International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 3.4, p. 273

Table 3.4.2 

A. Altomare,a* C. Cuocci,a A. Moliternia and R. Rizzia

aInstitute of Crystallography – CNR, Via Amendola 122/o, Bari, I-70126, Italy
Correspondence e-mail:  angela.altomare@ic.cnr.it

Table 3.4.2| top | pdf |
Examples of lattices leading to geometrical ambiguities

P = {Pij} is the transformation matrix from lattice I to lattice II, described by the vectors {ai} and {bi}, respectively, with [{\bf b}_i = \textstyle\sum_{j} P_{ij}{\bf a}_{j}].

Lattice ILattice IIP
Cubic P Tetragonal P [\pmatrix{ 0 &-1/2 &1/2\cr 0 &1/2&1/2 \cr -1& 0 & 0}]
Cubic I Tetragonal P [\pmatrix{ 0& -1/2 &1/2\cr 0 &-1/2 & -1/2\cr 1/2 & 0 & 0}]
Orthorhombic F [\pmatrix{-1/3 & -1/3 & 0\cr 0 & 0 & -1 \cr 1 & -1& 0}]
Orthorhombic P [\pmatrix{ 1/4 & -1/4 & 0 \cr 0 & 0 & 1/2 \cr -1/2 & -1/2 & 0}]
Cubic F Orthorhombic C [\pmatrix{ -1/2 & 0 & 1/2 \cr 0 & 1& 0 \cr -1/4 & 0 &-1/4}]
Orthorhombic I [\pmatrix{ -1/6 & 0 & -1/6\cr 1/2 & 0 &-1/2 \cr 0 &-1 &0}]
Hexagonal Orthorhombic P [\pmatrix{1/2 & 1/2 & 0 \cr 1/2 & -1/2& 0 \cr 0 & 0 &-1} ]
Rhombohedral Monoclinic P [\pmatrix{ -1/2 & 0 & -1/2 \cr 1/2 & 0 &-1/2 \cr 0 & -1 &0 }]