Electrical field gradient interaction

In the literature [55], typical energies involved in the nuclear quadrupole moments -crystalline electric field gradient interactions range up to A E 2x 10-25 J. The measured AE seems to confirm the hypothesis that the excess specific heat of the metallized wafer is due to boron doping of the Ge lattice. 

The polarizabilities of N2, O2, and Ar are nearly the same (1.74, 1.58, and 1.63 in units of 10 " cm, respectively), and are all nonpolar. Consequently, they adsorb nearly the same on all sorbents except zeolites. The fact that zeolites can distinguish between N2 and O2 was observed as early as 1938 (Barrer, 1937 1938). Barrer reported values for heats of adsorption of N2 on chabazite as high as 8 kcal/mol. The high heats of adsorption were subsequently explained quantitatively in terms of the quadrupole-electric field gradient interactions (Drain, 1953 Kington and Macleod, 1959). The unique adsorption properties of zeolites derive from the fact that their surfaces are composed of negatively charged oxides with isolated cations that are located above the surface planes. Despite... 

The nuclear quadrupole moment and the electric field gradient interaction... 

The electric field gradient is again a tensor interaction that, in its principal axis system (PAS), is described by the tluee components F Kand V, where indicates that the axes are not necessarily coincident with the laboratory axes defined by the magnetic field. Although the tensor is completely defined by these components it is conventional to recast these into the electric field gradient eq = the largest component,... 

In a molecule, a given nucleus will generally experience an electric field gradient due to the surrounding electrons. The energy of interaction U between the nuclear quadrupole and the electric field gradient E is given by... 

Terms up to order 1/c are normally sufficient for explaining experimental data. There is one exception, however, namely the interaction of the nuclear quadrupole moment with the electric field gradient, which is of order 1/c. Although nuclei often are modelled as point charges in quantum chemistry, they do in fact have a finite size. The internal structure of the nucleus leads to a quadrupole moment for nuclei with spin larger than 1/2 (the dipole and octopole moments vanish by symmetry). As discussed in section 10.1.1, this leads to an interaction term which is the product of the quadrupole moment with the field gradient (F = VF) created by the electron distribution. 

If the nucleus feels both a magnetic field and an electric field gradient, and the electric quadrupole interaction is small, then the excited levels shift further and make the sextet asymmetrical, as observed in the spectrum of Fe203. 

In the case of covalent compounds, crystal-field theory is a poor model for estimating electric field gradients because of the extensive participation of ligand atomic orbitals in the chemical bonds. MO calculations are a much better choice, since the corresponding interactions are considered, and realistic (noninteger) population numbers are obtained for the central metal as well as the ligand atomic orbitals. 

Spiering, H. The Electric Field Gradient and Quadmpole Interaction. In Long, G. (ed.) Mossbauer Spectroscopy Applied to Inorganic Chemistry, p. 79. Plenum, New York (1984)... 

Both the ground state and the 67.4 keV nuclear excited state of possess a nonzero electric quadrupole moment. If placed in an inhomogeneous electric field (electric field gradient, EFG 0) the Ni nucleus undergoes electric quadmpole interaction with the EFG at the nucleus, as a result of which the 67.4 keV level will split into three substates /, wi) = 5/2, 5/2), 5/2, 3/2), and 5/2, 1/2) and the ground level will split into two substates 3/2, 3/2) and 3/2, 1/2). 

As such, nuclear contributions to the heat capacity due to the interaction between germanium crystalline electric field gradients and the quadrupole moments of boron nuclei could account for the observed onset of the Schottky anomaly. 

The strength of the quadrupolar interaction is proportional to the quadrupole moment Q of a nucleus and the electric field gradient (EFG) [21-23]. The size of Q depends on the effective shape of the ellipsoid of nuclear charge distribution, and a non-zero value indicates that it is not spherically symmetric (Fig. 1). 

Fig. 1 (a) Schematic representation of the spherical and non-spherical charge distribution in a nucleus. The value of electric quadrupole moment Q for the quadrupolar nucleus depends on the isotope under consideration, (b) The quadrupolar interaction arises from the interaction of Q with surrounding electric field gradient (EFG)... 

Solid state 2H NMR parameters are almost exclusively governed by the quadrupole interaction with the electric field gradient (EFG) tensor at the deuteron site.1 8 The EFG is entirely intramolecular in nature. Thus molecular order and mobility are monitored through the orientation of individual C-2H bond directions. Therefore, 2H NMR is a powerful technique for studying local molecular motions. It enables us to discriminate different types of motions and their correlation times over a wide frequency range. Dynamics of numerous polymers has been examined by solid state 2H NMR.1 3,7,9 Dynamic information on polypeptides by NMR is however limited,10 26 although the main-chain secondary structures of polypeptides in the solid have been extensively evaluated by 13C and 15N CP/MAS NMR.27,28... 

If the spin-quantum number, Ik, of a spin k is larger than 1/2, we have an additional term in the Hamiltonian, the quadmpolar coupling, hPk. The quadmpolar Hamiltonian arises from the interaction between the electric-field gradient and the nuclear spin. The first-order quadrupolar Hamiltonian is given by ... 

Because the interactions measured in Mossbauer experiments are products of atomic and nuclear factors, experiments on iodine isotopes have yielded values of the change of nuclear radius between the ground state and the excited state, AR/R, quadrupole moment values Q, and magnetic moment values, fi, as well as electric field gradients and internal magnetic fields. 

SSNMR studies based on Li, Na, and Cs nuclei for 1100 EW samples whose sulfonate groups were exchanged with these cations (no excess counterions or co-ions being present) were conducted versus water content.The spectra reflect the influence of the immediate chemical environment about these cations that have spins greater than /2 and, therefore, possess quadrupole moments. It is the interaction of these quadrupole moments with local electric field gradients that influences the chemical shift (d) and line width of the observed resonance. In this case, the electric field is mainly due to —SO3 anions as shielded by water molecules. 

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... 

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