VIBRATIONS OF A BORON $ICOSAHEDRON^{*}$
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Date
1985
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Ohio State University
Abstract
The $B_{12}$ icosahedron is a unit of $\alpha$- and $\beta$- boron crystals and of a number of boron molecules. Group properties of a regular icosahedron are well-known, but the normal modes have not been pictured heretofore. There are eight distinct frequencies for the thirty modes with 1-fold, 3-fold, 4-fold, and 5-fold degeneracies. Oscillations are here pictured in terms of three equilibrium icosahedral descriptions: one involves two parallel regular pentagons and two polar atoms, a second has two polar triangles and an equatorial puckered hexagon, while the third consists of six pairs of atoms on opposite faces of a cube. The visualizations should prove useful in application to heat conduction, substituent atom localization, and polaron electrical conduction in boron-rich borides.
Description
$^{*}$Supported by the Center for High Technology Materials, University of New Mexico and the Jet Propulsion Laboratory sponsored by NASA.
Author Institution: Department of Physics and Astronomy, The University of New Mexico
Author Institution: Department of Physics and Astronomy, The University of New Mexico