GTBL042-10 GTBL042-Callister-v2 August 13, 2007 18:16
10.18 The Gibbs Phase Rule • 379Consider the case of single-phase fields on the phase diagram (e.g.,α,β, and
liquid regions). Since only one phase is present,P=1 andF= 3 −P
= 3 − 1 = 2
This means that to completely describe the characteristics of any alloy that exists
within one of these phase fields, we must specify two parameters; these are composi-
tion and temperature, which locate, respectively, the horizontal and vertical positions
of the alloy on the phase diagram.
For the situation wherein two phases coexist, for example,α+L,β+L, and
α+βphase regions, Figure 10.7, the phase rule stipulates that we have but one
degree of freedom sinceF= 3 −P
= 3 − 2 = 1
Thus, it is necessary to specify either temperature or the composition of one of the
phases to define the system completely. For example, suppose that we decide to spec-
ify temperature for theα+Lphase region, say,T 1 in Figure 10.27. The compositions
of theαand liquid phases (CαandCL) are thus dictated by the extremities of the tie
line constructed atT 1 across theα+Lfield. Note that only the nature of the phases
is important in this treatment and not the relative phase amounts. This is to say that
the overall alloy composition could lie anywhere along this tie line constructed at
temperatureT 1 and still giveCαandCLcompositions for the respectiveαand liquid
phases.
The second alternative is to stipulate the composition of one of the phases for
this two-phase situation, which thereby fixes completely the state of the system. For(Cu) Composition (wt% Ag)Temperature (°C)0204060600800LCT 1 + L CL1000400Figure 10.27 Enlarged
copper-rich section of the
Cu–Ag phase diagram in
which the Gibbs phase rule
for the coexistence of two
phases (i.e.,αandL)is
demonstrated. Once the
composition of either phase
(i.e.,CαorCL)orthe
temperature (i.e.,T 1 )is
specified, values for the two
remaining parameters are
established by construction
of the appropriate tie line.