Another property of solids, whose relation to this same phe nomenon was formerly not recognized, is the thermal conductivity. All solids conduct heat to a greater or less degree, their con ductivity being measured by the amount of heat which flows through unit cross-section in unit time under the influence of unit temperature gradient. There are, however, two classes whose con ductivity differs considerably, the metals and the non-metals. The metals in general conduct very much better than the non-metals; the mechanism of their thermal conduction however is almost certainly of a different type being due to the dissociated electrons which give to them their specific property of electrical con ductivity. The non-metals conduct in a varying degree, some of them such as the precious stones, more especially the diamond conducting extremely well, whilst others such as glass or mica have a conductivity very much smaller. The reason for this is intelligible, when one considers the model we have described. If one had completely elastic substances obeying Hooke's law accurately, the heat conductivity, as measured in the ordinary way, would be infinite, for heat in the form of elastic waves would be propagated from one end to the other with the speed of sound, and in equilibrium no temperature gradient could exist. At first sight this may seem paradoxical since a perfect vacuum in which heat is transmitted by radiation, which for this purpose may be regarded as harmonic waves, is usually considered to be a bad conductor. Nevertheless if its conduc tivity were measured in the ordinary way, it would be found to be infinite, since the amount of heat transmitted is independent of the temperature gradient and the fact that it is small is a consequence not of bad conductivity, but because only a com paratively small amount of heat can be transferred from the solid wall to the vacuum. The fact that solids have a finite heat con ductivity is due to their elastic properties not being strictly linear. Thus an elastic wave passing over a region in which there happens to be, say, a small excess compression due to another elastic wave is slightly scattered, since owing to the compression already existing and the lack of the linearity of the compressibil ity, this latter is slightly reduced and the velocity of propagation slightly increased. Hence in traversing the solid, the waves are scattered and a certain proportion returns instead of going for ward. If one defines a lengths in which the elastic wave ampli tude is reduced by scattering to it may be shown that the ther mal psl mal conductivity will be given by — p being the density, q the 4 velocity of propagation of the wave and s the specific heat.
This consideration shows that there will be an essential dif ference between the heat conductivity of crystals and amorphous solids. A crystal, until one comes down to molecular dimensions, may be regarded at the absolute zero as a completely homogeneous body. As the temperature rises owing to the random distribu tion of energy, there will be regions of excess strain and the reverse. If the forces were strictly elastic this would not affect the velocity of propagation of compressional or torsional waves. But the forces are not strictly elastic, consequently as the tempera ture is raised the scattering of the elastic waves increases. Hence, as shown by the above expression, the thermal conductivity should decrease with rising temperature ; calculation shows that in the region in which the specific heat is constant, it should be in versely proportional to the absolute temperature. This result was confirmed by measurements of the thermal conductivity of crystals at different temperatures.
The amorphous solids behave quite differently. In these, as we have seen, the molecules do not form a space-lattice, but may be regarded as distributed more or less evenly, without being in any special regular order. In glasses therefore, there are inhomo
geneities of density and compressibility which are inherent in the structure itself, neither due to nor affected by the temperature. The elastic waves, therefore, will be scattered in an amorphous body even at the absolute zero, indeed an increase in tempera ture is just as likely to improve as to diminish the homogeneity of such a substance. Hence there should be no variation in thermal conductivity with temperature due to modification in scattering; any variation which occurs must be attributed to a change in the specific heat, in general a much less important factor. Thus the heat conductivity of glasses is not very much affected by temperature.
The metals as has been stated, form a class apart. In these, electrons are dissociated from the atoms and play a large part in conduction, as is shown by the proportionality of thermal and electrical conductivity. If one assumes that the electrons form an interleaved space-lattice with the parent ions, then, owing to their small mass, they would have a very high proper frequency. Such an electron space-lattice might thus be regarded, as far as thermal properties are concerned as corresponding to a crystal at a very low temperature. From this point of view, the high thermal conductivity of metals is intelligible, but it is a point of view which has certain difficulties and is not fully established.
We have seen that the properties characteristic of the solid state may all be explained on the assumption that the forces acting between the molecules are of the type indicated by the curve in figure I. The definite volume of the solid is due to the rapid increase of the force of repulsion when the atoms approach one another. Its density is determined by the molecular weight and the distance at which repulsion balances attraction. The shape of the solid is determined by the quasi-elastic forces arising when molecules are displaced from their positions of equili brium and these forces are merely another expression of the intramolecular forces holding the molecules in place. Crystals are solids in which the attractive forces have been given full play and the molecules have attained the closest packed order. Glasses are merely under-cooled liquids in which the viscosity is too high to permit crystallization to take place. The melting point is that temperature at which the oscillations of the mole cules are so great as to cause them to collide ; the latent heat is at any rate in part the work done against attraction when they expand on fusion.
Hooke's law expresses the fact that the law of force is approxi mately linear near the position of equilibrium. Deviations from it account for the thermal expansion and determine the heat conductivity. The variation of the atomic heat with temperature depends according to the very much more recondite quantum theory upon the molecular frequency; this is obviously deter mined merely by the molecular restoring force and the molecular weight. Thus substances with large intramolecular forces and small atomic weights such as occur in the middle columns of the periodic table, will be hard and incompressible with high melting points and latent heats, with small thermal expansion coefficients, but great thermal conductivities and their atomic heats will deviate even at high temperatures from the normal value. Where the intramolecular forces are small, more especially if the atomic weights are high, we have soft compressible, low melting solids with large expansion coefficients and small heat conductivity. Owing to the dissociation of the electrons, metals are in another category whose special characteristics lie outside the scope of this article. The same may be said of those other properties, whether optical or electrical, magnetic or radioactive which solids possess in common with matter in other states of aggregation.
(F. A. L.)