Difference between revisions of "Crystallographic basis"
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| − | = | + | <font color="blue">Base cristallographique</font> (''Fr''). <font color="red">Kristallographische Basis</font> (''Ge''). <font color="black">Base cristallografica</font> (''It''). <font color="purple">結晶基底</font> (''Ja''). <font color="green">Base cristalográfica</font> (''Sp''). |
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| − | === | ||
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| − | Base | ||
== Definition == | == Definition == | ||
| − | A basis of ''n'' vectors '''e<sub>1</sub>''', '''e<sub>2</sub>''', ... , '''e<sub>n</sub>''' of the vector space '''V<sup>n</sup>''' is a ''crystallographic basis'' of the vector lattice '''L''' if ''every'' integral linear combination '''t''' = ''u''<sup>1</sup>'''e<sub>1</sub>''' + ''u''<sup>2</sup>'''e<sub>2</sub>''' + ... + ''u<sup>n</sup>'''''e<sub>n</sub>''' is a lattice vector of '''L'''. | + | A basis of ''n'' vectors '''e<sub>1</sub>''', '''e<sub>2</sub>''', ... , '''e<sub>n</sub>''' of the vector space '''V<sup>n</sup>''' is a ''crystallographic basis'' of the vector lattice '''L''' if ''every'' integral linear combination '''t''' = ''u''<sup>1</sup>'''e<sub>1</sub>''' + ''u''<sup>2</sup>'''e<sub>2</sub>''' + ... + ''u<sup>n</sup>'''''e<sub>n</sub>''' is a lattice vector of '''L'''. It may or may not be a [[primitive basis]]. |
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| − | [[ | ||
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| − | + | == See also == | |
| + | *[[Direct lattice]] | ||
| + | *Chapter 1.3.2.1 of ''International Tables for Crystallography, Volume A'', 6th edition | ||
| − | [[Category:Fundamental crystallography]] | + | [[Category:Fundamental crystallography]] |
Latest revision as of 17:31, 9 November 2017
Base cristallographique (Fr). Kristallographische Basis (Ge). Base cristallografica (It). 結晶基底 (Ja). Base cristalográfica (Sp).
Definition
A basis of n vectors e1, e2, ... , en of the vector space Vn is a crystallographic basis of the vector lattice L if every integral linear combination t = u1e1 + u2e2 + ... + unen is a lattice vector of L. It may or may not be a primitive basis.
See also
- Direct lattice
- Chapter 1.3.2.1 of International Tables for Crystallography, Volume A, 6th edition