Thermal conductivity heat flow may not be exactly the same as the direction of the thermal gradient. In metals, thermal conductivity approximately tracks electrical conductivity according to the Wiedemann–Franz law, as freely moving valence electrons transfer not only electric current but also heat energy. However, the general correlation between electrical and thermal conductance does not hold for other materials, due to the increased importance of phonon carriers for heat in non-metals. Highly electrically conductive silver is less thermally conductive than diamond, which is an electrical insulator, but due to its orderly array of atoms it is conductive of heat via phonons. The
Electrical resistivity and conductivity inside the conductor. Conductivity is the inverse (reciprocal) of resistivity. Here, it is given by: For example, rubber is a material with large "ρ" and small "σ"—because even a very large electric field in rubber makes almost no current flow through it. On the other hand, copper is a material with small "ρ" and large "σ"—because even a small electric field pulls a lot of current through it. As shown below, this expression simplifies to a single number when the electric field and current density are constant in the material. When the resistivity of a material has a directional component,