GTBL042-10 GTBL042-Callister-v2 August 13, 2007 18:16
10.8 Interpretation of Phase Diagrams • 349mass fractions be represented byWLandWαfor the respective phases. From the
lever rule,WLmay be computed according toWL=
S
R+S
(10.1a)or, by subtracting compositions,WL=
Cα−C 0
Cα−CL(10.1b)Lever rule expression
for computation of
liquid mass fraction
(per Figure 10.3b)
Composition need be specified in terms of only one of the constituents for a binary
alloy; for the computation above, weight percent nickel will be used (i.e.,C 0 = 35
wt% Ni,Cα=42.5 wt% Ni, andCL=31.5 wt% Ni), andWL=
42. 5 − 35
42. 5 − 31. 5
= 0. 68
Similarly, for theαphase,Wα=R
R+S
(10.2a)
Lever rule expression
for computation of
α-phase mass
fraction (per
Figure 10.3b)= (10.2b)C 0 −CL
Cα−CL=
35 − 31. 5
42. 5 − 31. 5
= 0. 32
Of course, identical answers are obtained if compositions are expressed in weight
percent copper instead of nickel.
Thus, the lever rule may be employed to determine the relative amounts or
fractions of phases in any two-phase region for a binary alloy if the temperature
and composition are known and if equilibrium has been established. Its derivation
is presented as an example problem.It is easy to confuse the foregoing procedures for the determination of phase
compositions and fractional phase amounts; thus, a brief summary is warranted.
Compositionsof phases are expressed in terms of weight percents of the components
(e.g., wt% Cu, wt% Ni). For any alloy consisting of a single phase, the composition
of that phase is the same as the total alloy composition. If two phases are present, the
tie line must be employed, the extremities of which determine the compositions of
the respective phases. With regard tofractional phase amounts(e.g., mass fraction of
theαor liquid phase), when a single phase exists, the alloy is completely that phase.
For a two-phase alloy, on the other hand, the lever rule is utilized, in which a ratio of
tie-line segment lengths is taken.