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 individual matrix elements are not necessarily reciprocals of one another; for example, "σ" may not be equal to 1/"ρ". This can be seen in the Hall effect, where formula_34 is nonzero. In the Hall effect, due to rotational invariance about the z-axis, formula_35 and formula_36, so the relation between resistivity and conductivity simplifies to: If the electric field is parallel to the applied current, formula_34 and formula_40 are zero. When they are zero, one number, formula_41, is enough to describe the electrical resistivity. It is then written as simply formula_9, and this reduces to the simpler expression. According to elementary