Larson department of physics, brigham young university, provo, utah. Some materials, such as metals, are good conductors of electricity. Chapter 4 electronic structure the electronic properties of matter determines its macroscopic behavior. This page contains materials for the session on the band theory of solids.
Avogadrosnumberisthenumberof atomsinexactly12gramsof 12 c. The free electrons from the ntype semiconductor combine with the holes in the. Crystals and band theory boundless chemistry lumen learning. Dft sdft hohenbergkohnsham oep semiconductors and insulators density functional theory hohenbergkohn theorems 1964 1 external potential vr is uniquely determined by nr 2 the variational principle holds e0 ev0n0 n h. Topics covered range from the breakdown of classical theory to atomic spectra and the old quantum theory, as well as the uncertainty principle of heisenberg and the foundations of quantum mechanics.
We start here from the limit of free electrons assuming the periodic potential v r is. Type of material numbers of free electrons resitsivity. The electron theory of solids has been developed in three main stages. According to this theory, the free electrons move in a periodic field provided by the lattice. The average velocity and displacement of the electron along any direction over a period of time. If the wavelength of the electron is related to the lattice parameter a, then the electron cannot. Freeelectron theory of metals accessscience from mcgraw. The transfer of energy between electrons and ions in solids. According to this theory, the metals containing free electrons obey the laws of classical mechanics. Free electron theory of solids mini physics learn physics.
To a good approximation, the properties of solids can be divided into vibrational dynamics and electronic properties. Given its simplicity, it is surprisingly successful in. In solidstate physics, the electronic band structure or simply band structure of a solid. Mar 29, 2015 free electron theory of solids march 29, 2015 december 30, 2010 by mini physics electrons can be visualised as rattling around insde the metal, randomly changing direction when they collide with positive ions, much like a ball in a pinball machine. Introduction to the physics of electrons in solids by brian k. Mahan physics department, university of tennessee, knoxville, tennessee 37966, u. Our goal now is to understand the consequences of this, so that we can start to get a feel for some of the basic properties of materials. This study of the theory of electrical and thermal conduction in metals, semiconductors, and insulators is written at a level appropriate to graduate students and research workers and assumes some knowledge of wave mechanics in its reader.
The general approach and aim of this book is to provide a comprehensive introduction to the subjects on solid state physics as well as electronics to the undergraduate students in a coherent, simple and lucid manner. In metals, where the relaxation processes depend on both electrons and phonons, all thermodynamic and transport properties are dictated by electronphonon ep interaction. Solid state theory physics 545 electrons in metalselectrons in metals. We know that in an atom, the protons and the neutrons constitute the central part called the nucleus.
In the nearly free electron approximation, interactions between electrons are. Electronphonon coupling in metallic solids from density. Mar 10, 2010 electron liquids and solids in one dimension. Introduction during the past year several of my associates wilfried hsch and jiwei wu and i have been working on the theory of electron transport in solids 15. This leads to the idea of a reduced zone representation of the freeelectron expression. Jan 30, 2015 let us begin by considering the case of an isolated atom on the left in fig. The treatment of a metal as containing a gas of electrons completely free to move within it. Let us begin by considering the case of an isolated atom on the left in fig.
Surprisingly, while the calculation of the orbital magnetization in finite systems such as atoms and molecules is straight forward, in extended systems or solids it has long eluded calculations owing to the fact. Introduction to modern solid state physics i accept uio. Lecture notes for solid state physics rudolf peierls centre. This is totally inexplicable within the free electron model. Principles of the theory of solids, cambridge university press. Introduction during the past year several of my associates wilfried hsch and jiwei wu and i have been working on the theory of electron. 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.
Electron dynamics in solids in the previous chapter we have seen how the singleelectron energy states form a band structure in the presence of a lattice. Electron correlation in molecules and solids article pdf available in progress of theoretical physics supplement 80. Atomic and electronic structure of solids by efthimios kaxiras. I n homogeneous electron gas under the influence of an external potential vr and the mutual coulomb repulsion. It turns out that the nearly free electron approximation is quite reasonable for simplemetals withpredominant s. This database on electron solid interactions contains experimental results on secondary electron yields for elements and compounds as a function of energy, backscattered electron yields for elements and compounds as a function of energy, stopping powers for electrons in elements and compounds, and experimental xray. The free electrons, considered identical to the outermost, or valence, electrons of free metal atoms, are presumed to be moving independently of one another. In solid state physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. The core of the book deals with the physics of electron and phonon states in crystals and how they determine. Electron emission from solids is a fundamental process underlying electrical transmission in a gas or vacuum, and as such, was among the earliest phenomena to be observed scientifically. 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 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. Electronphonon in general, electronion interaction is an important and ubiquitous process in solids, affecting almost all physical properties.
Pdf we trace the fundamental developments and events, in their. It provides a modern treatment of the theory of solids dealing with the physics of electron and phonon states in crystals and how they determine the structure and properties of solids. Ost theories of electronic structure in solids are electron. Solid state physics part ii optical properties of solids mit.
This functional plays a central role in the present paper. This treats the electrons quantum mechanically but ignores the presence of ions, it is applied to the calculation of the specific heat and the thermopower. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Freeelectron theory of metals article about freeelectron. In an atom electrons revolue around the nucleus and a metal is composed of such atoms. If a battery is connected in series with an ammeter and a piece of some material copper, silicon, glass, or such, a deflection in the ammeter will indicate a flow of charged particles a current i through the circuit see fig. The valence electrons of atoms are free to move about the whole volume of the metal, like the molecules of a perfect gas in a container. 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. Electron correlations, magnetic ordering, and mott insulation in solids j. According to the theory of elasticity, one can write equations of motion as. Northholland, amsterdam electron transport in solids g.
Assumptions or salient features in classical free electron theory the classical free electron theory is based on the following postulates. Molecular orbital theory treats all solids as a very large collection of. So if two identical atoms combine to form a diatomic molecule, each atomic. Jan 09, 2003 atomic and electronic structure of solids book. Atomic and electronic structure of solids pdf atomic and electronic structure of solids pdf. The phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory.
Free electron theory of solids march 29, 2015 december 30, 2010 by mini physics electrons can be visualised as rattling around insde the metal, randomly changing direction when they collide with positive ions, much like a ball in a pinball machine. Simultaneously there will be a voltage drop v across the sample as measured by a voltmeter. Srit unit iii free electron theory applied physics. Band theory is only an approximation to the quantum state of a solid, which. The free electrons, considered identical to the outermost, or valence. Solids with free electrons that is electrons not directly involved in the interatomic bonding are the familiar metals cu, al, fe, au, etc. Pdf the development of the quantummechanical electron theory. This paper describes the theory of momentumresolved electron tunnelling into a liquid of particles with a. Electron liquids and solids in one dimension vikram v. Consider free electrons in a metal an electron gas. This graduate textbook designed for students in physics, chemistry and materials science provides a modern treatment of the theory of solids dealing with the physics of electron and phonon states in crystals and how they determine the structure and properties of solids.
Lecture 5 solids thefreeelectrongas in asolid state, afew loosely bound valence outermost and not in completely filled shells. Upperlevel undergraduate course taught at the university of pittsburgh in the fall 2015 semester by sergey frolov. The sommerfeld theory for the freeelectron gas is then introduced. The focus then changes to the quantum theory of crystalline solids. Cbse ncert notes class 12 physics semiconductor electronics. Electrons can be visualised as rattling around insde the metal, randomly changing direction when they collide with positive ions, much like a ball in a pinball machine. In a crystal of a monovalent element the arrangement of atoms and electrons must be such that there is one atom for each electron. Prominent examples are the alkali metals and aluminum. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i.
The overlap or size of the gap between the valence. Band theory also states that an electron cannot absorb an amount of energy that would place it in the energy gap. When i was an undergraduate, i thought solid state physics a subgenre of condensed matter. Solid state physics and electronics get best books pdf. Metallic bonding may be described as the sharing of free electrons among a lattice of. He develops the basic ideas of crystal lattice dynamics, electron zone structure, and transport theory from first principles. The course is based on steven simons oxford solid state basics textbook. In the mideighteenth century, jeanantoine nollet and william morgan conducted experiments showing that the passage of electrical discharge in partially. This book is of historic significance since it represents a mile stone in the development of the theory of transport phenomena in solids. Electron dynamics in solids in the previous chapter we have seen how the single electron energy states form a band structure in the presence of a lattice. The classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates.
The sommerfeld theory for the free electron gas is then introduced. In a substance, as many atoms are close to each other, the energy levels of the atom form a continuous band, where in the electrons move. Atomic and electronic structure of solids this text is a modern treatment of the theory of solids. An introduction to the electron theory of solids introduces the reader to the electron theory of solids. The free electron theory you can get solutions of the form. The basic ideas of crystal lattice dynamics, electron zone structure, and transport theory are developed from first principles, and. I lid h l f i h l b d hi h bi diin solids the electron states of tightly bound high binding energy electrons are very similar to those of the isolated atoms.
Bornoppenheimer based electronphonon coupling formalism 1203 3. Electron liquids and solids in one dimension nature. 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. Solids with no free electrons are the familiar insulators glass, quartz crystals, ceramics, etc. The first part of the book deals with electrons and atoms in a crystal, and the second part extends the discussion to defects in crystals and to structures. Cambridge core condensed matter physics, nanoscience and mesoscopic physics introduction to the physics of electrons in solids by brian k.
Strongly correlated electrons in solids scholarpedia. All electron optimized effective potential method for solids. Since the scf potential exhibits the symmetry based, at least in. Tanner skip to main content accessibility help we use cookies to distinguish you from other users and to provide you with a better experience on our websites. In contrast to electrons that participate in both ionic and covalent bonds. According to the classical free electron theory the value of specific heat of metals is given by 4. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid.
Introduction to the physics of electrons in solids by. Now we come to the opposite limiting case where electrons are almost free. Electron phonon in general, electron ion interaction is an important and ubiquitous process in solids, affecting almost all physical properties. To assign the peak in the optical absorption spectrum of alkalis observed in figure 1. The core of the book deals with the physics of electron and phonon states in crystals and how they determine the structure and properties of the solid. B harmonic oscillators, phonons, and the electronphonon interaction. In the ground state of a system of nfree electrons with an electron concentration of nv, where v is the volume, the occupied states may be represented as points. An introduction to the electron theory of solids 1st edition. In metals, where the relaxation processes depend on both electrons and phonons, all thermodynamic and transport properties are dictated by electron phonon ep interaction.
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