GENERAL METHOD TO SELECT CONVENIENT LATTICE VECTORS ON A SURFACE WITH ARBITRARY MILLER INDICES

K. Hermann
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K. Hermann: Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany

Surface Review and Letters (SRL), 1997, vol. 04, issue 05, 1063-1069

Abstract: Many theoretical methods dealing with electronic and structural properties of single crystal surfaces rely on a convenient description of the surface and bulk periodicity at the same time. This can be achieved by using surface adapted lattice vectors$({\bf R}^{\rm s}_1$, ${\bf R}^{\rm s}_2$, ${\bf R}^{\rm s}_3)$, where vectors${\bf R}^{\rm s}_1$, ${\bf R}^{\rm s}_2$define(h k l)net planes parallel to the surface while${\bf R}^{\rm s}_3$connects adjacent(h k l)net planes. For selected low index(h k l)surfaces of common crystals the construction of appropriate lattice vectors may be trivial. However, the general problem of determining a lattice basis adapted to a surface orientation which is described by Miller indices(h k l)in a general crystal lattice is more involved. In this paper we show that such bases,$({\hat{\bf R}}^{\rm s}_1, {\hat{\bf R}}^{\rm s}_2, {\hat{\bf R}}^{\rm s}_3), can be uniquely determined by linear transformations from the bulk lattice basis$({}{\bf R}_1$,\,${\bf R}_2$,\,${\bf R}_3)$. The transformations depend on Miller indices(h k l)butnoton the lattice type and can be quantified by number-theoretical methods. Thus, they are numerically stable and can be easily implemented in computational algorithms dealing with surfaces of most general crystals.

Date: 1997
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DOI: 10.1142/S0218625X97001310

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