The Electric Field in Crystals: The Refractivity of Rutile

Applications of the Ewald method. I. Calculation of multipole lattice sums

“…Similarly, the interpretation of electronic spectra of crystals requires the evaluation of dipole-dipole and higher-order lattice sums (Craig & Walmsley, 1963;Decius, 1968;Philpott & Lee, 1973;Frech, 1973). The response of crystals to electric fields as measured by their dielectric properties (Agranovich, 1974;Sinha, Gupta & Price, 1974;Bolton, Fawcett & Gurney, 1962;Tessman, Kahn & Shockley, 1953;Koikov & Rozova, 1967) or Stark spectroscopy (Hochstrasser, 1973;Dunmur & Munn, 1975;Chen, Hanson & Fox, 1975) again requires a knowledge of appropriate lattice sums for its microscopic interpretation. The effect of static or dynamic strain on all these properties is principally due to changes in the lattice sums, which in turn may be expressed in terms of higher-order lattice sums.…”

Electric Field Gradient Calculations in Hexagonal Tungsten Bronze Type Fe3+ Fluorides: (H2O)0.33FeF3 and Anhydrous FeF3

“…Summations are then performed in such a way that Ihe convergence requirements are fulfilled [4, 51. All of the calculations are performed in the international standard axes. The various sums are extrapolated to an infinite crystal by the so-called Neville plot method [6]. The calculated EFG tensor is diagonalized to obtain the set of principal axes OXYZ and the principal components (I V, , l s I V, , l 2 I Vzzl).…”

Techniques and Convergence Properties of EFG Lattice Summations

“…Not only did the lattice sums converge slowly, but they also oscillated as the radius was increased because the number of ions within a spherical boundary does not increase smoothly with the volume enclosed. When the cavity is changed to one having the same shape as the unit cell of the crystal and containing an integral number of such unit cells, the convergence of the lattice summations becomes regular because the ratio of the number of ions within the cavity to the volume of the cavity is a constant (Bolton et al 1962). Nijboer and de Wette (1958) introduced an alternative method for the computation of lattice sums and this was applied to the evaluation of lattice EFGs in crystals by de Wette (1961) and de Wette and Schacher (1965).…”

“…A convenient method of extrapolating lattice sums is by means of Neville tables (see Section 4) as used by Bolton et al (1962) in the calculation of the electric fields at the ionic sites in rutile due to induced dipoles at all the other sites. If N is the number of unit cells in the side of the rectangular cavity, these authors found that the extrapolations to N = Cf) went as N -1 for cavities with ions on their faces or edges and as N -2 for cavities with no surface ions.…”