Acoustic phonon branches

The calculated Rayleigh mode (SJ, the lowest lying phonon branch, is in good agreement with the experimental data of Harten et al. for all three metals. Due to symmetry selection rules the shear horizontal mode just below the transverse bulk band edge can not be observed by scattering methods. The mode denoted by Sg is the anomalous acoustic phonon branch discussed above. Jayanthi et al. ascribed this anomalous soft resonance to an increased Coulomb attraction at the surface, reducing the effective ion-ion repulsion of surface atoms. The Coulomb attraction term is similar for all three metals... 

For the investigation of crystal phonons, we may in a first approximation consider rigid molecules. Then we obtain 6s branches of phonons in a crystal with s molecules per unit cell. In these 6s branches, 6s-3 are optical phonon branches and 3 acoustical phonon branches for the latter Qs(k)t ocs k (cs... 

On the assumption that the electron correlations are relatively weak in the material, the model of Schulz [37], which takes into account the interaction between the conduction electrons and one acoustic phonon branch, has then been used to calculate the longitudinal phonon spectrum. In the model, two new optical modes are coming up at 2kF, corresponding to excitations in the phase and in the amplitude of the distortion. However, the agreement was still very poor in this case, the renormalization of the phase mode being considerably larger in the model than experimentally observed [34]. 

Of the three acoustic phonon branches, in each case that with the largest slope is the branch of the longitudinal acoustic phonons (LA), while the two others are the transverse acoustic branches (TA). From this we can derive immediately the longitudinal sound velocity... 

Other thermodynamic parameters like thermal expansivity and eom-pressibility follow directly from standard relationships (e.g., [50]. Elastic constants are readily calculated from the acoustic phonon branches of the VIB model (e.g., Chizmeshya, et al., [29]). MPIB elastic constants have not yet been calculated. 

It can be seen from Eqs. (11) and (12), that the acoustical phonon branch is folded into the new minizone and minigaps open at the zone center and boundary for 5 0 (see... 

Figure 9 Scheme of the folding of the acoustical phonon branch into the new artificial Brillouin zone of a superlattice with period length D = irlSa. The dots mark the intersections of the folded phonon branch and the wave vector of the incident light. 

Problem 2.3. Figure 2.27 represents the dispersion of phonons on the NaF(lOO) surface. Show the dispersion curves corresponding to surface phonons. Which of them are related to (a) acoustical phonon branches (b) optical phonon branches Which of them can be referred to as surface resonance phonons ... 

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