Electron microscopy
C-Centered Lattices/C-Centering
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There are totally three lattice types which are:
         i) Primitive (P) lattices. In this case, there is only one lattice point per unit cell.
         ii) Body-centered (I) lattices. In this case, there is a lattice point at the corners and one in the center of the cell.
         iii) A-, B-, C- or F-centered lattices. In this case, there is a lattice point at the corners and others at one (A, B, C) or all three (F) of the faces.

Table 2962. Reflections of different lattice centerings.

Centering Reflection condition Reflections involved Integral extinction law
A-centering k + l = 2n    
B-centering h + l = 2n all reflections  
C-centering h + k = 2n   h + k = 2n + 1 (h + k = odd)
F-centering h; k; l all even or all odd   h+ k, h+ l, k+ l = 2n + 1 (h+ k, h+ l = odd)
I-centering h + k + l = 2n   h + k + l = 2n + 1 (h + k + l = odd)
R (obverse) -h + k + l = 3n    
R (reverse) h - k + l = 2n    

As an example, the three space groups C2/m, C2 and Cm have the same systematic forbidden reflections which are caused by the C-centering (h+k = 2n+1). The other symmetry operations in the three space groups, e.g. 2-fold rotation axis (2) and mirror plane (m) in the C2/m space group, do not cause forbidden reflections.

For the enlarged tetragonal unit cells, i.e. C or F centred unit cells, the symbols selected to describe the symmetry with respect to the x and y axes, and with respect to the face-diagonal directions is simply the same as that selected for the equivalent P and I centred cells, but with the order of the symbols reversed e.g. the name C4/mmb is used for the enlarged unit cell of space group P4/mbm.



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