Drude model deals with conuctivity of the metals by assuming fixed ions with sea of free electrons. This model is mostly used to explain the transparency of the metallic thin films. Also please have a look on the following links to study it in more detail

1- http://physics.bu.edu/~okctsui/PY543/1_notes_Drude_2013.pdf

2- http://physics.bu.edu/~okctsui/PY543/1_notes_Drude_2013.pdf

3- http://www.physics.iisc.ernet.in/~aveek_bid/PH208/Lecture%201%20Drude%20model.pdf

Just read the chapter 1 of the text book "Solid State Physics' by N. W Ashcroft and N.D. Mermin, Saunders College Publishing (1976). Drude's theory is explained very well there.

It is the model of a "drude". ^^

explain dc, ac, hall and thermal conductivity

as always a very good approximation. ;)

Good evening Chao,

Drude (Free electron) Model is a model to predict some physical phenomena in solid state materials. It considers electrons involved metallic bonds as free that wanders in Brownian motion, hence called as electron gas. Based on these assumptions and using the ideal gas theory, the electrical and thermal conductivities of materials are predicted. Among others, the model successfully predicts the Ohm's law and electronic thermal conductivity in metals.

I confirm Tapan Chatterji answear, in that book you'll find a very good explanation.

In few words, Drude Model is the oldest model about metal structure that explains electrical and termal conduction.

Drude model deals with inversion domain boundaries in IV-nitrides semiductors

See Physical Review B 06/1999; 59(24):88343-15925

It deals with the transport properties of electron in the conductors (metals), in particular, to understand the electrical conduction mechanism of such materials.

Drude model is the classical picture of transport properties in metals. It is based on the following assumptions

1.Free electrons are responsible for conduction

2.They move randomly and the collision will be elastic. They behave much similar to gas, hence called as electron gas using MB distribution law

3.When an external field is applied, they drifted towards the higher potential end.

Based on these assumptions, drude proposed the electrical conductivity and thermal conductivity expression. But the main drawback, (since we all know that energies of electrons are discrete) it could not able explain many transport properties like hall effect, etc. But still it is classical one to be used in many problems.

In fact one can say that theory of solid state started with the Drude theory of metals. The theory of Drude was published in Annalen der Physik 1, 566 (1900) and 3, 369 (1900). Please remember that electron was discoved by J.J. Thomson in 1897, one three years ago and quantum hypothesis of Max-Planck was proposed in the same year 1900. With the intution of a genius Drude boldly proposed free electron (gas) theory of metal. He of course used classical Boltzman statistics because quantum statistics was still unknown and he still got surprisingly good results. Electrons are not really free. They are subject to strong ion-electron and electron-electron interaction. They do not obey classical Boltzman statistics but quantum Fermi-Dirac statistics. Sommerfield in fact took the Drude free electron model as such and just used Fermi-Dirac statistics and got even better results. For a long time physicists wondered why this simple free electron (gas) model worked so well. Then at the advent of quantum theory of solid state one understood why the independent electron approximation used so far worked relatively well and what was role of screening. Thomas and Fermi and then Lindhard published the detailed theories of screening and with these modification the long-standing problem of the cohesion in metal was better understood. But then came the genius Landau and introduced Fermi liquid theory and the bold idea of quasiparticles. Although the electrons are not really free but electrons can be effectively replaced by quasiparticles that act as qusi-free particles. This is an emergent behavior of a many particle system. To understand all these developments all condensed matter physicists should go through chapters 1, 2, 3 and 17 very carefully of the excellent text book by Ashcroft and Mermin that I mentioned and cited before. Without a through understanding of these four chapters ( I am stressing that these are best things one can read in the whole literature of solid state physics) the education of condensed matter physicist in not complete.

Wow! What a nice explanation. It looks like a live seminar. No one can better this answer. Tapan Sir seems to be so genius on solid state physics.

To appreciate Drude's achievement one must know that periodic arrangement of atoms in solid, though speculated, was not known experimentally. X-ray diffraction was twelve years later and only then the periodic arrangement of atoms in a solid became known and accepted. Drude ignored the details of atomic arrangement and considered valence electrons to be free like atoms in a gas and introduced the idea of electron gas. Like the particles in a gas the electrons behave like free particles except during the collision. In between collisions the electrons do not interact with the ions or the other electrons. However collisions are assumed to happen and these set the limit to the distance the electrons can move in the average with and the corresponding time. After each collision the speed and direction of the electron changes but these details do not enter into the calculations. Setting this scenario Drude then happily use the classical statistics of Boltzmann then available to him and go ahead with his calculations. This can only be the bold work of a genius which indeed he was. He went far far ahead in explaining electrical and thermal conductivity and even the optical properties (his favorite subject) of metals. Well then came Sommerfield and used the quantum Fermi-Dirac statistics, Thomas and Fermi with screeing, and finally Landau with his quasiparticles and Fermi liquid theory. All very good and would definitely happen eventually but just reflect on the genius of Paul Karl Ludwig Drude (1863-1906) who postulated free electron theory of metal at the age of thirty seven and committed suicide at the age of barely forty-three for unknown reason but he is always remembered for his great achievement. Today you guys encounter his name repeatedly in the different chapters of solid state textbook like that of Ashcroft and Mermin.

And could you please give me in formations regarding the contribution made by lorentz in this theory. Often this classical theory was called as drude-lorentz model.

And Tapan Sir, Recently I gone through a topic in solid state physics (C. Kittel) regarding metal insulator transition. I found that Mott predicted critical lattice parameter theoretically 4.5 times the bohr radius with in which metal insulator transition take place. And this take place by any external parameters like pressure, strain, etc. Also i could not understand- when lattice parameter is low, materials are metallic and non-metallic when lattice parameters are high. How and why? In my understanding, when lattice parameter are small, more interaction will take place between electron-electron or electron-phonon and material becomes non-metallic .Is I am correct?

Drude was basically an experimentalist but had good theoretical understanding of the properties of matter. His theory was based on elementary calculation which when applied to dynamical theory of gases is known to give incorrect numerical values. His strength was not detailed rigorous calculations but physical understanding and deep insight into the problem. But Hendrik Lorentz was a great Dutch theoretical physicist whose contributions to physics were outstanding by any measure. Even Einstein was afraid to be his successor at the University of Amsterdam. He shared Nobel prize with Peter Zeeman in 1902 in physics for the discovery and theoretical explanation of the Zeeman effect, His name is associated with "Lorentz transformation", "Lorentz contaction", "Lorentz force" etc. etc. Lorentz re-examined the "free electron theory" of Drude using the full statistical theory of Maxwell and Boltzmann and also re-investigated the dynamics of collision process more carefully. That is why the free electron theory is sometimes referred as Drude-Lorentz theory.

I shall come to the topic of metal-insulator transition whenever I find more time.

Thank you Sir, I will wait

Mott described metal-insulator transition by imagining a crystalline array of hydrogen-like atoms in a lattice a that could be varied. Experimentally we know that NiO which has larger values of a is insulating whereas monovalent metal like sodium that has a smaller a is a metal. The question was at what value of would a metal-insulator transition take place? Mott assumed that this would occur when the screened (Fermi-Thomas screening) potential around each positive charge

V(r) = - (e^2/r) exp(-qr)

(where e is the electronic charge, r is the inter-atomic separation and the screening q is calculated by the Thomas-Fermi method) was just strong enough to trap an electron. The transition would be discontinuous. This would occur with varying n (number of electrons per unit volume) and therefore with varying q. Mott found that the transition would occur when

n^(1/2)a_H= 0.2

where a_H is the hydrogen radius.

This was the first initial theory of metal-insulator transition. It was applied to the metal-insulator transition in doped semiconductors and argued that the disorder causes the transition to be continuous. This theory did not prove to be appropriate at least for the doped semiconductor where probably the theory of Anderson transition (another big topic) is more appropriate. Mott's theory was just a preliminary and intuitive theory and applicable in some cases only. For other situation the theory of Hubbard is more appropriate and for problems involving disordered and glassy system. So you many find situations where the Mott's simple argument given above fails.

The problem of electron-electron interaction or correlation is highly complex and is not solved satisfactorily. For a deep understanding you should read "Metal-Insulator Transition" by N. Mott, Taylor and Francis, Second Edition (1990)

For a more recent review see:

Imada, M.; Fujimori, Tokura (1998). "Metal–insulator transitions". REV. MOD. PHYS 70 (4). http://rmp.aps.org/abstract/RMP/v70/i4/p1039_1

For a more recent review see:

Imada, M.; Fujimori, Tokura (1998). "Metal–insulator transitions". REV. MOD. PHYS 70 (4). http://rmp.aps.org/abstract/RMP/v70/i4/p1039_1

For a more recent review see:

Imada, M.; Fujimori, Tokura (1998). "Metal–insulator transitions". REV. MOD. PHYS 70 (4), 1039 (1998).

you can find a good answer also in Bohren C.F., Huffman D.R. Absorption and scattering of light by small particles (Wiley, 1998)(K)(400dpi)(T)(545s)(ISBN 0471293407).

for these basic questions, I suggest you fisrt try to find the answer in a textbook and solve them by yourself. I find that you asked a lot of questions that can be easily found in textbooks or published papers.

Drude model is a model used for only metals when  external field (E)is applied which brings about oscillation to the sytem....no spring connected but with mass of electron being considered in this case for the modelling of the system

 Respected (Tapan )Sir ,

Sir as you told that Drude model was extended H.A.Lorentz.

Is this a  lorentz drude model for dispersion of permittivity and permeability ,where  Lorentz equation is for dielectric material and drude    equation is for metallic material Or this is a completely different model ?