Nuclear Magnetic Resonance Study of <i>β</i>-Rhombohedral Boron and Boron Carbide

Abstract

The 11B nuclear magnetic resonance (NMR) in β-rhombohedral boron and in boron carbide has been investigated at room temperature. Continuous wave (cw) measurements were performed at NMR frequencies 2–22 MHz, and pulse measurements at 29.5 MHz. Because of the crystal symmetry and the large number (105) of atoms per unit cell, the NMR in single-crystal β-rhombohedral boron is characterized by a very complex first-order quadrupole spectrum which is extremely sensitive to crystal orientation in the magnetic field. Measurements were made on powders to observe the orientation average of the spectrum, and first- and second-order quadrupole interactions were observed. The cw spectrum is a superposition of spectra corresponding to quadrupole coupling constants νQ1 = 680 ± 70 kHz (this apparently being the central value for a distribution of electric field gradients whose spectra cannot be resolved) and νQ2 in the range 90 ≲ νQ2 ≲ 170 kHz. There may also be a few sites for which νQ3 ≅ 0 (νQ = eqQ / 2). The intensities of the spectra corresponding to the various quadrupole couplings were measured by a cw technique, and also by a pulse technique which utilizes the fictitious spin-12 formalism. 80% ± 5% of 11B nuclei in β-rhombohedral boron were found to experience the quadrupole coupling νQ1 = 680 kHz, corresponding to the fact that 80% of the atoms in the crystal are six coordinated with icosahedral nearest-neighbor linkages. The spin–lattice relaxation mechanism in β-rhombohedral boron was found to be quadrupolar in nature. The spin–lattice recovery following a saturation pulse sequence can be fitted by the sum of two exponentials having time constants 5 and 52 msec (the central transition was observed). When the time constants are “normalized” so that only phonon contribution to the relaxation is considered, the strength of the spin–phonon interaction is found to be extremely large (more than an order of magnitude greater than in any alkali halides). The cw spectrum in a powder of boron carbide was found to be similar to that of β-rhombohedral boron in that it is characterized by quadrupole couplings νQa = 520 ± 30 and νQb &amp;lt; 30 kHz. At higher NMR frequencies an additional powder pattern was observed which has divergences corresponding to νQc = 2.74 ± 0.10 MHz. Intensity measurements showed that 4 ± 2 times as many 11B nuclei experience the coupling νQa as experience νQb; the powder pattern which has divergences corresponding to νQc arises from 17%–58% of all 11B nuclei in the boron carbide crystal. These results lend support to a model of the boron carbide crystal which assigns a boron atom to the central position of the three-atom chain and a carbon atom to the icosahedron (which, in the usual simple models of boron carbide, is assumed to be occupied only by boron atoms).