THE QUANTUM PHYSICS OF SOLIDS 



T23 



tions, the specific heat has a peak at the Curie temperature. For invar, 

 however, the thermal expansion suffers a dip at the Curie temperature. 

 Hence the proportionaUty between specific heat and thermal expansion 

 coefiicient does not hold. Even for cases where the expansion coei^- 



< 1.0 



-100 -50 50 100 150 200 250 300 350 400 450 



TEMPERATURE IN DEGREES CENTIGRADE 



Fig. 35 — Expansion of invar versus temperature. 



cient has a peak, as in nickel for example, the proportionality does not 

 hold. The reason for the failure of Griineisen's law is easily found 

 and reflects in no way upon validity of the law for the cases to which 

 it is intended to apply. Griineisen's law is derived by assuming that 

 the crystal has a single definite energy versus volume curve. For 

 ferromagnetic materials this is not true as is evinced by the two 

 curves of Fig. TfTta. 



In this paper we have been concerned with the important but inactive 

 attributes of electrons associated with their energies. We have seen 

 how the variations of the electronic energy levels can be used to explain 

 a number of the important properties of solids. In the next paper, we 

 shall discuss the more dynamic subjects of electron velocities and 

 accelerations. 



ACKNOWLEDGMENTTS 



The writer would like to express his gratitude to Dr. R. M. Bozorth 

 for discussions of the section on magnetism, to Dr. K. K. Darrow for 

 criticisms and suggestions, to Mr. A. N. Holden for many valuable 

 comments on the manuscript and for the preparation of the crystal 

 of Fig. 1, and to Mr. B. A. Clarke for much valuable advice and 

 assistance with the figures. 



