Thus we see that the characteristic of having shape, in the case of a solid reduces to the fact that the molecules are held in position by the forces they exert upon one another, whether in regular array as in a crystal, or distributed irregularly as in a glass, until external agencies intervene. Unless forces large compared to the molecular forces are applied no great movement of the molecules or change in the shape can be expected. The effect of smaller forces, as might be expected, is to modify slightly the relative positions of the molecules. If, say, a solid is sub jected to pressure from all sides this corresponds to a general increase of the attractive forces. The positions of equilibrium approach one another, the solid is compressed into a smaller vol ume. The compressibility is thus a measure of the forces holding the molecules in their positions of equilibrium. Its small value shows how large these forces are.
There is one very remarkable class of objects, the metallic crystals in which the stress necessary to produce a change of shape is comparatively small. It has been found that metals which normally consist of an agglomeration of small crystals may be converted into large single crystals by alternate stretch ing or heating at appropriate temperatures. These single crystals exhibit a very small resistance to deformation, so much so that they are apt to bend and break up under their own weight. The reason for this abnormal behaviour has not been clearly estab lished, though it is possible that it is due to the constitution of the metallic space-lattice. Reasons have been adduced for the view that this consists of two interleaved lattices, one consisting of electrons and the other of the ions formed by their dissociation from the parent atoms. It has been suggested by Hume-Rotheray that such a lattice consisting alternately of particles of finite size and particles of comparatively negligible size would have a very small resistance to deformation.
The best known characteristic of crystals is their regular shape. This is readily explained on the view put forward above. The number of atoms in any given volume being fixed, the distance between planes of closely packed atoms must be greater than the distance between planes in which the atoms are farther apart. If the attractive force between the atoms diminishes with dis tance, the strength of the crystals at right angles to such a closely packed plane must be a minimum and hence cleavage will tend to occur along such a plane. The same argument explains why molecules which are deposited upon a crystal will seek out this plane and thus give rise to the shapes so well known to crystallographers.
The mutual attraction of the molecules gives rise of course on the surface of a solid to an uncompensated inward attraction which is known in liquids as surface tension. This corresponds to an external pressure of a very considerable amount. Its order
of magnitude may be gauged by considering the work consumed in causing the solid to expand. The amount which varies from substance to substance is measured in tens of thousands of at mospheres. Connected with this, in theory though not in practice, is the tensile strength of a solid. As shown by the curve, the attraction between two neighbouring molecules grows as they are removed from one another up to a limit after which it decreases. This limit should be a measure of the ultimate strength of the material and the point at which it is reached should bear some relation to the maximum tension. Though we do not know the exact form of the curve an estimate of the amount can be made. The shaded area represents the work done in removing a molecule to infinity, i.e., the latent heat of evaporation which of course is known; the angle under which the curve cuts the abscissa, gives the measure of the restoring force acting upon the mole cules; as mentioned above, it is related to the compressibility. An estimate of the theoretical strength of some of the metals is some twenty or thirty times higher than anything observed, pre sumably because the metals form an agglomeration of small crystals and their tensile strength no more gives a measure of the ultimate forces between the molecules than does the strength of a piece of wool, of the fibres composing it. Tensile strengths of the theoretical order of magnitude are found in glass immedi ately after and in silica for some hours after drawing in a flame. This presumably represents the period before submicroscopic crystallization sets in.
The forces acting upon a molecule in the interior of a solid, are obviously equal from all sides when it is in its position of equilibrium. No matter what the law of force may be a small displacement from this position will give rise to a restoring force proportional to the displacement. For by Taylor's Theorem, the function of a given argument, plus a small quantity, is equal to the function of the argument plus the small quantity multiplied by the derivative of the function. Since the forces from both sides are equal at equilibrium and the small displacement corre sponds in the one case to an addition to, and in the other a sub traction from the argument, the resultant restoring force is twice the derivative of the function multiplied by the displacement. This result which of course means no more physically than that every curve may over a sufficiently small distance be treated as a straight line, is the reason for the approximate validity of Hooke's law, that the strain is proportional to the stress, the extension to the applied force or the compression to the applied pressure. Though accurate to a first approximation, it has long been known that it is really only true as a limiting case for small forces.