In Chapter 9 nearly free-electron energy bands were discussed. In this chapter we discuss the energy bands of a crystal for which the electronic states are derived from atomic-like orbitals. For molecules this approach is the LCAO model. Applied to crystalline solids, it is referred to as the tight-binding model. In either case the wavefunctions are linear combinations of atomic-like orbitals. We shall analyze the energy bands of a class of perovskite oxides known as the d-band perovskites.

The structure of the ABO3 perovskites

We consider the cubic ABO3 oxides having the perovskite structure with the transition metal B ions. Examples include insulators, such as SrTiO3, BaTiO3, and KTaO3, and metals, such as NaWO3 and ReO3 (a perovskite without an A ion). The structure of these oxides is shown in Fig. 10.1. Many oxides (e.g., BaTiO3 and SrTiO3) undergo structural phase transitions at lower temperatures, leading to non-cubic lattices and ferroelectric and piezoelectric properties. Here we are concerned with the cubic phase.

As illustrated in Fig. 10.1, the B ions are at the center of a cube, the oxygen ions are on the faces of a cube, and the A ions are on the corners of a cube.

The five ions of the unit cell are labeled A, B, 2, 3, and 5 in Fig. 10.1. The origin is taken at the B site and the oxygen ions are located at a(1, 0, 0), a(0, 1, 0), and a(0, 0, 1).