Temperature Dependence of Electrical Resistivity of Metals

A general formula for the electrical resistivity of metals is obtained. This formula is applicable to any metals. When it is applied to crystalline metals, the usual phonon scattering resistivity is derived. When it is applied to amorphous or disordered metals, an increase in T 2 is predicted at low temperatures in addition to the increase in T 5 . The coefficient of the T 2 -term is shown to be proportional to the residual resistivity. For highly resistive metals, it is shown that the usual phonon scattering is suppressed, and that the temperature dependence of the resistivity becomes small: A kind of random phase model for the resistivity is presented. It is also shown that the resistivity due to impurity scattering increases in T 2 at low temperatures and increases in (- T ) -1 at high temperatures. The theory can also explain the saturation behavior of the resistivity with increasing temperatures observed in A -15 compounds.