Crystallographic Orbit  Practical Electron Microscopy and Database   An Online Book  

Microanalysis  EM Book http://www.globalsino.com/EM/  


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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 threedimensional (3D) 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 spacegroup E ⊇ S is generated by S, then E is at least S, or it may be a supergroup of S. E is socalled the eigensymmetry (characteristic) spacegroup 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 spacegroup S of the noncharacteristic orbit is a subgroup of the eigensymmetry spacegroup E of the orbit (see Figure 1459). Figure 1459. Orbit types. An infinite number of crystallographic orbits for a given space group E can be subdivided into sets of socalled Wyckoff positions of E. All the crystallographic orbits that have the same sitesymmetry 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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