Electric Field Gradients in Point-Ion and Uniform-Background Lattices

The lattice contribution to the field gradient in ionic crystals and metals is a quantity which has a well-defined value. However, for an actual evaluation, the field gradient is usually broken up into a number of conditionally convergent series with poor convergence. Rapidly convergent expressions for these series, and consequently, for the field gradient can be obtained by applying the method of plane-wise summation. This method is applied to the field gradient in ionic crystals with tetragonal and hexagonal symmetry and to the field gradient in tetragonal and hexagonal close-packed metal structures. As an example, an expression for the field gradient at the position of the anion is derived for ionic crystals with the Cd${\mathrm{I}}_{2}$ structure. This expression is numerically evaluated for Co${\mathrm{Br}}_{2}$, Fe${\mathrm{Br}}_{2}$, Mg${\mathrm{Br}}_{2}$, Mn${\mathrm{Br}}_{2}$, Ca${\mathrm{I}}_{2}$, Cd${\mathrm{I}}_{2}$, Co${\mathrm{I}}_{2}$, Fe${\mathrm{I}}_{2}$, Ge${\mathrm{I}}_{2}$, Mg${\mathrm{I}}_{2}$, and Mn${\mathrm{I}}_{2}$. Rather extensive numerical results are also presented for both close-packed metal structures, including values for the field gradient in Li, Be, Zn, In, and Rh.

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