According to this theory, the free electrons obey quantum laws. Sommerfeld theory of metals problems in solid state. The lectures are uploaded as pdf files, so you will need adobe acrobat reader in order to read them. The bohrsommerfeld quantization rule lies at the heart of the modern semiclassical theory of a bloch electron in a magnetic field. Please notice the word tend exceptions do occur and we will meet some of these before the end of the course. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. Before sommerfeld mucked it up, the simple drude model provided a very good explanation of dc and ac conductivity in metals, the hall effect, and thermal conductivity due to electrons in metals near room temperature. Pdf understanding of physics on electrical resistivity in metals. If the address matches an existing account you will receive an email with instructions to reset your password. He realised the role played by pauli exclusion principle in restricting the energy values of. Outline the sommerfelds theory of electrical conductivity. Chapter 5 the drude theory of metals delaware physics. According to this theory, the metals containing free electrons obey the laws of classical mechanics.
This rule is predictive of landau levels and quantum oscillations for conventional metals, as well as for a host of topological metals which have emerged in the recent intercourse between band theory, crystalline symmetries and topology. The classical free electron theory of metals drude lorentz theory of metals postulates. Based on the debroglie wave concept, he assumed that a moving electron. In this chapter the free electron theory of metals as developed by sommerfeld and others will be discussed. Baffling as well was the curious phenomenon of super conductivity, first observed in 1911by gilles hoist, work. For an historical survey of the contributions of physicist to the theory of metals, see p. Arnold johannes wilhelm sommerfeld, formemrs german. Butler, electrical conduction in metals, physics today. Handout 2 sommerfeld model for metals free fermion gas in this lecture you will learn.
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 metals are all electrons moving around with about the same energy. His theory also predicts a linear dependence of the specific heat for metals at low temperatures. Handout 2 sommerfeld model for metals free fermion gas. Quantum free electron theory could successfully explain the electronic sp. Sommerfeld and the spread of the electron theory of metals article pdf available in historical studies in the physical and biological sciences 172. To account for these shortcomings sommerfeld in 1927 developed a model for electrons in metals that took into consideration the fermidirac statistics of electrons note added. Butler, electrical conduction in metals, physics today, 1978, 3112, 4449. Pdf how sommerfeld extended bohrs model of the atom. The valence electrons of atoms are free to move about the whole volume of the.
The model also explains the wiedemannfranz law of 1853. The crucial idea was that a spectral line is made up of coinciding. Metals contain free electrons that move through a lattice of positive ions. The pauli exclusion principle strongly modifies classical maxwellboltzmann expressions for electronic specific heat and electron velocities. The assumptions of the drudelorentz classical theory of freeelectrons are the following. Understanding of physics on electrical resistivity in metals. Freeelectron theory of metals accessscience from mcgraw. 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. Sommerfeld free electron theory of electrons in metals. The theory is now understood as the semiclassical approximation to modern quantum mechanics the main tool of the old quantum theory was the bohrsommerfeld. As in that development, the steps leading to the quantum theory of metals may be divided into three periods. Condensed matter physics iii electrons and phonons in. Microscopic variables for electrical transport drude. In 1928 sommerfeld has proposed a simple model describing the motion of electrons. Sommerfeld theory of metals in 1928, arnold sommerfeld discovered that free electrons in metals follow fd statistics. Theory and properties provides the basis for the examination and explanation of thermoelectric phenomena and their correlations with other physical properties. Lecture 4 sommerfeld model, quantum ground state of free electron gas. It was developed in 1927, principally by arnold sommerfeld, who combined the classical drude model. Introduction to the electron theory of metals 1st edition.
Quantum theory of metals room temperature than the interatomic distance and even longer at low temperatures. Fundamental concepts of the electron theory of metals. The dimensionless number r s is introduced as the ratio between coulomb energy and kinetic energy. The smallscale details of the potential due to the ionic cores shown schematically in b are replaced by an average potential v 0. Besides his important contributions to the study of condensed matter systems, among which his seminal electron gas theory of metallic conduction probably stands out, he. Then you can start reading kindle books on your smartphone, tablet, or computer no kindle device required. The drude and sommerfeld models of metals in other words, the collisions produce a frictional damping term. Sommerfelds electrontheory of metals pdf free download epdf. His approach is based upon quantization of electrical energy levels. The main peculiarities of such electrons are connected with the form of their isoenergy surfaces, which is different from those of the free electrons.
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. In an atom electrons revolue around the nucleus and a metal is composed of such atoms. Arnold sommerfeld and condensed matter physics annual. The free electron model considers that metals are composed of a quantum electron gas where ions. Sommerfelds free electron theory of metals physics. Quantum free electron theory of metals science key. 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.
Get a printable copy pdf file of the complete article 823k, or click on a page image below to browse page by page. The development of the quantum mechanical electron theory. 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. Wojciechowski, in metal surface electron physics, 1996. Quantum free electron theory was proposed by arnold sommerfeld. Topological aspect of the dynamics of electrons in crystals band electrons is discussed. 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. Sommerfeld s extension of bohrs atomic model was motivated by the quest for a theory of the zeeman and stark effects.
He served as doctoral supervisor for many nobel prize winners in physics and chemistry only j. The classical period was dominated by the model of drude and lorentz in which a metal contained an ideal gas of conduction electrons governed by kinetic theory. Elements can be more clearly classified as metals and non metals on the basis of their chemical properties. Apr 10, 20 according to this theory, the metals containing free electrons obey the laws of classical mechanics. But according to quantum theory, the free electrons occupy different energy levels, up to fermi level at 0 k. The treatment of a metal as containing a gas of electrons completely free to move within it. Bohrsommerfeld theory first gived the fine structure constant 17. Oct 11, 2017 the bohr sommerfeld quantization rule lies at the heart of the modern semiclassical theory of a bloch electron in a magnetic field. Nonmetals tend to react with oxygen to form acidic oxides. Pdf formulation of heat conduction and thermal conductivity of. Similarly, the heat conductivity at high temperatures was computed to be propor tional to t, but observed to go in direct proportion to t.
The theory was never complete or selfconsistent, but was rather a set of heuristic corrections to classical mechanics. The discussions assume the readers familiarity with the material pertaining to appendixes b, c, d, and e. When we recall the fact sommerfeld has recently expressed. Conductivity, hall effect and other transport phenomena will be treated separately in chapter 11.
Full text is available as a scanned copy of the original print version. He nevertheless played a crucial role for the history of the field. Six of sommerfeld s students werner heisenberg, wolfgang pauli, peter debye, hans bethe, linus pauling, and isidor i. Boltzmann, sommerfeld, and landaus kinetic theory of electrons in metals electrical and thermal conductivity electrical transport in weak magnetic fields thermoelectric and thermomagnetic e ects highfrequency conductivity skin e ects quantum e ects at high magnetic fields phonon propagation in metals acoustic attenuation. Nov 05, 2016 quantum free electron theory could successfully explain the electronic sp. Some appreciation of the term of relaxation time dt. In such a picture, the ionic cores merely maintain charge.
The salient features of quantum free electron theory sommerfeld proposed this theory in 1928 retaining the concept of free electrons moving in a uniform potential within the metal as in the classical theory, but treated the electrons as obeying the laws of quantum mechanics. These results are applied and account for the properties and deviations of commercial materials in the temperature ranges of most common industrial usage. 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. Schematic of the electronic potential assumed in the drude and sommerfeld models of metals a. Sommerfeld 1928 applied the principles of quantum mechanics to classical free electron theory. Sommerfeld theory of metals in 1928 arnold sommerfeld. Lorentz, the theory of electrons and its application to the phenomena of light and radiant heat, teubner. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. It also gives the correct value for the lorentz number. Ine here, saw the realization that the new quantum theory could explain, at. This idea will have many applications, even beyond the drude model.
This lecture series constitutes a first undergraduate course in solid state physics delivered in an engaging and entertaining manner by professor steven h. Atomic selectrons are delocalised due to overlap of outer orbits. Ponderomotive interaction of steady currents and their magnetic field in the absence of magnetizing media 218. In this section, we calculate the bohrsommerfeld model, and explain the original meaning and derivation of this fine structure constant. The development of the quantummechanical electron theory. Enter your mobile number or email address below and well send you a link to download the free kindle app.
The old quantum theory is a collection of results from the years 19001925 which predate modern quantum mechanics. In 1928, by applying quantum mechanical principles, arnold sommerfeld succeeded in overcoming many of drawbacks of the classical free electron theory, while retaining all the essential features of the classical free electron theory. The classical theory fails to explain the heat capacity and the magnetic. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with each other. Arnold sommerfeld 18681951, one of the founders of modern theoretical physics and a pioneer of quantum theory, was no condensed matter physicist. 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. This leads to a temperature independent n since the fermi energy for metals is in the 10 4. Metals tend to react with water to form basic hydroxides. This textbook gives a complete account of electron theory in both periodic and nonperiodic metallic systems. According to classical theory, the free electrons in a metal have random motions with equal probability in all directions. Drude theory of metals problems in solid state physics.
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