Thermal Conductivity: Nonmetal Impact on Change

[aaaa202]

For a nonmetal what determines thermal conductivity is the propagation of lattice vibrations. As T increases these lattice vibrations collide with each other more often. Does this mean that the thermal conductivity will de- or increase?

 

[DrDu]

What would you guess?

 

[aaaa202]

Im guessing the phonon collisions act as a sort of resistance, so the conductivity drops with increasing temperature. But on the other hand, what if there were no collisions? What would then transmit heat?

 

[DrDu]

If there are no collisions, e.g. at very low temperatures, you have ballistic transport which is very rapid.
I think that only so-called Umklapp scattering processes actually can reduce the heat transport and this requires the sum of the crystal momenta of the two phonons to be larger than a reciprocal lattice vector. So it is only important at relatively high energies ~ Debye energy. Whether this includes room temperature depends on the material.