By means of the nearly free electron model explained in this lecture. In solidstate physics, the nearly free electron model or nfe model is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. Essential concepts centers on the unifying, essential theoretical concepts and tools of modern condensed matter physics that every reader should know to read the literature. Generalizations from molecules to solids the source of the binding energy is primarily the electrostatic potential. The last electron we put in has the highest energy. An important quantity which characterizes electronic properties of a solid is the density of states. The model is closely related to the more conceptual empty lattice approximation. Solid inert gases which have the electronic structure. The number of collisions the electron has is equal to the number of ions centered within the volume, where r is the radius of the ion. 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. The free electron model the quantum state of an electron is described by the timeindependent schrodinger equation. Well examine the assumption of a constant potential. Given its simplicity, it is surprisingly successful in. Equation 107 in 1 which follows the presentation in the textbook solid state physics by neil w.
Bloch theorem, phonons in one dimension, periodicity, effect of a basis on the electronic structure, crystal structures, the reciprocal lattice. Handout 2 sommerfeld model for metals free fermion gas. Mermin, holtsanders this is the standard complete introduction to solid state physics. In a crystal, the atoms are arranged in a periodic lattice. The localization energy can also play a role metal. 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. Mean free path classically, we can calculate the mean free path.
The clear and concise introduction not only describes all the basic phenomena and concepts, but also such advanced issues as magnetism and superconductivity. Thus, solidstate physics forms a theoretical basis of materials science. This successful brief course in solid state physics is now in its second edition. Free electron model a free electron model is the simplest way to represent the electronic structure of metals.
Pauli exclusion principle was needed to account for the bound electron states in atoms, sommerfeld applied the same principle to the free electron gas of metals. In this chapter we discuss the free electron theory of metals, originally developed by sommerfeld and others. Solid state theory physics 545 kronnigpenney modelpenney model. The free electron model, with its parabolic energywavevector dispersion curve, provides a reasonable description for conduction electrons in simple metals. Intended for a two semester advanced undergraduate or graduate course in solid state physics, this treatment offers modern coverage of the theory and related experiments, including the group theoretical approach to band structures, moessbauer recoil free fraction, semiclassical electron theory, magnetoconductivity, electron selfenergy and. The nearlyfree electron model university of oxford. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. However, the free electron circles c 2 and c 3 intersect the zone boundaries.
Each electron occupies an orbital having quantum numbers \n\, \l\, and \m\, with the energies of the orbitals given above in terms of the zeros \\z. Solid state physics download book free computer books. In this chapter we discuss the freeelectron theory of metals, originally developed by sommerfeld and others. The weak periodic potential causes a distortion of the fermi circle of a twodimensional electron gas as it approaches the zone boundary. Access study documents, get answers to your study questions, and connect with real tutors for phys 563. Solid state physics free electron model lecture 14 a. The free electrons, considered identical to the outermost, or valence, electrons of free metal atoms, are presumed to be moving independently of one another throughout the.
The evolution of the fermi surface of a divalent twodimensional metal with a square lattice as a band gap is opened at the brillouin zone boundary. In this exercise, we will find the band structure of this crystal in two ways. Before solving the model, the professor gives a brief recap of perturbation theory and defines the normalization of the free wave solutions to be 1 in the unit cell. Translational symmetry is not essential for producing a band gap amorphous solids also have band gaps. Luth, springerverlag another very popular book on the subject, with quite a bit of information in it. The model enables understanding and calculating the electronic band structure of especially metals. In this model the potential is weak and the solutions of the hamiltonian can be treated as perturbed solutions of the free electron model. Free solid state physics books download ebooks online. The 3s electrons in the outermost shell becomes conduction electrons and moves freely through the whole system. The scattered eld is an outgoing sph erical wave represented by u 0 f e a d eikd. Sep 01, 20 first semester solid state physics short videos produced by the colorado school of mines.
This is totally inexplicable within the free electron model. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. Problems forsolid state physics 3rdyearcourse6 hilary. Explaining the difference between type i and type ii superconductors. Describe the classical free electron model of metals in terms of the. At the end of this course, students should have the conceptual and mathematical tools to read current research papers in solid state physics and to understand the physical process underlying many solid state devices. Drude model of electric conductivity thermal conductivity free electron fermi gas model 5. Introduction to solid state physics, 8th edition wiley.
A musthave textbook for any undergraduate studying solid state physics. Solid state physics phys 40352 by mike godfrey spring 2012 last changed on may 22, 2017. Free electron theory of solids mini physics learn physics. This material is contained as part of the lectures on applications of quantum mechanics. To describe this in terms of a probability fe that a state of energy e is occupied, we write for \t 0 \, k\. Under the meanfield approximation, electrons are largely independent. For details of the calculation, see for example kittel introduction to solid state physics. Ncu 5 classifications of materials according to their viscosity, materials are classified into solids, liquid, and gas phases. Please do email me if you find any typos or mistakes. Orlando february 9, 2004 the source of the binding energy is primarily the electrostatic potential between the nuclei and the electrons. Since the publication of the first edition over 50 years ago, introduction to solid state physics has been the standard solid state physics text for physics majors. Ueep2024 solid state physics topic 3 free electron in metals 2. Unit1 classical free electron theory physics duration.
Drudes classical theory of electrical conduction drude assumed that a metal is composed of ions, which are stationary, and valence electrons, which are free to move. It covers the basics of band structure, fermi surfaces, phonons, and particles in magnetic fields. Low diffusivity, high density, and high mechanical strength means. The freeelectron quantum gas model still predicts a hall coe. More advanced than hook and hall solid state physics, by n. Solid state theory spring semester 2010 manfred sigrist institut fur theoretische physik hit k23. Crystallography electron motion in periodic structures. Free electron model of polyenes chemistry libretexts. 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.
L z the electrons inside the box are confined in a threedimensional infinite. In solid state physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. Lecturenotesforsolidstatephysics 3rdyearcourse6 hilaryterm2012. Solid state theory institute for theoretical physics. It is the largest branch of condensed matter physics. Solid state physics nearly free electron model contd.
The average is over all directions in sklid the electron emerged from the first collision. Finished with phonons, optical and thermal properties. In solidstate physics, the free electron model is a simple model for the behaviour of valence electrons in a crystal structure of a metallic solid. 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. Problems forsolid state physics 3rdyearcourse6 hilary term2011. It is envisioned as a graduate text for a 1semester course although the reader is not assumed to have prior knowledge of solid state physics because results are derived from first principles. Sharing electrons between nuclei lowers the energy of the solid. Solidstate physics studies how the largescale properties of solid materials result from their atomicscale properties. With valence electrons wandering around fixed ion cores in metals, the chargeneutral environment experienced by each electron justifies the freeelectron model. Free electron model of metals, in solid state physics, representation of a metallic solid as a container filled with a gas composed of free electrons i.
Solidstate physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. David mermin should illustrate the meaning of the central equation. Solid state physics studies how the largescale properties of solid materials result from their atomicscale properties. The emphasis in the book has always been on physics rather than formal mathematics. Nevertheless, a useful model when results independent of justification in retrospect. Pdf lecture note on solid state physics free electron. Velocities in the free electron theory a assuming that the free electron theory is applicable. In solid state physics, the nearly free electron model or nfe model is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The periodic lattice, bragg diffraction, brillouin zones. Solid state theory physics 545 electrons in metalselectrons in metals. As an example we consider a na atom, which has an electron configuration of 1s 2 2s 2 2p 6 3s 1. Previously we used the nearlyfree electron model to discuss the propagation of electrons in the presence of a periodic crystal potential.
The free electrons, considered identical to the outermost, or valence. Physics of the solid state at washington state university. The freeelectron model, with its parabolic energywavevector dispersion curve, provides a reasonable description for conduction electrons in simple metals. We see that the velocity of electrons is relatively large. Each section starts with a gentle introduction, covering basic principles. Ictp video portal solid state physics lecture of 20. In solid state physics, the electronic band structure or simply band structure of a solid describes the range of energies of an electron that the solid may have within it called energy bands, allowed bands, or simply bands and also about the ranges of energy that it may not have called band gaps or forbidden bands.
Solid state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. Solid state physics phys 40352 theoretical physics. The authors goal from the beginning has been to write a book that is accessible to undergraduate and consistently teachable. May 10, 2020 the last electron we put in has the highest energy.
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