Field gradient tensor

Fig. 4a-c. Sketch of simple motional mechanisms and resulting averaged field gradient tensors a Kink-3-bond motion b crankshaft-5-bond motion c 180° jump of phenyl ring... 

Electric field gradient tensor 24 Entanglements 124 Entropy model 200,201 Epoxy composites 192... 

The first derivative of the potential T at r = (0,0,0), taken as negative value, represents the ekctric field E, and the second derivative represents the electric field gradient tensor V at the nucleus,... 

When inserting into (4.5), the term ZeR will be multiplied with the elements of the electric field gradient tensor V. Fortunately, the procedure can be restricted to diagonal elements Vu, because V is symmetric and, consequently, a principal axes system exists in which the nondiagonal elements vanish, = 0. The diagonal elements can be determined by using Poisson s differential equation for the electronic potential at point r = 0 with charge density (0), AV = Anp, which yields... 

Physical Interpretation of the Electric Field Gradient Tensor... 

Table 5.7 Breakdown of the contributions to the largest field gradient tensor element in a.u. from spin-polarized B3LYP DPT calculations (from [60])...

JJor chemists interested in modem theories of chemical bonding, the most useful data obtainable by the Mossbauer technique are the magnitude and sign of the electric quadrupole field gradient tensor and the magnitude of the shift, 8, (which we prefer to call the chemical isomeric. Cl, shift), of the center of the Mossbauer spectrum relative to some standard absorber. Although a considerable amount of chemical and structural information is potentially available from quadrupole data on iron compounds, relatively little use has been made of such data in the literature, and we will not discuss this parameter here. We will instead restrict ourselves to two main points review of the explanations put forth to explain Cl shift data in iron compounds, and a survey of some of the correlations and generalizations which have been found. 

Considering only bonding between adjacent atoms on the same chain, the principal axes of the field gradient tensor are shown in Figure 5b. 

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). 

For a nonzero electric field gradient tensor V at the Ti sites, we expect for each Ti isotope 27 resolved quadrupole perturbed NMR fines. The frequency... 

B. Winkler, P. Blaha and K. Schwarz, Ab initio calculation of electric-field-gradient tensors of forsterite. Am. Miner., 1996,81,545-549. 

What is the orientation of the principal axes of the electric-field-gradient tensor q at O17 in H2017 ... 

Electric-field-gradient tensor, 230 Electric potential, 230 Electric quadrupole moment, 229-231, 365-366... 

If nuclei or their surroundings have any mobility, the resonance fine will narrow and become Lorentzian in shape. The cause of this behaviour is an averaging process of the components of the field gradient tensor. Quantitative considerations of the mobility mechanisms in zeolites are difficult to make and are beyond the scope of this article. 

Proton and fluorine are the most frequently studied nuclei in the solid state NMR of polymers. However, useful information can be obtained from deuterium resonance, (2H I = 1). In the presence of nuclei with spin I > 1/2, which possess a quadrupolar moment, the most dominant interaction occurs between the quadrupolar moment and an electric field gradient tensor V, generated by the C—D bonding electrons. Consequently, the only dominant interaction, besides Hz (Eq. (1)), will be described by the quadrupolar Hamiltonian, which for a single spin has the form ... 

The three components of the electric field gradient tensor are related by Poisson s equation, as shown earlier. However, the electrons that have a finite probability density at the nucleus, the s and p1/2 electrons, have a spherically symmetric distribution around the nucleus and as such do not contribute to E2. Thus, in the computation of E2, the Un can be related by... 

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