In the lectures we have derived two simple rules, which are away from brillouinzone boundaries the electronic bands i. In this exercise, we will find the band structure of this crystal in two ways. Ravindran, phy075 condensed matter physics, spring 20 16 july. Origin of energy bands and nearly free electron model. Energy bands nearly free electron model electron diffraction and energy gap bloch theorem the central equation emptylattice approximation tightbinding model see chap 9 nfe model is good for na, k, al etc, in which the lattice potential is only a small perturbation to the electron sea. Moreover, the sharp spectral features observed in photoemission remain well defined with little additional broadening for more than 500 mev below e f, pointing to suppressed electronelectron scattering. By means of the nearly free electron model explained in this lecture. Besides, in the freeelectron model electrons can travel long distances. One dimensional electron energy bands for the nearly free electron model shown in the extended brillouin zone scheme. Using density functional theory dft, it is revealed that the nearly free electron nfe states are near the fermi levels in hydroxyl oh functionalized mxenes. Failure of the nearlyfreeelectron approach for energy bands that are higher in energy e. That is, the electron eigenstates are initially assumed to. While in gaps at the brillouin zone boundary one finds such a state only for positive potential matrix element, there a surface state. Nearly free electron model what is the dispersion curve of the free electron model.
From atomic theory, we are used to the idea that different electronic. Nearly free electrons in a 5d delafossite oxide metal. Simplest extension of the electron gas model nearly free electron gas very small potential variation with the periodicity of the crystal. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. Nearly free electron superatom states of carbon and boron.
Nearly free electron approximation and tight binding. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the. Quantum free electron theory was proposed by arnold sommerfeld. The phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. In the nearly free electron model, we take the opposite approach. Treating the nearly free electron model using degenerate perturbation theory has been shown on the blackboard during lectures 3. Energy spectrum of a nearlyfree electron model in 1d the eigenstates of free problem in 1d. Together, our findings establish ptcoo2 as a model nearlyfreeelectron system in a 5 d delafossite transitionmetal oxide. Atomic selectrons are delocalised due to overlap of outer orbits. This is true for any k,but a periodic perturbation has nonzero matrix elements only between particular states. This is totally inexplicable within the free electron model. Introduction to the electron theory of metals uichiro mizutani department of crystalline materials science, nagoya university. Derive the electron band structure when the interaction with the lattice is weak using the nearly free electron model describe what momentum states of particles in a crystal may couple through the periodic lattice potential.
Drude model fails to predict hall and conductivity for all metals except for alkaline metals metal li na k ag au al inr h en 0780. One corresponding to a plane wave, or a free electron, and another corresponding to a periodic correction factor. The electrons, however, are treated using quantum mechanics. The free electron approximation remains a good approximation well away from the edges of the brillouin zone only wavevectors close to a multiple of. Perturbation theory and nearlyfree electron model pdf. The treatment of a metal as containing a gas of electrons completely free to move within it. Chapter 4 electronic structure the electronic properties of matter determines its macroscopic behavior.
Mod01 lec9 the free electron theory of metals youtube. Drawing a dispersion relation i the reduced zone scheme for free electron and nearly free electrons case things we need to know. So it leads to much larger predicted quantities than that is actually observed. By firstprinciples theory we study the nearly free electron nfe states of carbon and boron nitride nanotubes. Energy bands nearlyfree electron model electron diffraction and energy gap bloch theorem the central equation emptylattice approximation tightbinding model see chap 9 nfe model is good for na, k, al etc, in which the lattice potential is. Maslov department of physics, university of florida.
Recall nature of free electron gas free electrons in box of size l x l x l artificial but useful. Doublewell and tightbinding models pdf lecture notes. Chapter 6 free electron fermi gas national tsing hua. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. Lecture 4 week 19 origin of energy bands and nearly free electron model intuitive picture braggreflection for nearly free electrons gap opening for nearly free electrons kronigpenney model empty lattice approximation. Simple bandstructure diagrams for a one dimensional periodic solid in the limit vr 0 expressed in the extended zone a, repeated zone b, and reduced zone c schemes. 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. A natural extension of the freeelectron model is the nearly free electron nfe model, which applies to crystals, because it is assumed that the electrons are subjected to a periodic potential inside them. The nearlyfree electron model university of oxford. Modulation of nearly free electron states in hydroxylfunctionalized mxenes. In the bulk of the material, the surface is disregarded altogether and the electrons are completely free. Handout 8 linear combination of atomic orbitals lcao. Electrons in a periodic potential nearly free electron.
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. Most of the ohterminated mxene are metallic, but some of them, e. Drude theory of conduction basics of free electron theory and electrical conductivity part. This in turn will affect the way the electron gas can absorb energy from an external source. On the theory of surface states in nearly free electron. If 0, we assume the electron to be traveling in a weak potential, and can thus expand the wave function into two parts.
The energy e of free electrons which is plotted versus k in fig. Nearly free electron in the tight bonding model, the electron eigenstates are initially assumed to be localized around the atoms, then a hopping term is introduced to allow them to delocalize. This page contains selected lecture notes and inclass presentations lecture notes solid state i. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. According to the classical free electron theory the value of specific heat of metals is given by 4. Also according to this theory the value of electronic specific heat is equal to 32 r. Sc2coh2, are semiconductors and the nfe states are conduction bands. Mod01 lec9 the free electron theory of metals nptelhrd. The dashed curve corresponds to the case of free 1 1. Note, however, that although the free electron wave vector is simply p, where p is the momentum of the electron, in the bloch case k is not proportional to the. This model, like the free electron model, does not take into account electron electron interactions. The existence of surface states in band gaps of a nearly free electron band structure is investigated. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals.
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