Techniques and Convergence Properties of EFG Lattice Summations

Abstract

The calculation of electric field gradient (EFG) lattice sums over point charges in ionic crystals is considered. Although the de Wette method gives rapidly converging sums under favourable circumstances, direct summations over a unit cell-shaped cavity are found to produce lattice sums which converge regularly as N-2 (N is the number of unit cells in a side of the cavity), allowing accurate extrapolation to their values for an infinite lattice by means of Neville tables. This convergence behaviour can be explained mathematically for orthogonal lattices using the Euler-Maclaurin formula. A point charge calculation of the EFGs at low symmetry sites in GdFe03 has been carried out to compare the convergence of the direct summation and de Wette techniques and to illustrate the N-2 convergence of the direct lattice sums.

The effect of vacancy ordering on quadrupole shifts in Mössbauer spectra of maghemite

“…Many workers have used calculations of the electric field gradient (EFG) during Mössbauer analyses of materials. The calculations are usually based on a point charge model and seek convergence for the sum over a large crystal by using successively larger spherical shells [7], the de Wette slabsummation method [8] or electrically neutral unit cell shaped volumes [9]. We shall use the last method as described in section 2 because it produces the fastest convergence.…”