# Electrical Conductivity and Resistivity

It is well known that one of the subatomic particles of an atom is the electron. The electrons carry a negative electrostatic charge and under certain conditions can move from atom to atom. The direction of movement between atoms is random unless a force causes the electrons to move in one direction. This directional movement of electrons due to an electromotive force is what is known as electricity.

## Electrical Conductivity

Electrical conductivity is a measure of how well a material accommodates the movement of an electric charge. It is the ratio of the current density to the electric field strength. Its SI derived unit is the **Siemens per meter**, but conductivity values are often reported as percent IACS. IACS is an acronym for International Annealed Copper Standard, which was established by the 1913 International Electrochemical Commission. (More Information on the IACS.) The conductivity of the annealed copper (5.8001 x 10^{7}S/m) is defined to be 100% IACS at 20°C . All other conductivity values are related back to this conductivity of annealed copper. Therefore, iron with a conductivity value of 1.04 x 10^{7} S/m, has a conductivity of approximately 18% of that of annealed copper and this is reported as 18% IACS. An interesting side note is that commercially pure copper products now often have IACS conductivity values greater than 100% IACS because processing techniques have improved since the adoption of the standard in 1913 and more impurities can now be removed from the metal.

Conductivity values in Siemens/meter can be converted to % IACS by multiplying the conductivity value by 1.7241 x10^{-6}. When conductivity values are reported in microSiemens/centimeter, the conductivity value is multiplied by 172.41 to convert to the % IACS value.

Electrical conductivity is a very useful property since values are affected by such things as a substances chemical composition and the stress state of crystalline structures. Therefore, electrical conductivity information can be used for measuring the purity of water, sorting materials, checking for proper heat treatment of metals, and inspecting for heat damage in some materials.

## Electrical Resistivity

Electrical resistivity is the reciprocal of conductivity. It is the is the opposition of a body or substance to the flow of electrical current through it, resulting in a change of electrical energy into heat, light, or other forms of energy. The amount of resistance depends on the type of material. Materials with low resistivity are good conductors of electricity and materials with high resistivity are good insulators.

The SI unit for electrical resistivity is the ohm meter. Resistivity values are more commonly reported in micro ohm centimeters units. As mentioned above resistivity values are simply the reciprocal of conductivity so conversion between the two is straightforward. For example, a material with two micro ohm centimeter of resistivity will have ½ microSiemens/centimeter of conductivity. Resistivity values in microhm centimeters units can be converted to % IACS conductivity values with the following formula:

172.41 / resistivity = % IACS

**T**emperature Coefficient of Resistivity

As noted above, electrical conductivity values (and resistivity values) are typically reported at 20 ^{o}C. This is done because the conductivity and resistivity of material is temperature dependent. The conductivity of most materials decreases as temperature increases. Alternately, the resistivity of most material increases with increasing temperature. The amount of change is material dependent but has been established for many elements and engineering materials.

The reason that resistivity increases with increasing temperature is that the number of imperfection in the atomic lattice structure increases with temperature and this hampers electron movement. These imperfections include dislocations, vacancies, interstitial defects and impurity atoms. Additionally, above absolute zero, even the lattice atoms participate in the interference of directional electron movement as they are not always found at their ideal lattice sites. Thermal energy causes the atoms to vibrate about their equilibrium positions. At any moment in time many individual lattice atoms will be away from their perfect lattice sites and this interferes with electron movement.

When the temperature coefficient is known, an adjusted resistivity value can be computed using the following formula:

$R_{1}=R_{2}[1+a \times (T_{1}-T_{2})]$

Where: R_{1} = resistivity value adjusted to T_{1}

R_{2} = resistivity value known or measured at temperature T_{2 }a = Temperature Coefficient

T_{1} = Temperature at which resistivity value needs to be known

T_{2} = Temperature at which known or measured value was obtained

For example, suppose that resistivity measurements were being made on a hot piece of aluminum. Normally when measuring resistivity or conductivity, the instrument is calibrated using standards that are at the same temperature as the material being measured, and then no correction for temperature will be required. However, if the calibration standard and the test material are at different temperatures, a correction to the measured value must be made. Presume that the instrument was calibrated at 20^{o}C (68^{o}F) but the measurement was made at 25^{o}C (77^{o}F) and the resistivity value obtained was 2.706 x 10^{-8} ohm meters. Using the above equation and the following temperature coefficient value, the resistivity value corrected for temperature can be calculated.

$R_{1}=R_{2}[1+a \times (T_{1}-T_{2})]$

Where: R_{1} = ?

R_{2} = 2.706 x 10^{-8} ohm meters (measured resistivity at 25 ^{o}C)

a = 0.0043/ ^{o}C

T_{1} = 20 ^{o}C

T_{2} = 25 ^{o}C

R_{1} = 2.706 x 10^{-8}ohm meters * [1 + 0.0043/ ^{o}C * (20 ^{o}C – 25 ^{o}C)]

R_{1} = 2.648 x 10^{-8}ohm meters

Note that the resistivity value was adjusted downward since this example involved calculating the resistivity for a lower temperature.

Since conductivity is simply the inverse of resistivity, the temperature coefficient is the same for conductivity and the equation requires only slight modification. The equation becomes:

$s_{1}=s_{2}/[1+a \times (T_{1}-T_{2})]$

Where: s_{1} = conductivity value adjusted to T_{1}

s_{2} = conductivity value known or measured at temperature T_{2 }a = Temperature Coefficient

T_{1} = Temperature at which conductivity value needs to be known

T_{2} = Temperature at which known or measured value was obtained

In this example let’s consider the same aluminum alloy with a temperature coefficient of 0.0043 per degree centigrade and a conductivity of 63.6% IACS at 25 ^{o}C. What will the conductivity be when adjusted to 20 ^{o}C?

s_{1}= 63.6% IACS / [1 + 0.0043 * (20 ^{o}C – 25 ^{o}C)]

s_{1}= 65.0% IASC

The temperature coefficient for a few metallic elements is shown below.

Material | Temperature Coefficient (/ ^{o}C) |

Nickel | 0.0059 |

Iron | 0.0060 |

Molybdenum | 0.0046 |

Tungsten | 0.0044 |

Aluminum | 0.0043 |

Copper | 0.0040 |

Silver | 0.0038 |

Platinum | 0.0038 |

Gold | 0.0037 |

Zinc | 0.0038 |