Use of a drudelindhard model bulk dielectric function for describing a bulk plasmon excitation in a freeelectronlike material has yielded an analytical expression for the surface dielectric. We first consider the simple onedimensional case in which electrons move freely along a line, such as through a very thin metal rod. Such dynamical processes have been essential for drude s theory of electrical conductivity in metals 1 and will be discussed in detail in chapter 5. In metals, the free conduction electrons also contribute to the heat capacity. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. Jun 15, 2018 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. The alkali metals or nobel metals can be regarded as simple metals. According to this model, the valence electrons of the constituent atoms of the crystal become conduction electrons and travel freely throughout the crystal. Unlike the nearlyfree electron model in this problem we consider the case where the. Not all solids conduct electricity insulators, semiconductors, so the free electron model is not a valid description for all solids. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal.
Unit iii free electron theory engineering physics dr. Electron distribution described by fermidirac distribution function the wavevector k classically the kinetic energy of an electron is given by e p2 2m the free electron model gives the energy of an electron as. The scattering of conduction electrons are due to 1. The freeelectron model cannot explain why some elements are metals and others insulators. Band theory and electronic properties of solids, by john singleton, oup more advanced material on electrons in solids. Bound and free states in solids 0 the 1d potential energy of an electron due to an array of nuclei of charge 01 e vr 2 yg q separated by a distance.
The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. Solid state physics phys 40352 theoretical physics. In addition, there is a cubic term t 3 that contributes to the specific heat of metals but cannot be explained by the free electron model. Free electron model for solids engineering physics class. For pure metals, however, the electronic contributions dominate in the thermal conductivity.
It was developed in 1927, 1 principally by arnold sommerfeld, who combined the classical drude model with quantum mechanical fermidirac statistics and hence it is also known as the drudesommerfeld model. Because there is an energy gap between the electron states in the zone. In this script we follow closely the excellent textbook solid state physics by. One dimensional electron energy bands for the nearly free electron model shown.
Molecular orbital theory treats all solids as a very large collection of atoms bonded together and try to solve the schrodinger equation for a periodically repeating system. Amoleisdefinedasthisnumberofentitiesusually atomsormoleculesofany material. The electronic structures of solids aims to provide students of solid state physics with the essential concepts they will need in considering properties of solids that depend on their electronic structures and idea of the electronic character of particular materials and groups of materials. However, the free electron circles c 2 and c 3 intersect the zone boundaries. In the free electron model, we assume that the valence electrons can be treated as free, or at least moving in a region constant potential, and noninteracting. Also used in the condensed matter option 4th year course. The free electron model gives us considerable information about several electronic properties of the socalled simple metals.
In this model, one thinks of each valence electron being free to roam within a sphere of radius \r\ i. Drudes classical theory of electrical conduction drude assumed that a metal is composed of ions, which are stationary, and valence electrons, which are free to move. One dimensional electron energy bands for the nearly free electron model shown in the extended brillouin zone scheme. Rather than sharing and exchanging electrons, a metal is essentially held together by a system of free electrons that wander throughout the solid. Free electron model for solids according to this theory, a metal consists of electrons which are free to move about in the crystal like molecules of a gas in a container.
Path taken by a free electron in a metal under the in. In solid state physics the electron heat capacity or electronic specific heat describes the contribution of electrons to the heat capacity. Ashcroft and mermin, solid state physics, holt, rinehart and winston, 1976, chap. Free electron theory of solids march 29, 2015 december 30, 2010 by mini physics electrons can be visualised as rattling around insde the metal, randomly changing direction when they collide with positive ions, much like a ball in a pinball machine. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. 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. L l density of states calculate allowed values of k. The treatment of a metal as containing a gas of electrons completely free to move within it. Lecture notes theory of solids i physics mit opencourseware. The drude model of the free electron gas we start by considering propagation of electrons in a metal. The free electrons, considered identical to the outermost, or valence, electrons of free metal atoms, are presumed to be moving independently of one another.
To assign the peak in the optical absorption spectrum of alkalis observed in figure 1. Lecture notes mit opencourseware free online course materials. The metals form a unique type of bonding known as metallic bonding and form the lattice structure. Heat is transported by phonons and by free electrons in solids. Free electron theory of solids mini physics learn physics. Avogadrosnumberisthenumberof atomsinexactly12gramsof 12 c. Ohmsohms lawlaw andand electronelectron driftdrift electric fieldelectric field e drift velocity v d current densitycurrent densityjij ia volume element.
The uniqueness in such a type of bonding fashion lies in the fact that unlike ionic bonding and covalent bonding where the sharing of electrons is between two atoms and the electrons remain localized, in metallic bonding the bond is formed among all the atoms in the. Ginzburg landau free energy, meissner effect and flux quantization. The freeelectron model gives us considerable information about several electronic properties of the socalled simple metals. Mutual repulsion between electrons is ignored and hence potential energy is taken as zero.
The movements of free electrons obey the laws of the classical kinetic theory of gases. Free electron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. Srit unit iii free electron theory applied physics. The transport properties of solids are closely related to the energy dispersion relations ek. Heat capacity of the electron gas classical statistical mechanics a free particle should have 3kb2.
Freeelectron theory of metals article about freeelectron. Sources of electrical resistance in metals according to quantum free electron theory, the free electrons always collides with the positive ions or electrons present in the metal. In the free electron model of metals, the conduction electrons are treated as a perfect gas obeying fermidirac statistics. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. Rpascreened freeelectron model and for electronic density parameters rs 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. A free electron model is the simplest way to represent the electronic structure of. Well examine the assumption of a constant po tential. The weak periodic potential causes a distortion of the fermi circle of a twodimensional electron gas as it approaches the zone boundary. Each electron occupies an orbital having quantum numbers \n\, \l\, and \m\, with the energies of the orbitals given above in terms of the zeros \\z.
In the nearly free electron approximation, interactions between electrons are completely ignored. N atoms each give one valence electron and the electrons are freely mobile. Bloch theorem, phonons in one dimension, periodicity, effect of a basis on the electronic structure, crystal structures, the. Well examine the assumption of a constant potential. Finished with phonons, optical and thermal properties. Review of energy dispersion relations in solids references. Besides, in the free electron model electrons can travel long. However, this model is in general too simple to explain many electronic and optical properties of solids. Lecturenotesforsolidstatephysics 3rdyearcourse6 hilaryterm2012.
Use of a drudelindhard model bulk dielectric function for describing a bulk plasmon excitation in a free electron like material has yielded an analytical expression for the surface dielectric. The free electron model cannot explain why some elements are metals and others insulators. Drude model, the ratio of the thermal to the electrical conductivity does. The simplest model of a metal is the free electron model. Besides, in the freeelectron model electrons can travel long. Free classical electrons l consider a gas of free classical electrons moving under the influence of electric and area a magnetic fields. Bloch theorem, phonons in one dimension, periodicity, effect of a basis on the electronic structure, crystal structures, the reciprocal lattice.
The major failure of the free electron model is that it does not explain the significant difference between metals, insulators, and semiconductors. The free electrons, considered identical to the outermost, or valence. Free electron model periodic boundary conditions add a second piece of crystal the same size. Free electron model of metals up to this point, we have only considered contributions to the heat capacity from vibrations within the solid. Ueep2024 solid state physics topic 3 free electron in metals 2. Prominent examples are the alkali metals and aluminum. The phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. The valence electrons form a very dense electron gas.
Apr 05, 2014 this feature is not available right now. Solid state physics optical properties of solids download book. According to the classical free electron theory the value of specific heat of metals is given by 4. In impure metals, the electron mean free path is reduced by collisions with. Free electron model put free electrons into a very wide potential well the same size as the crystal i. It turns out that the nearly free electron approximation is quite reasonable for simplemetals withpredominant s. Electrons can become free of the nuclei and move between nuclei since we observe electrical conductivity electron gas simplest possible model for a metal electrons are completely free of the nuclei nuclei are replaced by a smooth background electrons in a box. To relate the charge density in a metal to the density of free electrons, let nbe the number of electrons. Free electron theory of metals nicholas research group. This idea was given by drude and he utilized it to explain many properties of metals satisfactorily such as electrical conductivity, thermal conductivity etc. Lecture 5 solids thefreeelectrongas in asolid state, afew loosely bound valence outermost and not in completely filled shells.
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