International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2006). Vol. D, ch. 3.3, p. 418

Table 3.3.8.1 

Th. Hahna* and H. Klapperb

aInstitut für Kristallographie, Rheinisch–Westfälische Technische Hochschule, D-52056 Aachen, Germany, and bMineralogisch-Petrologisches Institut, Universität Bonn, D-53113 Bonn, Germany
Correspondence e-mail:  hahn@xtal.rwth-aachen.de

Table 3.3.8.1| top | pdf |
Lattice planes (hkl) and lattice rows [uvw] that are mutually perpendicular (after Koch, 2004[link])

LatticeLattice plane (hkl)Lattice row [uvw]Perpendicularity condition and quantity [j' = hu + kv + lw]
Triclinic
Monoclinic (unique axis b) (010) [010]
Monoclinic (unique axis c) (001) [001]
Orthorhombic (100) [100]
(010) [010]
(001) [001]
Hexagonal and rhombohedral (hexagonal axes) ([hki0]) [[uv0]] [u = 2h + k], [v = h + 2k], [j' = 2 h^2 + 2k^2 + 2 hk]
(0001) [001]
Rhombohedral (rhombohedral axes) ([h, k, -h-k]) [[u, v, -u-v]] [u = h], [v = k], [j' = 2 h^2 + 2k^2 + 2 hk]
(111) [111]
Tetragonal ([hk0]) [[uv0]] [u = h], [v = k], [j' = h^2 + k^2]
([001]) [[001]]
Cubic ([hkl]) [[uvw]] [u = h], [v = k], [w = l]; [j' = h^2 + k^2 + l^2]