Conduction of electricity

Ultimately the conductivity of a material is decided by how easily the electrons are flowing through the material. Metals have a high conductivity of electricity.

A common way of explaining this is that the regular structure of the metal cations is surrounded by a “sea” of valence electrons. The electrons are very mobile and can thus easily conduct electricity and heat. In the so-called band model the electrons in metals are excited from a filled electron band to an empty electron band. In metals the energy needed to excite an electron to the next band, also called the energy gap, is very small. (Zumdahl 1998, pp. 744) Resistance is, very simplified, caused by the path of the electrons being obstructed, the electrons being slowed down. This effect is also called scattering.

If the temperature is increased the resistivity will increase for metals (Heaney 2003). This is because the scattering will increase with increasing temperature.

Single graphite crystallite consists of structural units as shown in Figure 2-16.

Each of the carbon atoms, grey in Figure 2-16, have four valence electrons available. Three of these valence electrons are used to form the rigid structure inside the graphene layers through forming s-bonds with the three nearest neighboring carbon atom within the plane. These three electrons do not participate in the conduction of electricity. The fourth valence electron has an axis of symmetry that is perpendicular to the graphene layer. (Wallace 1947) These valence electrons form p orbitals, which are important both as the p bonds, which stabilize the graphite layers, and due to the delocalized electrons.

The delocalized electrons in the closely spaced p orbitals are exactly analogous

to the conduction bands found in metals. (Zumdahl 1998) The energy gap is, as for metals, zero (Wallace 1947). This makes the electrons very mobile and the resistivity parallel to the graphene planes very low. However, the electrical resistivity perpendicular to the graphene planes much higher. The ratio between conduction in the two directions is more than 10⁵ (Krishnan and Ganguli 1939).

When heated, the material resistivity increases linearly with temperature. Single crystals of graphite have the same temperature dependence as metals, i.e. the resistivity increases with increasing temperature.

Polycrystalline graphite has a much higher resistivity compared to the single crystalline graphite. Whereas the single-crystalline graphite behaves as a metal, with an energy gap equal to zero, the polycrystalline graphite has a finite energy gap between the occupied valence band and the conduction band, similar to what is found for semiconductors. The degree of graphitization influences the size of the energy gap. Other factors that influence the material resistivity of polycrystalline graphite are listed below.

1) Due to the large ratio between the electrical conductivity parallel and normal to the graphene planes, the preferred direction of conduction is along the carbon crystals, i.e. parallel to the graphene planes.

2) Due to the preferred direction of conduction, the current path is increased due to the orientation of the crystals in relation to each other. The degree of graphitization or ordering of the graphene planes in relation to each other, and orientation of the graphene planes in relation to the axis of the current through the media will largely affect the material resistivity. An extruded graphite rod will have a higher conductivity parallel to the axis of the extrusion, compared to perpendicular to the axis of the extrusion. This is because the graphite crystallites will be oriented parallel to the extrusion axis.

3) The bonding between the crystallites is a barrier that will cause scattering of the electrons. The degree of scattering varies with degree of graphitization.

4) The distance between the graphene planes d₀₀₂ varies, and it is known that d₀₀₂ decreases with increasing crystallite size. A larger d₀₀₂ means fewer graphene planes per unit volume.

5) Micro- and macro porosity, and micro cracks also causes an increased current path. These factors are mainly influenced by the raw materials and production method.

As mentioned in the preceding section, the heat treatment temperature of the carbon material greatly influences the ordering of the carbon material. The heat treatment of the carbon materials also has an impact on the electrical conductivity. Mrozowski (1952) reports that the variation in room temperature resistivity as a function of heat treatment temperature can be divided into three different stages:

< 1000°C - The electrical resistivity decreases several orders of magnitude. This is largely due to the transition from a raw state to a baked carbon. Components such as hydrogen, nitrogen and oxygen are driven off in this region, causing a strong evolution of gasses as well as shrinking of the material. The foreign atoms are barriers for the conduction between crystallites. The concentration of free electrons also increases in this temperature region.

1000°C-2000°C - Only a very small change in the material resistivity is observed.

An increased growth of the crystallites decreases the number of free electrons.

These two effects are counteracting each other, thus causing a minimal change in the material resistivity. This region will stretch to higher temperatures for carbons that are not easily graphitizable.

> 2000°C - A drop in the material resistivity is observed when the carbon sample is graphitized. As the heat treatment temperature is increased further,

the gap between the graphene planes decreases, causing a further decrease in the material resistivity.

The material resistivity of polycrystalline graphite is known to decrease when heated from room temperature as the number of activated electrons increase, i.e.

the number of electrons that excited from the valence band to the conduction band. A minimum in the resistivity is then reached. Above this minimum, the material resistivity increases linearly with increasing temperature, as for the monocrystalline graphite. The temperature of the minimum resistivity varies with the degree of graphitization, decreasing with increasing degree of graphitization. (Mrozowski 1952)

Metallurgical coke is closer to polycrystalline graphite than to single crystalline graphite. The number of obstructions between the graphite crystallites will, however, be higher compared to the polycrystalline graphite. Thus the material resistivity of the metallurgical coke will be higher compared to the polycrystalline graphite. In the temperature range up to 1600°C, which has been the temperature range investigated in this thesis, a minimum in the material resistivity can not be expected to be observed. This is due to the low graphitizability of the coal used to produce metallurgical coke. A minimum in the material resistivity will probably be above 2000°C, which was the temperature of the material resistivity minimum of a baked carbon estimated by Mrozowski (1952).