Electron Theory of the Metallic Stale. 755 



§ 8. Thermal Conduction. 



Thermal conduction in non-metallic solids is generally 

 thought to-day to be due to elastic thermal waves. Tl e 

 classical electron theory interprets the quantitatively 

 superior metallic conductivity also in a qualitatively dif- 

 ferent manner, as due to an hypothetical electron gas. We 

 are now forced to give up this standpoint, as neither the 

 kinetic energy of the electrons nor their free paths are 

 great enough to explain the great conductivity of the 

 metals. We therefore are led to try if the conduction 

 cannot in the metals as in all other solids be referred to 

 the elastic waves ; and, indeed, we shall in this way find 

 reasons enough for the superiority of the conductivity of 

 the metals in their peculiar structure. In a salt of the 

 type NaCl, for example, the lattices of positive and 

 negative ions, as is known from the residual rays, have 

 different characteristic frequencies and thus transport 

 different elastic waves. Now as the two lattices have 

 like energy, there will, at high temperatures, be a lively 

 exchange of energy between them, so that the distance 

 within which the intensity of the wave diminishes to an 

 infinitely small part of its original value, will be but few 

 atom distances, which is also in good agreement with the 

 experimental values for the conductivity. In a metal, on 

 the other hand, the energy of the electron space-lattice 

 is relatively very small, so that the waves in the atom- 

 lattice will be very little damped, and thus give a great 

 conductivity. 



For a quantitative discussion we start with a general 

 formula * for the conductivity X, called forth by damped 

 elastic waves : 



X = ipcwL, (16) 



where p is the density, c the specific heat, w the velocity 

 of the waves, and L their mean range, defined by the 

 decrease dK of the intensity K over the distance dS by 

 the equation 



"K-17 ( 16 > 



We may, for high temperatures, transform this expression 

 for X in the following manner, pc is the specific heat for 

 the unit of volume, and as a molecule in a solid has the 



* P. Debye, ' Vortrage iiber d. kinet. Theorie,' Gottingen, 1914, p. 50. 



