Rather than go into a detailed explanation here, please have  a look at the pages in the link from the MATTER website. This section explains how the structure factor is calculated for simple cubic lattices and how the structure factor for some hkl values sum to zero, these are your forbidden reflections.

http://www.matter.org.uk/diffraction/intensity/structure_factor.htm

To my understanding forbidden reflection occur as the assumption of spherical electron density around "atoms" does not hold especially for strongly oriented covalent bonds, e.g. in silicon and diamond. There may be also other defect types that contribute to that effect.   

https://books.google.de/books?id=2CjYv3EuRx0C&pg=PA49&lpg=PA49&dq=the+forbidden+reflection+diamond+electron+density&source=bl&ots=4HtUissG7m&sig=_dTqKrhKMKHRDuWkd_HkNjc2pyg&hl=de&sa=X&redir_esc=y#v=onepage&q=the%20forbidden%20reflection%20diamond%20electron%20density&f=false

Just to add something to the last part.

http://dx.doi.org/10.1107/S0021889810049599

Sorry Dominique Ectors but forbidden reflections are not related to the type of bonding but to presence of the following crystallographic features: non primitive lattices, i.e. body centred (I), face centred (F), base centred (C) lattices; symmetry planes and rotation axes with fractional translation, i.e. glide planes and roto-translation axes. In other words forbidden reflections are related to the symmetry of a crystalline material. In some cases forbidden reflections can be present .... but here the explanation is longer. I suggest to read some basic book on crystallography, for example https://global.oup.com/academic/product/fundamentals-of-crystallography-9780199573660?cc=it&lang=en&

Dear Mr. Ferraris

Of course I know that forbidden reflections are related to symmetry aka. the structure factor being zero for those reflections. But there are cases where these are effectively non zero due to the effects mentioned above. To my interpretation that was the aim of the question in the first place, to know why these reflections appear even though they should be canceled out when calculated by the kinematical approach with the IAM.  

Regards

If I remember correctly, such phenomena have been observed many years ago and described as "Umweganregung" caused by multiple scattering and diffraction on perfect crystals only (as here reported). For these crystals the model of the mosaic structure is not valid which is the reason that the intensity does not scale with the square of the structure amplitude but it is direct proportional. If the here reported  result would be general,  any crystal structure determination and phase analysis would be highly questionable, or am I wrong? In electron diffraction this phenomena is known for the 222 which has arbitrarily a structure amplitude of zero. In EBSD patterns the 222 is well visible. Other reflections which are absent because of geometrical reasons as G. Ferraris listed are missing there as well, so that I would like to see the diffractogram before starting to irritate people reading our discussion here. Could you post it?

I did EBSD simulations using dynamical diffraction theory of electrons (A. Winkelmann et al, Ultramicroscopy (2007)). 222 well visible (better than the 111 which is actually the strongest) but no hint for 200. But never say never... :-) 

The appearance of reflections that are forbidden on the basis of the symmetry as expressed by the space group symbol may appear because a diffracted strong beam is diffracted in its turn. That is known as Renninger effect. I have already suggest to consult a textbook of crystallography e.g. the one edited by C. Giacovazzo quoted in my previous answer. For example, the space group of diamond is Fd3m; the presence of the F lattice allows only reflections whose indices hkl are either all odd or all even. Thus, e.g., the reflection 100 is forbidden but may appear because of the Renninger effect.  

Hi Nita, what irritates me is that following our current believe of bonding all covalent bondings do not fulfill the imagination about spherical "atoms" or electron shells. And how do you explain the 222 in EBSD where the interaction does not happen with the "deformable" electron shell but with the core...and here I have problem to imagine the core shows significant deviations from a spherical arrangements. I've never seen in XRD powder a 002 or even a 222. Did you? 

...and btw: 222 is no forbidden interference for Fd3m...in contrast to 002.

00L : L=4n

0K0 : K=4n

0KL : K+L=4n

H00 : H=4n

H0L : H+L=4n

HK0 : H+K=4n, H=2n, K=2n

HKL : H,K,L odd/even

HHL : H+L=2n

HKK : H+K=2n

HKH : H+K=2n

Maybe that I am biased by my half-century activity as crystallographer but about forbidden and allowed diffractions I rely on space group theory and Renninger effect. If non-sphericity of atoms, directional bonds and similar things do not affect the crystal symmetry the GEOMETRICAL pattern of diffraction is not affected. Renninger effect depends on the mosaicity of a crystal and on the orientation of the crystal. It cannot be explained in few words. Please look, e.g., in this site https://books.google.it/books?id=77pUdgxcar0C&pg=PA209&lpg=PA209&dq=renninger+effect+diffraction+crystallography&source=bl&ots=pRKowi6RIX&sig=TA7HQI44v780g2zflQvhLAlTN6Q&hl=en&sa=X&ved=0ahUKEwi34_mqtqDMAhXCFiwKHRmUAiMQ6AEIKTAB#v=onepage&q=renninger%20effect%20diffraction%20crystallography&f=false

Renninger effect...or Umweganregung...it is the same.

Hi Nita,

if you would be right with 222, why Magnetite has then a very strong 222? Same space group type: 227. Or we are using the term "absent" reflection in another meaning.

From my point of view, 222 is only accidentally absent because of the specific structure of Si only. 

This can happen due to multiple diffraction. Refer to following publication and you will find the answer

J Appl Crystallogr. 2015 Apr 1; 48(Pt 2): 528–532.

High-resolution characterization of the forbidden Si 200 and Si 222 reflections

Peter Zaumseila

Full paper is available on the link

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4379439/

@ I. Vali: if you rotate your sample around the sample normal the 002 should disappear if it is "Umweganregung". Does it?

As far as I understood Umweganregung correctly, it means that the measured intensity is NOT produced by the forbidden and absent 002 but by at least two lattice planes which are accidentally in reflection conditions and directing their intensity into the detector so that they only appear to come from 002. 002 does not contribute at all to this detected intensity...an is still forbidden to reflect.

Dear Nita, regarding the 222 of Si structure: Of course, the intensity should be zero, but not as consequence of the space group type but because of the structure. Si does not occupy a general position so that specific conditions for reflection are valid: To the above written

h+k=2n, h+l=2n and k+l=2n

additionally

h=2n+1 is required (for hkl). This only follows from this specific position. If you add any other position. e.g. a general x,x,x the interference 222 immediately appears. 

Regarding the german part (thanks!) it claims that the covalent bondings SEEM(!...in German: scheint) to be the reason. From my point of view a somehow  "strange" interpretation since also these bondings follow exactly the symmetry of the group with all consequences. This means that you need to go into another space group, but why? At the moment  I have only the idea of implemented defects which is explained to be not probable.  

Frankly speaking I am astonished to see that a lot of people is convinced that the type of bonding alone can either forbid or add reflections without checking if the space group (i.e. symmetry) has been affected.

:-) yes, it is easier to work with new instruments, with higher spatial and angular resolution, and finally use software which should do all automatically of course. I guess that the concept (importance) of symmetry is going lost, is totally underestimated nowadays, and improperly taught at universities since there is a common believe that crystallography cannot compete with new branches which get more money.

We also forget that only because something has been published it is forever true. A careful interpretation and validation is essential, otherwise it is also only copy and paste. I am sure that each author does not do it intentially, but sometimes it simply happens that we fail (maybe we fail more than find the correct reason for some observed investigation). Therefore it is from my point of view very fruitful to have these discussions here. Nobody knows everything...

Hi All,

The sample is n-type Si 100 substrate material. I have done only 2 theta scan. I have not seen the same peak in all of the samples but the one which was irradiated with electrons at a particular dose. Attached is the diffractogram.

I don't want argue about the existence of the detected 002 or 222. We only have to adjust our "models" for interpretation. The Renninger effect has been demonstrated on several materials. I am not sure how many people know it but there is from my point of view no doubt about a multiple diffraction. What happen with electrons (I have no idea about the intensity of the 002 in comparison to the 400) I cannot say presently. Since also simulations can be wrong :-) I checked an experimental pattern. Nothing remarkable...but I have to think about it first. At least 222 is the best visible interference order of (111).

The "covalent bonding effect" looks to me like a slight shift of the effective atomic position from 1/8, 1/8, 1/8 to x,x,x which would explain this effect (see my former comment). But this wouldn't explain the visible 002 since x,x,x has no specific conditions for h00.

I still forgot a short remark: peaks caused by Renninger effect should be clearly sharper than the usual reflections because of double or multiple diffraction!