Elementary mesh

An elementary mesh called that of the base vectors and a two-dimensional crystal lattice spanned parallelogram . It is the equivalent of the unit cell, restricted to two dimensions . A two-dimensional crystal structure can be thought of as an elementary mesh displaced by integer multiples of the two basis vectors. The covering of the plane by the elementary meshes is complete and does not overlap. This covering is a type of tiling . ${\ displaystyle {\ vec {a}}}$${\ displaystyle {\ vec {b}}}$

Two-dimensional lattice and crystallographic base

The set of all translation vectors G, which map a two-dimensional crystal lattice onto itself, forms a point lattice . In the general case, the grid is that after

${\ displaystyle B: = \ left \ {\ left. \ sum _ {u, v} u {\ vec {a}} + v {\ vec {b}} \; \ right | \, u, v \ in \ mathbb {Z} \ right \} \ subseteqq G}$

is formed, a subset of the grid G, this becomes clear in the rectangular face-centered grid. If the grids G and B are identical, one speaks of a primitive elementary mesh.

Two-dimensional grid, base and surface structure

The places that are formed by the lattice points of the grid G ​​are not always the places where atoms can be found in a crystal , they only reflect the symmetry of the surface structure. The basis shows where the atoms can be found within the elementary mesh. In surface physics, it is often the case that the surface atoms are not arranged in one plane. It is therefore necessary to indicate the position of the atoms not only in the surface plane, but also in the direction perpendicular to the surface.