Free electron model a free electron model is the simplest way to represent the electronic structure of metals. The simplest model of a metal is the free electron model. Besides, in the free electron model electrons can travel long. To zeroth order the valence electrons are assumed to form a free gas. Tightbinding model 1 electronic models find, read and cite. In the nearly free electron model, we take the opposite approach. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. Well examine the assumption of a constant potential. Nearlyfree electron model successes of the free electron model. The nearly free electron model is a modification of the freeelectron gas model which includes a weak periodic perturbation meant to model the interaction between the conduction electrons and the ions in a crystalline solid. The nearlyfree electron model condensed matter a spa5228. If 0, we assume the electron to be traveling in a weak potential, and can thus expand the wave function into two parts.
Jan 20, 2020 metals, such as copper and aluminum, are held together by bonds that are very different from those of molecules. The nearly free electron model, periodic potential, band structure. The corresponding eigenfunctions are plane waves with a realspace representation. Sep 06, 2017 this feature is not available right now.
Within the nearly free electron model we start from the dispersion relation of free electrons and analyze the effect of introducing a weak lattice potential. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. Nov 22, 2010 what should reassure you is that the properties that emerge are consistent with the nearly free electron model. That is, the electron eigenstates are initially assumed to be completely delocalized plane waves for free electrons, then a periodic potential is turned on to.
In the lectures we have derived two simple rules, which are away from brillouinzone boundaries the electronic bands i. Drawing a dispersion relation i the reduced zone scheme for free electron and nearly free electrons case things we need to know. Nearlyfreeelectron effective model for conducting nanotubes. Nearly free electron model k e entirely free electron model 2 k l for an electron in a monatomic linear lattice of lattice constant a, reciprocal lattice vectors, g first brillouin zone. The free electron model gives us considerable information about several electronic properties of the socalled simple metals. One corresponding to a plane wave, or a free electron, and another corresponding to a periodic correction factor. Positive hall coefficients r h values this gives rise to the nearly. Ashcroft and mermin, solid state physics, holt, rinehart and winston, 1976, chap.
A natural extension of the freeelectron model is the nearly free electron nfe model, which applies to crystals, because it is assumed that the electrons are subjected to a periodic potential inside them. Ohmsohms lawlaw andand electronelectron driftdrift electric fieldelectric field e drift velocity v d current densitycurrent densityjij ia volume element. The energy e of free electrons which is plotted versus k in fig. Bands always cross on brillouin zone boundariesalso sometimes accidental crossings. Although the free electron model is a great oversimplification of the reality, surprisingly in many cases it works pretty well, so that it is able to describe many important properties of metals. Sommerfield model for free electron theory 21 kf k a couple of muchused graphs relating to the sommerfeld model. Modern methods will yield essentially same, probably small differences. In solidstate physics, the nearly free electron model or nfe model is a quantum mechanical model of physical properties of electrons that can move almost. Kohn anomalies and enhanced superconductivity in simple. The freeelectron model gives us considerable information about several electronic properties of the socalled simple metals. Although the free electron model is a great oversimplification of the reality, surprisingly in many cases it works pretty well, so that it is able. That is, the electron eigenstates are initially assumed to. Lecture 4 week 19 origin of energy bands and nearly free electron model intuitive picture braggreflection for nearly free electrons gap opening for nearly free electrons kronigpenney model empty lattice approximation number of states in a band and filing of the bands.
A simple, free electron like model for the saline hydrides is discussed. Adding repulsive interactions between electrons does not change very much the picture presented here. Solutions due wednesday, 11 at the time of the class instructor. Does not explain why mean free paths can be so long does not explain why some materials are metals, some insulators and some are semiconductors successes. Handout 6 electrons in periodic potentials in this lecture you will learn. By means of the nearly free electron model explained in this lecture.
Of course, if the two atoms in the primitive cell were different then the crystal would lack inversion symmetry. Another example is the difference between the temperature dependence of the resistivity of metals and semiconductors. 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. Rather than sharing and exchanging electrons, a metal is essentially held together by a system of free electrons that wander throughout the solid. A free electron model is the simplest way to represent the electronic structure of metals. As per his investigation, the behavior of free electron in different possible energy states is explained, how the large number of electrons are disturbed in the energy states. Ravindran, phy075 condensed matter physics, spring 20 16 july. Metals, such as copper and aluminum, are held together by bonds that are very different from those of molecules. This is true for any k,but a periodic perturbation has nonzero matrix elements only between particular states. Nearlyfree electron model starts from the free electron perspective v 0 and adds a very weak periodic potential to represent the ions. This is where drudes free electron model of the metal the same model that explained electrical and thermal conductivity will help us through.
Origin of energy bands and nearly free electron model intuitive picture braggreflection for nearly free electrons gap opening for nearly free electrons kronigpenney model empty lattice approximation number of states in a band and filing of the bands. Energy spectrum of a nearlyfree electron model in 1d the eigenstates of free problem in 1d. Solid state physics nearly free electron model ucl. Nearly free electron in the tight bonding model, the electron eigenstates are initially assumed to be localized around the atoms, then a hopping term is introduced to allow them to delocalize. It is found that the phonon softening previously reported consist of simple kohn anomalies, the amplitudes of which are increased under pressure. Nearly free electron model bloch functions kronigpenney. The complications arise from several vanishing structure factors associated with certain reciprocal lattice vectors.
A nearly free electron model for crystalline mgh2 request pdf. In this exercise, we will find the band structure of this crystal in two ways. Chapternearly free electron model free download as pdf file. According to the classical free electron theory the value of specific heat of metals is given by 4. Free classical electrons l consider a gas of free classical electrons moving under the influence of electric and area a magnetic fields. Chapternearly free electron model electrical resistivity. As you saw in your homework, if the crystal potential lacked inversion symmetry w. The freeelectron model cannot explain why some elements are metals and others insulators. This is totally inexplicable within the free electron model. The phonon spectrum of sodium is studied using ab initio methods and a simple nearly free electron model in the pressure range where the fcc phase is stable. Periodic lattice there is an analogy between electron waves and lattice waves phonons for most value of the dispersion curve, the electrons move freely throughout the lattice there is a group velocity that is nonzero. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium.
Request pdf nearlyfreeelectron effective model for conducting nanotubes we study a nonrelativistic quantumfieldtheory model of a manyfermion system on a small cylindrical surface. Electron gas model nearly free electron gas very small potential variation with the periodicity of the crystal we will first consider electrons in one dimension very weak potentials with crystal periodicity. P3 20 points the kronigpenney model allows one to consider both the nearlyfreeelectron and tightbinding limits. The resistivity of metals, which is small at absolute zero, increases with increase of temperature. We note that in the free electron model, there is only one band. Origin of energy bands and nearly free electron model. In the nearly free electron approximation, interactions between electrons are completely ignored. Quantum free electron theory was proposed by arnold sommerfeld. A natural extension of the free electron model is the nearly free electron nfe model, which applies to crystals, because it is assumed that the electrons are subjected to a periodic potential inside them.
What should reassure you is that the properties that emerge are consistent with the nearlyfree electron model. Part ii the nearly free electron model 35 chapter 6 the drude model of conductivity 6. This model, like the freeelectron model, does not take into account electronelectron interactions. Drude model fails to predict hall and conductivity for all metals except for alkaline metals metal li na k ag au al inr h en 0780. Nearlyfree electrons model jacob shapiro march 30, 20 abstract the following is my attempt to explain to myself what is going on in the discussion of the. Nearly free electron model in the free electron model, the dispersion is. Nearly free electrons model jacob shapiro march 30, 20 abstract the following is my attempt to explain to myself what is going on in the discussion of the nearly free electron model which can be found in. Treating the nearly free electron model using degenerate perturbation theory has been shown on the blackboard during lectures 3. One dimensional electron energy bands for the nearly free electron model shown in the extended brillouin zone scheme.
The nearlyfreeelectron model and the fermi surface of. Energy bands nearlyfree electron model electron diffraction and energy gap bloch theorem the central equation emptylattice approximation tightbinding model see chap 9 nfe model is good for na, k, al etc, in which the lattice potential is only a small perturbation to the electron sea. The nearlyfreeelectron model for fermi surfaces becomes exceedingly complicated in structures containing a relatively large number of conduction electrons per primitive cell. Nearly free electron approximation use a travelling wavefunction for an electron, e ikx, with kinetic energy 2k22m assume that this is bragg scattered by the wavevector g. The former are localized in the vicinity of graphene plane within a distance of the. The evolution of the fermi surface of a divalent twodimensional metal with a square lattice as a band gap is opened at the brillouin zone boundary.
Energy bands nearly free electron model electron diffraction and energy gap bloch theorem the central equation emptylattice approximation tightbinding model see chap 9 nfe model is good for na, k, al etc, in which the lattice potential is only a small perturbation to the electron sea. Physical differences between conductors, semiconductors, insulators 2. Every algebraic nal result must be supplemented by a check of units. The phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory.
Besides, in the freeelectron model electrons can travel long. Nearly free electron approximation use a travelling wavefunction for an electron, e ikx, with kinetic energy 2k22m. Apr 10, 20 the phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. Blochs theorem and bloch functions electron bragg scattering and opening of bandgaps free electron bands and zone folding energy bands in 1d, 2d, and 3d lattices ece 407 spring 2009 farhan rana cornell university. The free electron model cannot explain why some elements are metals and others insulators.
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