Calculation of the Distortion in the Surface Region of an Alkali Halide Crystal Bounded by a {100} Face G. C. BENSON, P. I. FREEMAN, and EDWARD DEMPSEY
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Downloaded by TUFTS UNIV on June 3, 2018 | https://pubs.acs.org Publication Date: June 1, 1961 | doi: 10.1021/ba-1961-0033.ch005
Division of Pure Chemistry, National Research Council, Ottawa, Canada
The model described allows the ions of the first n layers at the free {100} face of a hemicrystal with sodium chloride structure to relax in a direction normal to the face and to be polarized by the electric field in the surface region. The equilibrium configuration is determined by minimizing the energy of the system. Numerical results for sodium chloride are presented for the five cases 1 ≤ n ≤5. A value of —107.4 erg cm. is estimated for the total correction to the surface energy of this material due to surface distortion. -2
m knowledge of the structure in the boundary region of a crystal is of considerable ^ importance to the understanding of surface phenomena in chemistry. It has been recognized for a long time that the relative configuration of the atoms or ions near the surface of a crystal will differ from that in the bulk of the material. Unfortunately, there is as yet no reliable experimental method for determining in detail what perturbations of the regular lattice structure occur and recourse must be made to the predictions of reasonable theoretical models. With few exceptions most theoretical investigations of surface distortion have been limited to the consideration of the outer layer and leave unanswered the question of how far significant distortion extends into the crystal. Recently Alder, Vaisnys, and Jura ( 1 ) have given a careful analysis of the depth of penetration of surface effects in inert gas crystals. It was found that the expansion between adjacent layers falls off as the inverse cube of the distance from the surface and that the deeper lying perturbations make relatively small contributions to the surface energy. In the case of ionic crystals, the presence of different ionic species and the possibility of polarization effects inherently complicate the estimation of surface distortion. Previous considerations of the depth of penetration of surface effects in these materials (7, 10) have used oversimplified interaction potential functions or have imposed rather severe constraints on the form of relaxation permitted. A fairly detailed treatment of the distortion in the outermost layer of a free {100 } 1
Present address, Union Carbide Corp. Research Institute, P. O. Box 278, Tarrytown, Ν. Y. 26
Copeland et al.; SOLID SURFACES Advances in Chemistry; American Chemical Society: Washington, DC, 1961.
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Downloaded by TUFTS UNIV on June 3, 2018 | https://pubs.acs.org Publication Date: June 1, 1961 | doi: 10.1021/ba-1961-0033.ch005
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Distortion of Alkali Halide Crystal
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Figure 1. Variables used to describe configuration in surface region of crystal with sodium chloride structure and bounded by {100} face
face of a semi-infinite alkali halide crystal has been given by Benson, Balk, and White (2); the present paper is a preliminary report of the extension of these calculations to a consideration of the distortion in the first five layers at the surface of a sodium chloride crystal. Further details of the calculations will be presented later, when results have been obtained for other alkali halides. Model and Method of Computation A section normal to the j 100} face of a semi-infinite crystal having a sodium chloride type structure is shown schematically in Figure 1. The nearest neighbor separation in the regular lattice is denoted by a. Layers parallel to the j 100 } face are indicated by an index λ, which for increasing depth takes on values 0, 1, 2, . . ., etc. The distortion is restricted to a surface region for which 0 ^ λ < η — 1; in the present work 1 < η < 5. Positive and negative ions of layer λ are as sumed to be displaced from the regular lattice sites, in the direction of the outward normal to the surface, by distances ζ I a and z^ a, respectively, and to have dipole moments ^ a n d μχίη this direction. Thus the values of four variables (z£, Ζχ, μ^ and μ, χ) are needed to specify the configuration of each layer in the surface region. The interaction energy of two ions, i and /, is taken to be "a
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