Electron microscopy
 
Crystallographic Orbit
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A crystallographic orbit includes symmetrically equivalent points and is defined as an 'infinite' set of atoms obtained from a given atom by operating the symmetry of a space group of the crystal. For a given space group E, all points in the three-dimensional (3-D) space are subdivided into sets of such crystallographic orbits. A crystal structure is composed of one or more crystallographic orbits.

Assuming an orbit with a space-group E ⊇ S is generated by S, then E is at least S, or it may be a supergroup of S. E is so-called the eigensymmetry (characteristic) space-group of the orbit. When E = S the orbit is then called a characteristic orbit of S, otherwise it is designated a noncharacteristic orbit. Therefore, the generating space-group S of the noncharacteristic orbit is a subgroup of the eigensymmetry space-group E of the orbit (see Figure 1459).

Crystallographic Orbit

Figure 1459. Orbit types.

An infinite number of crystallographic orbits for a given space group E can be subdivided into sets of so-called Wyckoff positions of E. All the crystallographic orbits that have the same site-symmetry group belong to the same Wyckoff position. In other words, if the corresponding coordinates are completely fixed by the symmetry, the orbit is then identical with the Wyckoff position. However, if one or more coordinates are variable, the Wyckoff position comprises many orbits.

 

 

 

 

 

 

 

 

 

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