The Electric Field Gradient eq Point Charge Model

From the components eqp, of the electric field gradient tensor with respect to the system of the crystal axes, the coupling constant, eqzz = eq, and 17 can be calculated by transformation of the tensor to its principal axes. 

For application, Eq. (II.4) has to be considerably simplified. The simplest model is the assumption of point charges. We take the crystal lattice as composed from the point charges nte, where e is the elementary charge. The index i, o i k, distinguishes the different kinds of charged points (particles) within the lattice. Assuming the system of crystal axes already transformed to the principal axes system of the tensor, we calculate the coupling constant from 

The summation over the index j takes into consideration all particles of the charge number nt. Similar equations can be written for eqyy and eqxx and then T) can be be calculated. There is no doubt about the crudeness of this model. 

For ions, ym is between +1 and (-200). Negative values of yx lead to an amplification of the external field gradients. There are numerous published calculations of for ions and atoms 4.10 12, is,22,34,40,41,77,85-87,97,106, 120 . 

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