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Integral reflection conditions

The integral reflections are the general reflection conditions due to the centering of cells. They are given in the table below:

Integral reflection conditions for centered lattices.

Reflection
condition
Centering type of cell Centering symbol
None Primitive P
R (rhombohedral axes)
h + k = 2n C-face centered C
k + l = 2n A-face centered A
l + h = 2n B-face centered B
h + k + l = 2n body centered I

h + kh + l and

k + l = 2n or:
hkl all odd or all

even (‘unmixed’)

all-face centered F
− h + k + l = 3n

rhombohedrally

centered, reverse

setting

R (hexagonal axes)
h − k + l = 3n

rhombohedrally

centered, obverse

setting (standard)

h − k = 3n hexagonally centered H
 

See also

Section 2.2.13.1 of International Tables of Crystallography, Volume A