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 the electronic thermal conductivity when the electrochemical potential gradient inside the sample is zero, as a starting point. As next step the transport coefficients are written as following where formula_56 and "a" the Bohr radius. The dimensionless integrals "I" are defined as where "s"("x") is the dimensionless transport distribution function. The integrals "I" are the moments of the function where "x" is the energy of carriers. By substituting the previous formulas for the transport coefficient to the equation for "λ" we get the following equation From the previous equation we see that "λ" to be zero the bracketed term