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
Thermal conductivity to 10 cm. The phonon mean free path has been associated directly with the effective relaxation length for processes without directional correlation. If V is the group velocity of a phonon wave packet, then the relaxation length formula_31 is defined as: where "t" is the characteristic relaxation time. Since longitudinal waves have a much greater phase velocity than transverse waves, "V" is much greater than "V", and the relaxation length or mean free path of longitudinal phonons will be much greater. Thus, thermal conductivity will be largely determined by the speed of longitudinal phonons. Regarding the dependence of wave velocity