Summary 958.4 Summary
This chapter discusses the properties of an ideal Fermi–Dirac gas.
Quantum statistics rather than MB statistics canbe appropriateforgases athigh
density, low temperature and light particle mass.
The exclusion principle dominates FD statistics, since the maximum occupation
number ofa one-particle stateis 1. States arefullor empty.
3 .AtT=0 there is a sharp Fermi energy, defined so that all lower energystates are
full, and all higher energy states are empty.
This energycanbe representedbya ‘Fermisurface’ink-space
At higher temperatures, the Fermi surface becomes blurred, with states withinkkkBT
ofthe surfacehavingintermediate occupation on average.
Manythermodynamic properties of thegas are related to those of the MBgas,
reduced by a factorkkkBT/εF.
Conduction electronsin metals provide a goodexampleofFD properties, even
thoughthedensityofstatesis not that ofanidealfreegas.
Liquid helium-3 is (surprisingly) another candidate, for reasons which will be
exploredfurtherinChapter 14.
Thephasediagram ofhelium-3 shows that thesolid is moredisorderedthan the
liquid, a demonstration that the lack of flexibility in the FD gas inhibits spin
disorder.