Direct space

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== Other languages ==
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<Font color="blue">Espace direct </Font>(''Fr''). <Font color="red">Direktes Raum </Font>(''Ge''). <Font color="green">Espacio directo (''Sp'').<Font color="black"> Spazio diretto (''It'')
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Espace direct (''Fr''). Direktes Raum (''Ge''). Espacio directo (''Sp'').<Font color="black"> Spazio diretto </Font>(''It'')
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== 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

See also

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