Copper greater strength than monocrystalline forms. The softness of copper partly explains its high electrical conductivity (59.6×10 S/m) and high thermal conductivity, second highest (second only to silver) among pure metals at room temperature. This is because the resistivity to electron transport in metals at room temperature originates primarily from scattering of electrons on thermal vibrations of the lattice, which are relatively weak in a soft metal. The maximum permissible current density of copper in open air is approximately 3.1×10 A/m of cross-sectional area, above which it begins to heat excessively. Copper is one of a few metallic elements with a
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