Lattice vibrations of the icosahedral solid. alpha. -boron
- Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico (USA)
Crystalline {alpha}-boron consists of B{sub 12} icosahedra in a rhombohedral lattice of {ital R}{bar 3}{ital m} space-group symmetry. We here carry out a classical force-field analysis of the lattice vibrations. The {bold q}={bold 0} Brillouin-zone vibrations are treated as those of a {ital D}{sub 3{ital d}}-point-group-symmetry B{sub 12} cluster perturbed by intericosahedral crystalline forces; valence-force constants are fitted to account for Raman and ir spectral data. Two-centered intericosahedral bonds are found to be twice as strong as intraicosahedral bonds, while three-centered crystalline bonds are almost as strong as those within a B{sub 12} unit. The highest-frequency Raman line arises from the breathing mode, strongly perturbed by the two-centered interactions. The lowest-observed-frequency Raman line is attributed to B{sub 12} libration. As crystal-force-field strengths are turned up, noncrossing of frequencies is encountered; we, therefore, correlate {alpha}-crystal modes with {ital I}{sub {ital h}} regular-icosahedral and {ital D}{sub 3{ital d}} B{sub 12}-cluster modes through eigenvector expansions. Useful classical predictions are made of ir intensities for wave vector {bold q}={bold 0} modes by considering adjacent bond stretching; a prediction of Raman intensities in terms of bond polarizabilities appears to be of very limited value. The phonon analysis is extended from the Brillouin-zone center to the edges by introducing phase-angle differences along two distinct (one {ital C}{sub 3} and one {ital C}{sub 2}) rotational-symmetry axes. The acoustical-branch wave speeds are predicted to be 1.1{times}10{sup 6} and 0.38{times}10{sup 6} cm/sec for the {ital c}-direction longitudinal and transverse components, respectively.
- OSTI ID:
- 5344319
- Journal Information:
- Physical Review, B: Condensed Matter; (United States), Vol. 44:6; ISSN 0163-1829
- Country of Publication:
- United States
- Language:
- English
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