I am trying to understand the systematic absences that occur for certain symmetry. The explantion above was given for fcc but I would have thought that both of them would not be seen if the above was the case.
does 200 planar diffraction have 2 or 3 times the intensity of 100 plane
This is due to the symmetry of a certain crystal structure, which is mathematically reflected in the form of a particular structure factor.
Write down the structure factor for the simplest case (for example Ni/Pt/Pd/Ag/Au fcc) and you will get, after simple calculations, the so called extinction rules. (If structure factor for a certain reflection will be zero, then the peak will not be visible in the XRD pattern.) For the fcc structure (pure Ni for example) you will get that reflections which could be observed in your pattern should have the same parity of h, k, and l (eg. (111), (200), (220), (311), ...). Please note that the reflections with mixed parity of (hkl) (for example (100), (110), (210), ...) will not be visible in the collected pattern. If you will do the same calculations for the bcc structure you will see that in this case the visible reflections will have the even sum of h+k+l (for example (110), (200), (220), ...).
For simple structures like fcc, bcc or hcp it is easy to calculate the extinction rules with a piece of paper and a pencil. However, for more complicated structure (triclinic, monoclinic, cubic structures with different atoms in different sites) it could be much more complicated or even impossible.
Cheers!
An example for Marcin's sentences are provided below link:
Reflection lines can be seen in accordance with a BCC structure. In page seven even sums are given for h+k+l .
http://bama.ua.edu/~mweaver/courses/MTE583/MTE%20583_Class_17.pdf
It helpful to remember that (200) plane is a reciprocal reflection of (1/2,0, 0) and (100) plane is a reciprocal reflection of (1, 0, 0). When a cube is taken into account, the most atomically crowded plane will provide relatively more intensity (regardsless of they are a member of corner atoms of surface atoms).
From Fourier theory, we know that a line crossing the origin in reciprocal space is the Fourier transform of a projection of a structure on this axis.
it is then easy to understand the serial systematic absences. If the projection has half periodicity (as compared to the structure) then the Fourier transform has double periodicity, i.e. only half of the peaks are present. The other one are systematically absent.
For example, if you project a structure with space group P1 2_1 1 along the b axis, the periodicity of the projected structure on b will be halved. Therefore only the 0k0 reflections with k=2n will be present, the other being systematically absent
With this method, you can easily find all the possible systematic absences !
Hi Tola, in your specific case the systematic or general absences are simply an effect of the introduction of lattice centerings. If you describe the same lattice (F, I, A, B, C, R (hexagonal axes)) by a primitive one - what you can simply dy by PowderCell transforming the structure description by a subgroup symmetry using a P lattice - you won't have these absences anymore. The reason are lattice translation vectors with non-integer components. Mathematically, the calculation principle is exacly the same as described above, e.g. by G. Chapuis. However, in his example (serial or zonal absences) the effects are not related to the lattice but to the symmetry within one lattice point. But again, the reason are translation components in glide planes and screw axes which are an exact fraction of the lattice vector, e.g. 1/2 for glide planes or two-forld screw axes, 1/3 for three- or sixfold screw axes etc.
By the way, the use of Miller indices, e.g. for lattice planes, require brackets or parenthesis, but then the h,k,l have to be relatively prime. If you use 002 - which are Laue indices - no brackets are used to express that we are talking about reciprocal lattice point, interferences etc. Then, and only then, h,k, and l can have any integer.
In order to prevent misunderstandings in discussion please use this internationally accepted convention correctly and don't mix it. Especially since students read these discussions and don't yet see the differences between (hkl), {hkl}, [uvw], and hkl.
all the previous answers are corrct , but the answer of Marcin Perzanowski is correct also and simple for those who are not crystallographer
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