Electric asymmetry parameter

Nuclear electric quadrupole QCC (quadrupole coupling constant), (asymmetry parameter) Line-shape analysis, nutation NMR Coordination symmetry... 

Here, I, I, and I are angular momentum operators, Q is the quadrupole moment of the nucleus, the z component, and r the asymmetry parameter of the electric field gradient (efg) tensor. We wish to construct the Hamiltonian for a nucleus if the efg jumps at random between HS and LS states. For this purpose, a random function of time / (f) is introduced which can assume only the two possible values +1. For convenience of presentation we assume equal... 

An instructive description of the first-order perturbation treatment of the quadrupole interaction in Ni has been given by Travis and Spijkerman [3]. These authors also show in graphical form the quadrupole-spectrum line positions and the quadrupole-spectrum as a function of the asymmetry parameter r/ they give eigenvector coefficients and show the orientation dependence of the quadrupole-spectrum line intensities for a single crystal of a Ni compound. The reader is also referred to the article by Dunlap [15] about electric quadrupole interaction, in general. 

The electric quadmpole interaction is described by A q = (c2Fzz/4)(l - -asymmetry parameter rj. The latter was assumed to be zero in the least-squares fits of the OSO2... 

Asymmetry in the ligand environment, either geometric or in charge distribution (or both), affect the asymmetry parameter, tp An r = 0 value corresponds to complete axial symmetry, whereas r = 1 corresponds to pure rhombic symmetry. Electric monopole interactions between the nuclear charge distributions and the electrons at the nucleus cause a shift of the nuclear ground and excited states. These interactions are known as the isomer shift, 8. Both the Mossbauer source and the absorber (the sample of interest) experience an isomer shift, and it is customary to quote 8 relative to a standard, usually Fe metal or Na2[Fe(CN)5NO] 2H2O at... 

To calculate the nuclear quadrupole moment from the measured quadrupole splitting, it is necessary to know the electric field gradient, q, at the Te nucleus as well as the asymmetry parameter, rj. These can be calculated in the Townes and Dailey approximation (4) by knowing the chemical bonding in Te. 

Its magnitude is governed by the amount of electronic and nuclear nuclear charge that lies along the z axis along the C—bond. The shape of the interaction (electric field gradient tensor) is described by the asymmetry parameter (ti), which... 

When the gradient of the electric field does not have axial symmetry another parameter must be introduced to describe the magnitude of the electric field gradients in the solid. This is the asymmetry parameter j , which is a measure of the deviation from axial symmetry (5, 94). In addition, the direction of the principal axis of the electric field gradient tensor must be specified. From single crystal rotation patterns, the values of these parameters may be deduced (94). 

B magnetic Reid strength, Tesla, T / asymmetry parameter for a one-electron process C coulomb, the unit of electric charge... 

Fig. 4. Quadrupolar powder patterns (a) Spin NMR powder pattern showing that the central -)<- ) transition is broadened only by dipolar coupling, chemical shift anisotropy, and the second-order quadrupolar interactions, (b) Spin 1 NMR powder pattern for a nucleus in an axially symmetric electric field gradient (see text). The central doublet corresponds to 6 = 90° in Eq. (10). The other features of low intensity correspond to 6 = 0° and 6 = 180°. (c) Theoretical line shape of the ) - -) transition of a quadrupolar nuclear spin in a powder with fast magic-angle spinning for different values of the asymmetry parameter t (IS) ...

Where (i, is the usual asymmetry parameter and is a function, in general, of E. An analogous expression holds in PES except that ip is then the angle between the direction of ejection and the electric vector of the incident radiation. 

Here 0dm is the angle between the director and the largest component, eq, of the electric field gradient tensor, and rj is the asymmetry parameter. The different coordinate systems used are shown in Figure 1. 

The latter equation assumes a 100% linearly polarized ionizing radiation, a is the fine structure constant, Nni is the number of electrons in a nl subshell, Dni->ei l is a radial dipole photoionization amplitude, fini is the dipole photoelectron angular asymmetry parameter, and A i2 is the electric dipole-quadrupole interference term arising due to the correction term ikr in the above expression for Mab,... 

X the 33S nuclear quadrupole coupling constant (expressed in frequency units), and r] the asymmetry parameter of the electric field gradient tensor (0[Pg.21]

In these studies, the parameters that could provide the most interesting information are likely to be the electric field gradient (nuclear quadrupole coupling constant) at the 33S nucleus and its asymmetry parameter. Indeed, modifications of the lattice structure in different cement matrixes are expected to influence the symmetry of the electronic distribution around the sulphur nucleus more than the chemical environment of sulphur. 

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... 

For nuclei with 7 1, the nuclear electric quadrupole moment interacts with the electric field gradient in a nonsymmetric environment of electrons around the nucleus. The electric field gradient is described by a tensor that can be expressed in diagonal form (components Vx, VY, and IQ) in a principal axis system fixed in the molecule. By Laplace s equation the sum of the three components is zero, so there are two independent parameters, usually taken as the largest of the three components, V7 = d2V/dz2, and the asymmetry parameter tj = (Vx — IQ)/ Vz, with the convention that VZ VX. The electrical interaction leads to... 

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