By Arya Hakimian, Application Scientist
The Wiedemann–Franz Law describes a proportional relationship between a material’s ability to conduct heat and its ability to conduct electricity. It is expressed mathematically as:
Where:
- k is the thermal conductivity (W/m·K)
- σ is the electrical conductivity (S/m)
- T is the absolute temperature (K)
- L is the Lorenz number, typically valued at:
This law assumes that free electrons are the primary carriers of both heat and electrical current. This assumption holds true for pure metals and simple metallic alloys, especially at moderate temperatures.
The Wiedemann–Franz Law arises from the free electron model of metals, where electrons behave like a gas of charged particles. These electrons transport both energy (as heat) and charge (as electricity). The law reflects that the exact scattering mechanisms, such as collisions with atoms or impurities, affect both types of transport similarly.
The Lorenz number is derived from quantum statistical mechanics, specifically the Sommerfeld theory, which refines the classical Drude model by incorporating Fermi-Dirac statistics.
Why is This Law Important?
1. Thermoelectric Materials Research
In thermoelectrics, the goal is to convert heat into electricity (or vice versa) efficiently. The Wiedemann–Franz Law helps researchers understand the trade-offs between electrical and thermal conductivity. Materials with high electrical conductivity but low thermal conductivity are ideal, and deviations from the law can signal promising thermoelectric behavior.
2. Electronics and Semiconductor Design
In microelectronics, managing heat is critical. Conductive pathways (like copper traces) must dissipate heat efficiently to prevent overheating. The law allows engineers to estimate thermal performance based on electrical measurements.
3. Quality Control and Diagnostics
In industrial settings, deviations from expected Wiedemann–Franz behavior can indicate a material’s impurities, defects, or phase changes.
Limitations and Considerations
While it can be helpful, the Wiedemann–Franz Law has its boundaries. It makes several assumptions that can present challenges in the practical implementation of its use:
- Material Type: Pure metals and simple alloys. In semiconductors or insulators, phonons (vibrational energy carriers) dominate heat transport. EV Motors, for example, use a mix of metals, including complex alloys which are engineered for high-performance.
- Temperature Range: Typically valid from room temperature up to a few hundred degrees Celsius. At very low or very high temperatures, electron scattering mechanisms change, affecting the Lorenz number.
- Electron Scattering: The law assumes minimal scattering from impurities or lattice vibrations. In real-world materials, especially those with complex microstructures, this assumption may not hold.
Figure 1: Schematic of an Electric Motor Showing Various Components
Conclusion
The Wiedemann–Franz Law remains a helpful equation in calculating the thermal and electrical transport properties of materials. While it offers a practical shortcut for thermal conductivity by providing estimates, direct measurements are always strongly recommended.
Interested in Learning More?
Whether you’re working with electrically insulating materials in electric motor applications or exploring metallic systems where the Wiedemann–Franz Law applies, C-Therm Technologies provides the precision and flexibility you need with industry-leading thermal conductivity solutions. If you want to learn more about C-Therm and our thermal conductivity testing products, contact us directly at info@ctherm.com and book a FREE technical consultation with a subject matter expert today.
If you are in need of testing support, C-Therm’s lab division, Thermal Analysis Labs, offers contract testing services using Trident and other advanced methods. For expert support in characterizing your materials, contact the team at info@thermalanalysislabs.com.
About the Author
Arya Hakimian is C-Therm’s resident Application Specialist. He has extensive experience in thermal analysis and materials characterization, and he holds a MSc in Chemistry and BSc in Medicinal and Pharmaceutical Chemistry from the University of New Brunswick.