Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

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12.8 Electrical Resistivity of Metals • 469

12.8 ELECTRICAL RESISTIVITY OF METALS

As mentioned previously, most metals are extremely good conductors of electricity;

room-temperature conductivities for several of the more common metals are con-

tained in Table 12.1. (Table B.9 in Appendix B lists the electrical resistivities of a

large number of metals and alloys.) Again, metals have high conductivities because

of the large numbers of free electrons that have been excited into empty states above

the Fermi energy. Thusnhas a large value in the conductivity expression, Equation

12.8.

At this point it is convenient to discuss conduction in metals in terms of the

resistivity, the reciprocal of conductivity; the reason for this switch should become

apparent in the ensuing discussion.

Since crystalline defects serve as scattering centers for conduction electrons in

metals, increasing their number raises the resistivity (or lowers the conductivity). The

concentration of these imperfections depends on temperature, composition, and the

degree of cold work of a metal specimen. In fact, it has been observed experimentally

that the total resistivity of a metal is the sum of the contributions from thermal

vibrations, impurities, and plastic deformation; that is, the scattering mechanisms act

independently of one another. This may be represented in mathematical form as

follows:

ρtotal=ρt+ρi+ρd (12.9)

Matthiessen’s

rule—for a metal,

total electrical

resistivity equals the

sum of thermal,

impurity, and

deformation

contributions in whichρt,ρi, andρdrepresent the individual thermal, impurity, and deforma-

tion resistivity contributions, respectively. Equation 12.9 is sometimes known as

Matthiessen’s rule Matthiessen’s rule.The influence of eachρvariable on the total resistivity is demon-

strated in Figure 12.8, a plot of resistivity versus temperature for copper and several

copper–nickel alloys in annealed and deformed states. The additive nature of the

individual resistivity contributions is demonstrated at –100◦C.

Influence of Temperature

For the pure metal and all the copper–nickel alloys shown in Figure 12.8, the resistivity

rises linearly with temperature above about –200◦C. Thus,

ρt=ρ 0 +aT (12.10)

Dependence of

thermal resistivity

contribution on

temperature

Table 12.1 Room-Temperature Electrical Conductivities

for Nine Common Metals and Alloys

Electrical Conductivity

Metal [(-m)−^1 ]

Silver 6.8× 107

Copper 6.0× 107

Gold 4.3× 107

Aluminum 3.8× 107

Brass (70 Cu–30 Zn) 1.6× 107

Iron 1.0× 107

Platinum 0.94× 107

Plain carbon steel 0.6× 107

Stainless steel 0.2× 107