The Electron Theory of Metals in the Light of New Experimental Data

Deviations from Ohm's Law at High Current Densities of 5 \ifmmode\times\else\texttimes\fi{} ${10}^{6}$ amp./${\mathrm{cm}.}^{2}$ have been detected in the case of Au and Ag foils, of the order of 1 per cent. Details will be reported elsewhere.Effect of Mechanical Tension on Electrical Resistance.---For Li, Ca and Sb, as in the case of most metals, the resistance increases with the tension, whereas for Bi and Sr the coefficient is negative. Details will be reported elsewhere.Modified Electron Theory of Electrical Conductivity has already been suggested by the author. It is assumed that the number of free electrons is relatively small; that their mean free path is many times the atomic diameter and depends on the amplitude of atomic vibration; and that the natural velocity of the electrons has the equipartition value. It is here discussed in the light of the above new experimental data. The deviations from Ohm's law support the theory since they require long mean free paths. For normal atoms for which the resistance decreases with increasing pressure, the electrons must pass directly from atom to atom through intervening atoms; but for the abnormal atoms Li, Ca and Sb, with both pressure and tension coefficients positive, the electrons seem to pass in channels between the atoms, somewhat as in Wien's theory. Diagrams are given showing the relation of the channels to the crystal structure. This simple conception enables the various coefficients of resistance to be connected quantitatively. The tension and temperature coefficients are calculated in terms of the pressure coefficients and the elastic constants and are found to agree approximately with the observed values.Pressure Coefficient of the Wiedemann-Franz Ratio has been found to be negative for nine out of the eleven metals tested; that is, the thermal conductivity increases with pressure less rapidly than the electrical conductivity. Details will be reported elsewhere.Elastic Wave Theory of the Atomic Part of Thermal Conduction in Metals.---The above result for the pressure coefficient means that an important part, probably at least one third, of the thermal conduction in these metals is performed by atoms, a conclusion confirmed by a comparison of Lorentz's theoretical value of the Wiedemann-Franz ratio with the experimental value. As a crude picture of the atomic conduction, it is suggested that the atoms are arranged in coherent strings separated from each other by gaps which each shift in position by the diameter of an atom each time the string on either side is hit, just like gaps between strings of billiard balls. Thermal energy is transferred when the gap shifts. By calculation, the maximum rate of propagation of a gap comes out about half the speed of sound in the metal, much less than the electronic velocity. The theory of electrical conduction already presented suggests that the length of the coherent strings of atoms is the same as the free path of the electrons, thus making possible a connection between the electronic and atomic contributions to thermal conductivity. If the number of atoms is of the order of 20 times the number of free electrons, as is to be expected from the above theory of electrical conductivity, then atomic conductivity comes out of the proper order of magnitude. A discussion of the temperature and pressure coefficients of the atomic conductivity adds further evidence in favor of the probability of this theory. Comparison with other theories. It is similar to Debye's concepts of thermal conduction in a crystal, but differs from Hall's ionization theory which, it is concluded, probably can account for only a small part of the conduction.