Page 342 - Materials Science and Engineering An Introduction

314 • Chapter 9 / Phase Diagrams

(for the a phase), and similarly for copper in silver (for the b phase). The solubility
limit for the a phase corresponds to the boundary line, labeled CBA, between the
a/(a + b) and a/(a + L) phase regions; it increases with temperature to a maximum
[8.0 wt% Ag at 779 C (1434 F)] at point B, and decreases back to zero at the melt-
ing temperature of pure copper, point A [1085 C (1985 F)]. At temperatures below
779 C (1434 F), the solid solubility limit line separating the a and a b phase re-
solvus line gions is termed a solvus line; the boundary AB between the a and a L fields is the
solidus line, as indicated in Figure 9.7. For the b phase, both solvus and solidus lines
solidus line
also exist, HG and GF, respectively, as shown. The maximum solubility of copper
in the b phase, point G (8.8 wt% Cu), also occurs at 779 C (1434 F). This horizon-
tal line BEG, which is parallel to the composition axis and extends between these
maximum solubility positions, may also be considered a solidus line; it represents
the lowest temperature at which a liquid phase may exist for any copper–silver alloy
that is at equilibrium.
There are also three two-phase regions found for the copper–silver system
(Figure 9.7): a + L, b + L, and a + b. The a- and b-phase solid solutions coexist for
all compositions and temperatures within the a + b phase field; the a + liquid and b +
liquid phases also coexist in their respective phase regions. Furthermore, composi-
tions and relative amounts for the phases may be determined using tie lines and the
lever rule as outlined previously.
As silver is added to copper, the temperature at which the alloys become
liquidus line totally liquid decreases along the liquidus line, line AE; thus, the melting tem-
perature of copper is lowered by silver additions. The same may be said for silver:
the introduction of copper reduces the temperature of complete melting along
the other liquidus line, FE. These liquidus lines meet at the point E on the phase
diagram, which point is designated by composition C and temperature T E ; for the
E
copper–silver system, the values for these two parameters are 71.9 wt% Ag and
779 C (1434 F), respectively. It should also be noted there is a horizontal isotherm
at 779 C and represented by the line labeled BEG that also passes through point E.
An important reaction occurs for an alloy of composition C E as it changes tempera-
ture in passing through T E ; this reaction may be written as follows:

cooling
The eutectic reaction L(C E ) m a(C aE ) + b(C bE ) (9.8)
(per Figure 9.7) heating

In other words, upon cooling, a liquid phase is transformed into the two solid a and b
phases at the temperature T E ; the opposite reaction occurs upon heating. This is called a
eutectic reaction eutectic reaction (eutectic means “easily melted”), and C E and T E represent the eutectic
composition and temperature, respectively; C aE and C bE are the respective compositions
of the a and b phases at T E . Thus, for the copper–silver system, the eutectic reaction,
Equation 9.8, may be written as follows:

cooling
L(71.9 wt% Ag) m a(8.0 wt% Ag) + b(91.2 wt% Ag)
heating
Often, the horizontal solidus line at T E is called the eutectic isotherm.
Tutorial Video: The eutectic reaction, upon cooling, is similar to solidification for pure components
Eutectic Reaction in that the reaction proceeds to completion at a constant temperature, or isothermally,
Vocabulary and at T E . However, the solid product of eutectic solidification is always two solid phases,
Microstructures whereas for a pure component only a single phase forms. Because of this eutectic reac-
Eutectic tion, phase diagrams similar to that in Figure 9.7 are termed eutectic phase diagrams;
Reaction Terms components exhibiting this behavior make up a eutectic system.