That time the valance electrons in metals were regarded as the noninteracting particles of an ideal gas. Thermal properties of the free 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 27 48. Prominent examples are the alkali metals and aluminum. 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. 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. The classical free electron theory is based on the following postulates. Sommerfelds free electron theory of metals physics assignment. Srit unit iii free electron theory engineering physics. According to this theory, the metals containing free electrons obey the. All metals share common properties excellent electrical conductors excellent thermal conductors shiny when polished all due to the free electrons of the metallic bond outline classical drude theory of metals successes and limitations of the classical model sommerfeld theory of metals. Later, quantum mechanics became the basis for the theory of most of the general properties of simple metals such as sodium, with one free electron per atom, magnesium with two, and aluminum with three. Atomic selectrons are delocalised due to overlap of outer orbits. Nov 05, 2016 behavior of free electron is different from electron in the potential field of the crystal as current is due to flow of charge, electron behavior in external electric field is important 9.
In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. 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 development of the quantummechanical electron theory of. Electron theory of complex metallic alloys sciencedirect. Electron theory synonyms, electron theory pronunciation, electron theory translation, english dictionary definition of electron theory. What are the drawbacks of classical free electron theory. It could not explain the negative temperature coefficient of resistivity for certain solids 2. Drude theory of conduction basics of free electron theory and electrical conductivity. This paper continues an earlier study of the first phase of the development from 1926 to 1928 devoted to finding the general quantummechanical framework.
Classical free electron theory of metals this theory was developed by drude and lorentz and hence is also known as drudelorentz theory. Such freely moving electrons cause electrical conduction under an applied field and hence referred to as conduction electrons. The valence electrons of atoms are free to move about the whole volume of the metals like the molecules of a perfect gas in a container. Dm represents documents in the archives of the deutsches museum in. Because it was unable to answer why the mean free path of electrons reaches 20nm in a good conducting metal like silver in room tempereture. Postulates of classical free electron theory 1 the free electrons of a metal are having like the moleculesof a gas in acontainer. In this chapter the free electron theory of metals as developed by sommerfeld and others will be discussed. It is free to move throughout the volume of the metal. The classical theory had several conspicuous successes, notably the. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal.
The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. Electron dynamics and fermi surfaces electron dynamics the next important subject we address is electron dynamics in metals. Apr 10, 20 the phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. To assign the peak in the optical absorption spectrum of alkalis observed in figure 1. Put free electrons into a very wide potential well the. Then sommerfelds elementary quantum mechanical theory of metals is discussed. The failure of the free electron theory of metals physics.
May 20, 2006 why did the free electron theory of metals fail the free electron of model my effort. Drude theory of conduction basics of free electron theory and electrical conductivity part 1. Especially classical free electron theory and quantum free electron theory of metals. 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. According to classical free electron theory of metals electrical conductivity is given by, from the above equation, relation between temperature and electrical conductivity is given by hence, classical free electron fails to explain the temperature dependence of electrical conductivity.
The collection of valence electrons from all the atoms in a given piece of metal forms electron gas. 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. In a metal conduction electrons move almost freely. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. Conductors classical free electron theory of metals electrical and thermal conductivity wiedemann franz law lorentz number draw backs of classical theory quantum theory fermi distribution function effect of temperature on fermi. Attempts to understand the stabilization mechanism of structurally complex metallic alloy cma phases dates back to 1936 when mott and jones interpreted the stabilization of cu 5 zn 8 and al 4 cu 9 gammabrasses containing 52 atoms per unit cell at particular electrons per atom ratio ea in terms of the contact of the free electron sphere with the brillouin zone. All due to the free electrons of the metallic bond. Engineering physics ii unit 1 conducting materials notes topic covered. 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.
However, the following assumptions of classical electron theory continue to be applicable in quantum free electron theory also. The free electrons are treated as equivalent to gas molecules and they are. Freeelectron theory of metals article about freeelectron. Quantum free electron theory was proposed by arnold sommerfeld. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in metals. In solidstate physics, the free electron model is a simple model for the behaviour of. Mar 18, 2018 classical free electron theory of metals physics video.
The treatment of a metal as containing a gas of electrons completely free to move within it. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. The main assumptions of classical free electron theory are. Solid state, by providing a large and ready number of concrete prob. 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. The discussions assume the readers familiarity with the material pertaining to appendixes b, c, d, and e.
Our consideration will be based on a semiclassical model. Unit1 classical free electron theory physics youtube. Some appreciation of the term of relaxation time dt. The development of the quantummechanical electron theory of metals. Free electron theory of metals nicholas research group. The valence electrons of metallic atoms are free to move in the spaces between ions from one place to another place within the metallic specimen similar to gaseous molecules so that these electrons are called free electron gas.
The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role. The free electron model solved many of the inconsistencies related to the drude model and gave insight into several other properties of metals. The classical free electron theory of metals drude lorentz theory of metals. From the instant of sudden disappearance of an electric field across a metal, the average velocity of the conduction electrons decays. The classical free electron theory was introduced by p. The main assumptions of quantum free electron theory are, the energy levels of the conduction electrons are quantised.
The term semiclassical comes from the fact that within this. This approximation starts with the notion that the metal contains a collection of ion cores, each core consisting of a nucleus and shells of tightly bound electrons, and a number of electrons that are not bound to any particular nucleus. The free electron model considers that metals are composed of a quantum electron gas where ions. This textbook gives a complete account of electron theory in both periodic and nonperiodic metallic systems. Drudes theory treated the electrons as an ordinary classical gas. Mar, 2017 start free trial sign in engineering physics by s. So it leads to much larger predicted quantities than that is actually observed. Conductivity, hall effect and other transport phenomena will be treated separately in chapter 11. Engineering physics ii unit 1 conducting materials notes. It turns out that the nearly free electron approximation is quite reasonable for simplemetals withpredominant s. Metals drudes classical theory theory by paul drude in 1900, only three years after the electron was discovered.
Ravindran, phy075 condensed matter physics, spring 20 16 july. A metal is imagined as the structure of 3dimensional array of ions in between which, there are free moving valence electrons confined to the body of the material. Assumptions we will first consider a gas of free classical electrons subject to external electric and magnetic fields. The distribution of electrons in various allowed energy levels occur as per pauli exclusion principle. About that time, geometrical terms such as extremal sections, curvatures, diameters, limiting points began to appear in papers on the electron theory of metals.
One of the earliest successful approximations in the theory of metals was the free electron theory. For the love of physics walter lewin may 16, 2011 duration. The classical free electron theory of metals drude lorentz theory of metals postulates. Freeelectron theory of metals accessscience from mcgraw. In an atom electrons revolue around the nucleus and a metal is composed of such atoms. It was developed in 1927, principally by arnold sommerfeld, who combined the classical drude model. Quantum free electron theory of metals science key. Electron theory definition of electron theory by the free. Expressions obtained will be useful when considering real conductors i free electrons. The valance electrons are not affected by theeltlectronion it tiinteraction. Drude model conductivity frequency dependence plasma. This idea was given by drude and he utilized it to explain many properties of metals satisfactorily such as electrical conductivity, thermal conductivity etc. Theory of free electrons in metals elefterios lidorikis room. Pdf free electron theory 201516 vtu shashank mohan.
854 1045 1080 1038 159 253 1311 1516 449 1368 1340 1038 374 297 373 301 559 1485 1156 787 1057 1121 1462 1435 1189 1179 1367 1030 495 969 1322