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 is reduced, with this behaviour governed by the Knudsen number, defined as formula_27, where formula_28 is the mean free path of gas molecules and formula_29 is the typical gap size of the space filled by the gas. In a granular material formula_29 corresponds to the characteristic size of the gaseous phase in the pores or intergranular spaces. Isotopically pure diamond can have a significantly higher thermal conductivity, increasing from 2,200 W·m·K (for pure natural diamond, 98.9% C) to 3,320 (for 99.9% enriched), possibly 41,000; with 200,000 "predicted" for 99.999% C.) At the atomic level, there are no simple, correct expressions