For example, magnetite (Fe3O4) does not contain 002 reflections but contains 004 reflections, though it has FCC structure. Is it because of the structure factor? In my case, I have an oxide that is most likely to be spinel from diffraction pattern (d-spacing and other parameters), but has additionally 002 reflections from [001] zone axis. Is it possible?
Thank you.
002 reflection is forbidden for Fd3m space group in the kinematic theory due to presence of the d-type gliding plane. However it can become visible in the electron diffraction experiments because of double diffraction.
Dear Alexander B. Missyul’
Thanks for the answer. It would be great if you provide any references for the phenomenon.
Thank you.
Dear Wiswanathan,
regarding the visibility of reflections, you can´t expect the same fashion in another structure only because it has the same lattice. Another structure may have differences in crystallography even though it has the same lattice. Always check the space group of structure, as Alexander suggested.
Structure factor is very important, and normally its zero value means that the reflection should absent in diffraction pattern. However, having thicker sample, you can expect the forbidden reflection in the position of systematic absents, caused by double diffraction. Another way how to see forbidden reflection is to have extremly thin sample area. In this case, you can see reflection even if its structural factor is zero, because the destructive component of interference can´t be completed on few atomic layers.
Dear Vladimír Girman and Alexander B. Missyul’
Thanks for the concise and informative answer. I checked few literatures, it seems that those forbidden reflections usually appeared very faint. But in my case it is strong and close to other possible reflections.
I will make my case clear here. The oxide composition from STEM-EDAX is very similar to AB2O4 spinel (only A-B-O compound possible). The FFT (not SAD) pattern is similar to ordinary FCC structure with 002 reflections (rather than Fd3m) as given in the attached image. Please note that the ratio and angle are slightly different (which I think is negligible). My question is can I ascertain it to be AB2O4 spinel?
Dear Viswanathan
What determines either {hkl} family planes are allowed or forbidden is the Structure factor whish is F = SUM [fn exp [2i (hxn + kyn + lzn)] where by SUM we define the sum over all n atoms in the unit cell with their respective atomic factor (fn) which is proportional to the atomic number (Z), that is, the number of electrons (e-) in the atom.
In other words, both the atomic coordinates x, y, z) and the "size" of the atom (Z) are responsible of the reflections.
So if you have a sample which is isostructural to the FCC magnetite and there is another metal different from iron (Z = 26 e-) in the octahedral or tetrahedral sites, the reflections are not necessarily identical two those of pure magnetite.
Read the first two chapters of Kittel (Introduction of Solid State Physics) for more details.
Hope this answer be useful. Good luck .
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