Page 353 - Materials Science and Engineering An Introduction

9.13 Equilibrium Diagrams Having Intermediate Phases or Compounds • 325

The fractions of total a, W a (both eutectic and primary), and also of total b, W b , are
determined by use of the lever rule and a tie line that extends entirely across the a + b
phase field. Again, for an alloy having composition C 4 ,
Lever rule expression
for computation of W a = Q + R
total a-phase mass P + Q + R
fraction

= 97.8 - C 4 = 97.8 - C 4 (9.12)
97.8 - 18.3 79.5
and
Lever rule expression
for computation of W b = P
total b-phase mass P + Q + R
fraction
C 4 - 18.3 C 4 - 18.3
= = (9.13)
97.8 - 18.3 79.5
Analogous transformations and microstructures result for alloys having composi-
tions to the right of the eutectic (i.e., between 61.9 and 97.8 wt% Sn). However, below
the eutectic temperature, the microstructure will consist of the eutectic and primary b
microconstituents because, upon cooling from the liquid, we pass through the b liquid
phase field.
When, for the fourth case represented in Figure 9.16, conditions of equilibrium are
not maintained while passing through the a (or b) liquid phase region, the following
consequences will be realized for the microstructure upon crossing the eutectic isotherm:
(1) grains of the primary microconstituent will be cored, that is, have a nonuniform dis-
tribution of solute across the grains; and (2) the fraction of the eutectic microconstituent
formed will be greater than for the equilibrium situation.

9.13 EQUILIBRIUM DIAGRAMS HAVING
INTERMEDIATE PHASES OR COMPOUNDS

The isomorphous and eutectic phase diagrams discussed thus far are relatively sim-
ple, but those for many binary alloy systems are much more complex. The eutectic
copper–silver and lead–tin phase diagrams (Figures 9.7 and 9.8) have only two solid
terminal solid phases, a and b; these are sometimes termed terminal solid solutions because they
solution exist over composition ranges near the concentration extremes of the phase dia-
gram. For other alloy systems, intermediate solid solutions (or intermediate phases)
intermediate solid may be found at other than the two composition extremes. Such is the case for the
solution
copper–zinc system. Its phase diagram (Figure 9.19) may at first appear formidable
because there are some invariant points and reactions similar to the eutectic that
have not yet been discussed. In addition, there are six different solid solutions—two
terminal (a and h) and four intermediate (b, g, d, and P). (The b phase is termed
an ordered solid solution, one in which the copper and zinc atoms are situated in a
specific and ordered arrangement within each unit cell.) Some phase boundary lines
near the bottom of Figure 9.19 are dashed to indicate that their positions have not
been exactly determined. The reason for this is that at low temperatures, diffusion
rates are very slow, and inordinately long times are required to attain equilibrium.
Again, only single- and two-phase regions are found on the diagram, and the same
rules outlined in Section 9.8 are used to compute phase compositions and relative