Symmetry in the atomic pattern

In addition to the symmetry within any particular cell, the points in the neighboring cells are related by symmetry to those in that particular cell. Thus we can add symmetry operations that contain an element of translation as well as the other elements appropriate to the finite figure. The addition of translation to the possible symmetry operations greatly increases the number of possible combinations of the symmetry elements. There are 230 possible combinations (space groups) any atomic arrangement in a crystal must have the symmetry corresponding to one of these 230 combinations of symmetry operations. To determine the space group requires a detailed examination of the crystal by x-rays. 

The new symmetry elements that are introduced are screw axes and glide planes. A screw axis in a pattern is exemplified in the structure of selenium, which has a threefold screw axis. The chain of selenium atoms winds around the edge of the unit cell. If we imagine a cylinder centered on the edge of a unit cell. Fig. 27.20(a), then a rotation of 120° with a translation of j the height of the cell moves atom a to position b, atom b to position c, atom c to a, atom a to a position in the next unit cell, and so on. Repetition of this operation three times moves a to a. The unit cell has been transformed into itself, but moved upward to the position of the next unit cell. 

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