Callister - An introduction - 8th edition

352 • Chapter 10 / Phase Transformations
G
0
r*
G * het
G * hom
r
Figure 10.6 Schematic freeenergy-versus-embryo/nucleusradius
plot on which are
presented curves for both
homogeneous and
heterogeneous nucleation.
Critical free energies and the
critical radius are also shown.
homogeneous), and, therefore, heterogeneous nucleation occurs more readily
(Equation 10.10). In terms of the nucleation rate, the N #
-versus-T curve (Figure
10.4c) is shifted to higher temperatures for heterogeneous. This effect is represented
in Figure 10.7, which also shows that a much smaller degree of supercooling
(T) is required for heterogeneous nucleation.
Growth
The growth step in a phase transformation begins once an embryo has exceeded
the critical size, r*, and becomes a stable nucleus. Note that nucleation will continue
to occur simultaneously with growth of the new phase particles; of course, nucleation
cannot occur in regions that have already transformed to the new phase. Furthermore,
the growth process will cease in any region where particles of the new
phase meet, because here the transformation will have reached completion.
Particle growth occurs by long-range atomic diffusion, which normally involves
several steps—for example, diffusion through the parent phase, across a phase
boundary, and then into the nucleus. Consequently, the growth rate G #
is determined
Figure 10.7 Nucleation rate versus temperature for
T m both homogeneous and heterogeneous nucleation.
Degree of supercooling (T ) for each is also shown.
T het
T hom
Temperature
Ṅhet
Ṅ hom
Nucleation rate