This chapter continues our overview of bulk materials, and introduces the major materials systems relevant for the remainder of the book.

One sensible way to classify materials is by the arrangement of their constituent atoms – their structure. Macroscopic materials consisting of large numbers of atoms are readily grouped into two categories: ordered and disordered. More precisely, one can examine the density–density correlation function,

S(r) ≡ 〈ρ(r0)ρ(r0 + r)〉.

The intensity of elastic diffraction at some wave vector transfer q from a bulk material is proportional to the Fourier transform of S(r).

In a completely disordered system, the position of one atom is uncorrelated with the position of any of the other atoms. Thus S(r) ∝ δ(r). This is the case for a dilute, classical gas. For a liquid or supercritical fluid, particles are squeezed together closely enough that the finite size of the constituent atoms becomes relevant. In that case there is some typical nearest-neighbor distance, though there is no long range pattern to the arrangement of atoms. Mathematically S(r) has a broad peak where |r| equals the nearest neighbor separation as well as at r = 0, but little other structure. An essentially identical pattern results for a completely amorphous solid such as a glass. With increasing positional order, additional peaks develop in S(r). The limit of this would be a perfect single crystal, in which S(r) would have delta function peaks at each lattice vector, r = R.

An alternative classification scheme can be built around a material's response to mechanical stresses. Fluids are defined by their inability to support shear stresses. That is, for a given patch of area at the boundary of a fluid, if a force is applied in the plane of that surface, the fluid will begin to deform, and will continue to deform at some rate as long as the shearing force is applied. In contrast, solids are said to resist shear.