Optic phonon branches

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... 

In positronium forming materials without optical phonons much longer Ps slowing-down times should be found. This may be tested by AMOC measurements in solid rare gases, crystallizing in the face centered cubic (fee) structure which, being a Bravais lattice, does not have optical phonon branches. 

Coupling of the electronic transition to the optical phonon branch (assumed to be dispersionless and of frequency yields for... 

We conclude this section by noting that, in contrast to a statement of Jones and Zewail in Ref. 90, the contribution of the optical phonon branch to optical dephasing may well be distinguished from that of exchange by studying the optical dephasing characteristics of several different guests in the same host crystal. 

Raman scattering has been performed by Stiisser et al. (1982) for the inter-mediate-valence phases of the solid solution systems Smj R S (R = Y, La, Pr, Gd, Tb, Dy, Tm 0.15cation mass has been observed in between the gap of the acoustic- and optical-phonon branches for all Sm concentrated (x < 0.5) intermediate-valence phases. The Raman spectra of Smi R S with R = Y, Pr, Gd, Dy in the upper jpart of fig. 45 show at 300 K a maximum of the scattering intensity near 200 cm . This gap mode for x <0.50 is due to first-order scattering as demonstrated by its temperature dependence (fig. 45... 

Period of the chain is equal to a. Let us suppose the linear relationship between the interaction force between the nearest neighbors and atomic displacement. Every internal motion of the lattice could be represented by the superposition of the mutually orthogonal waves as follows from the lattice dynamic theoiy (see e.g. Bom and Huang 1954 Leibfried 1955). Aiy lattice wave could be described by the wave vector K from the first Brillouin zone in the reciprocal space. Dispersion curve co K) has two separated branches (for 2 atoms in the primitive unit), which could be characterized as acoustic and optic phonons. If we suppose also the transversal waves (along with longimdinal ones), we can get three acoustic and three optical phonon branches. There is always one longitudinal (LA or LO) and two mutually perpendicular transversal (TA or TO) phonons. 

Let us consider the wave vectors K from the vicinity of the first Brillouin zone origin (i.e. K 0). It corresponds to the infrared active lattice vibrations with X > > a. The optical phonon branch has the highest vibration frequency possible for the atom chain in that case. The ions vibrate with the opposite phases and amplitudes inversely proportional to their masses. Dipole moments are effectively created in each elementary unit and therefore the crystal is polarized. Polarization of the crystal causes the internal periodical electric field E at the position of each atom. This field contributes to the additional electric force on each ion, either by - -eEi, or by —eE force. Let us further denote the stiffness of the nearest neighbor interaction (i.e. spring constant) by C and displacement of ions A and B by w.4, ub respectively. The ion displacements follow the differential equation of motion... 

This scenario holds for our model, too. The condition (Eq. 41) corresponds to the intersection of Ctq with the optical phonon branch (Fig. 21.1). In a computer simulation two very different time scales appear. Starting with any initial condition including the QCA re-... 

However, this effect is extremely small when a-helix parameters are used. The situation can be illustrated by drawing Fig. 21.1, now using the a-helix parameters of Section 21.5. As a is very small there is a wide gap between the acoustic and optical phonon branches and the intersection point qo is far outside of the first Brillouin zone (e.g. qo = 5n for c = 2cj). Therefore the above condition for the convergence of the iteration, i.e. ( o) and G (qo) are negligible, is indeed very well fulfilled and the energy loss due to emission of optical phonons is negligible. 

The solutions co- k) and u)+ k) correspond to the acoustic and optical phonon branches, respectively, in an infinite ID chain of atoms (Fig. 2.9). To ensure the finiteness of the atomic displacements given by Eq. (2.71) one has to require that the wave number k is real. However, this is not necessary if we consider an atomic chain which is terminated at one end. In that case k has an imaginary part ix (Eq. (2.41)) and, accordingly. 

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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