Nuclear quadrupole interactions

The eigenfunctions for nonaxial nuclear quadrupole interaction are mixtures of the 7, mj) basis functions and thus do not possess well-defined magnetic quantum numbers. Strictly speaking, the states should not be labeled with pure quantum numbers m/. ... 

Y2Ba4Cu7025 Nuclear quadrupole interaction at copper sites, EFG tensor at all sites is calculated using the point charge model, conclusion that holes in the Y2Ba4Cu70i5 lattice are localized predominantly at positions of chain oxygen... 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

In summary, NMR techniques based upon chemical shifts and dipolar or scalar couplings of spin-1/2 nuclei can provide structural information about bonding environments in semiconductor alloys, and more specifically the extent to which substitutions are completely random, partially or fully-ordered, or even bimodal. Semiconductor alloys containing magnetic ions, typically transition metal ions, have also been studied by spin-1/2 NMR here the often-large frequency shifts are due to the electron hyperfine interaction, and so examples of such studies will be discussed in Sect. 3.5. For alloys containing only quadrupolar nuclei as NMR probes, such as many of the III-V compounds, the nuclear quadrupole interaction will play an important and often dominant role, and can be used to investigate alloy disorder (Sect. 3.8). 

In the first row of (3.1) the terms denote the electron Zeeman (2 EZ), the hf (2 hft), the nuclear Zeeman (XNZ) and the nuclear quadrupole interaction (CXQ) of the central (metal) ion. The second row represents the hf, the nuclear Zeeman and the nuclear quadrupole interactions for sets of magnetically equivalent ligand nuclei. Each particular set is denoted by the index k, the individual nuclei of set k by kx. 

The spin Hamiltonian for the nuclear quadrupole interaction has the form2,149,150) ... 

Nuclear Quadrupole Interactions of Transition Metal Ions... 

Townes-Dailey Description of the I4N Nuclear Quadrupole Interaction... 

To resolve hf and nuclear quadrupole interactions which are not accessible in the EPR spectra, George Feher introduced in 1956 a double resonance technique, in which the spin system is simultaneously irradiated by a microwave (MW) and a radio frequency (rf) field3. This electron nuclear double resonance (ENDOR) spectroscopy has widely been applied in physics, chemistry and biology during the last 25 years. Several monographs2,4 and review articles7 11 dealing with experimental and theoretical aspects of ENDOR have been published. 

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. 

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... 

A comprehensive review of the theoretical and experimental background needed to determine these parameters is given by Das and Hahn 4S> and by Reif and Cohen 40). More recent treatments of the whole subject may be found in the monograph by Lucken 143> and the review article by Schempp and Bray 1S9L A review on studies of nuclear quadrupole interactions for the period 1960 and 1966 is given by Weiss 125) and experimental data up to 1966 have been compiled by Biryukov et al 139>. 

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... 

The nuclear quadrupole interaction energy tensor / is usually quoted in MHz, corresponding to the value of eQq/h, although the h is usually omitted. 

Segal, S. L., and R. G. Barnes Catalog of Nuclear Quadrupole Interactions and Resonance Frequencies, Pt. I, Elements and Inorganic Compounds. Ames Laboratory Research and Development Report, U.S.A.E.C., Physics, T1D 4500 (1962). 

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

The femperafure-dependenf linewidfhs of fhe ESR hfs of La Cs2, Sc C82 and Gd C82 have been discussed by Kato et al. (1993, 1995a,b, 1996) in terms of fhe spin-rofafion coupling interaction. Dinse and co-workers (Ruebsam et al., 1995,1996a,b) investigated temperature dependence of ESR line widths of La Cs2/ La C9o, and Sc Cs2 in different solvents and obtained irrformation on the nuclear quadrupole interactions in these metallofullerenes. Dunsch and co-workers (Bartl et al., 1994,1997 Seifert et al., 1998) studied Y satellite structures of M C82 (M = Sc, Y, La) in detail and reported that the manifold of hfc (hyperfine constants) could be interpreted by the calculated spin density distributions. 

Figure 2 Spectrum of the J = 8-7 rotational transition of I32xe65cu35ci xiig complicated hyperfine structure arises from nuclear quadrupole interactions of Cu (7cu = 3/2) and Cl (Id = 3/2). All transitions are split into Doppler doublets as a result of the molecular expansion traveling parallel to the microwave cavity axis. For clarity of the picture, the quantum number assignments of only a few hyperfine components are given as F -F". The...

DPPH = 2,2-diphenyl-1-picrylhydrazyl ENDOR= electron-nuclear double resonance EPR = electron paramagnetic resonance ESE = electron spin echoes ESEEM = electron spin echo envelope modulation EFT = fast fourier transformations FWHM = fidl width at half maximum HYSCORE = hyperfine sublevel correlation nqi = nuclear quadrupole interaction TauD = taurme/aKG dioxygenase TWTA = traveling wave tube amphfier ZFS = zero field sphtting. 

---