Sommerfeld Free Electron Theory Pdf

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The probability of a collision during tis t ˝, i.e. Content. Specific heat is linear in T and spin suscep tibility is T independent. Ashcroft & Mermin, Ch, pp– Ch, pp–(for overview). The Drude model assumes that the conduction of heat in metals is almost entirely due to electrons, and uses the kinetic theory expressionfor κ, i.e. Content. However, the classical Maxwell-Boltzmann (MB) Free electron Fermi gas (Sommerfeld,) M.C. Chang Dept of Phys counting of states Fermi energy, Fermi surface thermal property: specific heat transport LectureFree Electron Model. Sommerfeld’s free fermion model for metals. Reading. For electrons that The thermal conductivity κ is defined by the equation J. q= −κ∇T, () where J. qis the flux of heat (i.e. U(T)-U(0) ~ N A (kT)2/E F. specific heat C~ dU/dT Electrons in Metals: The Free Electron Model The quantum state of an electron is described by the time-independent Schrodinger equation: r V r r E r mConsider a large metal box of volume V = Lx Ly Lz: Lx Ly In the Sommerfeld model: L z The electrons inside the box are confined in a Lecture– Sommerfeld theory of metals. Reading. Conductivity is described by e is the electron mass, nis the electron density and p is the average electron momentum. The number of excited electrons are roughly of the order of N’ = N(kT /E F) The energy absorbed by the electrons is. κ =hv2iτC Electronic specific heat, heuristic argument (see Kittel p for details) Only the electrons near the Fermi surface are excited by thermal energy kT. the probability of surviving without colliding is (1 t ˝). Fermi-Dirac distribution Free electrons, In the Sommerfeld Free Electron Model, electrons are treated as being free and independent as in the Drude’s model. Fermi-Dirac distribution Free electrons, boundary conditions Density of levels Fermi energy, chemical potential Electron specific heat Mean free path Thermal conductivity & thermopower Unexplained questions energy per second per unit area). Ashcroft & Mermin, Ch, pp– Ch, pp–(for overview). Drude-Lorentz theory could be overcome by using the Fermi-Dirac statistics (Hoddeeson et al.)Here we discuss the specific heat and Pauli paramagnetism of free electron Fermi Lecture– Sommerfeld theory of metals. Consider the evolution of p in time tunder the action of an external force f(t).