Callister - An introduction - 8th edition

318 • Chapter 9 / Phase Diagrams
Temperature (°C)
1000
T 1
800
C
+ L
C L
L
Figure 9.23 Enlarged
copper-rich section of the
Cu–Ag phase diagram in
which the Gibbs phase rule
for the coexistence of two
phases ( and L) is
demonstrated. Once the
composition of either
phase (C or C L ) or the
temperature (T 1 ) is
specified, values for the
two remaining parameters
are established by
construction of the
appropriate tie line.
600
400
0 20 40 60
(Cu)
Composition (wt% Ag)
For binary systems, when three phases are present, there are no degrees of freedom,
because
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 9.7), it is the horizontal line that extends between points B
and G. At this temperature, 779C, the points at which each of the , L, and phase
fields touch the isotherm line correspond to the respective phase compositions;
namely, the composition of the phase is fixed at 8.0 wt% Ag, that of the liquid at
71.9 wt% Ag, and that of the phase at 91.2 wt% Ag. Thus, three-phase equilibrium
will not be represented 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 779C 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 9.7
F 3 P
3 3 0
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 www.wiley.com/college/callister (Student Companion Site).]