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Primitive cell (Read 2523 times)
Gerrit-Jan Linker
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Primitive cell
13.10.12 at 09:41:03
 
Primitive cell
 
Primitive cell:
A primitive cell is a unit cell built on the basis vectors of a primitive basis of the direct lattice, namely a crystallographic basis of the vector lattice L such that every lattice vector t of L may be obtained as an integral linear combination of the basis vectors, a, b, c.
 
It contains only one lattice point and its volume is equal to the triple scalar product (a, b, c).
 
Non-primitive bases are used conventionally to describe centred lattices. In that case, the unit cell is a multiple cell and it contains more than one lattice point. The multiplicity of the cell is given by the ratio of its volume to the volume of a primitive cell.  
 
Primitive basis:
A primitive basis is a crystallographic basis of the vector lattice L such that every lattice vector t of L may be obtained as an integral linear combination of the basis vectors, a, b, c.
 
Crystallographic basis:
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:
Conventional cell
http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1350114490/0#0
Unit cell
http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1350114408  
 
Source:
http://reference.iucr.org/dictionary/Primitive_cell
http://reference.iucr.org/dictionary/Primitive_basis
http://reference.iucr.org/dictionary/Crystallographic_basis
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« Last Edit: 13.10.12 at 13:10:53 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
Linker IT Software
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