Quadrupole

About: Quadrupole is a research topic. Over the lifetime, 14614 publications have been published within this topic receiving 261495 citations. The topic is also known as: quadrapole & electric quadrupole.

Quadrupole Effects in Nuclear Magnetic Resonance Studies of Solids

Abstract: 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.

Atomic polarizabilities and shielding factors

Abstract: A detailed discussion is given of the methods of calculating atomic polarizabilities and shielding factors and the relationships between them are demonstrated. The formulation of the uncoupled Hartree-Fock approximation is presented and it is shown that the methods are all approximate versions of it. A more accurate procedure, the coupled Hartree-Fock approximation, is described. Comprehensive tables of dipole and quadrupole polarizabilities and of quadrupole shielding factors are included together with an assessment of the probable accuracy.

Nuclear Magnetic Resonance Multiplets in Liquids

Abstract: Multiple magnetic resonance lines have been observed for H1, F19, and P31 nuclei in compounds such as PH3, PF3, F2PO(OH), and BrF5, in the liquid state. The multiplets consisted of two to seven equally spaced narrow components, symmetrically placed about a central frequency, and with splittings from 0.02 to 0.8 gauss. These multiplets arise from a new variety of interaction among the nuclear moments in a molecule. Resonance lines were found to be multiple either when a nucleus interacted with a different species of nucleus or when there was interaction between nuclei of the same species with resonance frequencies separated by a chemical shift. No compounds exhibited multiplets attributable to interactions among structurally equivalent nuclei. Nor were multiplets caused by nuclei whose electric quadrupole moments were coupled to a direction fixed in the molecule.The number and relative intensities of the components of a multiplet were determined by the number and statistical weights of the various nuclear spin orientations of the nuclei causing the splitting. In a given molecule, the ratio of the multiplet splittings of the two different resonance lines was inversely proportional to the ratio of the gyromagnetic ratios of the interacting nuclei. The splittings were independent of applied magnetic field at 4180 and 6365 gauss; they were independent of temperature over ranges from 55°C to −130°C. In PF5, the one gas examined, the splitting of the doublet fluorine resonance was the same in the gas and liquid phases; also, the doublet was demonstrated to arise from coupling with the phosphorus nucleus, rather than from a chemical shift between the resonances from the apex and meridian fluorines in the bipyramidal structure, as proposed earlier.All of the above characteristics are accounted for theoretically by assuming the magnetic nuclei interact via magnetic fields inside the molecule. The qualitative aspects are predicted by coupling of the form A12μ1·μ2 between the nuclear moments μ1 and μ2. The coupling constant A12 depends upon the detailed mechanism, which must involve the molecular electrons. Second‐order perturbation theory was used to calculate the relative magnitudes of coupling via the electron orbital and the electron spin magnetic moments. The electron spin mechanism was found to give splittings ten to twenty times the orbital. Approximate calculation of the electron spin mechanism in several simpler cases gave good agreement with experiment. The influence upon the splittings of electric quadrupole coupling and spin‐lattice relaxation was considered and is discussed briefly.

Electrodynamics of Noble Metal Nanoparticles and Nanoparticle Clusters

Abstract: In this paper we examine the electrodynamics of silver nanoparticles and of clusters of nanoparticles, with an emphasis on extinction spectra and of electric fields near the particle surfaces that are important in determining surface-enhanced Raman (SER) intensities. The particles and clusters are chosen to be representative of what has been studied in recent work on colloids and with lithographically prepared particles. These include spheres, spheroids, truncated tetrahedrons, and clusters of two or three of these particles, with sizes that are too large to be described with simple electrostatic approximations but small compared to the wavelength of light. The electrodynamics calculations are mostly based on the discrete dipole approximation (DDA), which is a coupled-finite element approach which produces exact or nearly exact results for particles of arbitrary size and shape if fully converged. Mie theory results are used to study the validity of the DDA for spherical particles, and we also study the validity of the modified long wavelength approximation (MLWA), which is based on perturbative corrections to the electrostatic limit, and of the single dipole per particle approximation (SDA). The results show how the dipole plasmon resonance properties and the electric field contours around the particle vary with particle shape and size for isolated particles. For clusters of particles, we study the effect of interparticle spacing on plasmon resonance characteristics. We also show that the quadrupole resonance is much less sensitive to particle shape and interparticle interactions than the dipole plasmon resonance. These results provide benchmarks that will be used in future comparisons with experiment.

Assignment of pre‐edge peaks in K‐edge x‐ray absorption spectra of 3d transition metal compounds: electric dipole or quadrupole?

Abstract: The characteristics of pre-edge peaks in K-edge x-ray absorption near edge structure (XANES) spectra of 3d transition metals were reviewed from viewpoints of the selection rule, coordination number, number of d-electrons, and symmetry of the coordination sphere. The contribution of the electric dipole and quadrupole transition to the peaks was discussed on the basis of the group theory, polarized spectra, and theoretical calculations. The pre-edge peak intensity for Td symmetry is larger than those for Oh symmetry for all 3d elements. The intense pre-edge peak for tetrahedral species of 3d transition metals is not due to 1s–3d transition, but transition to the p component in d–p hybridized orbital. The mixing of metal 4p orbitals with the 3d orbitals depends strongly on the coordination symmetry, and the possibility is predictable by group theory. The transition of 1s electron to d orbitals is electric quadrupole component in any of the symmetries. The d–p hybridization does not occur with regular octahedral symmetry, and the weak pre-edge peak consists of 1s–3d electric quadrupole transition. The pre-edge peak intensity for a compound with a tetrahedral center changes as a function of the number of 3d electrons regardless of the kind of element; it is maximized at d0 and gradually decreases to zero at d10. The features of pre-edge peaks in K-edge XANES spectra for 4d elements and the L1-edge for 5d elements are analogous with those for 3d elements, but the pre-edge peak is broadened due to the wide natural width of the core level. Copyright © 2008 John Wiley & Sons, Ltd.