Baffling as well was the curious phenomenon of super conductivity, first observed in 1911by gilles hoist, work. Deviations from the drude theory were observed, and the values of the optical mass and relaxation time of the conduction electrons are discussed. Sommerfeld theory of metals arnold sommerfeld 18681951 ece 407 spring 2009 farhan rana cornell university. Solid state physics part ii optical properties of solids. Normally the electrons are in a random motion throughout the.
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. This theory was developed by drude and lorentz during 1900 all the atoms are composed of and hence is also known as drudelorentz theory. 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. The drude theory of metals and the hall e ect by michele laino july 12, 2015 abstract in this brief tutorial i show the basic assumption of the drude model of conduction in metals, actually this tutorial represents a simpli ed version of the real drude model, since some properties, and consequences, have been omitted.
The quantum free electron theory somerfield developed this theory in 1928. Then sommerfelds elementary quantum mechanical theory of metals is discussed. Srit unit iii free electron theory applied physics. It features a 1hour lecture video, and also presents the prerequisites, learning objectives, reading assignment, lecture slides, homework with solutions, and resources for further study. The behaviour of free electrons moving inside the metals is considered to be similar to that of atoms or molecules in a perfect gas. Phase equilibria the equilibrium phase is always the one with the lowest free energy g h t s the driving force for a phase change is the minimization of free energy equilibrium state with minimum free energy under some specified combination of temperature, pressure, and composition e. Drude theory of metals university of california, irvine. Drudelorentz theory drude, in 1900, postulated that the metals consist of positive ion cores with the valence electrons moving freely among these cores. According to drude, the metals consists of positive ions cores with the valence electrons moving freely among these cores.
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. Drude theory of metals problems in solid state physics. Metals drudes classical theory theory by paul drude in 1900, only three years after the electron was discovered. Timevarying analysis the dynamics may also be described by introducing an effective drag force accuracy of the model simple classical drude model provides a very good explanation of dc and ac conductivity in metal it greatly overestimates the electronic heat capacities of metals quantum theory quantum theory is a collection of results. Many measurements of the optical properties of solids involve the normal incidence reectivity which is illustrated in fig. Drude theory of metals problems in solid state physics with. The development of the quantummechanical electron theory. Notes on the drude model assumptions of the drude model. Metals and the drudelorentz model oxford scholarship. The electrons are, however, bound to move within the metal due to electrostatic attraction between the positive ion cores and the electrons. Advanced electronic properties of materials classical drude theory of conduction contents.
In other words, the drude model is right about thermal conductivity, but wrong about heat capacity. Drude theory of conduction basics of free electron theory. Free electrons in a metal resemble molecules of a gas. The classical free electron theory of metals drude lorentz theory of metals drude and lorentz proposed this theory in 1900. Drudelorentz theory drudelorentz theory drude in 1900. This document is highly rated by electronics and communication engineering ece students and has been viewed 1449 times. Classical free electron theory of metals this theory was developed by drude and lorentz and hence is also known as drude lorentz theory.
The first case involves a metal while the second involves an insulator. The drude model was the rst attempt to use the idea of a \gas of electrons, free to move between positively charged ionic cores. According to this theory the free electrons obey quantum laws. Osa an experimental confirmation of the drude free. 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. 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. Drude formulated a theory for conduction in metals using the electron concept. He derives the valence and conduction band structures for electrons in metals e. 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. Drude model electrons shown here in blue constantly bounce between heavier, stationary crystal ions shown in red. As we shall see, this removes many thermal anomalies of the drude model. Drude applied equations of simple mechanics on the electrons to derive several expressions and also arrive at the ohms law.
Engineering physics ii unit 1 conducting materials notes. Drude model conductivity frequency dependence plasma. Mar 29, 2018 drude theory of conduction basics of free electron theory and electrical conductivity part 1. Similarly, the heat conductivity at high temperatures was computed to be propor tional to t, but observed to go in direct proportion to t. Jun 02, 2015 timevarying analysis the dynamics may also be described by introducing an effective drag force accuracy of the model simple classical drude model provides a very good explanation of dc and ac conductivity in metal it greatly overestimates the electronic heat capacities of metals quantum theory quantum theory is a collection of results. Goswamy associate professor in physics uiet, panjab university, chandigarh. Jun 15, 2018 this idea was given by drude and he utilized it to explain many properties of metals satisfactorily such as electrical conductivity, thermal conductivity etc. Here are some notes about the classical theory of metals and the. The classical free electron theory drude and lorentz proposed this theory in 1900. Metals contain free electrons that move through a lattice of positive ions.
Handout 2 sommerfeld model for metals free fermion gas. The treatment of a metal as containing a gas of electrons completely free to move within it. Schrodinger equation for a free electron 2 r v r r e r m. The classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in metals. Free electron theory of metals conductivity electrical. Based on the drude model we arrive at the equation of motion for electrons in an.
The classical free electron theory was introduced by p. Electrons in a metal behave much like particles in an ideal gas no coulombic interaction and no. Theory by paul drude in 1900, only three years after the electron was discovered. With no applied field, it can be seen that the electrons move around randomly. Engineering physics ii unit 1 conducting materials. Handout 2 sommerfeld model for metals free fermion gas in this lecture you will learn. Free electron theory drudes and lorentz free electron model.
Drude theory of conduction basics of free electron theory and electrical conductivity part 1. In an atom electrons revolue around the nucleus and a metal is composed of such atoms. 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 lattice and the free. The only possible interaction of a free electron with its environment is via. Assumptions or salient features in classical free electron theory. The drude theory of metals the model assumptions and approximations probabilityof collision per unit time. Lorenz model harmonic oscillator model without restoration force. Drude optical properties of metals 8 plasma frequency 1 to improve accuracy of drude model, effective number of free electron is usually introduced damping frequency damping frequency scattering time generally correlates with conductivity but not accurately 12 2 0 p 2 qn m z sq h. Comparison between drude and lindhard models article pdf available january 2017 with 947 reads how we measure reads. As per the experimental results there is no direct relation between electrical conductivity and concentration of electrons. Thompsons discovery of the electron, people became interested in understanding more about the mechanism of metallic conduction. The drude model peter hertel overview model dielectric medium permittivity of metals electrical conductors faraday e ect hall e ect paul drude, german physicist, 18631906. This page contains materials for the session on the band theory of solids.
Plasma oscillations plasmons can be described in the classical picture as an oscillation of free electron density. According to classical free electron theory of metals electrical conductivity is given by, then. The drude model can be visualised using the following simulation. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. The model, which is an application of kinetic theory, assumes that. Classical free electron theory of metals engineering. The metals form a unique type of bonding known as metallic bonding and form the lattice structure. This theory was developed by drude and lorentz during 1900 all the atoms are composed of and hence is also known as drude lorentz theory. This textbook gives a complete account of electron theory in both periodic and nonperiodic metallic systems. System upgrade on feb 12th during this period, ecommerce and registration of new users may not be available for up to 12 hours. The values of rs also vary between those of these two metals, from 5. The free electrons are, therefore, also referred to as free electron gas and the theory is accordingly known as drude and lorentz s classical free electron theory. I drude model derivation of freeelectron conductivity i scattering time estimates and matthiessens rule i mobility and hall coe cients i frequencydependent conductivity of freeelectron metals reading.
Classical free electron theory of metals this theory was developed by drude and lorentz and hence is also known as drudelorentz theory. The drude theory of metals the model kinetic theory of gases. The model, which is an application of kinetic theory, assumes that the microscopic behaviour of electrons in a solid may be treated classically and looks much like a pinball machine, with a sea of constantly jittering electrons bouncing. According to this theory, a metal consists of electrons which are free to move about in the crystal like molecules of a. Lecture1 drude model recap of kinetic theory of gases. Classical derivation of ohms law and drude conductivity. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. This model makes several key assumptions some of which are better approximations than others. You may notice the very high electron density found in metals, which is about. 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. Schulz, an experimental confirmation of the drude free electron theory of the optical properties of metals for silver, gold, and copper in the near infrared, j. Electrical conductivity as per free electron theory 3. This is about the right order of magnitude for many monovalent metals, such as sodium. The current theory explains this with ad hoc manipulations like screening and positive charge carriers, but the correct answer is much simpler.
Between collisions electrons move in straight line in the absence of a any. The assumptions of the drudelorentz classical theory of freeelectrons are the following. This chapter derives expressions for the following. The drude theory of metals and the hall e ect by michele laino july 12, 2015 abstract in this brief tutorial i show the basic assumption of the drude model of conduction in metals, actually this tutorial represents a simpli ed version of the real drude model, since some properties, and. The drude model of electrical conduction was proposed in 1900 by paul drude to explain the transport properties of electrons in materials especially metals. Classical free electron theory of metals in order to explain electrical conductivity in metals, lorentz and drude put forward a theory called free electron theory of metals. We assume for the present discussion that the solid is thick enough so that reections from the back surface can be neglected. Jul 31, 2015 free electron model page 4 theory of metals free electron theory of metals band theory of solids dr.
I drude model derivation of freeelectron conductivity i scattering time estimates and matthiessens rule i mobility and hall coe cients i frequencydependent conductivity. Plasma oscillation density fluctuation of free electrons 0 2. Atomic selectrons are delocalised due to overlap of outer orbits. Freeelectron theory of metals article about freeelectron. Notes on the drude model assumptions of the drude model the drude model provides a classical mechanics approach to describing conductivity in metals. The drude model provides a classical mechanics approach to describing conductivity in metals. The absorption edge was investigated very accurately. Ron ballinger gives todays lecture, explaining how the behavior of electrons in aggregate solids determines their electrical and thermal conductivities, optical absorption, and other physical properties. In its more modern context, the drudelorentz model views a material as consisting of an array of the following. Cu, be using lcaomo, and then extends this approach. Carrier dynamics of electrons and holes in moderately doped silicon pdf. Drude treated the free electrons as a classical ideal gas but the electrons should collide with the stationary ions, not with each other. Quantum theory of metals room temperature than the interatomic distance and even longer at low temperatures. The potential field of these ion cores, which is responsible for such an interaction, is assumed to.
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