Abstract
Introduction In the previous chapter, we saw how the long-range order of particle positions in a crystal could be described in a rather elegant manner using a space lattice that extends indefinitely. In this chapter, we examine instead disordered matter such as liquids or glasses in which a long-range repeated pattern is absent. These amorphous materials might not seem as glamorous as their crystalline counterparts, but they are increasingly prevalent in our world as they comprise the windows, computer screens and vast array of plastic components that surround us on a daily basis. In comparison with crystalline structures, these amorphous materials pose a challenge to describe, and their structure can only be defined in a statistical sense by introducing an ensemble-averaged, pair distribution function. In spite of their disordered nature, a robust pattern of particle positions emerges over short distances. This short-range order reflects the local coordination of particles and we briefly review the random close pack and the continuous random network systems as common examples of amorphous structure. A statistical structure Disordered or amorphous condensed matter has a clear disadvantage in that particle positions lack any long-range repeating pattern akin to that found in crystals. This is evident in Fig. 2.1, which illustrates the typical particle positions of either a glass or a liquid captured at a particular instant in time.