For instance, If in the JCPDS files of one element, the plane (110) is being indicated at 2- theta value of 35 degree but in the literature search, the same 2- theta value of the same element has been indicated as plane (101). Why? and How to consider which will be right for my XRD Graph? Is there any huge difference which I have to mention or will it affect my further experiment if I couldn't distinguish between these planes correctly? I want a detailed explanation about this. Thank you.
Dear Ipsita Priyadarshini ,
in order to understand this issue you should have a look at the lattice of your sample and figure out the lattice planes which are active your case.
For the case of a cubic lattice the lattice constant 'a' is valid for the x, the y and the z axes. In all these directions there is the same lattice constant.
In the attached drawing*) I have collected all the lattice planes which contribute to the (100), the (010) and the (001) reflections. These planes are parallel to the sides of a cube.
See also the active planes for the (110), the (101) and the (011) reflections. These planes are all diagonal planes of the cube.
The lattice plane distances 'd' of the cubic lattice are given by:
d = a /(h2 + k2 + l2)1/2
From this equation you see, that the lattice plane distances of (100), (010) and (001) planes are all the same; but also for the (110), (101) and (011) planes.
This outstanding behaviour is only valid for the cubic lattice...
*) made by me in the early 1990's as an example for the BCC lattice
Best regards
G.M.
These (hkl) are equivalent by symmetry in the case of cubic crystals, but not necessarily in the case of non-cubic crystals. It is (used to be?) common practice to indicate among the equivalent {hkl} with h > k > l if one hkl was used as representative in {}. However, unfortunately many computer programs appear to use some ascii or so sorting of the hkl, so often 011 is preferred by these programs rather than 110. In cubic materials there is little reason to indicate 101 as representative for the whole family.
In your case, when it was really a cubic material under consideration, probably by accident/individual ideas of the person who wrote the orginal literature, and during the editing process it became 110 due to conventions. In principle there is nothing wrong about indicating 101, but is uncommon or irritating to the user.
Note, however, it the material is e.g. orthohrhombic, then it depends on the choice of axes, whether the same lattice plane is named 101 or 110!
For this, please check the preprint article at DOI: 10.13140/RG.2.2.27720.65287/3
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