Electric field gradient fluctuations

S. Engstrdm and B. Jdnsson, Monte Carlo Simulations of the Electric Field Gradient Fluctuation at the Nucleus of a Lithium Ion in Dilute Aqueous Solution, Mol, Rhys., 43 (1981), 1235-1253. 

The orientation of the coordinate system in (1) is laboratory fixed with the z-axis along the static magnetic field Hq. The origin is chosen to coincide with the relaxing nucleus. In this coordinate system the components t) of the electric field gradient fluctuate due to the motion of the environment relative to the nucleus considered. 

Intermolecular quadrupolar 2 Fluctuation of the electric field gradient, moving multipoles Common for />1 In free Ions In solution [la... 

In the stochastic theory of lineshape developed by Blume [31], the spectral lines are calculated under the influence of a time-dependent Hamiltonian. The method has been successfully applied to a variety of dynamic effects in Mossbauer spectra. We consider here an adaptation due to Blume and Tjon [32, 33] for a Hamiltonian fluctuating between two states with axially symmetric electric field gradients (efg s), the orientation of which is parallel or perpendicular to each other. The present formulation is applicable for states with the same... 

While the nuclei 3H and 13C relax predominantly by the DD mechanism, relaxation of a quadrupole nucleus such as deuterium essentially involves fluctuating fields arising from interaction between the quadrupole moment and the electrical field gradient at the quadrupole nucleus [16]. If the molecular motion is sufficiently fast (decreasing branch of the correlation function, Fig. 3.20), the 2H spin-lattice relaxation time is inversely proportional to the square of the quadrupole coupling constant e2q Q/H of deuterium and the effective correlation time [16] ... 

Figure 10 A snapshot of the solvation of xenon in acetonitrile together with an ellipsoidal representation of electric field gradient (EFG). The EFG ellipsoid is on average rhombic, and fluctuates both in form and orientation. The fluctuations in the eigenvalues gives a fast vibrational averaging, and the long time decay in determined by reorientation of the EFG principal axis system.

It has been found that fluctuations in the orientation of the electric field gradient tensor due to torsional vibrations of the CIO3 group of KCIO3 account for the temperature dependence of the NQR frequency at low temperatures through changes in the values of the qa. Above 80 K, however, this does not adequately account for the variation since an expansion of the lattice occurs and the molecular vibrations cannot be approximated by harmonic oscillators. As the lattice expands, the distance between the ions increases, causing an additional decrease of qa and an increase in the sensitivity of the thermometer. 

The spin relaxation of most quadrupolar nuclei is completely given by the interaction of the nuclear quadrupole moment, eQ, with the electric-field gradient (e.f.g.) at the nucleus. To a good approximation the e.f.g. is generated in most molecular liquids exclusively by intramolecular charges. The interaction fluctuates in time because of the reorientation of the X—D or... 

The collapse of a six-line hyperfine spectrum with decreasing relaxation time is illustrated by the calculated spectra in Fig. 3.8 [44] for a " Fe nucleus in a fluctuating magnetic field and a fixed electric field gradient for different values of the electronic relaxation time. If the fluctuation rate is very slow compared to the precession frequency of the nucleus in the field H, the full six-line hyperfine pattern is observed. If the fluctuation rate is extremely rapid the nucleus will see only the time-averaged field which is zero and a symmetric quadrupolar pattern will be seen. At intermediate frequencies the spectra reflect the fact that the 2> -> transitions which make up the low-velocity component of the quadrupole doublet relax at higher frequencies than do the I I i> and -]-> -> transitions which... 

Fig. 3.8 Line shapes for an Fe nucleus in a fluctuating magnetic field and a fixed electric field gradient, for different values of the electronic relaxation time Tr. [Ref. 44, Fig. 2]...

Nuclear spin relaxation (NSR) does not require small particles because in certain cases nuclear spin depolarization occms by coupling of the nuclear electric quadmpole moment of the adsorbate to fluctuations in the substrate electric field gradient as the atom moves [95Chrl]. The depolarization of an initially prepared set of nuclear spins is monitored by thermal desorption into a special detector. Mathematical modeling is complicated, and only a small set of substrates and adsorbate nuclei can avoid competing depolarization processes. Spatial resolution depends on the length of diffusion before desorption, but lies near 10 nm. 

---