效性.     

Magnetization,magnetocrystalline anisotropy,magnetostriction and elastic constants of a ruthenium-nickel single crystal

The preparation of a single crystal of Ni:3.3 at.% Ru is described. The thermal variations of its main magnetic properties are given, namely magnetization, magnetocrystalline anisotropy and magnetostriction. The main feature of this compound is its small anisotropy energy, about 16 times smaller than that of pure nickel. Its elastic properties are identical to those of pure nickel. These data are briefly discussed.     

Influence of elastic strain on the density of phonon states and characteristics of discrete breathers in the gap of the phonon spectrum of a crystal with a NaCl structure

Appreciable elastic strain may considerably change the physical properties of crystals. This effect underlies the elastic stress technology, which has been intensively developed in recent years. The influence of elastic strain on the density of phonon states and on the properties of discrete breathers in the gap of the phonon spectrum of a crystal with a NaCl structure and a considerable difference between the anion and cation masses is studied using the molecular dynamics method. A number of crystal straining modes are considered. It is shown that the shear components of the strain tensor may significantly change the density of phonon states but slightly influence the frequencies of discrete breathers. Compression (tensile) strains raise (lower) the frequency of discrete breathers with a respective polarization.     

Universal relationships for the phonon spectra in BCC,FCC, and HCP crystals with a short-range interatomic interaction

The frequencies of the phonon branches that correspond to the vibrations of the close-packed atomic planes in bcc, fcc, and hcp crystals with short-range interatomic interaction are shown to be described by a universal relationship, which only contains two parameters for each branch, for any polarization λ. These phonon branches correspond to the (ξ, ξ, 0) direction in bcc crystals, the (ξ, ξ, ξ) direction in fcc crystals, and the (0, 0, ξ) direction in hcp crystals. This universal relationship can only be violated by long-range interactions, namely, the interactions outside the sixth coordination shell in a bcc crystal, the fifth coordination shell in an fcc crystal, and the eleventh or tenth coordination shell in an hcp crystal. The effect of these long-range interactions for each phonon branch can be quantitatively characterized by certain parameters Δ _nλ, which are simply expressed in terms of the frequencies of three phonons of the branch. The values of these parameters are presented for all bcc, fcc, and hcp metals whose phonon spectra are measured. In most cases, the proposed relationships for the frequencies are found to be fulfilled accurate to several percent. In the cases where the Δ _nλ parameters are not small, they can give substantial information on the type and scale of long-range interaction effects in various metals.     

Determination of the elastic constants of a composite plate using wavelet transforms and neural networks

An inverse method based on a combination of the wavelet transform and artificial neural networks is presented. The method is used to recover the elastic constants of a fiber-reinforced composite plate from experimental measurements of ultrasonic Lamb waves generated and detected with lasers. In this method, the elastic constants are not recovered from the dispersion curves but rather directly from the measured waveforms. Transient waveforms obtained by numerical simulations for different elastic constants are used as input to train the neural network. The wavelet transform is used to extract the eigenvectors from the Lamb wave signals to simplify the structure of the neutral network. The eigenvectors are then introduced into a multilayer internally recurrent neural network with a back-propagation algorithm. Finally, experimental waveforms recoded on a titanium-graphite composite plate are used as input to recover the elastic constants of the material.     

Temperature and pressure derivatives of elastic constants in single crystal Au-47.5 at.% Cd near martensitic phase transformation

The behavior of the elastic properties and their pressure derivatives near the martensitic transformation β→β′ was determined from sound velocity measurements at a frequency of 10 MHz, on a single crystal of Au-47.5 at.% Cd.The transformation of the β phase to the martensitic β' phase was obtained from the anisotropic elastic constants c₁₁, c₄₄ and c′, and their pressure derivatives. The behaviour of c₁₁ and c₄₄ is normal as a function of temperature, while the variation of c′ is positive with temperature. Before the β→β′ phase change the value of c′ is very small and exhibits high elastic anisotropy. The small value of c′ and the anisotropy were explained according to the crystallographic mechanism of the martensitic transformation and the Zener theory of instability of the b.c.c. structure. The pressure derivatives of c′ are negative and the variation of $\text{d}\text{c}{}_{44}\text{d}\text{P}$ with temperature is anomalous. This behavior can be explained by the influence of pressure on the transformation temperature, and by the instability of the β phase. It was found that the elastic constants c′ determine the mechanism of the transformation. From the pressure derivatives of c₁₁, c₄₄ and c′ the Grüneisen parameters for different modes of vibration were calculated. For the c′ mode the values are negative, for the c₄₄ mode the variation of the parameter with temperature is negative. This anomalous behavior can be explained as due to the anisotropic softening of the atom bonding on the (110) planes of the cubic structure, as a consequence of the phase transformation mechanism.     

Identification of a dynamical model for an acoustic enclosure using the wavelet transform

This paper presents results of research work in the identification of a dynamical model for an acoustic enclosure, a duct with rectangular cross-section, closed ends, and side-mounted speaker enclosures. An acoustic enclosure is excited randomly and random decrement functions are built to convert the random responses to free acoustic responses. It is shown that the estimation of resonance frequencies is possible using the wavelet transform of the system’s free response. Using a particular form of the son wavelet function, results are improved compared to those obtained with the traditionally Morlet wavelet function. An optimal value of a parameter of the son wavelet function is obtained by minimization of the wavelet entropy. The accuracy of this new technique is confirmed by applying it to a numerical example, and to an acoustic enclosure. The advantage of using the wavelet transform method over the Fourier-based modal analysis that would normally be used for the enclosure modes problem is established.     

Brillouin scattering in the nematic and isotropic phases of a liquid crystal

Brillouin scattering is the liquid crystal 5CB has been measured and the hypersonic speed and attenuation determined. At the nematic-isotropic transition a small discontinuity in the hypersonic speed is found. The results are compared with available ultrasonic data.