VERIFIED Free Electron Theory Of Solids Pdf Viewer
The free electron model solved many of the inconsistencies related to the Drude model and gave insight into several other properties of metals. The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role. The model can be very predictive when applied to alkali and noble metals.
Free Electron Theory Of Solids Pdf Viewer
The crystal lattice is not explicitly taken into account in the free electron model, but a quantum-mechanical justification was given a year later (1928) by Bloch's theorem: an unbound electron moves in a periodic potential as a free electron in vacuum, except for the electron mass me becoming an effective mass m* which may deviate considerably from me (one can even use negative effective mass to describe conduction by electron holes). Effective masses can be derived from band structure computations that were not originally taken into account in the free electron model.
where J \displaystyle \mathbf J is the current density, E \displaystyle \mathbf E is the external electric field, n \displaystyle n is the electronic density (number of electrons/volume), τ \displaystyle \tau is the mean free time and e \displaystyle e is the electron electric charge.
Other quantities that remain the same under the free electron model as under Drude's are the AC susceptibility, the plasma frequency, the magnetoresistance, and the Hall coefficient related to the Hall effect.
Many properties of the free electron model follow directly from equations related to the Fermi gas, as the independent electron approximation leads to an ensemble of non-interacting electrons. For a three-dimensional electron gas we can define the Fermi energy as
where the prefactor to n k B \displaystyle nk_B is considerably smaller than the 3/2 found in c V Drude \textstyle c_V^\textDrude , about 100 times smaller at room temperature and much smaller at lower T \textstyle T . The good estimation of the Lorenz number in the Drude model was a result of the classical mean velocity of electron being about 100 larger than the quantum version, compensating the large value of the classical heat capacity. The free electron model calculation of the Lorenz factor is about twice the value of Drude's and its closer to the experimental value. With this heat capacity the free electron model is also able to predict the right order of magnitude and temperature dependence at low T for the Seebeck coefficient of the thermoelectric effect.
An immediate continuation to the free electron model can be obtained by assuming the empty lattice approximation, which forms the basis of the band structure model known as the nearly free electron model.
Adding repulsive interactions between electrons does not change very much the picture presented here. Lev Landau showed that a Fermi gas under repulsive interactions, can be seen as a gas of equivalent quasiparticles that slightly modify the properties of the metal. Landau's model is now known as the Fermi liquid theory. More exotic phenomena like superconductivity, where interactions can be attractive, require a more refined theory.
In solid-state physics, the nearly free electron model (or NFE model) or quasi-free electron model is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The model is closely related to the more conceptual empty lattice approximation. The model enables understanding and calculation of the electronic band structures, especially of metals.
If the values of λ k \displaystyle \lambda _\mathbf k are non-degenerate, then the second case occurs for only one value of k \displaystyle \mathbf k , while for the rest, the Fourier expansion coefficient C k \displaystyle C_\mathbf k must be zero. In this non-degenerate case, the standard free electron gas result is retrieved:
Abstract:The Compton scattering process plays significant roles in atomic and molecular physics, condensed matter physics, nuclear physics and material science. It could provide useful information on the electromagnetic interaction between light and matter. Several aspects of many-body physics, such us electronic structures, electron momentum distributions, many-body interactions of bound electrons, etc., can be revealed by Compton scattering experiments. In this work, we give a review of ab initio calculation of Compton scattering process. Several approaches, including the free electron approximation (FEA), impulse approximation (IA), incoherent scattering function/incoherent scattering factor (ISF) and scattering matrix (SM) are focused on in this work. The main features and available ranges for these approaches are discussed. Furthermore, we also briefly introduce the databases and applications for Compton scattering.Keywords: compton scattering; bound electron; many-body interaction; ab initio approach