Publisher Summary This chapter discusses quadrupole effects in nuclear magnetic resonance studies of solids. The first evidence that many nuclei possess magnetic moments came from the study of the hyperfine structure of atomic spectra in the visible region. The interaction of the nuclear magnetic moment with the magnetic field produced by the atomic electrons gives rise to a hyperfine spectrum that is relatively simple, being characterized by the well known “interval rule.” Marked departures from this interval rule do occur in a few cases, however, and some of the departures can definitely be attributed to the presence of a nuclear electric quadrupole interaction. The methods of radio-frequency spectroscopy are very well adapted for the investigation of the very small interaction energies to which nuclear moments give rise. They have led not only to much more precise determinations of nuclear magnetic moments, but also to a vastly increased knowledge of nuclear electric quadrupole effects. The first outstanding success along this line was the discovery, by the molecular beam resonance method, of the quadrupole moment of the deuteron. The field of electric quadrupole interactions in nuclear magnetic resonance can be divided roughly into two areas according to the relative magnitude of the nuclear quadrupole interactions.

Quadrupole Effects in Nuclear Magnetic Resonance Studies of Solids

A ‘year-2008’ set of nuclear quadrupole moments, Q, is presented. Compared to the previous, ‘year-2001’ set, a major revision of the value or an improvement of the accuracy is reported for 38Sr, 49In, 50Sn (Mossbauer state), 51Sb, 57La, 80Hg and 88Ra. Slight improvements or valuable reconfirmations exist for 7N, 11Na, 13Al, 53I, 56Ba and 71Lu.

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Year-2008 nuclear quadrupole moments

Dependence of the Pure Quadrupole Resonance Frequency on Pressure and Temperature

The infinite‐layer compound CrCl3 is found to undergo a first‐order phase transformation near 240°K. The crystal structures of the high‐ and low‐temperature phases have been elucidated by detailed x‐ray diffraction and 35Cl nuclear quadrupole resonance studies. The previously reported structure for CrCl3 is shown to be incorrect. The present single‐crystal diffraction results at 298° and 225°K give monoclinic (C2/m: a0=5.959 A, b0=10.321, c0=6.114 A, β=108.49°) and rhombohedral (R3: a0=5.942 A, c0=17.333 A) structures, respectively. The 35Cl quadrupole resonance frequencies, measured in polycrystalline samples, have been compared with results of field‐gradient calculations based on the ionic point‐charge model. The ionic contribution accounts for a large fraction of the total gradient making it impossible to evaluate the covalency parameters of the Cr–Cl bonds from the measured quadrupole coupling constants.

X‐Ray Diffraction and Nuclear Quadrupole Resonance Studies of Chromium Trichloride

From nuclear structure to the quadrupolar NMR interaction and high-resolution spectroscopy

Experimental measurements on nuclear quadrupole resonances of chlorine and antimony isotopes in solids have been made to an accuracy of about 0.001 percent. The results are compared in detail with theoretical results for (1) nuclear quadrupole interaction, (2) interaction between quadrupole coupling and thermal vibrations, and (3) effects of a nuclear hexadecapole. The ratio $\frac{{(\mathrm{eQq})}_{{\mathrm{Cl}}^{35}}}{{(\mathrm{eQq})}_{{\mathrm{Cl}}^{37}}}$ varies between 1.268736 and 1.268973 while $\frac{{(\mathrm{eQq})}_{{\mathrm{Sb}}^{123}}}{{(\mathrm{eQq})}_{{\mathrm{Sb}}^{121}}}$ varies from 1.274714 to 1.274770. These variations may be attributed to zero-point vibrations and to thermal vibrations, so that no clear evidence is found for nuclear polarization by surrounding electric fields. For $p$-dichlorobenzene, the temperature coefficient of the coupling constant of Cl and the variation of isotopic coupling ratio with temperature are shown to be in fair quantitative agreement with the extension of Bayer's theory of vibrational effects. Relaxation times, Zeeman effects, and certain effects due to crystal structure are examined. Small discrepancies in the measured ratios of frequencies of transitions in ${\mathrm{Sb}}^{121}$ and ${\mathrm{Sb}}^{123}$, which can be attributed to nuclear hexadecapole interactions are found. These indicate a hexadecapole coupling constant in ${\mathrm{Sb}}^{123}$ of 24 kc/sec and a ratio of the ${\mathrm{Sb}}^{123}$ hexadecapole coupling to that of ${\mathrm{Sb}}^{121}$ of 0.8\ifmmode\pm\else\textpm\fi{}0.3. A convenient high-sensitivity circuit for observation of nuclear resonances in solids has been developed and is discussed.

Tien-Chuan Wang

Papers

Pure Nuclear Quadrupole Spectra of Chlorine and Antimony Isotopes in Solids