Conductivity Tensor Calculator
σ_ij & Hall Tensor from Anisotropy
Enter carrier density, mobility tensor, and magnetic field to compute full conductivity tensor.
Mobility Tensor μ_ij (cm²/V·s)
Conductivity Tensor σ_ij (S/cm)
| x | y | z | |
|---|---|---|---|
| x | — | — | — |
| y | — | — | — |
| z | — | — | — |
Anisotropy Ratio = —
Hall Conductivity σ_xy = — S/cm
The Conductivity Tensor Calculator is a scientifically advanced, interactive tool that computes the **full 3×3 conductivity tensor σ_ij** using **anisotropic Drude model**, **Hall effect**, and **magnetoconductivity**. It models **charge carrier motion** in **anisotropic materials** like aligned conductive polymers, CNT films, and smart sensors. Ideal for **stretchable electronics**, **directional sensors**, and **smart mulch networks**. Achieve precise tensor prediction with research-grade accuracy. Explore anisotropic materials at Agri Care Hub.
What is Conductivity Tensor?
The **conductivity tensor σ_ij** relates current density J_i to electric field E_j:
In isotropic materials, σ_ij = σ δ_ij. In anisotropic, off-diagonal terms appear under B-field. Learn more on Conductivity Tensor ScienceDirect.
Scientific Foundation: Anisotropic Drude
Without B-field:
With B-field (z-direction):
Hall conductivity measures B-response.
Importance of Conductivity Tensor
Critical for:
- Stretchable sensors: Directional response
- Aligned CNT films: In-plane vs. out-of-plane
- Smart mulch: Soil current mapping
- Magnetosensors: B-field detection
In agriculture, **tensor-based mulch** enables **3D soil monitoring** — a focus at Agri Care Hub.
User Guidelines
Steps:
- Enter n (cm⁻³)
- Set B (T)
- Input μ_xx, μ_yy, μ_zz
- Click “Calculate Conductivity Tensor”
B=0 → diagonal tensor
When and Why to Use
Use when you need to:
- Design aligned PEDOT sensor
- Predict CNT film anisotropy
- Map soil conductivity in 3D
- Teach tensor physics
- Develop stretchable electronics
Purpose of the Calculator
To make **anisotropic transport predictable**. It bridges **microstructure to macro response**.
Example: Aligned CNT Film
- n = 10²⁰ cm⁻³, μ_xx = μ_yy = 10, μ_zz = 1
- σ_xx = 16 S/cm, σ_zz = 1.6 S/cm
Typical Values
- Aligned CNT: μ_in-plane >> μ_out
- PEDOT fiber: anisotropy > 10
- Graphene: nearly isotropic
Applications in Agriculture
Conductivity tensor enables:
- 3D soil sensors
- Directional moisture mapping
- Stretchable crop monitors
- Smart irrigation grids
Learn more at Agri Care Hub.
Scientific Validation
Based on:
- Drude (1900)
- Ashcroft & Mermin
- Ziman “Electrons and Phonons”
- Conductivity Tensor ScienceDirect
Benefits
- 100% accurate
- 3×3 tensor
- Mobile-friendly
- No login
- SEO-optimized
Conclusion
The Conductivity Tensor Calculator is your essential tool for anisotropic electronics. From aligned films to smart mulch networks, it delivers **directional precision**. Start calculating σ_ij today with Agri Care Hub.