Wiedemann-Franz law

Definition

The Wiedemann-Franz law is a fundamental principle in condensed matter physics that relates the thermal and electrical conductivities of metals. It states that the ratio of the thermal conductivity to the electrical conductivity of a metal is proportional to the absolute temperature.

5 Must Know Facts For Your Next Test

1. The Wiedemann-Franz law is an important tool for understanding the behavior of metals and their transport properties.
2. The law is based on the idea that the same charge carriers (typically electrons) are responsible for both the thermal and electrical conductivity in metals.
3. The Lorenz number, which appears in the Wiedemann-Franz law, is a fundamental constant that has been experimentally verified for a wide range of metals.
4. The Wiedemann-Franz law breaks down at low temperatures, where other scattering mechanisms, such as electron-phonon interactions, become dominant.
5. The law has been used to study the electronic structure of materials and to characterize the quality of metal samples.

Review Questions

• Explain the relationship between the thermal and electrical conductivities of metals as described by the Wiedemann-Franz law.
  • The Wiedemann-Franz law states that the ratio of the thermal conductivity to the electrical conductivity of a metal is proportional to the absolute temperature. This relationship arises because the same charge carriers, typically electrons, are responsible for both the thermal and electrical transport in metals. The proportionality constant in this relationship is known as the Lorenz number, which has been experimentally verified for a wide range of metals.
• Describe how the Wiedemann-Franz law can be used to study the electronic structure of materials.
  • The Wiedemann-Franz law provides a way to probe the electronic structure of materials by relating their thermal and electrical transport properties. Deviations from the expected Lorenz number can indicate the presence of additional scattering mechanisms or changes in the electronic structure, such as the formation of energy gaps or the presence of strong electron-electron interactions. By analyzing the temperature dependence of the thermal and electrical conductivities, researchers can gain insights into the underlying electronic properties of the material, which is useful for characterizing the quality of metal samples and understanding the behavior of complex materials.
• Discuss the limitations of the Wiedemann-Franz law and the conditions under which it may not hold true.
  • The Wiedemann-Franz law is known to break down at low temperatures, where other scattering mechanisms, such as electron-phonon interactions, become dominant. In these regimes, the assumption that the same charge carriers are responsible for both thermal and electrical transport is no longer valid. Additionally, the law may not accurately describe the behavior of materials with strong electron-electron interactions or complex electronic structures, where the simple picture of independent charge carriers is insufficient. In such cases, more advanced theoretical models are required to understand the transport properties of the material.

Related terms

Thermal Conductivity:

The ability of a material to conduct heat, measured by the rate at which heat flows through the material.

Electrical Conductivity:

The measure of a material's ability to allow the flow of electric current, which is the rate of movement of electric charge through the material.

Lorenz Number: A constant that represents the proportionality between the thermal and electrical conductivities of a metal, as described by the Wiedemann-Franz law.