Characteristics of electrical conduction in Metals

The general characteristics of electrical conduction in metals are summarized as follows:

1) The electrical current density in the steady state is proportional to electric field strength
     (Ohm's law).

2)  For pure specimens, the electric conductivity (σ) and the thermal conductivity (σ') vary with temperature as follows:

      σ∝T⁻¹ and σ' =const (for T > θD); θD is characteristic Debye temperature.

       so that  σ' / σT is independent of temperature (Weidmann-Franz law)

For T < θD;

      σ∝T⁻⁵ and σ' = T⁻² where 'θD' is characteristic Debye Temperature. 

      The relation  ρ∝T⁵ is known as Bloch-Gruneisen T⁵ law.

 3) For metals that exhibit the phenomenon of superconductivity, their resistivity disappears at temperature above 0Kand below critical temperature for superconducting phase transition (critical temp=4.15K) for mercury.

4) For metals containing small amounts of impurities, the electrical resistivity(ρ) may be written as 

                                                          ρ = ρ₀ + ρᴘ(T)

where 'ρ₀' is a constant that increases with increasing impurity content and ρ(T) is temperature dependent part of resistivity. This is known as Mattheissen's rule.

5) For most metals, the electrical resistivity decreases with increasing pressure.

6) The resistivity of alloys that exhibit order-disorder transitions shows pronounced minima corresponding to ordered phases.