The solid state is that in which the energy of the molecules is insufficient to overcome their mutual repulsion sufficiently to enable them to collide. This distinction between mutual repul sion and collision presupposes an enormously rapid increase in the force at a given point corresponding to the distance which, in old fashioned language, would have been called the surface of the molecule. This very rapid increase certainly exists; exactly what causes it we need not here consider. At low tem peratures when the energy of the molecules is small they will approach one another until their average distance is such that their mutual attraction balances their mutual repulsion, in other words, until their mean distance corresponds to the point at which the curve cuts the axis in fig. 1. About this position of equilibrium the molecules oscillate under the influence of their mutual repul sion. As the temperature rises the magnitude of their excursions increases until the molecules reach a point at which the mutual repulsion becomes suddenly very large, in other words until they collide.
We must here call attention to the fact that there are two very definite classes of so-called solids, the crystalline and the amorphous solids. If one considers a number of molecules of similar type acting upon one another as described above it is clear that the most stable arrangement will be that in which the attractive forces have been able to exert themselves to the full, in other words the molecules will tend to arrange themselves in the closest packed order. If the fields of forces are symmetrical the closest packed form will correspond to the closest arrangement of a number of spheres. As has been known ever since cannon balls were piled into heaps, this closest array corresponds to a pyramid. Hence molecules with symmetrical fields of force will tend to arrange themselves in octahedral order, and will form a regular space-lattice. If the fields of force are not symmetrical they will still form a space-lattice, but the distance between them will not be the same along different axes, the axes will not be orthogonal, and the substance will not crystallize in the regular system. The crystalline state is characterized by the arrangement of molecules at regular intervals in the most stable condition.
One might almost question whether the amorphous bodies, some times called glasses, should properly be classed as solids. They are, strictly speaking, undercooled liquids and are formed when cooling from the liquid state takes place too rapidly for the forces of attraction to have time to collect the molecules into their most stable positions. In this state the positions of the molecules are irregular, though of course their average distance is not very much greater than in the crystal. They are close together but not equally spaced, they correspond to a crowd rather than to a regiment. When the attraction is great even the most rapid cooling may not suffice to prevent the molecules arranging them selves in regular order. If the energy to be gained by arranging them in regular array is not very great, i.e., if the work of attrac
tion is not very much greater than the work of repulsion, there is no great tendency to crystallize, and the substance may be supercooled, that is to say, solidified in the amorphous form even though cooled comparatively slowly. This is particularly likely to happen when one has large irregular molecules, especially if they are not all alike. Thus in the case of glass only a very prolonged exposure to an appropriate temperature causes devitrifi cation, i.e., crystallization to occur. Temperature in this connec tion is of supreme importance, for at low temperatures the energy of the particles is too small to enable them to make excursions from their position of equilibrium which might in favourable circumstances result in their changing places and achieving a more stable regular arrangement. It is high temperatures near, but not too near, the melting point where the viscosity is low, that favour crystallization.
Having defined these two classes we may examine the transi tion from the solid to the liquid state. As a crystal is heated the amplitude of the oscillations of the molecules about their posi tions of equilibrium increases until those molecules with an ex ceptionally high energy content collide with their neighbours. Such a collision results in the sharing of the momentum with a neighbour and the distribution of the energy between the two molecules. In this way the crystal may be heated without any material change until the temperature is reached at which the average amplitude of oscillation is such that all molecules collide. At this temperature sharing the energy does not diminish the oscillation below the point of collision and the whole structure collapses into a liquid. Thus the crystals have a perfectly well defined melting point which cannot be exceeded. No crystal can be heated in any circumstances above the melting point.
The amorphous bodies behave very differently. As the energy of the molecules is augmented the amplitude of oscillation of those which happen to be so placed that their neighbour's repulsion is small, increases very rapidly. In favourable circumstances, here and there collisions take place at temperatures well below that of liquefaction proper. The number of these go up rapidly as the temperature is raised. What might be called local liquefaction occurs in innumerable minute regions dispersed at random through the body. It becomes soft and viscous and changes gradually by imperceptible degrees into a liquid. It is precisely this property which gives glasses their valuable qualities. A temperature can always be found at which their viscosity is such that they can be worked and moulded, into any desired shape or form. From a scientific point of view this condition is less satisfactory; glasses have no definite melting point and in their case the solid state can only be defined as that in which few of the molecules have a sufficent amplitude of oscillation to collide.