# Interesting News – Vanadium Dioxide Violates the Wiedemann-Franz Law

It is an interesting news on conduction heat transfer.

The new article reports that vanadium dioxide conducts electricity much better than it conducts heat at near room temperature:

Abstract

In electrically conductive solids, the Wiedemann-Franz law requires the electronic contribution to thermal conductivity to be proportional to electrical conductivity. Violations of the Wiedemann-Franz law are typically an indication of unconventional quasiparticle dynamics, such as inelastic scattering, or hydrodynamic collective motion of charge carriers, typically pronounced only at cryogenic temperatures. We report an order-of-magnitude breakdown of the Wiedemann-Franz law at high temperatures ranging from 240 to 340 kelvin in metallic vanadium dioxide in the vicinity of its metal-insulator transition. Different from previously established mechanisms, the unusually low electronic thermal conductivity is a signature of the absence of quasiparticles in a strongly correlated electron fluid where heat and charge diffuse independently.

 Wiedemann–Franz(-Lorenz) Law

In solids, heat is transported by vibrations of the solid lattice (Phonon contribution) and motion of free electrons (Electronic contribution). In metals, thermal energy transport by electrons predominates. Thus, good electrical conductors are also good thermal conductors as the Wiedemann–Franz law states that:

\frac{\lambda}{\sigma} = LT \tag{1}

• $$\lambda$$: thermal conductivity
• $$\sigma$$: electrical conductivity
• $$T$$: absolute temperature
• $$L$$: Lorenz number ($$=2.45 \times 10^{-8}$$) [$${\rm W}\Omega/{\rm K}^2$$]

The news reports that vanadium dioxide does not obey this empirical law.

 Related Topics and Refereces (Japanese)

## Author: fumiya

CFD engineer in Japan

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