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Difference between revisions of "Crystallographic basis"

From Online Dictionary of Crystallography

(Tidied translations and added Spanish (U. Mueller))
 
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<Font color="blue"> Base cristallographique </Font>(''Fr'').
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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'').
  
 
== 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'''.  
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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]].
  
=== See also ===
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== See also ==
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*[[Direct lattice]]
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*Chapter 1.3.2.1 of ''International Tables for Crystallography, Volume A'', 6th edition
  
[[direct lattice]]<br>
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[[Category:Fundamental crystallography]]
Section 8.1 of ''International Tables of Crystallography, Volume A''
 
 
 
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[[Category:Fundamental crystallography]]<br>
 

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