| A technique has been developed to evaluate the Coulomb potential at sites near a semi-infinite crystal surface. Previously used slab calculations, which model the surface as being one face of an infinite slab, are inadequate for polar surfaces because of a nonvanishing influence due to the other face of the slab. The effects of this "second surface" can be eliminated by including a correction term in the slab calculation which, in effect, accounts for the potential due to all the ions in the semi-infinite crystal which are not contained in the slab. The semi-infinite crystal is therefore described by an infinite slab plus all the ions below the slab and the potential at a site is the sum of the potentials due to the ions in the slab and those ions below the slab. The latter potential is constant in space, depending only on the identity of the second surface. We refer to this technique as the "corrected sum-over-slabs" method.;A single crystal of nearly stoichiometric magnetite grown from the melt was oriented and cut to expose a (100) face. The surface stoichiometry was varied by exposure of the crystal to O(,2) or H(,2) at 400(DEGREES)C, 550(DEGREES)C, or 600(DEGREES)C. The surface structure at various surface stoichiometries was probed using LEED. It was found that the structure changed very little over the range of stoichiometries studied, namely from FeO(,1.26) to FeO(,1.50). LEED showed a pattern quite similar to that expected for the simple truncated bulk surface. The lattice spacing was very nearly that of the bulk Fe(,3)O(,4) (100) plane. Some of the spots were seen to fade upon reduction by H(,2) and some streaking occured. These observations are consistent with the bulk structural changes in the phase transitions between wustite, magnetite, and (gamma)-hematite.;The method is applicable to any surface. We have applied it to the (100), (110), (201), and (111) surfaces of NaCl and to the (100), (110), and (111) surfaces of the inverse, random, and normal spinel structures. In comparing the coulombic terms of the surface energies of the unrelaxed surfaces it was found that the (100) surface was the most stable surface in both the rock salt and spinel structures. |
