# Crystalline Properties of Solids

• Manijeh Razeghi
Chapter

This Chapter gives a brief introduction to crystallography, which is the science that studies the structure and properties of the crystalline state of matter. We will first discuss the arrangements of atoms in various solids, distinguishing between single crystals and other forms of solids. We will then describe the properties that result from the periodicity in crystal lattices. A few important crystallography terms most often found in solid state devices will be defined and illustrated in crystals having basic structures. These definitions will then allow us to refer to certain planes and directions within a lattice of arbitrary structure.

Investigations of the crystalline state have a long history. Johannes Kepler (Strena Seu de Nive Sexangula, 1611) speculated on the question as to why snowflakes always have six corners, never five or seven (Fig. 1.1). It was the first treatise on geometrical crystallography. He showed how the close-packing of spheres gave rise to a six-corner pattern. Next Robert Hooke (Micrographia, 1665) and Rene Just Haüy (Essai d’une théorie sur la structure des cristaux, 1784) used close-packing arguments in order to explain the shapes of a number of crystals. These works laid the foundation of the mathematical theory of crystal structure. It is only recently, thanks to x-ray and electron diffraction techniques, that it has been realized that most materials, including biological objects, are crystalline or partly so.

All elements from the periodic table (Fig. 1.2) and their compounds, be they gas, liquid, or solid, are composed of atoms, ions, or molecules. Matter is discontinuous. However, since the sizes of the atoms, ions and molecules lie in the 1 Å (10-10 m or 10-8 m) region, matter appears continuous to us. The different states of matter may be distinguished by their tendency to retain a characteristic volume and shape. A gas adopts both the volume and shape of its container, a liquid has a constant volume but adopts the shape of its container, while a solid retains both its shape and volume independently of its container. This is illustrated in Fig. 1.3. The natural forms of each element in the periodic table are given in Fig. A.1 in Appendix A.3.

## Keywords

Point Group Lattice Vector Reciprocal Lattice Translation Vector Miller Index
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