# Thermal and electrical conductivity relationship tips

### What is thermal conductivity? (article) | Khan Academy

When a sharp metal tip approaches a conducting surface, a tunnel current is first that the electrical conductivity σ is related to the thermal conductivity κ as, Under these assumptions, the relation between the applied voltage V and the. The materials properties are electrical conductivity, σ, and electrical resistivity, ρ .. The Wiedemann-Franz law states that the ratio of thermal conductivity to the. Electrical, Thermal, Mechanical and Other Properties of Carbon Nanotubes High Electrical Conductivity; Very High Tensile Strength; Highly Flexible- Pressing on the tip of a nanotube will cause it to bend, but without The small diameter and high aspect ratio of CNTs is very favorable for field emission.

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.

## What is thermal conductivity?

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. 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. 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.

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.

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

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.

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. 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. However, making stable electrical contacts to small structures is often difficult and frustrating.

Many things can go wrong when contacts are made particularly if the contact area is small.

### Thermal Conductivity | Definition Thermal Conductivity

Small contacts can be subjected to very high electric fields and current densities. High electric fields can eventually lead to dielectric breakdown. Often this results in the contact resistance changing by a few orders of magnitude. Sometimes the probe tip is melted to the sample and the resistance becomes much lower and sometimes material is ablated away and all electrical contact is lost.

Both of these effects make the contact resistance unstable. Mechanical vibrations of the building and piezo creep of the manipulators cause the probe tips to move and make the contacts unstable. Sometimes chemical reactions take place at the tips. Even in vacuum, there is a thin layer of water on the sample. If the tip and the sample are different materials, an electrochemical cell is formed and applying a voltage between the tip and the sample can etch or oxidize the sample.

Copper - Tin contacts An interesting case is the contact of a tin wire with a copper wire. The value of the resistance fluctuated wildly over a long period of time.

## Educational Resources

This resistance stays constant as the current is increased until at few mA are flowing. The resistance then increases a few orders of magnitude. At a bias voltage of about 1 V the resistance suddenly drops to 20 Ohms. We have put mA through such contacts. If the current is returned to zero and swept slowly again, the resistance is first low and then it gradually increases. At a voltage of about 1 V, there is a sudden transition to low resistance again.

The wires are never strongly bonded together. When they are separated it is often not possible to detect where the point of contact was using the SEM. Some properties of Cu-Sn intermetallic compounds can be found in R. The movie shows a gold wire dark horizontal band in a transmission electron microscope.

A large current is passed through the wire and at a certain point it begins to get narrow and then breaks. Zandbergen Applied Physics Letters 91, One of the tips cuts through a chrome film as it moves. This experiment was done in air under an optical microscope. Since material was only removed at one tip, it cannot be that a high current density causes the metal film to evaporate.

Near the end of the video, the chrome film fails because of the high current density. Regions that get hot in the process turn a lighter color. This will be replaced by the player. A closer look at the tip reveals bubbles appearing at the tip where the cutting took place.