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

GTBL042-10 GTBL042-Callister-v2 August 13, 2007 18:16

380 • Chapter 10 / Phase Diagrams

example, if we specifiedCαas the composition of theαphase that is in equilibrium

with the liquid (Figure 10.27), then both the temperature of the alloy (T 1 ) and the

composition of the liquid phase (CL) are established, again by the tie line drawn

across theα+Lphase field so as to give thisCαcomposition.

For binary systems, when three phases are present, there are no degrees of free-

dom, since

F= 3 −P

= 3 − 3 = 0

This means that the compositions of all three phases as well as the temperature are

fixed. This condition is met for a eutectic system by the eutectic isotherm; for the Cu–

Ag system (Figure 10.7), it is the horizontal line that extends between pointsBandG.

At this temperature, 779◦C, the points at which each of theα,L, andβphase fields

touch the isotherm line correspond to the respective phase compositions; namely,

the composition of theαphase is fixed at 8.0 wt% Ag, that of the liquid at 71.9 wt%

Ag, and that of theβphase at 91.2 wt% Ag. Thus, three-phase equilibrium will be

represented not by a phase field, but rather by the unique horizontal isotherm line.

Furthermore, all three phases will be in equilibrium for any alloy composition that

lies along the length of the eutectic isotherm (e.g., for the Cu–Ag system at 779◦C

and compositions between 8.0 and 91.2 wt% Ag).

One use of the Gibbs phase rule is in analyzing for nonequilibrium conditions.

For example, a microstructure for a binary alloy that developed over a range of

temperatures and consisting of three phases is a nonequilibrium one; under these

circumstances, three phases will exist only at a single temperature.

Concept Check 10.8

For a ternary system, three components are present; temperature is also a variable.

What is the maximum number of phases that may be present for a ternary system,

assuming that pressure is held constant?

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

The Iron–Carbon System

Of all binary alloy systems, the one that is possibly the most important is that for

iron and carbon. Both steels and cast irons, primary structural materials in every

technologically advanced culture, are essentially iron–carbon alloys. This section is

devoted to a study of the phase diagram for this system and the development of

several of the possible microstructures. The relationships among heat treatment,

microstructure, and mechanical properties are explored in Chapter 11.

10.19 THE IRON–IRON CARBIDE (Fe–Fe 3 C)

PHASE DIAGRAM

A portion of the iron–carbon phase diagram is presented in Figure 10.28. Pure iron,

upon heating, experiences two changes in crystal structure before it melts. At room

ferrite temperature the stable form, calledferrite,orαiron, has a BCC crystal structure.