ElectronGasLect25ME501F2011

ElectronGasLect25ME501F2011 - Purdue University ME 501:...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Patterned Border Template 1 Purdue University School of Mechanical Engineering ME 501: Statistical Thermodynamics Lecture 25: The Free Electron Gas in Metals Prof. Robert P. Lucht Room 2204, Mechanical Engineering Building School of Mechanical Engineering Purdue University West Lafayette, Indiana Lucht@purdue.edu , 765-494-5623 (Phone) November 9, 2011
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Patterned Border Template 2 Purdue University School of Mechanical Engineering Lecture Topics • Band theory of solids. • Free (valence) electrons in metals. • Fermi-Dirac statistics: further development. • The Fermi energy. • Contribution of free electrons to the heat capacity of a metal.
Background image of page 2
Patterned Border Template 3 Purdue University School of Mechanical Engineering Band Theory of Solids • As free atoms are brought closer together to form a solid lattice, the outer valence electrons of the free atoms begin to interact. The electronic energy levels in the atom split and then coalesce into bands as the distance decreases to the lattice spacing of the solid. J. Lay, Statistical Mechanics and Thermodynamics of Matter , 1990
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Patterned Border Template 4 Purdue University School of Mechanical Engineering Band Theory of Solids • The energy levels of the inner electrons do no split as much as the energy levels for the valence electrons because the inner electrons are not influenced nearly as much by the neighboring atoms. These inner electrons remain localized by a particular nucleus even in the solid lattice. The valence electrons are not localized to the region of a particular nucleus. In the case of a metal they are “free” to move within the crystal lattice formed by the positive ion cores. • Whether a solid is an insulator, semiconductor, or metal depends on the band structure that develops as the atoms are brought closer and closer together, and whether or not these energy bands are completely occupied. In metals, the valence bands are not fully occupied, or an empty band overlaps the fully occupied valence band. Because the electrons can be easily excited to a higher energy level by an applied electric field, metals are excellent conductors of electricity. J. Lay, Statistical Mechanics and Thermodynamics of Matter , 1990
Background image of page 4
Patterned Border Template 5 Purdue University School of Mechanical Engineering Band Theory of Solids • The band structure of Na (1s 2 2s 2 2p 6 3s 1 ), Mg (1s 2 2s 2 2p 6 3s 2 ), and Ne (1s 2 2s 2 2p 6 ) is shown below. Na and Mg are metals and are highly conductive, solid Ne is an insulator because of the energy gap between the fully occupied 2p valence band and the closest energy band above that, the empty 3s band. J. Lay, Statistical Mechanics and Thermodynamics of Matter , 1990
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Patterned Border Template 6 Purdue University School of Mechanical Engineering Band Theory of Solids • The development of the band structure of Na (1s 2 2s 2 2p 6 3s 1 ) is shown in more detail in this diagram.
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 21

ElectronGasLect25ME501F2011 - Purdue University ME 501:...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online