The free electron theory of metals

2018 ◽  
Author(s):  
L. Solymar ◽  
D. Walsh ◽  
R. R. A. Syms
Keyword(s):  
Distribution Function ◽  
Specific Heat ◽  
Work Function ◽  
Field Emission ◽  
Density Of States ◽  
Free Electron ◽  
Thermionic Emission ◽  
Photoelectric Effect ◽  
Electron Theory ◽  
Dirac Distribution

The model of the free electron theory is presented. The density of states and the Fermi–Dirac distribution function are discussed, leading to the specific heat of the electrons, the work function, thermionic emission, and the Schottky effects. As examples of applications the field-emission microscope and quartz–halogen lamps are discussed. The photoelectric effect and the energy diagrams relating to the junction between two metals are also discussed.

scholarly journals THE THERMAL FORM OF THE PHOTOEFFECT WITH THE DEBYE AND THE WIGNER CRYSTAL

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Miroslav Pardy ◽  
Keyword(s):  
Specific Heat ◽  
Work Function ◽  
Radiative Correction ◽  
Photoelectric Effect ◽  
Wigner Crystal ◽  
Photon Propagator ◽  
Crystal Medium

We define the photoelectric effect with the specific heat term replacing the work function. The photon propagator involving the radiative correction is also considered. We consider the Debye specific head for the 3D crystal medium, the specific heat for the 2D medium and specific heat for the Wigner crystal.

A Correlation between Critical Volumes and Work Function Data for Electrons in Liquid Hydrocarbons

1973 ◽  
Vol 51 (20) ◽  
pp. 3443-3444 ◽  
Author(s):  
H. T. Davis ◽  
L. D. Schmidt
Keyword(s):  
Work Function ◽  
Free Electron ◽  
Van Der Waals ◽  
Electron Work Function ◽  
Hard Core ◽  
Liquid Hydrocarbons ◽  
Electron Theory ◽  
Function Data ◽  
Van Der Waals Radii

Electron-molecule hard-core radii determined with the aid of Springett, Jortner, and Cohen's quasi-free electron theory from electron work function data are shown to correlate with the critical volumes of several hydrocarbons. The radii are approximately equal to the van der Waals radii determined from the critical volumes.

scholarly journals Квантовая теория эмиссии электронов из структуры "металл-диэлектрик" в сильных электрических полях

2020 ◽  
Vol 90 (6) ◽  
pp. 1035
Author(s):  
С.И. Берил ◽  
С.А. Баренгольц ◽  
Ю.А. Баренгольц ◽  
А.С. Старчук
Keyword(s):  
Work Function ◽  
Field Emission ◽  
Electric Fields ◽  
Electron Emission ◽  
Thermionic Emission ◽  
Emission Current ◽  
Electronic Work Function ◽  
Quantum Image ◽  
Field Emission Current ◽  
Increasing Temperature

A generalized formula is derived for the electron emission current in relation to the temperature, the electric field, and the electronic work function for a “metal–dielectric” system. The formula takes into account the quantum nature of the image forces. In deriving it, the Fermi–Dirac distribution and the quantum image potential obtained in terms of the electron–polaron theory are used. In the limit of the classical potential of image forces, the well-known Richardson–Schottky and Fowler–Nordheim formulas are obtained for thermionic emission and field emission, respectively. It is shown that at high temperatures and electric fields E ≥ 10 MV/cm, the polaron contribution to the electron emission current increases with increasing field and decreases with increasing temperature. The decrease in current is related to an increase in effective electronic work function due to the electron-polaron effect. Extrapolation formulas convenient to obtain theoretical estimates are derived for the thermionic and the field emission current.

A free-electron theory of conjugated molecules

1953 ◽  
Vol 49 (4) ◽  
pp. 650-658 ◽  
Author(s):  
J. Stanley Griffith
Keyword(s):  
Free Electron ◽  
Wave Functions ◽  
Electron Charge ◽  
Algebraic Equations ◽  
Electron Wave ◽  
Electron Theory ◽  
Conjugated Molecules ◽  
Electron Charge Density ◽  
Linear Polyenes ◽  
Alternant Hydrocarbons

ABSTRACTThe values of a free-electron eigenfunotion at the carbon nuclei of a conjugated hydrocarbon are found to satisfy a system of algebraic equations. These equations are similar in form to those obtained in the method known as the linear combination of atomic orbitale but only coincide with them for linear polyenes and benzene. The symmetry, degeneracy and energy of the eigenvectors of these free-electron equations correspond exactly to those of the free-electron wave functions found by the usual methods. From this correspondence, a theorem is deduced about the free-electron charge density in alternant hydrocarbons.

scholarly journals Carbon Nanotube Electron Sources: From Electron Beams to Energy Conversion and Optophononics

2014 ◽  
Vol 2014 ◽  
pp. 1-23 ◽  
Author(s):  
Alireza Nojeh
Keyword(s):  
Carbon Nanotubes ◽  
Field Emission ◽  
Electron Emission ◽  
Electron Beams ◽  
Thermionic Emission ◽  
Secondary Emission ◽  
Electron Sources ◽  
Field Emitters ◽  
Electron Microscopes ◽  
Electron Emitters

Carbon nanotubes have a host of properties that make them excellent candidates for electron emitters. A significant amount of research has been conducted on nanotube-based field-emitters over the past two decades, and they have been investigated for devices ranging from flat-panel displays to vacuum tubes and electron microscopes. Other electron emission mechanisms from carbon nanotubes, such as photoemission, secondary emission, and thermionic emission, have also been studied, although to a lesser degree than field-emission. This paper presents an overview of the topic, with emphasis on these less-explored mechanisms, although field-emission is also discussed. We will see that not only is electron emission from nanotubes promising for electron-source applications, but also its study could reveal unusual phenomena and open the door to new devices that are not directly related to electron beams.

A New Thermionic Cathode Based on Carbon Nanotubes with a Thin Layer of Low Work Function Barium Strontium Oxide Surface Coating

2008 ◽  
Vol 1142 ◽  
Author(s):  
Feng Jin ◽  
Yan Liu ◽  
Scott A Little ◽  
Chris M Day
Keyword(s):  
Work Function ◽  
Current Density ◽  
Enhancement Factor ◽  
Thermionic Emission ◽  
Field Enhancement ◽  
Oxide Coating ◽  
Emission Current Density ◽  
Emission Current ◽  
Strontium Oxide ◽  
Barium Strontium

ABSTRACTWe have created a thermionic cathode structure that consists of a thin tungsten ribbon; carbon nanotubes (CNTs) on the ribbon surface; and a thin layer of low work function barium strontium oxide coating on the CNTs. This oxide coated CNT cathode was designed to combine the benefits from the high field enhancement factor from CNTs and the low work function from the emissive oxide coating. The field emission and thermionic emission properties of the cathode have been characterized. A field enhancement factor of 266 and a work function of 1.9 eV were obtained. At 1221 K, a thermionic emission current density of 1.22A/cm2 in an electric field of 1.1 V/μm was obtained, which is four orders of magnitude greater than the emission current density from the uncoated CNT cathode at the same temperature. The high emission current density at such a modest temperature is among the best ever reported for an oxide cathode.

Excess Low Temperature Specific Heat and Related Phonon Density of States in a Modulated Incommensurate Dielectric

1996 ◽  
Vol 76 (13) ◽  
pp. 2334-2337 ◽  
Author(s):  
J. Etrillard ◽  
J. C. Lasjaunias ◽  
K. Biljakovic ◽  
B. Toudic ◽  
G. Coddens
Keyword(s):  
Low Temperature ◽  
Specific Heat ◽  
Density Of States ◽  
Phonon Density ◽  
Phonon Density Of States ◽  
Low Temperature Specific Heat

Transition from a Bloch-Wilson to a free-electron density of states in Znn− clusters

2005 ◽  
Vol 123 (22) ◽  
pp. 221102 ◽  
Author(s):  
Oleg Kostko ◽  
Gert Wrigge ◽  
Ori Cheshnovsky ◽  
Bernd v. Issendorff
Keyword(s):  
Electron Density ◽  
Density Of States ◽  
Free Electron ◽  
Free Electron Density ◽  
Electron Density Of States

Tight Binding Modeling of Properties Related to Field Emission from Nanodiamond Clusters

2000 ◽  
Vol 621 ◽  
Author(s):  
Denis A. Areshkin ◽  
Olga A. Shenderova ◽  
Victor V. Zhirnov ◽  
Alexander F. Pal ◽  
John J. Hren ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Field Emission ◽  
Density Of States ◽  
Electron Affinity ◽  
Potential Distribution ◽  
Tight Binding ◽  
Matrix Elements ◽  
Energy States ◽  
Bulk Diamond ◽  
Modeling Of Properties

ABSTRACTThe electronic structure of nanodiamond clusters containing between 34 and 913 carbon atoms was calculated using a tight-binding Hamiltonian. All clusters had shapes represented by an octahedron with (111) facets with the top and the bottom vertices truncated to introduce (100) surfaces. The tight-binding Hamiltonian consisted of environment-dependent matrix elements, and C-H parameters fit to reproduce energy states of the cyclic C6 and methane. The calculations predict a density of states similar to bulk diamond for clusters with radii greater than ∼2.5nm, and insignificant differences in the potential distribution between the clusters and bulk diamond for radii greater than ∼1nm. Hydrogen passivated nanodiamond clusters are estimated to have an electron affinity of approximately -1.8 eV.

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