# Thermal and electrical conductivity relationship help

In metals the things are quite easy because the thermal conductivity is mainly due to the density of electrons and the phonons are almost negligible. But when. Relationship between electrical and thermal conductivity in graphene-based of Sodium Dodecylbenzene Sulfonate (SDBS) by the aid of a bath sonicator for 3. For metals, there's a fairly strong relationship called the Wiedemann–Franz law. For semiconductors and other poorer electrical conductors there's at least a.

## Is there a relationship between electrical conductivity and thermal conductivity?

The thermal conductivity of this metal is, like electrical conductivity, determined largely by the free electrons. Suppose now that the metal has different temperatures at its ends. The electrons are moving slightly faster at the hot end and slower at the cool end. The faster electrons transmit energy to the cooler, slower ones by colliding with them, and just as for electrical conductivity, the longer the mean free path, the faster the energy can be transmitted, i.

In fact, the thermal conductivity is directly proportional to the product of the mean free path and thermal speed. Both thermal and electrical conductivity depend in the same way on not just the mean free path, but also on other properties such as electron mass and even the number of free electrons per unit volume.

The upshot is that the ratio of thermal to electrical conductivity depends primarily on the square of the thermal speed. But this square is proportional to the temperature, with the result that the ratio depends on temperature, T, and two physical constants: Boltzmann's constant, k, and the electron charge, e. Boltzmann's constant is, in this context, a measure of how much kinetic energy an electron has per degree of temperature.

There are simple models that can be used to predict the behaviour of many materials; close parallels exist between thermal and electrical conduction in metals, whereas the conduction mechanisms in non-metals are quite different.

Introduction to conduction It is important to not get confused by conduction, conductivity, resistance, and resistivity.

Resistivity and conductivity - Circuits - Physics - Khan Academy

For an isotropic material: For an actual sample of length l, and cross sectional area A, the resistance, R, is calculated by: Instead, the typical electron drift velocity their average velocity is much lower: This is expanded upon in the Drude model section. Another pertinent reminder is that of potential and current — current is the flow of electrons, and potential is the driving force that makes them flow.

With sufficient potential, electrons may carry charge through any material, including a vacuum see CRTthough they are powerless without any net current flow. The best electrical conductors apart from superconductors are pure copper and pure silver, with resistivities of To understand thermal conductivity in materials, it is important to be familiar with the concept of heat transfer, which is the movement of thermal energy from a hotter to a colder body.

It occurs in several circumstances: When an object is at a different temperature from its surroundings; When an object is at a different temperature to another object in contact with it; When a temperature gradient exists within the object. The direction of heat transfer is set by the second law of thermodynamics, which states that the entropy of an isolated system which is not in thermal equilibrium will tend to increase over time, approaching a maximum value at equilibrium.

This means heat transfer always occurs from a body at a higher temperature to a body at a lower temperature, and will continue until thermal equilibrium is reached. A transfer of thermal energy occurs only through 3 modes: Each mode has a different mechanism and rate of heat transfer, and thus, in any particular situation, the rate of heat transfer depends on how much a certain mode is prevalent. Conduction involves the transfer of thermal energy by a combination of diffusion of electrons and phonon vibrations — applicable to solids.

Radiation involves the transfer of thermal energy by electromagnetic radiation. The sun is a good example of energy transfer through a near vacuum. This TLP focuses on conduction in crystalline solids.

## Wiedemann–Franz law

The best metallic thermal conductors are pure copper and silver. At room temperature, commercially pure copper typically has a conductivity of about Wm-1K-1 although the thermal conductivity of a single crystal of copper was measured at 12, Wm-1K-1 at a temperature of In metals, the movement of electrons dominates the conduction of heat.

The bulk material with the highest thermal conductivity aside from the superfluid helium II is, perhaps surprisingly, a non-metal: The high conductivity is even used to test the authenticity of a diamond. Strong covalent bonds within the molecule are responsible for the high conductivity even though there are no free electrons, heat is conducted by phonons.

Most natural diamonds also contain boron atoms that replace carbon atoms in the crystal matrix, which also have high thermal conductance. Even with advanced models, this rapidly becomes far too complicated to model adequately for a material of macroscopic scale. Additionally, the electrons move in straight lines, do not interact with each other, and are scattered randomly by nuclei.

Rather than model the whole lattice, two statistically derived numbers are used: The Drude model can be visualised using the following simulation.

With no applied field, it can be seen that the electrons move around randomly. Use the slider to apply a field, to see its effect on the movement of the electrons. This animation requires Adobe Flash Player 8 and later, which can be downloaded here. However, it is important to note that for non-metals, multivalent metals, and semiconductors, the Drude model fails miserably.

To be able to predict the conductivity of these materials more accurately, quantum mechanical models such as the Nearly Free Electron Model are required. These are beyond the scope of this TLP Superconductors are also not explained by such simple models, though more information can be found at the Superconductivity TLP. Factors affecting electrical conduction Electrical conduction in most metallic conductors not semiconductors! There are three important cases: Pure and nearly pure metals For pure metals at around room temperature, the resistivity depends linearly on temperature.

Consequently, it is lower in annealed, large crystal metal samples, and higher in alloys and work hardened metals. You might think that at higher temperatures the electrons would have more energy to be able to move through the material, so perhaps it is rather surprising that resistivity increases and conductivity therefore decreases as temperature increases.

The reason for this is that as temperature increases, the electrons are scattered more frequently by lattice vibrations, or phonons, which causes the resistivity to increase. The temperature dependence of the conductivity of pure metals is illustrated schematically in the following simulation.

Use the slider to vary the temperature, to see how the movement of the electrons through the lattice is affected.

### Wiedemann–Franz law - Wikipedia

You can also introduce interstitial atoms by clicking within the lattice. This animation requires Adobe Flash Player 10 and later, which can be downloaded here. Alloys - Solid solution As before, adding an impurity in this case another element decreases the conductivity. Thus, solute atoms with a higher or lower charge than the lattice will have a greater effect on the resistivity.

Thermal conduction metals Metals typically have a relatively high concentration of free conduction electrons, and these can transfer heat as they move through the lattice. Phonon-based conduction also occurs, but the effect is swamped by that of electronic conduction.

The following simulation shows how electrons can conduct heat by colliding with the nuclei and transferring thermal energy. Wiedemann-Franz law Since the dominant method of conduction is the same in metals for thermal and electrical conduction i.

The Wiedemann-Franz law states that the ratio of thermal conductivity to the electrical conductivity of a metal is proportional to its temperature. The thermal conductivity increases with the average electron velocity since this increases the forward transport of energy.

However, the electrical conductivity decreases with an increase in particle velocity because the collisions divert the electrons from forward transport of charge. Ionic conduction For certain materials, there is no net movement of electrons, yet they still conduct electricity. The mechanism is that of ionic conduction, whereby some charged ions can move through the bulk lattice by the usual diffusion mechanisms, except with an electric field driving force. Such ionic conductors are used in solid oxide fuel cells — though for the example of yttria stabilised zirconia YZToperational temperatures are between and degrees C.

Because they conduct by a diffusion like mechanism, higher temperatures lead to higher conductivity, the reverse of what the simple Drude model would predict. Breakdown voltage There is an important, and potentially lethal mechanism by which an insulator can become conductive. In air, it may be commonly recognised as lightning. Gases are commonly ionised in domestic lighting devices.

The most common are fluorescent tubes and neon lights. To initially excite the mercury vapour in a fluorescent tube type light, a voltage spike exceeding the breakdown voltage is needed. This can be noticed when switching such a light on as a sudden ignition, with an associated radio interference spike.

### Is there a relationship between electrical conductivity and thermal conductivity?

A faulty tube may not fully ionise, leading to only a small glow at the ends. Under high voltages, even plexiglass may conduct. The temporarily ionised path is opaque on cooling, giving a Lichtenberg figure in this case. For non metals, there are relatively few free electrons, so the phonon method dominates.

Heat can be thought of as a measure of the energy in the vibrations of atoms in a material. As with all things on the atomic scale, there are quantum mechanical considerations; the energy of each vibration is quantised and proportional to the frequency.

• There was a problem providing the content you requested

A phonon is a quantum of vibrational energy, and by the combination superposition of many phonons, heat is observed macroscopically. The energy of a given lattice vibration in a rigid crystal lattice is quantised into a quasiparticle called a phonon. This is analogous to a photon in an electromagnetic wave; thermal vibrations in crystals can be described as thermally excited phonons, which can be related to thermally excited photons.

Phonons are a major factor governing the electrical and thermal conductivities of a material.

A phonon is a quantum mechanical adaptation of normal modal vibration in classical mechanics. A key property of phonons is that of wave-particle duality; normal modes have wave-like phenomena in classical mechanics but gain particle-like behaviour under quantum mechanics.

This is defined as the lowest possible energy that the system possesses and is the energy of the ground state. If a solid has more than one type of atom in the unit cell, there will be two possible types of phonons: The frequency of acoustic phonons is around that of sound, and for optical phonons, close to that of infrared light.

They are referred to as optical because in ionic crystals they are excited easily by electromagnetic radiation. If a crystal lattice is at zero temperature, it lies in its ground state, and contains no phonons.

When the lattice is heated to and held at a non-zero temperature, its energy is not constant, but fluctuates randomly about some mean value. These energy fluctuations are caused by random lattice vibrations, which can be viewed as a gas of phonons. Because the temperature of the lattice generates these phonons, they are sometimes referred to as thermal phonons.