# Direct space

(Difference between revisions)
 Revision as of 15:28, 17 March 2006 (view source) (→Other languages)← Older edit Revision as of 05:50, 18 March 2006 (view source)Newer edit → Line 1: Line 1: - == Other languages == + Espace direct (''Fr''). Direktes Raum (''Ge''). Espacio directo (''Sp''). Spazio diretto (''It'') - + - Espace direct (''Fr''). Direktes Raum (''Ge''). Espacio directo (''Sp''). Spazio diretto (''It'') + == Definition == == Definition ==

## Revision as of 05:50, 18 March 2006

Espace direct (Fr). Direktes Raum (Ge). Espacio directo (Sp). Spazio diretto (It)

## Definition

The direct space (or crystal space) is the point space, En, in which the structures of finite real crystals are idealized as infinite perfect three-dimensional structures. To this space one associates the vector space, Vn, of which lattice and translation vectors are elements. It is a Euclidean space where the scalar product of two vectors is defined. The two spaces are connected through the following relations:

(i) To any two points P and Q of the point space En a vector PQ = r of the vector space Vn is attached

(ii) For each point P of En and for each vector r of Vn there is exactly one point Q of En for which PQ = r holds

(iii) If R is a third point of the point space, PQ + QR = PR