Brillouin zone phonon distribution

It is found [138] that the increase of the corrugation due to the inclusion of axially symmetric (experimentally determined bulk) quadrupole moments located at the carbon sites [361] which model the aspheiical charge distribution in the graphite substrate [see (3.9) and (3.10) in Section III.D.l] stabilizes the commensurate herringbone structure. This structure is head-tail-ordered as in Ref. 17 (see Fig. 53a or Fig. 54Z>, where the molecular axes have a systematic out-of-plane tilt) the unit cell is deformed because of the displacement of the molecular centers on the two sublattices. The Brillouin-zone-center frequency gap in the phonon spectrum is estimated [138] to amount to about 10 K in the ground state,... 

If we calculate how the frequencies vary between different points in the Brillouin zone the results are a series of phonon dispersion curves. More generally, the distribution of frequencies in reciprocal space may be sampled by inelastic neutron scattering as the scattering function, S(Q,o), which may also be calculated via interatomic potential methods. 

Rush (1967) measured the inelastic incoherent neutron scattering from solid benzene and determined the phonon frequency distribution. Nakamura and Miyazawa (1969) carried out a complete Brillouin zone lattice dynamics calculation using the potential constants of Harada and Shimanouchi (1967), assuming the benzene molecule to be a nonvibrating rigid body. These authors first obtained agreement to better than 6% with Harada and Shimanouchi for the q = 0 modes. They then calculated the frequency distribution and were able to fit the experimental specific heat to better than 2 % by taking into account the internal modes as well and... 

The phonon confinement model [23] attributes the redshift of the asymmetric Raman line to relaxation of the -vector selection rule for the excitation of the Raman active phonons due to their locahzation. The relaxation of the momentum conservation rule arises from the finite crystalline size and the diameter distribution of the nanosolid in the films. When the size is decreased, the rule of momentum conservation will be relaxed and the Raman active modes will not be limited at the center of the Brillouin zone [21]. The large surface-to-volume ratio of a nanodot strongly affects the optical properties mainly due to introducing surface polarization states [28]. 

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