Nuclear Quadrupole Interactions in Solids

Besides NQR spectroscopy and the study of nuclear quadrupole interaction effects in broad-line NMR spectroscopy, paramagnetic electron resonance 6°1, Mossbauer spectroscopy, and the study of perturbed angular correlation of y-rays, are suitable methods for studying nuclear quadrupole interactions in solids. Indirect methods are also available for acquiring information about the nuclear quadrupole couplinjg constant from the liquid state (particularly NMR spectroscopy in liquids and in liquid crystals in some cases gives information about this constant). By microwave spectroscopy, the nuclear quadrupole interaction may be studied in the gaseous phase (see the paper by Zeil). We shall deal here only with the aspect of NQR spectroscopy in solids since this method has the broadest applicability to chemical problems in comparison with the other methods mentioned. 

Bersohn 76) has calculated the crystal field created by the molecular dipoles in the lattice of CH3C1. The static dipole moment of the molecules induces through the polarizability of the molecules an additional dipole moment which increases the dipole moment of the free molecule by a factor of about 1.05. This in turn means that the C—Cl bond has increased in ionic character under the influence of the intermolecular electric fields and therefore (see Eq. (II.9 the quadrupole coupling constant will be lower relative to the gaseous state. Besides the dipole moment induced in the direction of the static dipole, a perpendicular partial moment should be induced, too. Therefore the axial symmetry of the C—Cl bond will be disturbed and the asymmetry parameter 77 may become unequal zero. A small asymmetry parameter 17 = 0.028 has been observed for the nuclear quadrupole interaction in solid CH3I. Bersohn also calculated from the known crystal structure of 1,3,5-trichlorobenzene the induced... 

Smith JAS (1986) Nuclear quadrupole interactions in solids. Chemical Society Reviews 15 225-260. 

The second term in Eq. (II. 1) is the crucial one in discussing NQR investigations in the frame of chemical bonding in the solid state. In a general form, we may write the nuclear quadrupole interaction energy as... 

Segal, S. Unreported data quoted in Catalog of nuclear quadrupole interactions and resonance frequencies in Solids, Pt. I. 

Although solid state 2H NMR techniques are also used widely in structural studies, the principal use of these techniques has been to obtain detailed information on reorientational motions in the solid state, and our discussion is focused on this aspect of 2H NMR. As discussed above, the quadrupole interaction is usually the dominant nuclear spin interaction in 2H NMR, and other nuclear spin interactions (e.g. dipole-dipole interaction, CSA and scalar J-coupling) are generally negligible in comparison. For 2H, the quadrupole interaction is typically about 150-250 kHz, whereas the direct dipolar interactions and CSA are typically about 10 kHz and 0.7 kHz (at 11.7 T) respectively. Since the EFG originates from... 

This section presents a phenomenological description of those aspects of solid-state NMR spectroscopy that are most useful for obtaining structural and dynamical information on phase transitions in minerals and the nature of disordered phases. The chemical shift and nuclear quadrupole interactions and their anisotropies receive particular emphasis, because they provide sensitive probes of the short-range structure, symmetry, and dynamics at the atomic position. Frequency shifts arising from these interactions can also serve as physical properties from which order parameters can be obtained for use in Landau-type treatments of the evolution toward a phase transition. 

Nuclear magnetic resonance (NMR) is perhaps the simplest technique for obtaining deuterium quadrupole coupling constants in solids or in liquid crystalline solutions. In ordinary NMR experiments with a magnetic field Hq > 104 gauss, the nuclear quadrupole interaction [Eq. (6)1 for deuterium is much smaller than the Zeeman interaction and can be treated as a perturbation to the Hamiltonian... 

The electron-spin echo envelope modulation (ESEEM) phenomenon [37, 38] is of primary interest in pulsed EPR of solids, where anisotropic hyperfme and nuclear quadrupole interactions persist. The effect can be observed as modulations of the echo intensity in two-pulse and three-pulse experiments in which x or 7 is varied. In liquids the modulations are averaged to zero by rapid molecular tumbling. The physical origin of ESEEM can be understood in terms of the four-level spin energy diagram for the 5 = / =i model system... 

Structural information has been obtained for solid HfL4 (L = tropolone, iV-benzoyl-, or JV-nitroso-iV-phenylhydroxylamine) complexes by obtaining the nuclear quadrupole interactions of Ta, produced by the p-decay of isoRf Xwo Ta sites were observed for the last two ligands suggesting that they exist in two isomeric forms. For the tropolonato-complex, a rapid interconversion between isomeric forms appears possible, and [Hf(tropolone)4]-CHCI3 seems to involve an interaction between the occluded solvent molecule and the ligand aromatic rings. °... 

Almost all quadrupolar nuclei in the Periodic Table have been studied experimentally in one or more of their compounds. A current list 0f these results is available in a database published by the JAICI (Japan Association for International Chemical Information, Tokyo, Japan). Biennial International Symposia on nuclear quadrupole interactions are also excellent sources of the latest experimental and theoretical works. As an illustration of the kind of solid-state problems that may be studied, we give some recent examples of such investigations. Sensitivity. or signal-to-noise ratio (SNR) in WQR spectroscopy, as well as NMR, depends on the observed frequency, which in turn, depends, inter alia, on the value of Q. The lighter elements tend to have low values of Q and low NQR frequencies and low sensitivities. for example, a... 

In the case that the energy levels are determined solely by the nuclear quadrupole interaction magnetic dipole transitions may still be observed in the radio frequency region. This specialization of NMR is referred to as nuclear quadrupole resonance (NQR), and furnishes a means of measiuing the quadrupole interaction parameters with great precision. The theoretical background, experimental methods, and reviews of results obtained in many areas of solid state physics and chemistry are contained in a number of standard books on the subject [Lucken (1969), Smith (1974)]. 

As outlined in section 1.3.2., the nuclear quadrupole interaction is characterized by two parameters, the coupling constant eQVz expressed in suitable energy units, and an asymmetry parameter tj indicating the degree of departure of the electric field gradient (efg) tensor Fy from axial symmetry. Information relevant to the lanthanide-containing metal, alloys, or compound is contained in these two parameters, since from the standpoint of the physics or chemistry of solids the quadrupole moment Q is taken to be a known property of the nuclear state. 

The main NMR interactions in solution of interest to chemists are the chemical shift relative to some stated standard (6), the indirect coupling constant (7) and the relaxation times T1 (spin-lattice) T2 (spin-spin related to the line width) and T p, the relaxation time in the rotating frame. In the case of solids and oriented samples both the direct dipole-dipole and the electric quadrupole interactions assume greater importance. We shall confine our attention in this chapter to diamagnetic compounds so that we may neglect nuclear interactions with electron spins. 

The usefulness of quadrupolar effects on the nuclear magnetic resonance c I 7 yi nuclei in the defect solid state arises from the fact that point defects, dislocations, etc., give rise to electric field gradients, which in cubic ciystals produce a large effect on the nuclear resonance line. In noncubic crystals defects of course produce an effect, but it may be masked by the already present quadrupole interaction. Considerable experimental data have been obtained by Reif (96,97) on the NMR of nuclei in doped, cubic, polycrystalline solids. The effect of defect-producing impurities is quite... 

Static quadrupole effects in NMR are observed in solids (9) and also in anisotropic liquid crystals (10, 11, 12). For nuclei with spin quantum numbers, I, greater than V2, the distribution of positive charge over the nucleus can be nonspherical and the situation can be described in terms of a nuclear electric quadrupole moment. The interaction between the quadrupole moment, eQ and electric field gradients, eq, shifts the energy levels of the nuclear spin states. 

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