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

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 [Formula: see text], where vectors [Formula: see text] define (h k l) net planes parallel to the surface while [Formula: see text] 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, [Formula: see text], can be uniquely determined by linear transformations from the bulk lattice basis [Formula: see text]. The transformations depend on Miller indices (h k l) but not on 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.