Solid-state nuclear magnetic quadrupole interaction

Principles and Characteristics An interaction that is never directly seen in liquid spectra but that, if present, always dominates solid-state spectra is quadrupole interaction. Nuclei with I > Vi have an electric quadrupole moment Q that is a measure of the deviation of the nuclear charge distribution from spherical symmetry. Nuclei with 7 = 0, Vi do not care about electric field gradients their charge distribution is spherical. Some 74% of all NMR-active nuclei have I > V2, as listed elsewhere [763]. The nuclear electric quadrupole moment, 2, of an 7 > 1 nucleus can interact with the electronic environment near that nucleus to affect the nuclear spin angular momentum energy levels, even in zero magnetic field. Quadrupole interactions can... 

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... 

It can now be predicted with confidence that machine calculations will lead gradually toward a really fundamental quantitative understanding of the rules of valence and the exceptions to these toward a real understanding of the dimensions and detailed structures, force constants, dipole moments, ionization potentitils, and other properties of stable molecules and equally unstable radicals, anions, and cations, and chemical reaction intermediates toward a basic understanding of activated states in chemical reactions, and of triplet and other excited states which are important in combustion and explosion processes and in photochemistry and in radiation chemistry and also of intermolecular forces further, of the structure and stability of metals and other solids of those parts of molecular wave functions which are important in nuclear magnetic resonance, nuclear quadrupole coupling, and other interaction involving electrons and nuclei and of very many other aspects of the structure of matter which are now understood only qualitatively or semi-empirically. 

The term microenvironment is of fundamental importance in M5ssbauer spectroscopy. It is directly related to the hyperfine interactions sensed by the nucleus. In a solid studied by Mdssbauer spectroscopy, there are a large number of nuclei of the M5ssbauer isotope. They all sense local hyperfine interactions, which are determined by the product of a nuclear parameter (charge equivalent nuclear radius, Ry nuclear quadrupole moment, Q, and nuclear magnetic moment, /r) and a solid-state parameter (electronic density, p, electric field gradient represented by V22 and rj, and magnetic flux density, B) (see OEqs. (25.60), (0 25.68), and (025.74)). 

It is usual in magnetic solids for the main influence on the Mdssbauer spectrum to be felt through the interactions [1] and [2]. That is, the nucleus senses its own atom and the state of the solid via the effect of the solid on that atom. The interactions of class [1] are (i) the magnetic hypeifine interaction between the atomic spin S and the nuclear spin /, (ii) the interaction between the nuclear quadrupole moment Q (which is proportional to the deviation from a spherical distribution of nuclear charge) and the electric field gradient (EFG) produced by the electronic charge distribution of the atom, and (iii) the electrostatic interaction of the... 

The last three terms of the spin Hamiltonian shape the Mossbauer spectrum because they describe the interaction of the nucleus with the atom, the solid and the external magnetic field. The term I - A - S describes the magnetic interaction between the nucleus and the atom. This acts through components of the atomic spin which are determined by the Boltzmann population of the spin Hamiltonian states shown in Figure 4.2. Thus the first three terms of the spin Hamiltonian act to determine values for the components of S that are used in the magnetic interaction that shapes the Mossbauer spectrum. The mechanisms involved in this nucleus-atom interaction I A S will be discussed in detail in the next section. The quadrupole interaction term represents the interaction of the nuclear quadrupole moment with the EFG produced by the atom and the lattice. The principal component of the EFG is V — d Vldz (V is the electric potential at the nucleus) and the asymmetry parameter =... 

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)]. 

Low natural abundances, low gyromagnetic ratios and high quadrupole moments of several NMR active isotopes of the series from yttrium to cadmium can cause difficulties in solution state NMR. How ever, these formidable obstacles in the solution state can be turned to advantages in solid state NMR. Low natural abundance (i.e. dilute spins) can help in solid state measurements because the problem raised by dipolar interactions between like spins is elimi nated. Sensitivity problems found with low gyromag netic ratios in the solution state can be overcome in the solid state by the cross-polarization (CP) tech nique by which the magnetization of the observed nucleus (S) can be increased by a factor, Th/Ts- Fur ther, a nuclear quadrupole moment can result in con siderable sensitivity to local nuclear site symmetry, thus giving useful structural information. 

---