Phonon dispersion relations for potassium thiocyanate

Measurements of some low frequency phonon dispersion curves in potassium thiocyanate have been made using inelastic neutron scattering techniques. The measured phonon frequencies are presented along with ones calculated from a simple model comprising axially-symmetric force constants between nearest neighbour atoms. The applicability of such a model in describing the lattice dynamics of this crystal structure is discussed.     

Model for lattice dynamics of fcc metals

A lattice dynamical model which satisfies the requirement of static force equilibrium of fcc crystals is proposed. It incorporates central, angular and electron-ion interactions. The calculated dispersion curves for copper are in good agreement with neutron scattering data.     

Effects of Cl-Cl interaction on phonon dispersion in perovskite type CsPbCl3

The phonon dispersion curves in three symmetry directions of phase I of CsPbCl₃ superionic conductor are calculated by applying the de'Launay angular force model. With the third neighbor interaction between Cl-Cl ions, considerable agreements are obtained for all phonon frequencies at zone center (ZC) and also for the acoustic modes in the Δ direction. Two high energy phonon modes at ZC-point are reasonably understood.     

Phonon dispersion curves of V B group of metals

The phonon frequencies of vanadium, niobium and tantalum along the principal symmetry directions are computed using an angular force model. The calculated dispersion curves are in very good agreement with the experimental results.The author is grateful to Dr. V. Ramamurthy and Dr. S. B. Rajendraprasad of IIT Delhi for many valuable and stimulating discussions.     

Lattice vibrational spectrum of diamond

The lattic dynamics of covalent crystals are discussed with reference to known models. The dispersion curves of diamond have been computed on the basis of the shell model of Cochran applicable to covalent crystals. Parameters have been determined using elastic constants and dispersion curves along the Δ and A directions from the neutron spectrometric data of Warren et al. In general there is good agreement between the calculated curves and experiment. The average error is about 4.8%. Although the calculated curves seem to be a definite improvement over the curves calculated by Smith there appears to be a certain discrepancy between theory and experiment. Plausible causes of this discrepancy are pointed out.     

Phonon dispersion in mixed alkali halide crystal Na0.5K0.5Cl

In the present paper we have calculated the phonon dispersion curves of the mixed alkali halide Na_0.5K_0.5Cl using the modified three body force shell model, in all the three symmetry directions (q, o, o), (q, q, o) and (q, q, q). The model consists of long range three body interactions and the short range overlap repulsion. The repulsive parameters are calculated from the expressions for elastic constants derived for NaCl structure. The results will stimulate the experimentalist.     

Pseudopotential theory of effective interaction in simple metal

The second order pseudopotential theory suggests the possibility of a break-up of the total energy of simple metals into a purely volume-dependent part and an effective central pairwise interaction between ions. In the present paper finite contributions for these two parts of the energy have been extracted in a form convenient for calculation. Using the local Heine-Abarenkov model potential, a reliable effective ion-ion interaction is generated and the volume-dependent energy is calculated for Al. The relative contributions of the effective interaction and the volume-dependent energy term to various metallic properties are also calculated. The importance of volume dependence on the effective interaction is also discussed. The interactomic force constants upto eighth neighbour are derived from the effective interaction and it is found that the force constants beyond the third neighbour are negligibly small. This result is also confirmed by the calculation of dispersion curves with force constants obtained from the effective interaction upto the third neighbour which is found to reproduce the results of the full pseudopotential calculations. The force constants obtained are also used to study some finite temperature properties of Al in the quasi-harmonic approximation and the limitations of the theory are pointed out.     

Crystal dynamics of magnesium oxide

Phonon dispersion curves, for MgO, have been calculated, for the first time, in the framework of the modified three body force shell model (TSM), assuming both the positive and negative ions to be polarizable. The results are in good agreement with the inelastic neutron scattering measurements and are somewhat better than our earlier one-ion polarizable TSM calculations. It has been possible to conclude that a revised set of values of the elastic constants which are relatively larger, is essentially responsible to lead to a better set of model parameters and hence of the phonon frequencies.     

Lattice vibrational properties of uranium pnictides

Lattice vibrational properties of uranium pnictides have been studied using breathing shell model (BSM) which includes breathing motion of electrons of the U-atoms due tof−d hybridization. The phonon dispersion curves of U-pnicitides calculated from the present model agree reasonably well with the measured data. A comparison has been made between BSM and our results reported earlier obtained from three-body force rigid ion model to reveal the importance of the short-range electron-phonon interactions in these compounds. We also report, for the first time, the two phonon density of states and specific heat for these compounds.     

Laser-induced thermoelastic Leaky Lamb waves at the fluid–solid interface

A model based on the theory of fluid–structure interaction is developed to simulate the laser thermoelastic generation and propagation of Leaky Lamb waves at the water–aluminum interface. Each component of displacement, stress, and temperature are derived in transform domain by the photothermoelastic transfer matrix method. The time domain solutions are obtained by numerically inverting the transforms while the dispersion curves and attenuation curves for the leaky waves are also calculated. Then the propagation characteristics of different modes are analyzed. The model establishes a quantitative relation between the laser parameters, the material parameters, the corresponding waveforms, and the dispersion curves, which provides a useful tool for the Leaky Lamb waves applied to nondestructive evaluation.     

Phonon dispersion and dielectric behaviour of mixed alkali halide crystal NaCl0.5Br0.5

In the present paper we have calculated the phonon dispersion curves and dielectric constants, their volume derivatives and the Gruneisen parameters of the mixed alkali halide NaCl_0.5Br_0.5, using the extended three body force shell model. The results of dielectric constants, their volume derivatives and Gruneisen parameters are found to agree reasonably well with the experimental values, which establishes the validity of the three body charge transfer parameter. With this concept the phonon dispersion curves are obtained in all the three symmetry directions (q,o,o), (q,q,o) and (q,q,q), which will be of interest for experimental workers, since no experimental values have so far been obtained for phonon frequencies.     

Lattice dynamics of silver

The phonon dispersion curves of silver have been measured in the main symmetry directions at room temperature by coherent inelastic scattering of thermal neutrons using a correlation technique. The experimental results have been analyzed with parametrized expressions which have been derived from interatomic model potentials. With the Born-von Karman force constant model thermodynamic properties of silver could be calculated in good agreement with experimental results. Through the use of electron-ion model potentials the lattice dynamics of silver was correlated with its electronic properties. The results for some of those properties are compared with corresponding experimental values.     

Si(111)理想、弛豫及2×1重构表面的声子谱研究

本文利用微扰的方法考虑了占据态与空态间的耦合对能带能量的影响,给出延展键轨道近似下半导体力常数的解析表达式.利用这些表达式求出Si(111)的理想、1×1弛豫及2×1Haneman模型重构表面的声子色散曲线及其表面振动的振幅分布.不同表面结果的比较显示弛豫及重构对表面声子性质具有决定性的影响.同时,分析表明Haneman的2×1表面重构模型不足以满意地解释有关实验结果.     

Non-destructive evaluation of elastic material properties in anisotropic circular cylindrical structures

In this paper, non-axisymmetric guided wave propagation in circular cylindrical, anisotropic structures is studied in a frequency range up to 1 MHz. The investigations are carried out with carbon fibre reinforced tubes. The aim is the experimental determination of their effective linear elastic material properties in a non-destructive way. Therefore, an analytical model of the dispersion equation is fitted to the experimentally detected dispersion curves by systematically adjusting the desired material properties. A total least square scheme accompanied by an outlier detection criterion is used for this optimization task. Since the raw data of the measured dispersion curves contain a lot of noise, these outliers have to be detected and excluded, to achieve accurate results. Good agreement is found between the measured curves and the analytically calculated curves based on the estimated parameters. This fact indicates a high accuracy of the determined material properties.     

Non-destructive evaluation of elastic material properties in anisotropic circular cylindrical structures

In this paper, non-axisymmetric guided wave propagation in circular cylindrical, anisotropic structures is studied in a frequency range up to 1 MHz. The investigations are carried out with carbon fibre reinforced tubes. The aim is the experimental determination of their effective linear elastic material properties in a non-destructive way. Therefore, an analytical model of the dispersion equation is fitted to the experimentally detected dispersion curves by systematically adjusting the desired material properties. A total least square scheme accompanied by an outlier detection criterion is used for this optimization task. Since the raw data of the measured dispersion curves contain a lot of noise, these outliers have to be detected and excluded, to achieve accurate results. Good agreement is found between the measured curves and the analytically calculated curves based on the estimated parameters. This fact indicates a high accuracy of the determined material properties.     

Measurement of the dispersion relation of guided non-axisymmetric waves in filament-wound cylindrical structures

To determine the dispersion relation, guided waves are excited in specimens over a broad frequency range. The surface displacements are measured over time and space. The recorded data are analysed using a quasi-three-dimensional spectrum estimation algorithm. In the time domain a fast Fourier transform is used to extract the frequencies. To obtain the wave numbers, in space a two-dimensional matrix-pencil approach is applied to the data set. Using a suitable constitutive model (transversely isotropic or orthotropic) dispersion curves are calculated. Good agreement was found between the experimental and the numerically calculated dispersion relations after adjusting the material parameters. Since the dispersion relation of a structure depends on the mechanical material properties frequency-dependent material parameters can be extracted from the above-mentioned relation between frequency and wave number.     

Comparison between the dispersion curves calculated in complex frequency and the minima of the reflection coefficients for an embedded layer

Analytical solutions of Lamb functions for symmetric and antisymmetric elastodynamic modes propagating within a solid layer embedded in an infinite medium are presented. Alternative theoretical analyses of such modes are performed, first in terms of the usual approach of harmonic heterogeneous plane waves (real frequency and complex slowness) and then in terms of transient homogeneous plane waves (complex frequency and real slowness). An example structure of a 0.1-mm-thick "alpha case" (an oxygen-rich phase of titanium that is relatively stiff) plate embedded in titanium is used for the study. A large difference between the usual dispersion curves calculated in real frequency and complex slowness and those calculated in complex frequency and real slowness is shown. Thus the choice between a spatial and a temporal parameter to describe the imaginary part of the guided waves is shown to be significant. The minima and the zeros of the longitudinal and shear plane-wave reflection coefficients are calculated and are compared with the dispersion curves. It is found that they do not match with the dispersion curves for complex slowness, but they do agree quite well with the dispersion curves for complex frequency. This implies that the complex frequency approach is better suited for the comparison of the modal properties with near-field reflection measurements.     

Phonon dispersion and symmetry of solid-J2

The phonon dispersion curves, spectrum and specific heat of solid J₂ and Br₂ are calculated using a general central force parameter model, which is fitted to the available experimental data. The influence of the intramolecular degrees of freedom on the elastic constants and the compressibility is shown. The usefulness of group theoretical methods in the investigation of normal modes of vibrations in crystals is illustrated by applying them to the decomposition of the dynamical matrix.     

Lattice dynamics of CsF by extended three-body force shell model

Detailed calculations are presented for the phonon dispersion curves and two-phonon Raman spectra of cesium fluoride. The model applied for the purpose is the extended three-body force shell model which takes account of three-body and second-neighbour interactions. Theoretical predictions and experimental data are in almost exact agreement.