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

International Tables for Crystallography (2006). Vol. C, ch. 9.8, p. 935


T. Janssen,a A. Janner,a A. Looijenga-Vosb and P. M. de Wolffc

aInstitute for Theoretical Physics, University of Nijmegen, Toernooiveld, NL-6525 ED Nijmegen, The Netherlands,bRoland Holstlaan 908, NL-2624 JK Delft, The Netherlands, and cMeermanstraat 126, 2614 AM, Delft, The Netherlands

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Centring reflection conditions for (3 + 1)-dimensional Bravais classes

The centring reflection conditions are given for the 24 Bravais classes, belonging to six systems (with number and symbol according to Table[link]a). If qi = q these are the usual conditions for hklm, the indices of the reflections expressed with respect to a*, b*, c*, q. Otherwise the conditions are for indices HKLm with respect to a conventional basis [{\bf a}_c^*, {\bf b}_c^*, {\bf c}_c^*, {\bf q}^i] of the vector module M*. The relation between indices HKLm and hklm is given in the fourth column. Planar monoclinic and axial monoclinic mean a monoclinic lattice of main reflections and with the (irrational part of the) modulation wavevector in the mirror plane, or along the unique axis, respectively.

Systemqi vectorReflection conditionsRelation of indicesBravais class
Triclinic (αβγ)     1 [{\bar 1}]P(αβγ)
Planar monoclinic (αβ0)     2 2/mP(αβ0)
  [L+m=2n] [L = 2l+ m] 3 2/mP(αβ[{{1}\over{2}}])
  [h+l=2n]   4 2/mB(αβ0)
Axial monoclinic (00γ)     5 2/mP(00γ)
  [H+m=2n] [H=2h+m] 6 2/mP([{{1}\over{2}}]0γ)
  [h+l=2n]   7 2/mB(00γ)
  [H+L=2n, K+m=2n'] [K=2k+m] 8 2/mB(0[{{1}\over{2}}]γ)
Orthorhombic (00γ)     9 mmmP(00γ)
  [K+m=2n] [K=2k+m] 10 mmmP(0[{{1}\over{2}}]γ)
  [K+m=2n, H+m=2n'] [K=2k+m, H=2h+m] 11 mmmP([{{1}\over{2}}{{1}\over{2}}]γ)
  [h+k+l=2n]   12 mmmI(00γ)
  [h+k=2n]   13 mmmC(00γ)
  [H+K+m=2n] [H=h+m] 14 mmmC(10γ)
  [k+l=2n]   15 mmmA(00γ)
  [H+m=2n, K+L=2n'] [H=2h+m] 16 mmmA([{{1}\over{2}}]0γ)
  [h+k=2n, h+l=2n']   17 mmmF(00γ)
  [H+K+m=2n, K+L=2n'] [H=h+m] 18 mmmF(10γ)
Tetragonal (00γ)     19 4/mmmP(00γ)
  [H+K+m=2n] [H=h+k+m, K=k-h] 20 4/mmmP([{{1}\over{2}}{{1}\over{2}}]γ)
  [h+k+l=2n]   21 4/mmmI(00γ)
Hexagonal/Trigonal (00γ) [h-k-l=3n]   22 [{\bar 3}]mR(00γ)
  [H-K-m=3n] [H=2h+k+m, K=k-h] 23 [{\bar 3}]1mP([{{1}\over{3}}{{1}\over{3}}]γ)
      24 6/mmmP(00γ)