What factors affect the temperature dependence of electrical conductivity?

In summary, the conversation discusses the use of the Drude model to explain the temperature dependence of electrical conductivity. The model involves the density of mobile electrons and the relaxation time between collisions. However, the model becomes unreliable at high temperatures due to the frequent thermal collisions. Alternative models, such as quantum mechanics, can be studied to better understand this phenomenon. The conversation also briefly mentions the estimation of mean free path and the relationship between thermal conductivity and temperature.
  • #1
JohanL
158
0
How do you with a simple model explain the temperature dependence of the
electrical conductivity.
If you use the Drude model you get for the electrical conductivity

sigma = ne^2t / m

where n is the density of mobile electrons and t is the relaxation time.
t is the time between collisions and must be the only variabel here that depends on temperature. How can you estimate t(T).

Maybe there is a better model that describes the temperature dependence of the electrical conductivity.
 
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  • #2
I never liked the way the drude model gets bogus at the end:

"The only relevant quantity with dimensions of time is the time between collisions".

Alright, thermal collisions are much more frequent than conduction drift collisions. Calculate the distance between electrons N (number of conductivity electrons per cubic meter) arranged in a 1m^3 sphere (fun!). Then calculate the speed of the electrons from temperature using:

KE = 3/2 *k*T

where KE is kinetic energy, k is boltzmans and T is temperature.

Use the mean free path and velocity to compute time between collision.


After all that, throw away the drude model and study quantum mechanics.
 
  • #3
thx for your answer. :smile:

I have a question about mean free path p.
I calculate it from the density of electrons n (electrons/m^3)
then p = 1/(third root of n),

and then it should be indepent of temperature.
But I know that it should be different for different temperatures.
How can you estimate p for different temperatures?

_____________________

Then I used your model to estimate the temperature dependence of the thermal conductivity of the free electrons in a metal.

K = C*T*t = D * sqrt(T)

Where C and C are constants and t again is the time between collisions.
But the experimental curve of K doesn't have this form. Only for low temperatures it has. Then it reaches a maximum and goes down.
Why?
 
  • #4
Briefly :

The effective relaxation time comes from two contributions : scattering off of the lattice/phonons (not other electrons - the Drude model does not include electron-electron interactions), and scattering off of impurities and lattice imperfections.

[tex] \frac{1}{\tau} = \frac{1}{\tau _{lat}} + \frac{1}{\tau _{imp}} [/tex]

Speaking of resistivities instead of conductivities, you have

[tex] \rho = \rho _ {lat} + \rho _{imp} [/tex]

For most elemental metals, [itex] \tau _ {imp} [/itex] is fairly independent of the temperature. The lattice interactions are largely result of the fact that the lattice is vibrating rapidly, providing a large scattering cross section, so much so, that as [itex]T \rightarrow 0 [/itex], [itex] \rho _ {lat} << \rho _{imp} [/itex]

So, at 0 K : [itex] \rho \approx \rho _ {imp} [/itex]

INCOMPLETE...

Just realized you are now suddenly talking about thermal conductivity [itex]\kappa[/itex], rather than electrical conductivity [itex]\sigma [/itex]. Which one is it ? Drude does NOT try to explain thermal conductivity, and can not, because this is a largely phonon process. Seminal work on thermal conductivity was done by Debye and Pierls.
 
Last edited:

1. What is electrical conductivity?

Electrical conductivity is the measure of a material's ability to conduct electricity. It is a physical property that describes how easily electrons can flow through a material.

2. How is electrical conductivity measured?

Electrical conductivity is typically measured in siemens per meter (S/m) or mho per meter (mho/m). It is measured by applying a voltage across a material and measuring the resulting current that flows through it.

3. What factors affect electrical conductivity?

The main factors that affect electrical conductivity are the type of material, its composition, and its temperature. Generally, metals have high electrical conductivity due to their free electrons, while insulators have low conductivity due to their lack of free electrons.

4. Why is electrical conductivity important?

Electrical conductivity is an important property in many fields, including electrical engineering, materials science, and chemistry. It allows for the transmission of electricity, which is essential for powering devices and machines. It also plays a crucial role in the properties and behavior of materials.

5. How can electrical conductivity be increased?

Electrical conductivity can be increased in a material by adding impurities or alloying elements that increase the number of free electrons, or by reducing the temperature. In some cases, applying an external electromagnetic field can also increase conductivity.

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