In the last chapter, the formal description of linear elasticity was introduced. It was shown that knowledge of the elastic constants for a particular material allows one to describe the strains produced by any arbitrary state of stress. In materials science one is often interested in ‘controlling’ a material property and, thus, this chapter is concerned with the influence of structure on the elastic constants. At the most basic level, the elastic constants reflect the ease of deformation of the atomic bonds but it will be shown that other levels of structure can be very important, especially with the use of composite materials.

Relationship of elastic constants to interatomic potential

In Section 2.1, linear elasticity was considered from the perspective of a single atomic bond. It was shown that the elastic constant was related to the shape of the interatomic potential, notably the curvature of the potential in the vicinity of the equilibrium spacing. For example, consider the interatomic potentials shown in Fig. 3.1 that are typical of the extremes for (a) ionic and (b) covalent ceramics. The strong directional bonding associated with covalency leads to a deep potential well. For atomic interactions acting over similar distances this would lead to a sharper curvature at the potential minimum, compared to the purely ionic case.