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 remaining 3"p"("q" − 1) are accommodated through the optical branches. This implies that structures with larger "p" and "q" contain a greater number of optical modes and a reduced "λ". From these ideas, it can be concluded that increasing crystal complexity, which is described by a complexity factor CF (defined as the number of atoms/primitive unit cell), decreases λ. This was done by assuming that the relaxation time "τ" decreases with increasing number of atoms in the unit cell and then scaling the parameters of the expression for thermal conductivity in high temperatures accordingly. Describing of anharmonic effects is complicated