Dielectric Properties of Materials

Abstract

In crystallography, a crystal structure is a unique arrangement of atoms, ions, or molecules in a crystalline solid. It describes a highly ordered structure, occurring due to the intrinsic nature of its constituents to form symmetric patterns. The crystal lattice can be thought of as an array of "small boxes" infinitely repeating in all three spatial directions. Such a unit cell is the smallest unit of volume that contains all of the structural and symmetry information to build up the macro-scopic structure of the lattice by translation. The crystal structure and symmetry play a role in determining many of its physical properties, such as electronic band structure and optical transparency. To discuss the behavior of electrons in a crystal, we consider an isolated atom of the crystal. If Z is the atomic number, the atomic nucleus has a positive charge Ze. At a distance r from the nucleus, the electrostatic potential due to the nuclear charge is (in SI units) V (r) = Ze 4í µí¼‹í µí¼€ 0 r (1.1) where í µí¼€ 0 is the permittivity of free space. Since an electron carries a negative charge, the potential energy of an electron at a distance r from the nucleus is E p (r) = −eV (r) = − Ze 2 4í µí¼‹í µí¼€ 0 r (1.2) V (r) is positive, while E p (r) is negative. Both V (r) and E p (r) are zero at an infinite distance from the nucleus. Figure 1.1a,b shows the variation of V (r) and E p (r), respectively, with r. We now consider two identical atoms placed close together. The net potential energy of an electron is obtained as the sum of the potential energies due to the two individual nuclei. In the region between the two nuclei, the net potential energy is clearly smaller than the potential energy for an isolated nucleus (Figure 1.2). The potential energy along a line through a row of equispaced atomic nuclei, as in a crystal, is diagrammatically shown in Figure 1.3. The potential energy between the nuclei is found to consist of a series of humps. At the boundary AB Ferroelectrics: Principles and Applications, First Edition. Ashim Kumar Bain and Prem Chand.