Permitted hkl reflections for the 17 cubic aspects


In the following table the permitted hkl-reflections for powder diffraction (Debye-Scherrer mode) by each of the 17 cubic aspects, corresponding to different crystallographic cubic space groups (sg), with P-, I-, F-(sym)metry, are listed up to s = 40, where s is the sum of the squared hkl-Miller indices: s = h*h+k*k+l*l. If two different hkl combinations give the same s-value (doublets), s is indicated as s* (like for s = 9, h/k/l can be 3/0/0 and 2/2/1, respectively). A reflection is indicated by '+', no reflection by '-' and 'x' if only half of the planes contribute to the reflection. In case of douplets (s*) the sum of reflections from both hkl combinations is given: combinations +/+, +/-, -/+ result in '+' and combination -/- results in '-', respectively. For a table which lists the 36 space groups and their space symmetry for the 17 cubic aspects click here.

Nr: 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17
sym: P... P42.. P41.. Pn.. P..n Pn.n Pa. I... I41.. Ia. I..d Ia.d F... F41.. Fd.. F..c Fd.c
sg: 195 198 212 201 218 222 205 197 214 206 220 230 196 210 203 219 228
sg: 200 208 213 224 223 --- --- 199 --- --- --- --- 202 --- 227 226 ---
sg: 207 --- --- --- --- --- --- 204 --- --- --- --- 209 --- --- --- ---
sg: 215 --- --- --- --- --- --- 211 --- --- --- --- 216 --- --- --- ---
sg: 221 --- --- --- --- --- --- 217 --- --- --- --- 225 --- --- --- ---
sg: --- --- --- --- --- --- --- 229 --- --- --- --- --- --- --- --- ---


s 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17
1 + - - - - - - - - - - - - - - - -
2 + + + + + + - + + - - - - - - - -
3 + + + + - - + - - - - - + + + - -
4 + + - + + + + + - + - - + - - + -
5 + + + - + - x - - - - - - - - - -
6 + + + + + + + + + + + + - - - - -
8 + + + + + + + + + + + + + + + + +
9* + + + + - - + - - - - - - - - - -
10 + + + + + + - + + - + - - - - - -
11 + + + + - - + - - - - - + + + - -
12 + + + + + + + + + + - - + + + + +
13 + + + - + - x - - - - - - - - - -
14 + + + + + + + + + + + + - - - - -
16 + + + + + + + + + + + + + + + + +
17* + + + + + - + - - - - - - - - - -
18* + + + + + + + + + + - - - - - - -
19 + + + + - - + - - - - - + + + - -
20 + + + + + + + + + + + + + + - + -
21 + + + + + + + - - - - - - - - - -
22 + + + + + + + + + + + + - - - - -
24 + + + + + + + + + + + + + + + + +
25* + + + - + - x - - - - - - - - - -
26* + + + + + + + + + + + + - - - - -
27* + + + + + + + - - - - - + + + - -
29* + + + + + + + - - - - - - - - - -
30 + + + + + + + + + + + + - - - - -
32 + + + + + + + + + + + + + + + + +
33* + + + + - - + - - - - - - - - - -
34* + + + + + + + + + + + - - - - - -
35 + + + + + + + - - - - - + + + + +
36* + + + + + + + + + + - - + + + + +
37 + + + - + - x - - - - - - - - - -
38* + + + + + + + + + + + + - - - - -
40 + + + + + + + + + + + + + + + + +


Reference: J.S.Kasper and K.Lonsdale, Eds (1967), in: International Tables for X-Ray Crystallography, Vol 2, page 147 (Table 3.8.6C)

Author: Manfred Kriechbaum Manfred.Kriechbaum@tugraz.at (2002, 2025)