International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 1.6, p. 113

Table 1.6.3.1 

U. Shmuelia

Table 1.6.3.1| top | pdf |
Effect of lattice type on conditions for possible reflections

Lattice type[{\bi w}^{T}_{L}][{\bf h}{\bi w}_{L}]Conditions for possible reflections
P (0, 0, 0) Integer None
A [(0, \textstyle{{1}\over{2}} ,\textstyle{{1}\over{2}})] [(k+l)/2] hkl: [k+l=2n]
B [(\textstyle{{1}\over{2}}, 0 ,\textstyle{{1}\over{2}})] [(h+l)/2] hkl: [h+l=2n]
C [(\textstyle{{1}\over{2}}, \textstyle{{1}\over{2}}, 0)] [(h+k)/2] hkl: [h+k=2n]
I [(\textstyle{{1}\over{2}}, \textstyle{{1}\over{2}}, \textstyle{{1}\over{2}})] [(h+k+l)/2] hkl: [h+k+l=2n]
F [(0, \textstyle{{1}\over{2}}, \textstyle{{1}\over{2}})] [(k+l)/2] h, k and l are all even or all odd (simultaneous fulfillment of the conditions for types A, B and C).
  [(\textstyle{{1}\over{2}}, 0, \textstyle{{1}\over{2}})] [(h+l)/2]
  [(\textstyle{{1}\over{2}}, \textstyle{{1}\over{2}}, 0)] [(h+k)/2]
Robv [(\textstyle{{2}\over{3}}, \textstyle{{1}\over{3}}, \textstyle{{1}\over{3}})] [(2h+k+l)/3] hkl: [-h+k+l=3n]
  [(\textstyle{{1}\over{3}}, \textstyle{{2}\over{3}}, \textstyle{{2}\over{3}})] [(h+2k+2l)/3] (triple hexagonal cell in obverse orientation)
Rrev [(\textstyle{{1}\over{3}}, \textstyle{{2}\over{3}}, \textstyle{{1}\over{3}})] [(h+2k+l)/3] hkl: [h-k+l=3n]
  [(\textstyle{{2}\over{3}}, \textstyle{{1}\over{3}}, \textstyle{{2}\over{3}})] [(2h+k+2l)/3] (triple hexagonal cell in reverse orientation)