The calculated striped and shaded regions, corresponding to transverse and longitudinal polarizations respectively, are the slab-adapted bulk phonon bands, while the solid line is a calculation for the Rayleigh wave based on the Dispersive Linear Chain Model (shown schematically in Fig. All the data were obtained at 60 K, well into the low-temperature phase. The HAS data are shown as solid circles except for weak points which appear in the TOP spectra as hybridized longitudinal modes that are shown as crosses. The vertical lines in the lower panel denote the widths in the energy transfer distributions of these points. The edges of the transverse acoustic (TA) and longitudinal acoustic (LA) bulk bands are given by the hatched lines. The data in the upper panel were obtained at 1200 K, while in the lower panel the data shown by open circles were obtained at 500 K and those represented by closed circles were obtained at 300 K. Surface phonon dispersion for W(OOl) in the FM portion of the SBZ showing the measured Rayleigh wave (R) and longitudinal (L) modes. Note that the transverse branches, labeled TA (transverse acoustic) and TO (transverse optical), are doubly degenerate in these directions. Both crystals have fee lattices and rocksalt structures. Bulk phonon dispersion curves for KBr and RbCl in their and high-symmetry directions. Copyright 1992 by the American Physical Society.įigure 7. Along the directions (E), the modes are neither purely longitudinal nor transverse, and three branches exist for each category. The frequencies are expressed in wavenumber v = uj/2itc. Phonon dispersion curves of diamond along the main symmetry directions calculated from a Born-von Karman model fitted to neutron scattering experimental data (after ). The remaining curves correspond to the dispersion relation of transverse modes. The dotted curve is the result for a ID adsorbate at the same density. LI, L2, and 元 are longitudinal branches, i.e., molecular motion parallel to the groove. relative wave vector) for the three-stripe phase of CH4 on the external surface of a bundle. įigure 9-19 Phonon dispersion relation (angular frequency vs.
#Phonon dispersio dahed vertical series#
Here we want to show two series of spectra recorded by Claus. The phonon and polariton spectra were investigated by Claus 26>27> and Otaguro et al. Vibrations of species A, E, and E2 are allowed in the Raman effect, but only A and E, are infrared-active, therefore polariton dispersion is expected for the transverse phonons of these two species. LiI03 is a uniaxial hexagonal crystal ( factor group C6). The further solution ejj - n2 = 0 describes the dispersion of another set of strictly transverse phonons which do not degenerate with the ordinary phonons because of the anisotropy of the crystal. Similar to the fee FcsNi phase, a soft transversal mode is detected in bcc CuZn. Our result compares well with the experimental findings marked as diamonds in Fig. We have investigated the phonon dispersion of the B2 phase. those contain just one or two atoms per unit cell) but for general three-dimensional lattices of the vibrations are a mixture of transverse and longitudinal motions, the exceptions. Such motions can be observed in simple systems (e.g. A purely transverse ition is one where the displacement of the atoms is perpendicular to the direction of on of the wave in a pmely longitudinal vibration tlie atomic displacements are in the ition of the wave motion. The phonon density of states is ariation in the number of frequencies as a function of frequency. A phonon dispersion curve indicates how the phonon frequencies vary over tlie luin zone, an example being shown in Figure 5.37. For periodic solids it is necessary to take this periodicity into account the effect on the id-derivative matrix is that each element x] needs to be multiplied by the phase factor k-r y). As with calculations of the electronic structure of periodic lattices these cal-ions are usually performed by selecting a suitable set of points from within the Brillouin. Iditional importance is that the vibrational modes are dependent upon the reciprocal e vector k.
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