The Theory of the Electrical Resistance of Metals

Abstract

From a study of the experimental results of the previous chapter, the following are the main features that emerge regarding the electrical resistance of the metallic elements:

• 1. Metals have low resistivities lying in the range 1.5 to 150 πΩ-cm at room temperature, whereas semiconductors have resistivities that are 10⁶ to 10¹² times larger than these and insulators 10⁶ to 10¹² times larger still.

• 2. To a first approximation the resistivity is linear in temperature for most metals above 0.5θ.

• 3. Below 0.25θ the ideal or thermal component of the resistivity decreases faster than linearly—roughly as T ³ in many metals and as T ⁵ in several others, particularly the monovalent ones.

• 4. Some dependence of the magnitude of the resistivity on position in the periodic table is evident from Table I, both as regards valency and atomic number.

• 5a. The total resistivity is composed of thermal and impurity contributions; in magnetic metals there is a term of magnetic origin as well.

• 5b. The separation of the total resistivity into the above independent components, commonly known as Matthiessen’s rule, may be said to be generally valid [Equation (1.5)].

• 6. In some supposedly pure metals, notably Cu, Ag, Au, and Mg, a minimum occurs in the resistance close to the 5 to 15°K temperature region.

• 7. Nearly half the metals and a good many alloys and compounds become superconducting at low-enough temperatures.