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

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

368 • Chapter 10 / Phase Diagrams

+ L

 + L

C 4

Composition (wt % Sn)

Temperature (

°C)

L

(Pb) (Sn)

18.3 61.9 97.8

100

0

200

300

PRQ



Figure 10.18 The lead–tin

phase diagram used in

computations for relative

amounts of primaryαand

eutectic microconstituents

for an alloy of composition

C′ 4.

composition of 61.9 wt% Sn. Hence, the lever rule is applied using a tie line between

theα−(α+β) phase boundary (18.3 wt% Sn) and the eutectic composition. For

example, consider the alloy of compositionC′ 4 in Figure 10.18. The fraction of the

eutectic microconstituentWeis just the same as the fraction of liquidWLfrom which

it transforms, or

We=WL=

P

P+Q

=

C 4 ′− 18. 3

61. 9 − 18. 3

=

C 4 ′− 18. 3

43. 6

(10.10)

Lever rule expression

for computation of

eutectic

microconstituent and

liquid phase mass

fractions

(compositionC′ 4 ,

Figure 10.18) Furthermore, the fraction of primaryα,Wα′, is just the fraction of theαphase

that existed prior to the eutectic transformation or, from Figure 10.18,

Wα′=

Q

P+Q

=

61. 9 −C 4 ′

61. 9 − 18. 3

=

61. 9 −C 4 ′

43. 6

(10.11)

Lever rule expression

for computation of

primaryαphase

mass fraction

The fractions oftotalα,Wα(both eutectic and primary), and also of totalβ,Wβ,

are determined by use of the lever rule and a tie line that extendsentirely across the

α+βphase field. Again, for an alloy having compositionC′ 4 ,

Wα=

Q+R

P+Q+R

=

97. 8 −C 4 ′

97. 8 − 18. 3

=

97. 8 −C 4 ′

79. 5

(10.12)

Lever rule

expression for

computation of total

αphase mass fraction