Phonon dispersion branches in α quartz

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Abstract
The authors measured the six lowest phonon dispersion branches in alpha quartz at room temperature for the ( xi 00) and ( xi xi 0) directions. The qualitative agreement with lattice dynamical calculations by Barron et al. (1976) is good. Among the quantitative differences the most striking appears in the acoustic modes in the ( xi xi 0) direction. The symmetric ('longitudinal') branch has a lower initial slope (4.70 km s-1) and then one antisymmetric ('transverse') branch (5.4 km s-1). This unusual behaviour, which appears at relatively small phonon wavelengths observable by inelastic neutron scattering is in contrast to the long-wavelength sound velocities calculated from elastic constants which give 5.724 km s-1 for the symmetric and 5.114 km s-1 for the upper antisymmetric branch. They explain this observation by the different sound velocities in the first and zero sound regimes.