Abstract
This chapter explains the formal geometry of crystal lattices. Amorphous and quasi-crystalline forms of solids have been investigated in recent years but most solid metals are crystalline and some appreciation of crystallography is essential to a study of metallic transformations. The ideal crystal is classified by considering the symmetry properties of the atomic arrangement. The symmetry properties of the lattice are much more restricted, and there are only fourteen Bravais lattices, obtained from relations among the vectors ai. Instead of the primitive unit cell, it is often convenient to use a larger unit cell that illustrates the symmetry of the lattice positions. The scientific concept of a crystal has evolved gradually from the original classification by external shape to modern views on the internal atomic arrangement. The development of X-ray methods enabled the structure of a crystal to be investigated on a finer scale. The ideal crystal may be regarded as the repetition in three dimensions of some unit of structure, within which the position of each atom is specified exactly by a set of spatial coordinates.
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