Page 333 - Materials Science and Engineering An Introduction

9.8 Interpretation of Phase Diagrams • 305

9.8 INTERPRETATION OF PHASE DIAGRAMS
For a binary system of known composition and temperature at equilibrium, at least three
kinds of information are available: (1) the phases that are present, (2) the compositions
of these phases, and (3) the percentages or fractions of the phases. The procedures for
making these determinations will be demonstrated using the copper–nickel system.
Phases Present
The establishment of what phases are present is relatively simple. One just locates the
temperature–composition point on the diagram and notes the phase(s) with which the cor-
responding phase field is labeled. For example, an alloy of composition 60 wt% Ni–40 wt%
Cu at 1100 C would be located at point A in Figure 9.3a; because this is within the a region,
: VMSE
Isomorphous only the single a phase will be present. However, a 35 wt% Ni–65 wt% Cu alloy at 1250 C
(Sb-Bi) (point B) consists of both a and liquid phases at equilibrium.
Determination of Phase Compositions
The first step in the determination of phase compositions (in terms of the concentrations
of the components) is to locate the temperature–composition point on the phase dia-
gram. Different methods are used for single- and two-phase regions. If only one phase
is present, the procedure is trivial: the composition of this phase is simply the same as
: VMSE
Isomorphous the overall composition of the alloy. For example, consider the 60 wt% Ni–40 wt% Cu
alloy at 1100 C (point A, Figure 9.3a). At this composition and temperature, only the a
(Sb-Bi)
phase is present, having a composition of 60 wt% Ni–40 wt% Cu.
For an alloy having composition and temperature located in a two-phase region,
the situation is more complicated. In all two-phase regions (and in two-phase regions
only), one may imagine a series of horizontal lines, one at every temperature; each of
tie line these is known as a tie line, or sometimes as an isotherm. These tie lines extend across
the two-phase region and terminate at the phase boundary lines on either side. To
compute the equilibrium concentrations of the two phases, the following procedure
is used:
1. A tie line is constructed across the two-phase region at the temperature of the alloy.
2. The intersections of the tie line and the phase boundaries on either side are noted.
3. Perpendiculars are dropped from these intersections to the horizontal composition
axis, from which the composition of each of the respective phases is read.
For example, consider again the 35 wt% Ni–65 wt% Cu alloy at 1250 C, located at
point B in Figure 9.3b and lying within the a + L region. Thus, the problem is to deter-
mine the composition (in wt% Ni and Cu) for both the a and liquid phases. The tie line
is constructed across the a + L phase region, as shown in Figure 9.3b. The perpendicular
from the intersection of the tie line with the liquidus boundary meets the composition
axis at 31.5 wt% Ni–68.5 wt% Cu, which is the composition of the liquid phase, C L .
Likewise, for the solidus–tie line intersection, we find a composition for the a solid-
solution phase, C a , of 42.5 wt% Ni–57.5 wt% Cu.

Determination of Phase Amounts
The relative amounts (as fraction or as percentage) of the phases present at equilibrium
may also be computed with the aid of phase diagrams. Again, the single- and two-phase
situations must be treated separately. The solution is obvious in the single-phase region.
: VMSE Because only one phase is present, the alloy is composed entirely of that phase—that
Isomorphous is, the phase fraction is 1.0, or, alternatively, the percentage is 100%. From the previous
(Sb-Bi) example for the 60 wt% Ni–40 wt% Cu alloy at 1100 C (point A in Figure 9.3a), only
the a phase is present; hence, the alloy is completely, or 100%, a.