Infra-Red Vibrations in NaCl

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Abstract
A detailed calculation has been made of the propagation properties of the lattice vibrations in NaCl. The phase velocity, the group velocity, displacement angle (angle between the particle displacement and the direction of propagation), and the displacement ratio were calculated as a function of wave‐length for three directions of propagation. In these calculations, Born's theory was used. The crystal has a low pass (acoustical) and at times overlapping upper band (optical). At the lowest frequency the waves are simply elastic ones. As the frequency increases, the structure exhibits strong dispersion. In the limit of shortest wave‐length, the group velocity approaches zero. The optical branch is highly dispersive at all frequencies. The group velocity is negative (on the single‐zone scheme), and approaches zero at both the short and long wave‐length limits. Generally, for both branches at the short wave‐length limit the particle displacement lines up along the direction of nearest neighbors. Exceptions to this occur for propagation along some highly symmetrical direction.

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