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Circuit Protection, Grounding, and Service
Published in Radian Belu, Building Electrical Systems and Distribution Networks, 2020
Shielded cables contain a metallic layer just beneath the jacket to distribute evenly the electric field gradient throughout the insulation. This shield is sometimes provided in the form of a thin copper tape, or tape shield, which is grounded at the cable terminations. Typically, in three-phase circuits, each cable has enough copper strands in its concentric neutral to make up one-third of the system neutral. Conduits subjected to large temperature variations, usually in outdoor and some industrial applications, can expand or contract depending on the temperature fluctuations. The amount of the conduit expansion or contraction is computed by using the thermal expansion relationship: ΔLcond=Lrun×TECCond×ΔT
Basic Principles of EPR and NMR Spectroscopy
Published in Evgenii Talsi, Konstantin Bryliakov, Applications of EPR and NMR Spectroscopy in Homogeneous Catalysis, 2017
Evgenii Talsi, Konstantin Bryliakov
Another important relaxation mechanism appears for nuclei with I > 1/2 because these have nonzero electric quadrupole moments Q, which is able to interact with electric field gradients. The electric field gradient is provided by an asymmetric distribution of electron density around the nucleus. In liquids, the effect of quadrupolar interactions on the position of NMR resonances is averaged due to diffusional motions, but these interactions effectively induce spin relaxation. For all quadrupolar nuclei, quadrupolar relaxation dominates over all other relaxation mechanisms. Therefore, the NMR resonances of quadrupolar nuclei (that are ubiquitous in inorganic and organometallic chemistry) can be several kHz wide, which complicates their detection and masks the observation of scalar couplings that the observed nuclei are involved in, as well as small chemical shift differences.
Catalytic Surfaces and Catalyst Characterization Methods
Published in James J. Carberry, Arvind Varma, Chemical Reaction and Reactor Engineering, 2020
W. Nicholas Delgass, Eduardo E. Wolf
The second spectral parameter is quadrupole splitting (QS). This effect removes the magnitude but not the sign degeneracy of the nuclear spin states. In 57Fe, for example, the I = 3/2 excited state is split into Iz = ±3/2 and Iz = ±1/2 states. The ground state, with I = 1/2, is un-split. A quadrupole split spectrum for 57Fe in an isotropic powered sample has two lines of equal density (Greenwood and Gibb, 1971). The size of the splitting depends on the nuclear quadrupole moment (a constant) and the electric field gradient (EFG) at the nucleus. The EFG is a measure of the symmetry of the electronic environment of the atom. It is zero for cubic and tetrahedral symmetry, but increases in magnitude for more highly asymmetric arrangements. There are two important contributions to the EFG. The lattice component arises from the surroundings of the atom. The electronic component is a result of the valence election configuration of the atom itself. High-spin Fe3+ has an electron EFG of zero. The extra d electron on Fe2+ causes a strong, temperature-dependent quadrupole splitting when 57Fe is in a low-symmetry environment (Wertheim, 1964), The combined effects of isomer shift and quadrupole splitting are shown in Fig. 17, which illustrates oxidation/reduction of Fe/Y-zeolite (Garten et al., 1970). Spectrum 17a shows two ferrous states, with spectra corresponding to a large outer and smaller inner doublet. Spectrum 17b corresponds to Fe3+ and spectrum 17d to ferrous ions whose bonding to the zeolite has been weakened by hydration.
Effect of correlated hyperfine theory errors in the determination of rotational and vibrational transition frequencies in HD+
Published in Molecular Physics, 2022
In , the hyperfine structure arises from magnetic interactions between the proton, deuteron, electron, and molecular rotation, as well as the interaction of the deuteron electric quadrupole moment with the molecular internal electric field gradient. These interactions are described (to lowest order) by the Breit-Pauli Hamiltonian, but in practice it is more convenient to capture all interactions within an effective spin Hamiltonian that is specific to a given rovibrational state v, N. The currently most elaborate version of the effective spin Hamiltonian contains nine interaction terms [26]. The strength of each of the nine terms is characterised by a spin coefficient, (), which are obtained numerically by averaging the corresponding terms of the Breit-Pauli Hamiltonian, as well as possible high-order terms derived using the nonrelativistic quantum electrodynamics (NRQED) approach, over the rovibrational wavefunction [21,22,26].
Study on variable temperature Mössbauer spectra of GdFe0.5Cr0.5O3 perovskite
Published in Phase Transitions, 2021
Lebin Liu, Jiajun Mo, Haiwen Chen, Min Liu, Yanfang Xia, Anguo Peng
Superfine field, valence state and symmetry of 57Fe can be obtained by superfine interaction force (IS, QS, Γ, H) between 57Fe nucleus and external environment [24]. According to IS, the chemical bonds, valence states and coordination groups of Mössbauer nuclides can be determined, and IS is affected by the s electron density around the atomic nucleus. The electric field gradient (EFG) causes the change of QS, and EFG originates from the asymmetric distribution of valence electrons around the atomic nucleus or the asymmetric distribution of ionic charge in the crystal [25,26]. The structural information of atoms in the sample can be obtained by QS. In addition, when in a magnetically ordered state, the quadrupolar and magnetic interactions coexist, and their joint action leads to the quadruple shift, namely, on the basis of the existing magnetic splitting energy level, the spectral line increases or decreases an offset caused by the quadrupole interaction. QS at 120 K and 12 K (Table 1) is the quadruple shift. Based on previous research [27], in general, larger linewidths and broadenings refer to superparamagnetic behavior and chemical inhomogeneity, which are derived from local environment and size of nanocrystalline. simultaneously, this phenomenon also implies a helpful information that the nanocrystallinity of the sample is better maintained within the entire measurement temperature range.
Aspects of structural order in 209Bi-containing particles for potential MRI contrast agents based on quadrupole enhanced relaxation
Published in Molecular Physics, 2018
Hermann Scharfetter, Christian Gösweiner, Paul Josef Krassnig, Carina Sampl, Martin Thonhofer, Roland Fischer, Stefan Spirk, Rupert Kargl, Karin Stana-Kleinschek, Evrim Umut, Danuta Kruk
Recently, it was suggested to apply quadrupolar relaxation enhancement (QRE) as the central mechanism for a new class of extrinsic magnetic resonance imaging (MRI) contrast agents which rely on the shortening of the T1 relaxation time constant of water protons [1,2]. QRE effects stem from the fact that protons can transfer their magnetisation to a quadrupolar nucleus (QN, i.e. a nucleus with spin quantum number ≥1) via a mutual, dipole–dipole (DD) coupling. This process can only occur at magnetic fields at which the proton resonance frequency matches one of the transition frequencies of the QN between its energy levels. It manifests itself as a fast decay of the proton magnetisation interpreted as an enhanced spin–lattice relaxation rate R1 = 1/T1 [1-8] referred to as quadrupole peaks. The position of the quadrupole peaks is a function of the static magnetic field B0, the electric field gradient (EFG) at the location of the nucleus, the electrical quadrupole moment of the QN, its spin quantum number I and the angle between EFG and B0 [1-11].