Macroscopic Symmetry and Properties of Crystals

The chapter is written with the point of view and the needs of the modern solid-state physicist in mind. There is a tendency to neglect a systematic presentation of the macroscopic symmetry properties of crystals in current curricula. The chapter may serve to bridge the gap in part. However, most of the readers will possess a rudimentary knowledge of the structures of the simpler crystals and of the language of crystal geometry—for example, Miller indices. Such knowledge is assumed. General familiarity with tensor language and matrix algebra is assumed. However, the mathematical argument leading to the reduction of property representation by means of crystal symmetry is supplemented throughout by equivalent physical argument. Most crystalline materials that are found in nature or are produced by man are polycrystalline—that is, they are composed of many minute crystals. If the orientation of the single crystals is random, the typical polycrystalline specimen behaves isotropically with respect to its physical properties.