Table 1.1.1.1

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C. ch. 1.1, p. 3

E. Koch^a

^a Institut für Mineralogie, Petrologie und Kristallographie, Universität Marburg, Hans-Meerwein-Strasse, D-35032 Marburg, Germany

Table 1.1.1.1 | top | pdf |
Direct and reciprocal lattices described with respect to conventional basis systems

Direct lattice			Reciprocal lattice
$[{\bf a}_c, {\bf b}_c, {\bf c}_c]$			$[{\bf a}^_c, {\bf b}^_c, {\bf c}^*_c]$
Bravais letter	Centring vectors	Unit-cell volume	Conditions for reciprocal-lattice vectors $[h{\bf a}^_c+k{\bf b}^_c+l{\bf c}^*_c]$	Unit-cell volume	Bravais letter
A	$[{1\over2}{\bf b}_c+{1\over2}{\bf c}_c]$	2V		$[{1\over2}V^*]$	A
B	$[{1\over2}{\bf a}_c+{1\over2}{\bf c}_c]$	2V		$[{1\over2}V^*]$	B
C	$[{1\over2}{\bf a}_c+{1\over2}{\bf b}_c]$	2V		$[{1\over2}V^*]$	C
I	$[{1\over2}{\bf a}_c+{1\over2}{\bf b}_c+{1\over2}{\bf c}_c]$	2V		$[{1\over2}V^*]$	F
F	$[{1\over2}{\bf a}_c+{1\over2}{\bf b}_c,]$ $[{1\over2}{\bf a}_c+{1\over2}{\bf c}_c,]$ $[{1\over2}{\bf b}_c+{1\over2}{\bf c}_c]$	4V		$[{1\over4}V^*]$	I
R	$[{1\over3}{\bf a}_c+{2\over3}{\bf b}_c+{2\over3}{\bf c}_c]$ , $[{2\over3}{\bf a}_c+{1\over3}{\bf b}_c+{1\over3}{\bf c}_c]$	3V		$[{1\over3}V^*]$	R