168 CHAPTER 15. INVAR ALLOYSfigure. It is seen that here the non-magnetic state has the lower energy. Computational
results for the Invar alloy are shown in the middle part of the figure. There is not
much difference in energy between the non-magnetic state and the ferromagnetic state.
At low temperatures, only the ferromagnetic state will be populated, having its minimum
energy at a comparatively high volume. Williams and co-workers ascribe the Invar prop
erties to thermal excitations into the non-magnetic state for which the energy minimum
is seen to occur at a significantly lower volume. Increasing temperature, therefore, leads
to a gradual loss of the spontaneous volume expansion associated with the ferromagnetic
state.
Invar alloys are employed in many devices for which a low thermal expansion is desir
able. A detailed description of the physics and application of Invar alloys is presented in the