FUNDAMENTALS OF CRYSTALLINE STATE

The concepts of crystalline state and symmetry are just about synonymous today, although the general sense of symmetry is much older than the idea of symmetrical arrangement of atoms in the structures of crystalline solids. Following Webster s dictionary, symmetry is the beauty of form arising from balanced proportions , and to be symmetrical is to have the correspondence in size, shape and relative position or parts on opposite sides of a dividing line or median plane or about a center or axis . 

Humans constantly deal with symmetry, often without even noticing its significance in daily life. For instance, our exposure to symmetry begins every morning with a glimpse in a mirror, and it ends every night when we fall asleep in a bed with balanced proportions. In addition to the fact that intuitive perception of symmetry is familiar to almost everyone, it has multiple applications in science and engineering. A much more comprehensive and formal description of symmetry, when compared to that found in dictionaries is, therefore, necessary. 

In this chapter, we consider basic concepts of crystallographic symmetry, which are essential to the understanding of how atoms and molecules are arranged in space and how they form crystalline solids. Furthermore, the detailed knowledge of crystallographic symmetry is important to appreciate both the capabilities and limitations of powder diffraction techniques when they are applied to the characterization of the crystal structure of solids. We begin with the well-established notions of the three-dimensional periodicity 

Without a doubt, it is impossible to include each and every detail about crystallographic symmetry in this chapter, which is a part of the book about powder diffraction. We hope, however, that after the main concepts introduced here are understood, the reader will be ready to take on a much more comprehensive description of crystallographic symmetry, e.g. that found in the International Tables for Crystallography.  

---