In metals there are large number of free electrons moving freely in all possible directions 2. Properties of materials and the classical free electron theory. Free electron theory of metals request pdf researchgate. This is roughly the same as the interatomic distances in metals, a result consistent with the drude picture of electrons colliding with the ionic cores. The classical theory had several conspicuous successes, notably the. Then sommerfelds elementary quantum mechanical theory of metals is discussed. Free electron theory conductivity in metals by using. However, we shall see later that the drude model very seriously underestimates typical electronic. Freeelectron theory of metals accessscience from mcgrawhill. To introduce the free electron model for the physical properties of metals. Handout 2 sommerfeld model for metals free fermion gas. In this chapter the free electron theory of metals as developed by sommerfeld and others will be discussed.
This paradox was only removed after the advent of quantum theory. The simplest approach is the classical free electron model that was successful in explaining some of the properties of metals. According to free electron theory, the properties of a metal depends on gas of free electrons. 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. Free electrons do not bind to the ions cores as they are surrounded by core. This was succeded by the more sophisticated band theory of solids. Despite the success with respect to the wiedemannfranz law, the contribution to the speci. In several previous papers1 i have developed a statistical model of the metals which gives an account of the metallic bond of the alkali and the alkaline earth metals, and permits the computation. Electron theory of metals 419 on the view explained above, therefore, if a substance such as nio were. Fundamentals of the theory of metals pdf free download. Metals are good conductors both electrical and thermal. Free electron approximation crystal lattice may change the typical velocity, say, fermi velocity density of states lattice contribution to specific heat and thermoconductivity independent electron approximation fermiliquid theory another source of collision compressibility relaxation time approximation. Postulates of classical free electron theory 1 the free electrons of a metal are having like the moleculesof a gas in acontainer.
Periodic crystal potential and blochs theorem for the wavefunction. Free electron model for metals metals are very good at conducting both heat and electricity. 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. 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. In metals there are large number of free electrons moving freely in all possible. The basis of the electron theory of metals, with special. Drudes theory of metalsin this model electrons are considered as solid spheres.
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. Free electron theory of metal and density of state. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. The free electron gas, however, differs from an ordinary gas in some respects. In this theory ions are surrounded by core electrons and outermost electron considered as valance electrons in atomic context and conduction electrons in metallic context are free to roam on the body of metal. Applying perturbation theory to free electron wavefunctions and creation of energy gap. Metals, such as copper and aluminum, are held together by. It is the simplest theory for these materials, but still gives a very good description of many properties of metals which depend on the dynamics of the electrons. Quinn and others published free electron theory of metals find, read and cite all the research you need on. The free electron model considers that metals are composed of a quantum electron gas where ions play. The outer most electrons of metal atoms are also known as valence electrons. These free electrons are considered as electron gas.
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. Especially classical free electron theory and quantum free electron theory of metals. Drudes theory of metalsin this model electrons are considered as solid spheres as gas molecules in kinetic theory of ideal gas. Electrons in metals are treated as a free electron gas. Conductivity, hall effect and other transport phenomena will be treated separately in chapter 11. Assumptions or salient features in classical free electron theory the classical free electron theory is based on the following postulates. L z the electrons inside the box are confined in a threedimensional infinite.
These valence electrons are weakly bound with the atoms. Goswamy associate professor in physics uiet, panjab university, chandigarh. The density of states and the fermidirac distribution function are discussed, leading to the specific heat of the electrons, the work function, thermionic emission, and the schottky effects. This document is highly rated by electronics and communication engineering ece students and has been viewed 1743 times. Find powerpoint presentations and slides using the power of, find free presentations research about free electron theory of metals ppt. Pdf free electron theory of metals aryan gurung academia. A lattice of in a sea of electrons shared between all nuclei moving freely between them. Drude theory of conduction basics of free electron theory. As examples of applications the fieldemission microscope and quartzhalogen lamps are discussed. The classical free electron theory was introduced by p. Free electron theory drudes and lorentz free electron model.
Solid state physics problems and solutions download book. The simplest model of a metal is the free electron model. The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role. Clearly, the free electrons in a metal are trapped inside the surface, at least at room temperature. Thus all states are filled up to an energy e f, known as the fermi energy, determined by the requirement that the number of states with e 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. The drude theory of metals the model free electron densities densityof the electron gas. Free electron theory of metal and density of state engineering dr. The free electron model solved many of the inconsistencies related to the drude model and gave insight into several other properties of metals. Free electron model page 4 theory of metals free electron theory of metals band theory of solids dr. Apr 10, 20 the classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates.
Applying perturbation theory to free electron wavefunctions and nearly free electron model. This model explains many of the properties of metals. Atomic selectrons are delocalised due to overlap of outer orbits. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. These free electrons are, therefore, also referred to as free electron gas and the theory is accordingly named as free electron gas model. For an infinite potential well, where, and are positive integers. Free electron theory of metals conductivity electrical. Given its simplicity, it is surprisingly successful in. An icon used to represent a menu that can be toggled by interacting with this icon.
The basis of the electron theory of metals, with special reference to the transition metals view the table of contents for this issue, or go to the journal homepage for more. Bloch theorem, phonons in one dimension, periodicity, effect of a basis on the electronic structure, crystal structures, the reciprocal lattice. Free electrons in a metal resemble molecules of a gas. A classical free electron theory is a macroscopic theory proposed by paul drude in 1900.
Hence, classical free electron fails to explain the temperature dependence of electrical conductivity. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. This is referred to as the free electron model for metals. Classical free electron theory of metals engineering. According to this theory, the metals containing the free electrons obey the. The model of the free electron theory is presented. If any questions please contact me whatsap number 9416939577. The treatment of a metal as containing a gas of electrons completely free to move within it. Srit unit iii free electron theory applied physics. Conductivity in metals by applying quantum free electron theory, free electron theory. The general characteristics of electrical conductors are. The behaviour of free electrons moving inside the metals is considered to be similar to that of atoms or molecules in perfect gas.
L z the electrons inside the box are confined in a. In the ground state of this free electron gas, electrons will fill up n m states of lowest energy. The development of the quantummechanical electron theory of metals. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. Rather than sharing and exchanging electrons, a metal is essentially held together by a system of free electrons that wander throughout the solid. Metallurgy and material science physics of materials nptel. In a solid, the valence electrons interact and form a gas of electrons. Classical drude theory of metals successes and limitations of the classical model sommerfeld theory of metals. According to this theory, the metals containing the free electrons obey the laws of classical mechanics. Allowed energy levels for an electron are quantized, i.
The discussions assume the readers familiarity with the material pertaining to appendixes b, c, d, and e. The discussions assume the readers familiarity with the material pertaining to. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in metals. View and download powerpoint presentations on free electron theory of metals ppt. 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. 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. Metals, such as copper and aluminum, are held together by bonds that are very different from those of molecules. 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. 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.
Thus all states are filled up to an energy e f, known as the fermi energy, determined by the. Rakesh kumar singh center for nanoscience and nanotechnology aryabhatta knowledge university, patna objective and practical applications in science, engineering and technology in this chapter, we will study on the role of electrons in deciding the behavior of metals, material. 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 quantum statistics and semi. Put free electrons into a very wide potential well the. In solidstate physics, the free electron model is a simple model for the behaviour of charge. Quantum free electron theory was proposed by arnold sommerfeld. Electron theory of metals pes college of engineering. Freeelectron theory of metals article about freeelectron. Calculate the energy levels and energylevel spacing of a free electron in a metal. Electrons in metals electrons do not pop out of a piece of copper lying on the table.
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 to describe many important properties of metals. The free electron model the quantum state of an electron is described by the timeindependent schrodinger equation. Sommerfeldsmodel for metals consider a metal of a free electron density n m. Quantum free electron theory of metals science key.
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