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Certain lattice, such as body centered cubic (Cubic I) and face centered cubic (Cubic F), have "kinematically" forbidden reflections. In other words, due to the arrangements of the atoms in the unit cell, these are reflections where the intensity of the scattered wave is zero, given by,
 [3897]
where,
x_{i}, y_{i}, and z_{i}  The positions of the atoms in the unit cell.
Those reflections are destructive and thus they do not show up in the diffraction patterns, however, the relevant crystalline planes certainly exist in the crystals.
Table 3897a lists the symmetry elements that cause systematic forbidden reflections.
Table 3897a. Symmetry elements that cause systematic forbidden reflections.
The reflections that are kinematically forbidden due to the presence of screw axes or glide planes will appear in the diffraction pattern of a crystal that scatters dynamically. However, the kinematically forbidden reflections due to unitcell centering [2] do not show in the dynamical scattering.
Table 3897b. Conditions of forbidden and allowed reflections (h k l)
of common crystal structures
(F: the Structure Factor).
Bravais Lattice 
Forbidden reflections 
Allowed reflections 
F 
Number of lattice points
per cell 
Example Compounds 
Primitive Cubic 
None 
Any h, k, l 
f 
1 
αPo 
fcc 
h, k, l are mixed odd and even 
h, k, l are all odd or all even 
4f 
4 
fcc metals, GaAs, NaClrocksalt, ZnSzincblende 
bcc 
h + k + l is odd 
h + k + l is even 
2f 
2 
bcc metals 
fcc 
h, k, l are mixed odd and even; or, all even and h + k + l ≠ 4n 
As fcc, but if all even and h + k + l ≠ 4n, then absent (n is integer)



Si, Ge, Sn  diamond cubic 
Base centered 

h, k and l all odd or all even 
2f 
2 


h + k + l is odd




bct 
Primitive Hexagonal 
h + 2k = 3m and l is odd 
All other cases 


Hexagonal closed packed (hcp) metals 
Hexagonal closepacked (hcp) 



Reflection example 


h + 2k = 3n with l odd 
0 
0001 


h + 2k = 3n with l even 
2f 
0002 


h + 2k = 3n ± 1 with l odd 
f3 
0111 


h + 2k = 3n ± 1 with l even 
f 
0110 

For hcp crystals, the (0 0 0 l) reflections, e.g. for the case with 164 (P3m1) space group, are forbidden when l is odd. However, those reflection positions often show diffraction intensity, which is probably caused by chemical order on the basal planes, or by double or multiple diffraction (scattering).
Table 3897c. Miller indices of diffracting planes, and allowed and forbidden reflections.
{hkl} 
Σ[h^{2} + k^{2} + l^{2} ] 
FCC 
Diamond cubic 
BCC 
{100} 
1 
 
 
 
{110} 
2 
 
 
110 
{111} 
3 
111 
111 
 
{200} 
4 
200 
200 
200 
{210} 
5 
 
 
 
{211} 
6 
 
 
211 

7 
 
 
 
{220} 
8 
220 
220 
220 

9 
 
 
 
{310} 
10 
 
 
310 
{311}

11 
311 
331 
 
{222} 
12 
222 
 
222 

13 
 
 
 
{321} 
14 
 
 
321 

15 
 
 
 
{400} 
16 
400 
400 
400 

17 
 
 
 
{411} 
18 
 
 
411 
{330} 
18 
 
 
330 
{331} 
19 
331 
331 
 
{420} 
20 
420 
 
420 

21 
 
 
 
{332} 
22 
 
 
332 

23 
 
 
 
{422} 
24 
422 
422 
422 

25 
 
 
 
{431} 
26 
 
 
431 
{511} 
27 
511 
511 
 
{333} 
27 
333 
333 
 

28 
 
 
 

29 
 
 
 
{521} 
30 
 
 
521 

31 
 
 
 
{440} 
32 
440 
440 
440 
Table 3897d. Forbidden and allowed reflections (h k l)
of some materials.
Lattice 
Examples of forbidden reflections 
Examples of allowed reflections 
Example Compounds 
Cubic perovskite structure 
{1 0 0} 

SrTiO_{3} 
For symmetry determination with both XRD and electron diffraction crystallography, we are looking for symmetryrelated reflections. Then, the difference between the two techniques is mainly on systematically forbidden reflections:
i) In XRD profiles, the forbidden reflections typically have absolutely zero intensity.
ii) In SAED patterns, such forbidden reflections always have some degree of intensity due to double diffraction from multiple scattering.
Therefore, in SAED analysis, to minimize the multiple scattering, we need to use extremely thin specimens. Fortunately, precession electron diffraction (PED) gives an opportunity to provide closer kinematical conditions and are less dynamical than SAED. Given a large precession angle, the kinematical forbidden reflections can be identified [1]. However, in most cases, the forbidden reflections in PED patterns will not be fully absent since the patterns are produced as a sum of many misaligned electron diffraction patterns and screw axes can only be completely absent if the zone axis of the crystal is perfectly aligned.
Furthermore, for CBED patterns, we have:
i) The odd order reflections in the direction of the axis will be forbidden if the glide plane is parallel to the electron beam.
ii) For a screw axis or glide plane, if the projection of the unit cell in the beam direction has a symmetry, then the forbidden reflections would not be fully forbidden but would obviously be very weak.
[1] J. P. Morniroli, A. Redjaïmia, S. NIcolopoulos, Ultramicroscopy 107
(2007) 514.
[2] D. E. Sands. Introduction to crystallography. Dover Publications, 1993.
