Difference between revisions of "Direct space"
From Online Dictionary of Crystallography
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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''). <Font color="purple"> 直空間 </Font>(''Ja'') | + | <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''). <Font color="purple"> 直空間 </Font>(''Ja''). |
== Definition == | == Definition == | ||
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(i) To any two points ''P'' and ''Q'' of the point space ''E<sup>n</sup>'' a vector '''PQ''' = '''r''' of the vector space | (i) To any two points ''P'' and ''Q'' of the point space ''E<sup>n</sup>'' a vector '''PQ''' = '''r''' of the vector space | ||
| − | ''V<sup>n</sup>'' is attached | + | ''V<sup>n</sup>'' is attached. |
(ii) For each point ''P'' of ''E<sup>n</sup>'' and for each vector '''r''' of ''V<sup>n</sup>'' there is exactly one point ''Q'' of | (ii) For each point ''P'' of ''E<sup>n</sup>'' and for each vector '''r''' of ''V<sup>n</sup>'' there is exactly one point ''Q'' of | ||
| − | ''E<sup>n</sup>'' for which '''PQ''' = '''r''' holds | + | ''E<sup>n</sup>'' for which '''PQ''' = '''r''' holds. |
| − | (iii) If ''R'' is a third point of the point space, '''PQ''' + '''QR''' = '''PR''' | + | (iii) If ''R'' is a third point of the point space, '''PQ''' + '''QR''' = '''PR'''. |
== See also == | == See also == | ||
| − | [[ | + | *[[Direct lattice]] |
| − | ''International Tables | + | *''International Tables for Crystallography, Volume A'', 6th edition |
[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] | ||
Revision as of 13:16, 13 May 2017
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
- International Tables for Crystallography, Volume A, 6th edition