ABSTRACT
In Chapter 7 we gave a quantum mechanical framework for the theory of solids. We noted, in section 7.1, the central role played by the atomic nuclei in determining the structure and properties of a solid. Furthermore, we have commented, in section 1.1, on the fact that under ‘terrestrial’ conditions, solids are composed of identifiable atoms. The purpose of this chapter is to conceptually bridge the gap between the atomistic description of a solid, represented in Chapter 7, and the continuum description represented in Chapter 1. To that end we shall first, in section 9.2, describe qualitatively how a classical atomistic model may be inferred from the quantum-mechanical formulation of Chapter 7. Also in section 9.2 we shall specify the classical atomistic shell model for insulating crystals. The remainder of this chapter will then be largely devoted to derivations from the shell model of various bulk properties that are defined in terms of the continuum model of a solid. Thus in section 9.3 we derive the cohesive energy of the crystal. In section 9.4 we use this to derive the elastic constants: see section 1.4.1, especially equation (1.48). In section 9.5 we derive the dielectric and piezoelectric constants. The content of sections 9.3-9.5 is based on the report by Harding (1982).
