Conductivity – Ability to Conduct Electricity or Heat

1. Introduction

Conductivity refers to a material’s ability to allow the transfer of energy in the form of electrical current or heat. This fundamental property shapes applications across physics, engineering, and materials science. Materials are often classified as conductors, semiconductors, or insulators based on their conductivity values, directly influencing their roles in technology and nature.

Electrical conductivity (σ) quantifies how freely electrons move through a substance when an electric field is applied, forming the basis for electrical systems, electronics, and power networks. Thermal conductivity (κ) denotes the ability to transfer heat—vital for insulation, heat exchangers, and managing temperatures in critical systems.

Conductivity is not a static attribute; it depends on composition, structure, temperature, and impurities. For example, metals usually lose electrical conductivity as temperature rises, while semiconductors become better conductors. These nuances are essential when selecting materials for wiring, insulation, heat sinks, and advanced technologies such as superconductors or thermoelectrics.

2. Key Definitions and Terminology

3. Fundamentals of Conduction

3.1 Electrical Conduction

Electrical conduction is the movement of electric charge (typically electrons) through a material under an applied electric field. In metals, this flow is enabled by the conduction band, where electrons move freely. Insulators have a large band gap, restricting electron movement, while semiconductors have a smaller, tunable gap.

• Usage: All electrical and electronic systems rely on conductive materials for wiring, circuits, and shielding.
• Operation: Free electrons accelerate in an electric field, but their movement is limited by collisions (scattering).
• Equation: ( J = \sigma E ), where J is current density, σ is conductivity, E is electric field.

Typical values:
Copper (σ ≈ 5.96 × 10⁷ S/m), Silver (σ ≈ 6.3 × 10⁷ S/m), Teflon (σ < 10⁻¹² S/m).

3.2 Thermal Conduction

Thermal conduction is the process by which heat flows through a material from hot to cold regions, driven by a temperature gradient.

• In metals: Heat is transferred mainly by free electrons.
• In non-metals: Heat is carried by phonons (lattice vibrations).
• Equation (Fourier’s Law): ( q = -\kappa \frac{dT}{dx} ), where q is heat flux, κ is thermal conductivity, and ( \frac{dT}{dx} ) is the temperature gradient.

Typical values:
Copper (κ ≈ 390–400 W·m⁻¹·K⁻¹), Glass (κ ≈ 0.8 W·m⁻¹·K⁻¹), Air (κ ≈ 0.023 W·m⁻¹·K⁻¹), Diamond (κ ≈ 2200 W·m⁻¹·K⁻¹).

4. Physical Mechanisms and Models

4.1 Conduction in Metals (Drude Model)

The Drude model explains high electrical and thermal conductivities in metals by treating electrons as a “gas” moving freely among fixed positive ions. When an electric field is applied, electrons gain a net drift velocity.

[ \sigma = \frac{n e^2 \tau}{m} ]

Where n is electron density, e is charge, τ is average time between collisions, and m is electron mass.

Limitations: While the Drude model predicts the order of magnitude of conductivity, it cannot explain detailed temperature dependence or phenomena like superconductivity. Modern quantum models account for band structure and electron statistics.

4.2 Conduction in Non-metals (Phonons and Ionic Conduction)

• Phonons: In insulators and ceramics, heat is carried by lattice vibrations. Phonon scattering (by defects or other phonons) limits thermal conductivity.
• Ionic Conduction: In some solids and electrolytes, ions move as charge carriers. This mechanism is crucial in batteries and fuel cells.

Breakdown: High electric fields can cause insulators to become temporarily conductive (dielectric breakdown), as seen in lightning or electrical arcing.

5. Mathematical Models and Equations

5.1 Ohm’s Law and Electrical Conductivity

[ V = I R ] [ R = \rho \frac{l}{A} ] [ \sigma = \frac{1}{\rho} ] [ J = \sigma E ]

These formulas are essential for calculating current, voltage, and resistance in circuits and for selecting materials in electrical systems.

5.2 Fourier’s Law of Heat Conduction

[ \frac{Q}{t} = \kappa A \frac{\Delta T}{d} ]

Used to analyze and design heat flow in solids, critical for thermal management in engineering.

5.3 Wiedemann-Franz Law

[ \frac{\kappa}{\sigma} = L T ]

Where L (Lorenz number) ≈ ( 2.45 \times 10^{-8} ) W·Ω·K⁻² for most metals. It shows that electrons carry both electrical current and heat in metals.

6. Factors Affecting Conductivity

6.1 Material Composition and Structure

• Metals: High conductivity due to free electrons and ordered lattice.
• Non-metals/Amorphous solids: Lower conductivity due to lack of free electrons or disordered structure.
• Alloys: Adding elements increases scattering, reducing conductivity.

Example: Pure copper has much higher conductivity than brass (copper-zinc alloy).

6.2 Temperature Effects

• Metals: Increasing temperature increases atomic vibrations, which scatter electrons and decrease conductivity.
• Semiconductors: Higher temperature increases charge carriers, increasing conductivity.
• Thermal conductivity: In metals, generally decreases with temperature; in non-metals, may peak then drop.

6.3 Impurities, Defects, and Alloying

• Impurities/Defects: Interrupt electron or phonon flow, lowering conductivity.
• Alloying: Deliberate addition of atoms increases electron scattering (increases resistivity).
• Grain boundaries: Scatter carriers, further reducing conductivity in polycrystalline materials.

7. Examples, Data, and Applications

7.1 Electrical Conductors, Insulators, Semiconductors

Applications:

• High conductivity: Used in wiring, busbars, circuit boards, and heat sinks.
• Low conductivity: Used for electrical insulation, thermal barriers, and protective coatings.
• Semiconductors: Used in diodes, transistors, integrated circuits.

7.2 Thermal Conductors and Insulators

Applications:

• High κ: Heat exchangers, engine parts, electronics cooling.
• Low κ: Building insulation, thermal protection in aerospace.

8. Advanced Topics

8.1 Superconductivity

At very low temperatures, some materials exhibit superconductivity—zero electrical resistance and expulsion of magnetic fields. Applications include MRI magnets, maglev trains, and quantum computing.

8.2 Thermoelectrics

Thermoelectric materials enable direct conversion between heat and electricity (Seebeck and Peltier effects). Used in power generation for spacecraft and electronic cooling.

9. Summary

Conductivity—both electrical and thermal—is a cornerstone property in physics and engineering, governing how materials are used in everything from power grids to aircraft insulation. Its value depends on atomic structure, temperature, and purity, and is essential for safe, efficient, and innovative design.

For more information about how to select and use materials based on their conductivity, contact our team or schedule a demo.

Further Reading

• Ashcroft, N. W., & Mermin, N. D. (1976). Solid State Physics.
• Callister, W. D. (2018). Materials Science and Engineering.
• International Electrotechnical Commission (IEC) standards on material properties.

This glossary entry is part of our comprehensive reference for engineers and scientists.