Handout 2 sommerfeld model for metals free fermion gas. What should reassure you is that the properties that emerge are consistent with the nearlyfree electron model. According to the classical free electron theory the value of specific heat of metals is given by 4. Atomic selectrons are delocalised due to overlap of outer orbits. That is why band theory fails in some cases ferromagnetic systems, mott insulators. A conductor is a material which contains movable electric charges. Band theory periodic potential approach we have seen that the periodic potential in crystalswe have seen that the periodic potential in crystals can give rise to energy bands. These free electrons are mostly valence electrons, because the. Treating the nearly free electron model using degenerate perturbation theory has been shown on the blackboard during lectures 3. Free electron model drudesommerfeld model when electrons move freely in the lattice without any obstacle like potential due to ions or any impurity, these are called free electrons. Drawing a dispersion relation i the reduced zone scheme for free electron and nearly free electrons case things we need to know.
According to this theory, the metals containing free electrons obey the laws of classical mechanics. Nearly free electron model issues that are addressed in this chapter include. Schrodinger pronouns pdf download equation for a free electron. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. The free electrons, considered identical to the outermost, or valence. Groundstate properties of the electron gas 1 groundstate properties of the electron gas 2 the fermidirac distribution 3 thermal properties of the free electron gas 4 the sommerfeld theory of conduction in metals daniele to oli january 11, 2017 3 48. In solidstate physics, the nearly free electron model is a model of electron behavior in solids that enables understanding the electronic band structure of crystalline materials the nearly free electron model is a modification of the free electron gas model which includes a weak periodic perturbation meant to model the interaction between the conduction electrons and the ions in a. Nearly free electron model 7 nearly free electron model. The energy of these bands is between the energy of the ground state and the free electron energy the energy required for an electron to escape entirely from the material. Adding repulsive interactions between electrons does not change very much the picture presented here.
Ravindran, phy075 condensed matter physics, spring 20 16 july. Note, however, that although the free electron wave vector is simply p, where p is the momentum of the electron, in the bloch case k is not proportional to the. Solid state physics nearly free electron model ucl. The classical theory had several conspicuous successes, notably the. Srit unit iii free electron theory engineering physics. The nearlyfree electron model key reference for weeks 1012. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. Find materials for this course in the pages linked along the left. Electrons in a periodic potential nearly free electron. Ohmsohms lawlaw andand electronelectron driftdrift electric fieldelectric field e drift velocity v d current densitycurrent densityjij ia volume element. We first discuss essential elements of group theory. What is the difference between free electron theory and. So we will make a few more observations about the nature of the wave function relating to the periodic potential, and then solve the schroedinger equation.
By firstprinciples theory we study the nearly free electron nfe states of carbon and boron nitride nanotubes. Handout 2 sommerfeld model for metals free fermion gas in this lecture you will learn. Quantum free electron theory of metals science key. Lecture notes theory of solids i physics mit opencourseware. The energy e of free electrons which is plotted versus k in fig.
Nearly free electron state in graphane nanoribbon superlattice. That is, the electron eigenstates are initially assumed to. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. The valence band in any given metal is nearly filled with electrons under usual conditions. This model, like the free electron model, does not take into account electron electron interactions. Pdf modulation of nearly free electron states in hydroxyl. Nearly free electron approximation and tight binding. Sep 08, 2019 gate 2020 syllabus for physics pdf file download link is given below. Article nearly free electron state in graphane nanoribbon.
Maslov department of physics, university of florida. Energy bands nearlyfree electron model electron diffraction and. In metallic conductors, such as copper or aluminum, the movable charged. Unit iii free electron theory engineering physics dr. Sidebottom, fundamentals of condensed matter and crystalline physics, chapters 12 so far we have seen that the free electron gas model can explain a surprising number of the properties of metals, including their heat capacity and bulk modulus.
Energy spectrum of a nearlyfree electron model in 1d the eigenstates of free problem in 1d. Sommerfeld theory of metals arnold sommerfeld 18681951 ece 407 spring 2009 farhan rana cornell university does not say anything about the electron energy distribution in metalsare all electrons moving around with about the same energy. Using density functional theory dft, it is revealed that the nearly. However, the free electron circles c 2 and c 3 intersect the zone boundaries. We note that in the free electron model, there is only one band.
Neglecting the electron electron interaction and the electron ion interaction, it appears as if the electrons move in a confined box with periodic collision with ions in the lattice. One corresponding to a plane wave, or a free electron, and another corresponding to a periodic correction factor. Realizing nearlyfreeelectron like conduction band in a. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. In the bulk of the material, the surface is disregarded altogether and the electrons are completely free. The nearly free electron model is a modification of the free electron gas model which includes a weak periodic perturbation meant to model the interaction between the conduction electrons and the ions in a crystalline solid. 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. Every algebraic nal result must be supplemented by a check of units. Jul 29, 2019 nearly free electron like lumo band of c 60 monolayer on bp. The phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. The treatment of a metal as containing a gas of electrons completely free to move within it. Also according to this theory the value of electronic specific heat is equal to 32 r. Band theory of electrical conductivity boundless chemistry.
Free classical electrons l consider a gas of free classical electrons moving under the influence of electric and area a magnetic fields. The theory of electrons, and its applications to the phenomena of light and radiant heat by lorentz, hendrik antoon, 18531928. Chapter 4 electronic structure the electronic properties of matter determines its macroscopic behavior. We can use the extended zone scheme left or displace all the segments of the dispersion curve back into the. The logic is very similar to getting optical and acoustic phonon branches by changing atom masses and thereby reducing the size of the brillouin zone. In the nearly free electron model, we take the opposite approach. Tr 3 pm4 pm please help your instructor by doing your work neatly. The free electron model cannot explain why some elements are metals and others insulators. The corresponding eigenfunctions are plane waves with a realspace representation. The electrons, however, are treated using quantum mechanics. The free electron approximation remains a good approximation well away from the edges of the brillouin zone only wavevectors close to a multiple of.
Besides, in the free electron model electrons can travel long distances. Page 3 mobility of electrons the mobility of electrons is defined as the magnitude of drift velocity acquired by the electron in a unit field. Chapter 6 free electron fermi gas national tsing hua. Simplest extension of the electron gas model nearly free electron gas very small potential variation with the periodicity of. According to this theory, the free electrons obey quantum laws. 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. 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. This period finished with the establishment of quantum. Some appreciation of the term of relaxation time dt. In the nearly free electron approximation, interactions between electrons are completely ignored.
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. Handout 6 electrons in periodic potentials in this lecture you will learn. Free electron theory of conductor was proposed by p. This in turn will affect the way the electron gas can absorb energy from an external source. Apply the concept of band theory to explain the behavior of conductors. A conductor is a material that is able to conduct electricity with minimal impedance to the electrical flow. The weak periodic potential causes a distortion of the fermi circle of a twodimensional electron gas as it approaches the zone boundary. Quantum free electron theory was proposed by arnold sommerfeld. Band theory does not consider electronelectron interactions. Given its simplicity, it is surprisingly successful in explaining.
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. Electronic structure 103 in the following chapter, we will also learn some experimental techniques that are currently used to investigate the electronic properties of the bulk and the surface. Unlike the nearly free electron model in this problem we consider the case where the. Nearly free electron model what is the dispersion curve of the free electron model.
Jun 15, 2018 these free electrons move freely throughout the lattice and hence are termed as electron gas. Sommerfield model for free electron theory 11 success of quantum free electron theory according to classical theory, which follows maxwellboltzmann statistics, all the free electrons gain energy. Chapternearly free electron model free download as pdf file. This is totally inexplicable within the free electron model. Apr 10, 20 the phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. The nearlyfree electron model university of oxford. In this case, the perturbation theory constructed in this section diverges, and one has to select the eigenfunctions of the zeroth order in a di. Modulation of nearly free electron states in hydroxylfunctionalized mxenes. Freeelectron theory of metals article about freeelectron. So it leads to much larger predicted quantities than that is actually observed.
What is the difference between nearly free electron model. 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. 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. 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. This is true for any k,but a periodic perturbation has nonzero matrix elements only between particular states.
Both in the nearly free electrons and tight binding models, the only interaction is between electrons and the ions. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. The third period was a period of striving to understand and finally accept the wave and spin properties of the electron through formulating wave mechanics and relativistic quantum theory of the electron. Syllabus for general aptitude ga common to all papers. Apr 01, 2015 the free electron empty lattice approximation forms the basis of the band structure model known as nearly free electron model.
In the lectures we have derived two simple rules, which are away from brillouinzone boundaries the electronic bands i. Nearly free electron model in the free electron model, the dispersion is. Chapternearly free electron model electrical resistivity and. Nearly free electron nfe state 1421 exists widely in low dimensional materials, and it is an attractive candidate for electron transport. Nearlyfree electron model starts from the free electron perspective v 0 and adds a very weak periodic potential to represent the ions. 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. Because there is an energy gap between the electron states in the zone. Recall nature of free electron gas free electrons in box of size l x l x l artificial but useful. Introduction to the electron theory of metals the electron theory of metals describes how electrons are responsible for the bonding of metals and subsequent physical, chemical and transport properties. Nearly free electron superatom states of carbon and boron. 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.
What is the difference between free electron theory and nearly free electron theory. Solid state physics nearly free electron model contd lecture 19 a. These bands are 1d counterparts of the recently discovered superatom orbitals of 0d fullerenes. If 0, we assume the electron to be traveling in a weak potential, and can thus expand the wave function into two parts. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. Solutions due wednesday, 11 at the time of the class instructor. This model, like the freeelectron model, does not take into account electronelectron interactions.
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