We envisage a solid as a collection of atoms whose average positions are fixed with respect to one another.
When studying gases we all but ignored the potential energy of interaction of the atoms except for intermittent interactions as molecules transiently approached one another. But in solids we cannot do this: solids exist because of the potential energy of interaction between atoms.
The atoms of a solid are constrained to vibrate about their average position by the electrical interactions with their neighbours. Only exceptionally change their position with respect to their neighbours. This picture will probably be familiar to you, but just in case it is not, the figure below illustrates how we imagine the motion of the atoms in a solid.
In the illustration left, the arrows indicate the direction of atomic motion. Notice the small separation between the atoms and the random orientation of their vibrations. The atoms themselves are shown as a central darkly-shaded region, where the electron charge density is high, and a peripheral lightly-shaded region. The electric field in this peripheral region significantly affects the motion of neighbouring atoms, and disturbs the electronic charge density of neighbouring atoms.
When we discussed the properties of gases we were able to arrive at the theory of an ‘ideal gas’, which for many purposes was a good approximation to the properties of real gases. Solids, however have many fewer properties that can be explained in terms of a theory of an ‘ideal solid’. The diversity of properties exhibited by solids (e.g. the difference between metals and insulators) calls for us to make multiple simple models to serve as starting points for attempts to understand the behaviour of real solids.
Despite the diversity in the properties of solids, it is important to realise that in all the materials, the only force acting between atoms is the electrostatic coulomb force. The coulomb force, coupled with the different configurations of electrons in the outer parts of the 100 or so different types of atoms, is sufficient to produce solids with the diversity that you find around you.
In Chapter 6 we will discuss four simplified models of solids which represent idealised categories. However, most real solids do not fall neatly into one category or another. The idea is that by looking at a few (rather rare) ‘simple solids’ which do fit this categorisation scheme, we will be able to shed light on what is happening in more common, but more complex, solids.