Thermodynamics of the Nonrelativistic Free-Electron Fermi Gas in One, Two, and Three Dimensions from the Degenerate to the Nondegenerate Temperature Regime
Iowa State University Digital Repository, Ames IA (United States)
Is Version Of
Ames National LaboratoryPhysics and Astronomy
The thermodynamic properties of a nonrelativistic free-electron Fermi gas is of fundamental interest in condensed matter physics. Properties previously studied in three-dimensions (3D) in the lowand high-temperature limits include the internal energy, heat capacity, zero-field magnetic spin susceptibility, and pressure. Here we report solutions for the temperature dependence spanning these two temperature regimes of the chemical potential, internal energy, magnetic susceptibility, and the heat capacity at constant volume in 1D, 2D, and 3D. Also calculated are the pressure, enthalpy, heat capacity at constant pressure, isothermal compressibility, and thermal expansion coefficient versus temperature in 2D and 3D. Of primary interest here are the detailed dimension-dependent crossovers of these properties between the degenerate and nondegenerate temperature regime, which are graphically illustrated for each of the above properties.
This article is published as Johnston, David C. "Thermodynamics of the nonrelativistic free-electron Fermi gas in one, two, and three dimensions from the degenerate to the nondegenerate temperature regime." Journal of Physics and Chemistry Research 4, no. 2 (2022). DOI: 10.36266/JPCR/149E. Copyright 2022 Johnson DC. Attribution 4.0 International (CC BY 4.0). Posted with permission. DOE Contract Number(s): AC02-07CH11358.