THE QUANTUM PHYSICS OF SOLIDS 



721 



imagine it maintained in the unmagnetized state; in this state the 

 equilibrium lattice constant is smaller than for the magnetized case 

 and the expansion curve is shown dashed. The curves for fixed 



LATTICE CONSTANT 



ec 



TEMPERATURE 



Fig. 33 — Theory of the thermal expansion of iron. 



(a) Energy in magnetized (M) and unmagnetized {U) 



states versus lattice constant. 



(b) Difference in energies versus lattice constant. 



(c) Lattice constant versus temperature. 



(d) Thermal expansion coefificient versus temperature. 



intermediate degrees of magnetization are shown as light lines. Now 

 as the iron is heated the magnetization does not stay constant but 

 decreases with temperature and becomes zero at the Curie temperature 

 Q^. In Fig. ZZc this corresponds to a continuous shifting from the 

 line of higher magnetization to the lines of lesser magnetization with 

 increasing temperature as indicated by the curve with circles. We see 

 that the rate of expansion — that is, the thermal expansion coefficient, 

 which is defined as the derivative of the curve divided by a — should 

 have an irregular form as shown in Fig. TfZd. 



In Fig. 34 we show observed thermal expansion curves for a series of 

 iron nickel alloys,*^ showing that the expansion for iron rich alloys agrees 

 with that predicted from Fig. ZZ. The reader may verify that had 

 the curve of Fig. ZZh been adjusted to correspond to nickel, the anom- 

 alous expansion would have been in the opposite direction, as is found 

 experimentally for the nickel rich alloys. 



The more rapid the transition from the magnetized to the unmag- 



" Figures 34 and 35 are taken in a modified form from J. S. Marsh, " Alloys of 

 Iron and Nickel," Vol. I, Special-Purpose Alloys, 1938, McGraw-Hill Book Co. 



