GTBL042-10 GTBL042-Callister-v2 August 13, 2007 18:16
10.12 Development of Microstructure in Eutectic Alloys • 361whereCSn(α)andCPb(α)denote the concentrations in weight percent of tin
and lead, respectively, in theαphase. From Example Problem 10.2, these
values are 10 wt% and 90 wt%. Incorporation of these values along with
the densities of the two components yieldsρα=100
11
7 .24 g/cm^3+
89
11 .23 g/cm^3= 10 .59 g/cm^3Similarly for theβphase:ρβ=100
CSn(β)
ρSn+
CPb(β)
ρPb=
100
98
7 .24 g/cm^3+
2
11 .23 g/cm^3= 7 .29 g/cm^3Now it becomes necessary to employ Equations 10.6a and 10.6b to deter-
mineVαandVβasVα=Wα
ρα
Wα
ρα+
Wβ
ρβ=
0. 67
10 .59 g/cm^3
0. 67
10 .59 g/cm^3+
0. 33
7 .29 g/cm^3= 0. 58
Vβ=Wβ
ρβ
Wα
ρα+
Wβ
ρβ=
0. 33
7 .29 g/cm^3
0. 67
10 .59 g/cm^3+
0. 33
7 .29 g/cm^3= 0. 42
10.12 DEVELOPMENT OF MICROSTRUCTURE
IN EUTECTIC ALLOYS
Depending on composition, several different types of microstructures are possible
for the slow cooling of alloys belonging to binary eutectic systems. These possibilities
will be considered in terms of the lead–tin phase diagram, Figure 10.8.
The first case is for compositions ranging between a pure component and the
maximum solid solubility for that component at room temperature [20◦C (70◦F)].
For the lead–tin system, this includes lead-rich alloys containing between 0 and about
2 wt% Sn (for theαphase solid solution), and also between approximately 99 wt%