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Unformatted text preview: 1 MAE 581 Advanced Materials Science Lecture note 5 Symmetry All single crystals possess translational symmetry, and most possess other symmetry elements as well. In this chapter we describe the 32 crystallographic point groups used for single crystals. The seven Curie groups used for textured polycrystalline materials are enumerated in the next chapter. Symmetry operations We live in a three-dimensional world which means that there are basically four kinds of geometric symmetry operations relating one part of this world to another. The four primary types of symmetry are translation , rotation , reflection , and inversion . As pictured in Fig. 3.1, these symmetry operators operate on a point with coordinates Z 1 , Z 2 , Z 3 and carry it to a new position. By definition, all crystals have a unit cell that is repeated many times in space, a point Z 1 , Z 2 , Z 3 is repeated over and over again as one unit cell is translated to the next....
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- Fall '11
- Advanced Materials Science, rotational symmetry operation