Phonon Dispersion Curves in Bismuth

Dispersion curves for phonons propagating in the trigonal direction in bismuth at room temperature and at 75°K have been obtained in a neutron inelastic scattering experiment. Observed frequencies (units 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">13</sup> rad/sec) at 75°K are as follows: at the zone center, ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TO</inf> = 1.40 ± 0.02, ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LO</inf> = 1.89 ± 0.02; at the zone boundary in the trigonal direction, ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TA</inf> = 0.73 ± 0.01, ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LA</inf> = 1.12 ± 0.02, ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TO</inf> = 1.91 ± 0.02, ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LO</inf> = 2.03 ± 0.02. At room temperature, the observed frequencies were about 1.5 percent lower. Data were also obtained for longitudinal phonons propagating in the binary direction at 75°K. It is interesting to note that the splitting between the zone boundary frequencies for the optical and acoustic branches for each polarization is quite large. This splitting is difficult to understand if bismuth is thought of as a slightly distorted simple cubic lattice. The experimental results may be qualitatively understood if bismuth is considered to be made up of a series of double layers normal to the trigonal axis. The atoms in each double layer form a crinkled hexagonal net with strong, probably covalent, bonds between atoms. The forces between atoms on adjacent double layers are relatively weak. This model is consistent with the easy cleavage of bismuth normal to the trigonal axis. Analysis of the trigonal dispersion curves in terms of a linear chain model indicates that there are significant forces connecting a given atom with atoms situated on the four planes on either side of it.

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