I have calculated electronic components of thermal conductivity by wiedmanfranz law. Then the lattice thermal conductivity is derived from it. But some of those values are negative. at the end of What is the reason of it? Are they acceptable?
Dear Ganesh Hegde :
I think all is about a misunderstanding about the "law".
This "law" does n't work for Phonons, just for Electrons. This means that it is not applicable for the Lattice Thermal Conductivity part, but just for the electronic contribution to kTot.
This is the reason of why this "law" is only valid for metallic materials, and is a rough approximation for degenerated, or highly doped semiconductors.
If you search in a solid state physics textbook how this Law was derived, it was done using the Drude's model for electrons; using this model, the expressions for Specific Heat and Thermal Conductivity were put in place using the Maxwell-Boltzmann statistics, and the Electric Conductivity (this is the most important derivation form the Drude's model) was considered just looking at the free carriers in the solid only as charged free particles (electrons) in a static periodic lattice of static massive ions. However, neither the thermal fluctuations of the lattice, nor the vibrations of it are taken into account.
So you cannot calculate kL using the Wiedemann-Franz's Law., kL is not involved whatsoever in the derivation of this model.
The model which the W-F Law was derived didn't considered the Lattice Thermal part.
What I mean to say is: It is not correct to separate the electronic component and the phononic component of the Thermal Conductivity when you have computed this using the W-F Law. Since the materials the "Law" is applicable for, cannot have an important component of phononic (or lattice thermal ) conductivity., maybe not more than a 20%, if not less, but anyways, will be always an approximation.
Regards!
Dear Ganesh Hegde :
I think all is about a misunderstanding about the "law".
This "law" does n't work for Phonons, just for Electrons. This means that it is not applicable for the Lattice Thermal Conductivity part, but just for the electronic contribution to kTot.
This is the reason of why this "law" is only valid for metallic materials, and is a rough approximation for degenerated, or highly doped semiconductors.
If you search in a solid state physics textbook how this Law was derived, it was done using the Drude's model for electrons; using this model, the expressions for Specific Heat and Thermal Conductivity were put in place using the Maxwell-Boltzmann statistics, and the Electric Conductivity (this is the most important derivation form the Drude's model) was considered just looking at the free carriers in the solid only as charged free particles (electrons) in a static periodic lattice of static massive ions. However, neither the thermal fluctuations of the lattice, nor the vibrations of it are taken into account.
So you cannot calculate kL using the Wiedemann-Franz's Law., kL is not involved whatsoever in the derivation of this model.
The model which the W-F Law was derived didn't considered the Lattice Thermal part.
What I mean to say is: It is not correct to separate the electronic component and the phononic component of the Thermal Conductivity when you have computed this using the W-F Law. Since the materials the "Law" is applicable for, cannot have an important component of phononic (or lattice thermal ) conductivity., maybe not more than a 20%, if not less, but anyways, will be always an approximation.
Regards!
Dear Ganesh,
how F. Hernandez wrote, the W. F. law cannot applied for the lattice thermal conductivity.
Furthermore, the thermal conductivity cannot be negative. Both components, the electronic and phononic conductivity are additive.
With Regard
R. Mitdank
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