International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2010). Vol. B, ch. 1.4, p. 121

Table 1.4.4.1 

U. Shmuelia

Table 1.4.4.1| top | pdf |
Correspondence between types of centring in direct and reciprocal lattices

Direct latticeReciprocal lattice
Lattice type(s)Centring translationsLattice type(s)Restriction on hklMultiple unit cell
P, R   P, R   [{\bf a}^{*}], [{\bf b}^{*}], [{\bf c}^{*}]
A 0, [{1 \over 2}], [{1 \over 2}] A [k + l = 2n] [{\bf a}^{*}], [2{\bf b}^{*}], [2{\bf c}^{*}]
B [{1 \over 2}], 0, [{1 \over 2}] B [h + l = 2n] [2{\bf a}^{*}], [{\bf b}^{*}], [2{\bf c}^{*}]
C [{1 \over 2}], [{1 \over 2}], 0 C [h + k = 2n] [2{\bf a}^{*}], [2{\bf b}^{*}], [{\bf c}^{*}]
I [{1 \over 2}], [{1 \over 2}], [{1 \over 2}] F [h + k + l = 2n] [2{\bf a}^{*}], [2{\bf b}^{*}], [2{\bf c}^{*}]
F 0, [{1 \over 2}], [{1 \over 2}] I [k + l = 2n] [2{\bf a}^{*}], [2{\bf b}^{*}], [2{\bf c}^{*}]
  [{1 \over 2}], 0, [{1 \over 2}]   [h + l = 2n]  
  [{1 \over 2}], [{1 \over 2}], 0   [h + k =2n]  
[R_{\rm hex}] [{2 \over 3}], [{1 \over 3}], [{1 \over 3}] [R_{\rm hex}] [-h + k + l = 3n] [3{\bf a}^{*}], [3{\bf b}^{*}], [3{\bf c}^{*}]
  [{1 \over 3}], [{2 \over 3}], [{2 \over 3}]