# Heat conduction coefficient in tungsten

• rayman123

## Homework Statement

Hello! I am supposed to explain the behaviour of the thermal conductivity of tungsten. I have plotted the relation
http://img340.imageshack.us/img340/9776/heatcond.jpg [Broken] is also experimental data
Temp[0 10 50 100 300 500 1000 2000 3400]
and thermal conductivity coefficient
$$\lambda$$ 0 97,1 4,28 2,08 1,74 1,46 1,18 1 0,9]
Can someone explain the mechanism to me? Why does the thermal conductivity reache its maximum for T=10K ? and after that it gradually decreases and after some temp is behaves almost like constant?
How this can be explained?
Thank you!

## The Attempt at a Solution

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Well, I'm not an expert in solid state physics but here are some background issues.

Heat conduction in a crystalline material such as tungsten will be expressible at the quantum level in terms of random phonon propagation (quantized vibrations i.e. sound particles) and thermal electron conduction.

Typically in metals electron based heat conduction dominates while in non-metalic crystalline materials phonon propagation dominates. However given Tungsten is a very hard crystalline metal with lower conductivity both may be significant.

Now with the crystaline structure you have via the somewhat regular atomic spacing, bands of phonon transparency where the wavelengths are matching up with the spacing.

Heat conductivity due to electron motion may be more significant in Tungsten, it being a metal. The electrons also conduct in certain energy (and thus wavelength) bands affected by atomic spacing which is affected by the temperature.

I got quite a few good "pops" googling: "heat conductivity electron phonon mechanisms"

So I would begin, if I were you, to see what other materials show similar heat conductivity vs temperature effects, compare the thermal conductivity curves to electrical conductivity curves, thermal expansion curves, speed of sound measurement curves. Possibly there is a transition point which of phonon vs electron based heat conduction dominates.

thank you for your reply. The mechanism itself I am familiar with but I do not know how to explain this behaviour, why suddenly the heat conductivity decreases as the temp raises. I will do some researches:)