# 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 (indicated as symbols P..., I..., F...) are listed up to s = 40, where s is the square sum of the hkl-reflections: s = h*h+k*k+l*l. If two different hkl combinations give the same s-value (dublets), 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 duplets (s*) the sum of reflections from boths hkl combinations is given: combinations +/+, +/-, -/+ result in '+' and combination -/- results in '-', respectively. For a table which lists the 36 possible space groups and their space symmetry for the 17 possible cubic aspects click here.

 Nr: 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 symbol: P... P42.. P41.. Pn.. P..n Pn.n Pa. I... I41.. Ia. I..d Ia.d F... F41.. Fd.. F..c Fd.c

 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@oeaw.ac.at (Nov.18th 2002)