WiedemannFranz

The Wiedemann-Franz law is a principle in solid-state physics that relates electrical conductivity to thermal conductivity in metals. It is named after German physicists Gustav Wiedemann and Rudolf Franz, who formulated it in 1853. The law states that the ratio of the total thermal conductivity κ to the electrical conductivity σ times the absolute temperature T is approximately constant: κ/(σT) ≈ L, where L is the Lorenz number. For many metals at room temperature, L is close to the theoretical value L0 = π^2/3 (k_B/e)^2 ≈ 2.44×10^-8 WΩK^-2.

The law arises from the free-electron model, in which electrons are the dominant carriers of both heat and charge, and scattering processes affect electrons similarly for both transports. Phonons carry heat as well, but in many metals at moderate to high temperatures electronic contributions dominate κ. The law works best for simple, monovalent metals and at temperatures where electron scattering is largely elastic.

Limitations and deviations: the Wiedemann-Franz law can fail at very low temperatures where electron-phonon scattering changes, in metals with strong inelastic scattering, in highly impure or strongly correlated materials, or where phonon contributions to κ are significant. In such cases the measured Lorenz number L can deviate from L0, revealing information about scattering mechanisms and electronic structure.

The law remains a foundational result in metallurgy and condensed matter physics, used to estimate electronic thermal conductivity and to test models of electron transport.