# Atomic surface

### From Online Dictionary of Crystallography

##### Revision as of 13:34, 18 May 2009 by TedJanssen (talk | contribs)

Surface atomique, fenêtre, domaine d'acceptation (Fr.)

Definition

Quasiperiodic structures may be considered as the intersection of a higher-dimensional
lattice periodic structure and the physical space. For point atoms or the vertices of
a tiling, the higher-dimensional structure consists of a periodic array of
objects with a dimension equal to *n-m*, the difference between the rank of the
Fourier module and the dimension of the physical space (usually three), and
transverse ( *i.e.* not tangential) to the physical space. The *atomic surface*
is the (*n-m*)-dimensional object in superspace (see there) corresponding to a point atom
in physical space.

For incommensurately modulated crystals with a smooth modulation function, these atomic surfaces are unbounded (cf. Fig. \ref{embed}). They have the same dimension as the internal space and they have lattice periodicity. For other aperiodic crystals, the atomic surfaces consists of disjoint components, the atomic domains (also called windows, atomic surfaces, or acceptance domains).

See also: Superspace, acceptance domain.

Figure Caption. A one-dimensional incommensurate phase with a two-dimensional modulation is the intersection of the one-dimensional physical space with an periodic array of two-dimensional surfaces, with three-dimenisonal lattice periodicity.