Electrical conductivity

Electrical conductivity or specific conductivity is a measure of a material's ability to conduct an electric current. When an electrical potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current. The conductivity σ is defined as the ratio of the current density $$\mathbf{J}$$ to the electric field strength $$\mathbf{E}$$:


 * $$\mathbf{J} = \sigma \mathbf{E}$$

It is also possible to have materials in which the conductivity is anisotropic, in which case σ is a 3&times;3 matrix (or more technically a rank-2 tensor) which is generally symmetric.

Conductivity is the reciprocal (inverse) of electrical resistivity and has the SI units of siemens per metre (S·m-1) i.e. if the electrical conductance between opposite faces of a 1-metre cube of material is 1 siemens then the material's electrical conductivity is 1 Siemens per metre. Electrical conductivity is commonly represented by the Greek letter σ, but κ or γ are also occasionally used.

An EC meter is normally used to measure conductivity in a solution.

Classification of materials by conductivity

 * A conductor such as a metal has high conductivity.
 * An insulator like glass or a vacuum has low conductivity.
 * The conductivity of a semiconductor is generally intermediate, but varies widely under different conditions, such as exposure of the material to electric fields or specific frequencies of light, and, most important, with temperature and composition of the semiconductor material.

The degree of doping in solid state semiconductors makes a large difference in conductivity. More doping leads to higher conductivity. The conductivity of a solution of water is highly dependent on its concentration of dissolved salts and sometimes other chemical species which tend to ionize in the solution. Electrical conductivity of water samples is used as an indicator of how salt-free or impurity-free the sample is; the purer the water, the lower the conductivity.

Complex conductivity
To analyze the conductivity of materials exposed to alternating electric fields, it is necessary to treat conductivity as a complex number (or as a matrix of complex numbers, in the case of anisotropic materials mentioned above) called the admittivity. This method is used in applications such as electrical impedance tomography, a type of industrial and medical imaging. Admittivity is the sum of a real component called the conductivity and an imaginary component called the susceptivity. 

Temperature dependence
Electrical conductivity is strongly dependent on temperature. In metals, electrical conductivity decreases with increasing temperature, whereas in semiconductors, electrical conductivity increases with increasing temperature. Over a limited temperature range, the electrical conductivity can be approximated as being directly proportional to temperature. In order to compare electrical conductivity measurements at different temperatures, they need to be standardized to a common temperature. This dependence is often expressed as a slope in the conductivity-vs-temperature graph, and can be used:


 * $$\sigma_{T'} = {\sigma_T \over 1 + \alpha (T - T')}$$

where


 * σT&prime; is the electrical conductivity at a common temperature, T&prime;
 * σT is the electrical conductivity at a measured temperature, T
 * α is the temperature compensation slope of the material,
 * T is the measured absolute temperature,
 * T&prime; is the common temperature.

The temperature compensation slope for most naturally occurring waters is about 2 %/°C, however it can range between (1 to 3) %/°C. This slope is influenced by the geochemistry, and can be easily determined in a laboratory.

At extremely low temperatures (not far from absolute 0 K), a few materials have been found to exhibit very high electrical conductivity in a phenomenon called superconductivity.