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

GTBL042-10 GTBL042-Callister-v3 October 4, 2007 11:56

2nd Revised Pages

364 • Chapter 10 / Phase Diagrams

+ L

L

L

+

















Composition (wt% Sn)

Temperature (

°C)

300

200

100

g

f

e

d

x

C 2

L

(C 2 wt% Sn)

C 2 wt% Sn

0 10 203040 50

x

Solvus

line

Figure 10.12 Schematic

representations of the

equilibrium microstructures

for a lead–tin alloy of

compositionC 2 as it is cooled

from the liquid-phase region.

of compositionC 2. Upon crossing the solvus line, theαsolid solubility is exceeded,

which results in the formation of smallβ-phase particles; these are indicated in the

microstructure inset at pointg. With continued cooling, these particles will grow

in size because the mass fraction of theβphase increases slightly with decreasing

temperature.

The third case involves solidification of the eutectic composition, 61.9 wt% Sn

VMSE

Eutectic

(Pb–Sn)

(C 3 in Figure 10.13). Consider an alloy having this composition that is cooled from

a temperature within the liquid-phase region (e.g., 250◦C) down the vertical lineyy′

in Figure 10.13. As the temperature is lowered, no changes occur until we reach

the eutectic temperature, 183◦C. Upon crossing the eutectic isotherm, the liquid

transforms to the twoαandβphases. This transformation may be represented by

the reaction

L(61.9 wt% Sn)Δ

cooling

heating

α(18.3 wt% Sn)+β(97.8 wt% Sn) (10.9)

in which theα- andβ-phase compositions are dictated by the eutectic isotherm end

points.

During this transformation, there must necessarily be a redistribution of the lead

and tin components, inasmuch as theαandβphases have different compositions

neither of which is the same as that of the liquid (as indicated in Equation 10.9). This