Free electron model

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In physics, the free electron model is a simple model for the behaviour of electrons in a crystal structure of a metallic solid. Developed principally by Drude and Sommerfeld, the free electron model neglects not only the Coulomb interaction between electrons, but also the interaction between the electrons and the atomic lattice through which they move. The free electron model is a quantum model as opposed to the Drude model, which is classical. Once the effects of quantum mechanics are taken into account, many of the experimental predictions of the model are surprisingly accurate, given its simplicity.

The free electron model should be contrasted with the tight-binding model, which uses the opposite simplification of treating the electrons as tightly bound to the atomic cores. (Coulomb interactions between electrons are still neglected.) The predictions of these two complementary models are reassuringly similar.

Contents 1 Ideas and assumptions 2 Predictions of the model 3 Problems 4 See also 5 External articles and references

[edit] Ideas and assumptions

In solid-state physics valence electrons are modeled as completely detached from their ions in an "electron gas". While this model is the simplest model, it reproduces the main electronic properties of metals. The two fundamental asumptions are:

• the independent electron approximation that considers the electrons as independent. Electron screening is one justification for ignoring electron-electron interactions.
• the electrons move in a constant energy potential (the structure of the material is completely ignored). Bloch's Theorem states that a periodic potential (such as a regular array of atoms) cannot scatter an electron.

[edit] Predictions of the model

This very simple model of metals more or less correctly predicts:

• the shape of the electronic density of states.
• the range of binding energy values.
• the functional form of the heat capacity .
• electrical conductivities.
• the Wiedemann-Franz law.
• The energy of an electron is equal to

h² * k² / ((2pi)² * 2m

[edit] Problems

As not all the forces on the electrons are taken into account the electrons have an effective mass that is larger than the free electron model predicts.

[edit] See also

Free electron

• Nearly-free electron model
• Free electron laser

People

• Hendrik A. Lorentz
• Arnold Sommerfeld
• Joseph Larmor

Other

• Thermal conductivity
• Electrical conductivity
• Pauli exclusion principle
• Band theory
• Fermi gas
• Drude model

[edit] External articles and references

• "Free-electron model of metals". Encyclopædia Britannica, Inc., 2006.
• "The free electron model". cmmp.ucl.ac.uk.
• Evgeny Y. Tsymbal, "Introduction to Solid State Physics; Section 7: Free electron model". University of Nebraska-Lincoln (physics.unl.edu).
• "Semiconductor Physics; 2.1 Basic Band Theory; 2.1.1 Essentials of the Free Electron Gas". tf.uni-kiel.de.
• Oleg Krupin, "Dichroism and Rashba effect at magnetic surfaces of crystalline rare-earth metals : Dichroism and Rashba effect RK magnetic crystal surfaces OF rare earth metals; Appendix C: Free-Electron Model".
• Chia-Hung Yang, "Handout : Electron I: Free electron model". ENEE 600 - Solid State Electronics.
• "From Thomson's Corpuscles to the Electron". American Institute of Physics, 2006.
• "Electrons in free space". BlackLight Power Inc.

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