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

GTBL042-17 GTBL042-Callister-v2 September 14, 2007 9:36

Revised Pages

17.2 Heat Capacity • 707

Normal lattice positions for atoms

Positions displaced because of vibrations

Figure 17.1

Schematic

representation of the

generation of lattice

waves in a crystal by

means of atomic

vibrations. (Adapted

from “The Thermal

Properties of

Materials” by

J. Ziman. Copyright

©c1967 by Scientific

American, Inc. All

rights reserved.)

The vibrational thermal energy for a material consists of a series of these elastic waves,

which have a range of distributions and frequencies. Only certain energy values are

allowed (the energy is said to be quantized), and a single quantum of vibrational

phonon energy is called aphonon.(A phonon is analogous to the quantum of electromagnetic

radiation, thephoton.) On occasion, the vibrational waves themselves are termed

photon phonons.

The thermal scattering of free electrons during electronic conduction (Section

12.7) is by these vibrational waves, and these elastic waves also participate in the

transport of energy during thermal conduction (see Section 17.4).

Temperature Dependence of the Heat Capacity

The variation with temperature of the vibrational contribution to the heat capacity

at constant volume for many relatively simple crystalline solids is shown in Figure

17.2. TheCvis zero at 0 K, but it rises rapidly with temperature; this corresponds

Temperature (K)

Heat capacity,

Cv

(^00) D
3 R Figure 17.2 The temperature dependence
of the heat capacity at constant volume;θD
is the Debye temperature.