Sommerfeld and the spread of the electron theory of metals article pdf available in historical studies in the physical and biological sciences 172. In the bulk of the material, the surface is disregarded altogether and the electrons are completely free. The drude theory of metals the model kinetic theory of gases. 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. Ece 407 spring 2009 farhan rana cornell university. Atomic selectrons are delocalised due to overlap of outer orbits. Sommerfeld theory of metals describe the electron behavior in metals. Pdf sommerfelds extension of bohrs atomic model was motivated by the quest for a theory of the zeeman and stark effects. Sommerfeld theory of metals problems in solid state.
Classical derivation of ohms law and drude conductivity. Understanding of physics on electrical conductivity in. In 1928 sommerfeld has proposed a simple model describing the motion of electrons confined in a metal. 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. Full text is available as a scanned copy of the original print version. Drude sommerfeld kubo masatsugu sei suzuki and itsuko s. Arnold johannes wilhelm sommerfeld, formemrs german. System upgrade on feb 12th during this period, ecommerce and registration of new users may not be available for up to 12 hours. Using the method of kinetic theory of gases and maxwell boltzmann distribution law, drude and lorentz explained the phenomenon of electrical conduction. Apr 10, 20 according to this theory, the metals containing free electrons obey the laws of classical mechanics. The great electrical conductivity of metals, as well as their high reflectivity suggest that they contain a large number of electrons which can move freely in the crystal skeleton build up from the positively charged ioncores.
Content fermidirac distribution free electrons, boundary conditions density of levels fermi energy, chemical potential electron speci. Retains almost all aspects of drude model with the. In classical free electron theory, proposed by drude and later developed by lorentz, it is assumed that valence electrons in a metal are analogous to a gas in a box. Pdf how sommerfeld extended bohrs model of the atom. Overview around 1900, drude paul karl ludwig drude improved the theory of. It can also serve as a desirable reference book to solve typical problems and grasp. Nov 05, 2016 failures of quantum free electron theory.
This lecture series constitutes a first undergraduate course in solid state physics delivered in an engaging and entertaining manner by professor steven h. 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. Sommerfeld 1928 applied the principles of quantum mechanics to classical free electron theory. Understanding of physics on electrical conductivity in metals. Metals form in crystal structures which have relatively large numbers n nn of nearest neighbours, e. 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. However, thoughout the course the material that i write on the blackboard will not necessarily be covered in this transcript. The treatment of a metal as containing a gas of electrons completely free to move within it. Based on the debroglie wave concept, he assumed that a moving electron. I recommend the book band theory and electronic properties of solids, by john singleton oxford. Ganesh the drude model is inadequate in many respects, e. Sommerfelds electrontheory of metals pdf free download. His approach is based upon quantization of electrical.
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. Assumptions most are very similar to those of drude. Sommerfelds free electron theory of metals home sommerfelds free electron theory of metals 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. According to classical theory, the free electrons in a metal have random motions with equal probability in all directions. 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. Sommerfelds extension of the bohr theory in 19151916, it was turned into a powerful tool of atomic research and adopted and further developed by german physicists in particular. 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. The electrons, however, are treated using quantum mechanics.
The course is based on steven simons oxford solid state basics textbook. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. It was developed in 1927, principally by arnold sommerfeld, who combined the classical drude 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. The pauli exclusion principle strongly modifies classical maxwellboltzmann expressions for electronic specific heat and electron velocities.
Many of these errors occur because the electrons velocity and energy are deduced from a classical distribution. The drude and sommerfeld models of metals this series of lecture notes covers all the material that i will present via transparencies during this part of the c3 major option. Get a printable copy pdf file of the complete article 823k, or click on a page image below to browse page by page. Quantum free electron theory of metals pdf the turn of the twentieth century, of a freeelectron theory of metals and the writing by arnold sommerfeld and.
According to this theory, the free electrons obey quantum laws. The discussions assume the readers familiarity with the material pertaining to appendixes b, c, d, and e. This textbook gives a complete account of electron theory in both periodic and nonperiodic metallic systems. Full text full text is available as a scanned copy of the original print version. The problems in this book can be used as homework assignments in an introductory or advanced course on solid state physics for undergraduate or graduate students.
Chapter 6 free electron fermi gas national tsing hua. Sommerfelds free electron theory of metals physics. Sommerfelds free electron theory of metals physics assignment. Jan 11, 2016 upperlevel undergraduate course taught at the university of pittsburgh in the fall 2015 semester by sergey frolov. The sommerfeld theory was simply the lorentz theory with the fermidirac distribution function replacing the boltzmannmaxwell distribution function.
Handout 2 sommerfeld model for metals free fermion gas. The new and more general bohrsommerfeld theory described the atom in terms of two quantum numbers, while bohr had originally used only one quantum number. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. 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. It could not explain the negative temperature coefficient of resistivity for certain solids 2. Metals and insulators measured resistivities range over more than 30 orders of magnitude. However, thoughout the course the material that i write on the. Conduction current in metals em wave propagation in metals skin depth plasma frequency. According to this theory, the metals containing free electrons obey the laws of classical mechanics. Ine here, saw the realization that the new quantum theory could explain, at. Sommerfeld theory of metals problems in solid state physics. Quantum free electron theory of metals science key.
It was developed in 1927, 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. The development of the quantummechanical electron theory of. In the free electron model, there is no lattice, and no electronelectron interaction, but it gives nice. The sommerfeld model was, however, unable to answer why the mean free path of electrons reaches 20 nm in a good conducting metal like silver at room. Drudes theory treated the electrons as an ordinary classical gas.
Sommerfeld theory of metals free download as pdf file. When we recall the fact sommerfeld has recently expressed. Given its simplicity, it is surprisingly successful in. Sommerfeld free electron theory of electrons in metals. A natural step was to formulate a quantum theory of electrons in metals. The discussions assume the readers familiarity with the material pertaining to. Despite the success with respect to the wiedemannfranz.
The classical theory had several conspicuous successes, notably the. The development of the quantummechanical electron theory of metals. Effect of impurity and temperature on electrical resistivity of metals. Metals tend to come from the lefthand side of the periodic table. But according to quantum theory, the free electrons occupy different energy levels, up to fermi level at 0 k. Iii the sommerfeld free electron theory of metals 2000. In this chapter the free electron theory of metals as developed by sommerfeld and others will be discussed. The development of the quantummechanical electron theory. Pdf how sommerfeld extended bohrs model of the atom 19.
The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. Handout 2 sommerfeld model for metals free fermion gas in this lecture you will learn. Quantum free electron theory was proposed by arnold sommerfeld. Upperlevel undergraduate course taught at the university of pittsburgh in the fall 2015 semester by sergey frolov.
The classical theory fails to explain the heat capacity and the magnetic. The free electron model considers that metals are composed of a quantum electron gas where ions. Conductivity, hall effect and other transport phenomena will be treated separately in chapter 11. This is totally inexplicable within the free electron model. Standard topics such as crystal structure, reciprocal space, free electrons, band theory, phonons, and magnetism are covered. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. Free and independent electrons, but no assumptions about the nature of the scattering. Iii the sommerfeld free electron theory of metals 2000 solid state physics free download as pdf file. It could not classify a solid on the basis of their conductivity property 3.
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