Phonon Dispersion Curves in Bismuth

Abstract

Dispersion curves for phonons propagating in the trigonal direction in bismuth at room temperature and at 7S oK have been obtained in a neutron inelastic scattering experiment. Observed frequencies (units 10 1S rod/sec> at 7S oK are as follows: at the zone center, WTO 1,40 ± 0.02, (tJLO = 1.89 ± 0.02; at the zone boundary in the trigonal direction, WTA 0.73 0.01, Wr,A = 1.12 ± 0.02, WTO = 1.91 ± 0.02, UiLo = 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 7S oK. 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 laltice. 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. 234 ffiM JOURNAL • JULY 1964 235 " -,

Collective excitations and viscosity in liquid Bi

“…They make up 29% of the total at 573 K, increasing to 42% at 1023 K. At frequencies above 3-4 meV, the vibrational component dominates, showing a distinct peak around 9 meV at 573 K that moves to slightly lower frequencies at higher temperatures. This peak is within the range of frequencies found in crystalline Bi, 50 and its weakening at higher temperatures suggests that aspects of the crystalline structure are still present at 573 K and other temperatures near the melting point. 12,20 The diffusion coefficient, heat capacity at constant volume, entropy, and zero point energy determined by the TwoPT program 35 are shown in Table I.…”

“…1 Particularly striking is the deep minimum near q = 2.0 Å, which is close to the reciprocal lattice vector where a minimum occurs in the phonon spectrum of crystalline Bi. 50 A second, weaker minimum occurs at approximately twice this wave vector. This does not imply that the modes are "phononlike," but it does suggest that a process resembling umklapp scattering can occur in liquids as well as solids.…”

First‐ and second order Raman scattering in Sb and Bi at high pressure

“…The four features of the second order band all shift to higher frequencies under compression, as does the band above 400 cm , slightly lower than previous results [14,15,18], which is due to heating of the sample during laser irradiation as a result of not having good thermal contact to the diamond. Temperature estimates from the temperature dependence of the E 2g mode using the inelastic neutron data [11,12] give approximately 370 K. In addition there are rather weak features on the low frequency side of the E g mode at 47 cm -1 and 59 cm , marked by the asterisk in Fig. 3a, and more clearly to be seen in the background-subtracted spectra of Fig.…”

“…Investigations of Sb and Bi at normal pressure include phonon dispersion curves of Sb and Bi in the A7 phase by inelastic neutron scattering [11][12][13] and Raman spectroscopy [14][15][16][17]. High-pressure studies with the latter method were performed for both substances up to 0.7 GPa [18], in a recent study of Sb to 15 GPa [19], and for the lighter homologue As to 40 GPa [20].…”

Structure and dynamics in liquid bismuth and Bin clusters: A density functional study

“…6) cover the range of phonon frequencies measured in crystalline Bi [74-108 cm −1 , INS at 300 K; 60 …”