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

GTBL042-11 GTBL042-Callister-v3 October 4, 2007 11:59

2nd Revised Pages

11.4 Metastable Versus Equilibrium States • 413

Fraction of transformation,

y

Nucleation Growth

t0.5

Logarithm of heating time, t

0

0.5

1.0 Figure 11.10 Plot of fraction

reacted versus the logarithm of

time typical of many solid-state

transformations in which

temperature is held constant.

By convention, the rate of a transformation is taken as the reciprocal of time

required for the transformation to proceed halfway to completion,t 0. 5 ,or

rate=

1

t 0. 5

(11.18)

Transformation

rate—reciprocal of

the halfway-to-

completion

transformation time

Temperature will have a profound influence on the kinetics and thus on the

rate of a transformation. This is demonstrated in Figure 11.11, wherey-versus-logt

S-shaped curves at several temperatures for the recrystallization of copper are shown.

A detailed discussion on the influence of both temperature and time on phase

transformations is provided in Section 11.5.

11.4 METASTABLE VERSUS EQUILIBRIUM STATES

Phase transformations may be wrought in metal alloy systems by varying tem-

perature, composition, and the external pressure; however, temperature changes

by means of heat treatments are most conveniently utilized to induce phase

Time (min)

(Logarithmic scale)

Percent recrystallized

110102 104

0

20

40

60

80

100

135 C 119 C 113 C 102C88C4 3 C

Figure 11.11 Percent recrystallization as a function of time and at constant temperature for

pure copper. (Reprinted with permission fromMetallurgical Transactions, Vol. 188, 1950, a

publication of The Metallurgical Society of AIME, Warrendale, PA. Adapted from B. F.

Decker and D. Harker, “Recrystallization in Rolled Copper,”Trans. AIME,188,1950,

p. 888.)