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

GTBL042-12 GTBL042-Callister-v2 August 13, 2007 18:22

468 • Chapter 12 / Electrical Properties

Net electron motion

Scattering events

 Figure 12.7 Schematic diagram showing the

path of an electron that is deflected by

scattering events.

continuously increasing with time. However, we know that a current reaches a con-

stant value the instant that a field is applied, indicating that there exist what might be

termed “frictional forces” that counter this acceleration from the external field. These

frictional forces result from the scattering of electrons by imperfections in the crys-

tal lattice, including impurity atoms, vacancies, interstitial atoms, dislocations, and

even the thermal vibrations of the atoms themselves. Each scattering event causes

an electron to lose kinetic energy and to change its direction of motion, as repre-

sented schematically in Figure 12.7. There is, however, some net electron motion in

the direction opposite to the field, and this flow of charge is the electric current.

The scattering phenomenon is manifested as a resistance to the passage of an

electric current. Several parameters are used to describe the extent of this scattering;

mobility these include thedrift velocityand themobilityof an electron. The drift velocityvd

represents the average electron velocity in the direction of the force imposed by the

applied field. It is directly proportional to the electric field as follows:

vd=μee (12.7)

Electron drift

velocity—

dependence on

electron mobility and

electric field intensity The constant of proportionalityμ

eis called the electron mobility, and is an indication

of the frequency of scattering events; its units are square meters per volt-second

(m^2 /V-s).

The conductivityσof most materials may be expressed as

σ=n|e|μe (12.8)

Electrical

conductivity—

dependence on

electron

concentration,

charge, and mobility wherenis the number of free or conducting electrons per unit volume (e.g., per

cubic meter), and|e|is the absolute magnitude of the electrical charge on an electron

(1.6× 10 −^19 C). Thus, the electrical conductivity is proportional to both the number

of free electrons and the electron mobility.

Concept Check 12.1

If a metallic material is cooled through its melting temperature at an extremely

rapid rate, it will form a noncrystalline solid (i.e., a metallic glass). Will the elec-

trical conductivity of the noncrystalline metal be greater or less than its crystalline

counterpart? Why?

[The answer may be found at http://www.wiley.com/college/callister (Student Companion Site).]