# Thermal and electrical conductivity relationship questions

The first mechanism is based on electrons with strong correlation to the electrical conductivity of solid (for a non metal solid: possibility of a long range. Ask the experts your physics and astronomy questions, read answer archive, and The upshot is that the ratio of thermal to electrical conductivity depends. More fundamental questions arise when you examine the reasons for wide This means that the ratio of thermal to electrical conductivity depends upon the.

Heat can be thought of as a measure of the energy in the vibrations of atoms in a material.

### DoITPoMS - TLP Library Introduction to thermal and electrical conductivity

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. 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.

Thermal phonons can be created or destroyed by random energy fluctuations. It is accepted that phonons also have momentum, and therefore can conduct energy through the lattice.

Unlike electrons, there is a net movement of phonons - from the hotter to the cooler part of the lattice, where they are destroyed. Electrons must maintain charge neutrality in the lattice, so there is no net movement of electrons during thermal conduction. The following simulation shows schematic optical and acoustic phonons in a 2D lattice, and has the option to animate a 2D wavevector defined by clicking inside the green box.

Umklapp scattering When two phonons collide, the resulting phonon has the vector sum of their momenta.

The way of treating particles moving in a lattice quantum mechanically under the reduced zone scheme which is beyond the scope of this TLP but is explored in more depth in the Brillouin Zones TLPleads to a conceptually strange effect. If the momentum is too great outside the first Brillouin zone then the resulting phonon moves in almost the opposite direction.

This is Umklapp scattering, and is dominant at higher temperatures- acting to reduce thermal conductivity as the temperature increases. Applications Silicon chips As electrical properties vary with microstructure, a type of computer memory called phase-change random-access memory PC-RAM has been developed.

## What is thermal conductivity?

The amorphous state is semiconducting, while in a poly crystalline form it is metallic. Heating above the glass transition, but below the melting point, crystallises a previously semiconducting amorphous cell.

Likewise, fully melting, then rapidly cooling a cell leaves it in the metallic crystalline state. This variation of resistivity with microstructure is crucial to the operation of such devices. This allows for multiple distinguishable levels of resistance per cell, increasing the storage density, and reducing the cost per megabyte.

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

The more common problem with silicon devices is dissipating heat. A modern processor has a thermal design power of above 70w Intel i722 nm process. It is common for heat sinks to have a copper block attached to the microprocessor casing by thermal paste, and pressure. The bulk of the heat sink is usually made from much cheaper aluminium, though the high thermal conductivity of copper is necessary for the interface.

Thermal paste, whilst a better thermal conductor than air, is much worse than most metals, so it is only used as a thin layer to replace air gaps. Conduction is not the most efficient method to carry heat to a separate heat sink, so convection and the latent heat of evaporation can be used.

Heat pipes, typically made from copper are filled with a low boiling point liquid, which boils at the hot end, and condenses at the cool end of the pipe.

This is a much faster way of transferring heat over longer distances.

Space There are many applications of thermal insulators, with development coming from attempts to improve bulk mechanical properties, while retaining insulating properties, i. They are such good insulators, that the outside may glow red-hot, while inside the shuttle the astronauts are still alive.

One of the best thermal insulators is silica aerogel. An aerogel is an extremely low-density solid-state material made from a gel where the liquid phase of the gel has been replaced with gas. The result is an extremely low density solid, which makes it effective as a thermal insulator.

One use of aerogels is for a lightweight micrometeorite collector, aerogel was used. While extremely light, it is strong enough to capture micrometeors. Matches stay cool millimetres from a blowtorch, a large array of aerogel bricks is ready to be launched into space, and the resulting space dust is photographed upon return to earth Aerogels can be made from a variety of materials, but share a universal structure style.

However, a common material used is silicate. Silica aerogels were first discovered in Aerogels have extreme structures and extreme physical properties. The highly porous nature of an aerogel structure provides a low density. Aerogels are good thermal insulators because they eliminate the three methods of heat transfer convection, conduction and radiation. They are good convective insulators due to the fact that air cannot circulate throughout the lattice. Silica aerogel is an especially good conductive insulator because silica is a poor conductor of heat - a metallic aerogel, on the other hand, would be a less effective insulator.

Carbon aerogel is an effective radiative insulator because carbon is able to absorb the infrared radiation that transfers heat.

Hence, for maximum thermal insulation, the best aerogel is silica doped with carbon. Power transmission One of the largest scale uses of electrical conductors is in power transmission. Unfortunately, the properties that are desirable for a strong cable seem opposed to those for a good conductor. There are a huge variety of steels, but again, the interstitial carbon atoms increase the resistance compared to pure iron.

This means that a larger diameter cable is needed, which, due to the density of steel, ends up being very heavy and expensive. Heavier cable also means we must construct additional pylons, which is a large component of the cost. Copper, while appropriate for home wiring, is dense, and increasingly expensive. For most overhead power cables, the solution is to use two materials — a steel core, surrounded by many individual aluminium cores.

This achieves light, high strength, and acceptable conductivity cables. Superconductors have been trialled for power transmission, though only underground, and at a considerably higher cost and efficiency! Thermoelectric effect The thermoelectric effect is the direct conversion of a difference in temperature into electric voltage and vice versa.

Simply put, a thermoelectric device creates a voltage when there is a different temperature on each side of the device.

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

This effect can be used to generate electricity, to measure temperature, to cool objects, or to heat them. Because the sign of the applied voltage determines the direction of heating and cooling, thermoelectric devices make very convenient temperature controllers. The Peltier effect is that when a direct current flows through a metal-semiconductor junction, and heat is either absorbed or released. This is because the average energy of electrons in the two materials is different, and heat makes up this difference.

A fuller understanding requires knowledge of the band structure, explored further in the TLP on Semiconductors. Summary We have now gone over the foundation behind electrical and thermal conduction, as well as some of the more common applications.

You should understand the role of electrons and phonons in thermal conduction, as well as how the interactions between them lead to changes in electrical conductivity with temperature.

You should appreciate that metals have more heat transfer mechanisms than their non-metal counterparts, therefore explaining why they have higher thermal conductivity.

Also, this TLP should have touched on some of the major applications of thermal and electrical conductors and insulators. Finally, the connections between thermal and electrical conductivity in metals have been made, including the Wiedemann-Franz Law.

To summarise the factors affecting conductivity: Temperature — as temperature increases, the average energy per phonon increases, and by the umklapp scattering mechanism, thermal conductivity is decreased.

Phonons also scatter electrons more. Electron density in metals — if electrons are the conductors, more valence electrons usually leads to better conduction. Alloying — interstitials scatter electrons, and decrease conductivity. Phase boundaries, impurities, dislocations, etc. Please follow this link if you would like to provide a short review for this TLP Questions Quick questions You should be able to answer these questions without too much difficulty after studying this TLP.

If not, then you should go through it again! For phonons, the normal modes a Gain particle like behaviour under quantum mechanics. The resistance depends on the specific type of metal we're dealing with. The greater the distance an electron can travel without bumping into an ion core, the smaller is the resistance, i.

The average distance an electron can travel without colliding is called the 'mean free path. The electrons which are free to respond to the electric field have a thermal speed a sizable percentage of the speed of light, but since they travel randomly with this high speed, they go nowhere on average, i.

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.