Electric field gradient quadrupole interaction

An obvious candidate for a standard Na sample is NaCl dissolved in water. A better solid standard at room temperature is NaCN (preferably sealed in a tube — it is poisonous). Even though its crystal structure is the same as that of NaCl, i.e., the sodium nuclei reside at sites of cubic symmetry, the sodium nuclei have much shorter T s due to the hindered rotation of the CN units which modulate the EFG (about the average value of zero) at the sodium sites. The cubic site is important because it allows the full intensity to be observed. In compounds with distorted Na sites, the electric field gradient will interact with the quadrupole moment to split the line so that only the central transition with only 20% of the... 

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. 

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. 

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 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... 

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. 

In Formulas (19) and (20) the actual value of the quadrupole moment Q that occurs is not that of the bare nucleus, but the bare nucleus value multiplied by a parameter 1 — This is necessary because the electron distribution of the atom is distorted when the atom is in an electric field gradient, due to the interaction of the electrons with the field gradient. This distortion produces an additional gradient which is —7 times the... 

The usefulness of quadrupolar effects on the nuclear magnetic resonance c I 7 yi nuclei in the defect solid state arises from the fact that point defects, dislocations, etc., give rise to electric field gradients, which in cubic ciystals produce a large effect on the nuclear resonance line. In noncubic crystals defects of course produce an effect, but it may be masked by the already present quadrupole interaction. Considerable experimental data have been obtained by Reif (96,97) on the NMR of nuclei in doped, cubic, polycrystalline solids. The effect of defect-producing impurities is quite... 

Numerous X-ray investigations have unravelled the solid state structure of contact and solvent-separated ion pairs. It was therefore considered to be of interest to evaluate also the potential of solid state NMR as a tool for the investigation of this structural problem. In addition to the study of chemical shifts discussed above (Section II.B), the quadrupole coupling constant of the nuclide Li, x( Li), was expected to be an ideal sensor for the bonding situation around the lithium cation because, due to its dependence on the electric field gradient, the quadrupolar interaction for this spin-3/2 nucleus is strongly influenced by local symmetry, as exemplified in Section II.C.3. This is also shown with some model calculations in Section ILF. 

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