. The Bell System technical journal . 32, comes at the equilibrium distance or minimum ofthe Em curve. Adding the solid curves of (a) and (h) (adjusting theenergy scales, of course) gives the dashed curve representing the energyEv of the unmagnetized state shown in Fig. 33a. We are now in aposition to make predictions about the thermal expansion of iron. Let us imagine that the iron is somehow made to stay in the mag-netized state. Then its expansion curve, lattice constant versustemperature, will be shown as in Fig. Zic by the solid heavy line. Next * J. C. Slater, Phys. Rev., 36, 57 (1930).
. The Bell System technical journal . 32, comes at the equilibrium distance or minimum ofthe Em curve. Adding the solid curves of (a) and (h) (adjusting theenergy scales, of course) gives the dashed curve representing the energyEv of the unmagnetized state shown in Fig. 33a. We are now in aposition to make predictions about the thermal expansion of iron. Let us imagine that the iron is somehow made to stay in the mag-netized state. Then its expansion curve, lattice constant versustemperature, will be shown as in Fig. Zic by the solid heavy line. Next * J. C. Slater, Phys. Rev., 36, 57 (1930). THE QUANTUM PHYSICS OF SOLIDS 721 imagine it maintained in the unmagnetized state; in this state theequilibrium lattice constant is smaller than for the magnetized caseand the expansion curve is shown dashed. The curves for fixed il -*^ xx A u^^/ 1 \\ • / \\ • / \V / / M \\ / / \\ \—\ (a) y/ / / / ^X y / / ^KyWy ^ o (0 ^yyyypZ ^^^^^,,.^^^^^y^^^ < ^»^^/]^/]^/^£:^ Q. ^- 1 (c). 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. Nowas the iron is heated the magnetization does not stay constant butdecreases with temperature and becomes zero at the Curie temperatureQ^. In Fig. ZZc this corresponds to a continuous shifting from theline of higher magnetization to the lines of lesser magnetization withincreasing temperature as indicated by the curve with circles. We seethat the rate of expansion—that is, the thermal expansion coefficient,which is defined as the derivative of the curve divided by a—shouldhave an irregular form as shown in Fig. TfZd. In Fig. 34 we show observed thermal expansion curves for a series ofiron nickel alloys,*^ sho
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