25-08-2014, 11:57 AM
Free Electron theory of metals On Seminar Report
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Drude Model
Drude (~1900) assumed that the charge density associated with the positive ion cores is spread uniformly throughout the metal so that the electrons move in a constant electrostatic potential.
According to FEM, this potential is taken as zero and the repulsive force between conduction electrons are also ignored.
Electron gas is free and independent, means ‘no electron-electron or electron-ion interactions
Demerits of Drude Theory
From the classical free electron theory the value of specific heat of metals is given by 4.5R, where ‘R’ is called the universal gas constant. But the experimental value of specific heat is nearly equal to 3R.
With help of this model we can’t explain the electrical conductivity of semiconductors or insulators.
The theoretical value of paramagnetic susceptibility is greater than the experimental value.
Ferromagnetism cannot be explained by this theory
It is assumed that the valance electrons travel in constant potential inside the metal but they are prevented from escaping the crystal by very high potential barriers at the ends of the crystal.
In this theory, though the energy levels of the electrons are discrete, the spacing between consecutive energy levels is very less and thus the distribution of energy levels seems to be continuous
FEM: At a Glance
Classical Model:
Metal is an array of positive ions with electrons that are free to roam through the ionic array
Electrons are treated as an ideal neutral gas, and their total energy depends on the temperature and applied field
In the absence of an electrical field, electrons move with randomly distributed thermal velocities
Quantum Mechanical Model:
Electrons are in a potential well with infinite barriers: They do not leave metal, but free to roam inside
Electron energy levels are quantized and well defined, so average energy of electron is not equal to (3/2)kBT
Electrons occupy energy levels according to Pauli’s exclusion principle