Anisotropy coupling , Electric field gradient

The expressions for the various parts of the Hamiltonian (equation 1) are well documented and for our purpose and the following discussion it suffices to summarize the results for axially symmetric situations in angular frequency units with the equations 2-6, where and Ashielding tensor and the shielding anisotropy, respectively, D is the dipole coupling, eq or V is the electric field gradient at the nucleus, eQ is the nuclear quadrupole moment and the other symbols have their usual meaning ... 

Fig. 4. Quadrupolar powder patterns (a) Spin NMR powder pattern showing that the central -)<- ) transition is broadened only by dipolar coupling, chemical shift anisotropy, and the second-order quadrupolar interactions, (b) Spin 1 NMR powder pattern for a nucleus in an axially symmetric electric field gradient (see text). The central doublet corresponds to 6 = 90° in Eq. (10). The other features of low intensity correspond to 6 = 0° and 6 = 180°. (c) Theoretical line shape of the ) - -) transition of a quadrupolar nuclear spin in a powder with fast magic-angle spinning for different values of the asymmetry parameter t (IS) ...

Fig. 3.1.1 Anisotropic spin interactions, (a) Quadrupole coupling of nucleus to the electric field gradient of a C- H bond, (b) Dipole-dipole coupling between C and H. (c) Anisotropic magnetic shielding of C nuclei. Left Geometry of the interaction and principal axes of the coupling tensor. Middle NMR spectrum for a single molecular orientation. Right The average over all orientations is the powder spectrum. The parameters A>, denote the anisotropy of the interaction k. S is the chemical shift. Adapted from [Blii3] with permission from Wiley-VCH.

The value of coefficient B is defined by crystalline fields originated from equilibrium positions of lattice ions. Magnetic spins are coupled with these fields via weak relativistic spin-orbit interaction (giving rise to above magnetic anisotropy energy), while electric dipoles are coupled with electric crystalline field electrostatically. In ferroelastics, the elastic dipoles constituting order parameter interact with elastic strain or gradients of crystalline field. 

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