Direct space

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

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

See also

direct lattice
Section 8.1 of International Tables of Crystallography, Volume A