Page 338 - Materials Science and Engineering An Introduction

310 • Chapter 9 / Phase Diagrams

liquidus line (point b, ~1260 C). At this point, the first solid a begins to form, which
has a composition dictated by the tie line drawn at this temperature [i.e., 46 wt%
Ni–54 wt% Cu, noted as a(46 Ni)]; the composition of liquid is still approximately
35 wt% Ni–65 wt% Cu [L(35 Ni)], which is different from that of the solid a. With
continued cooling, both compositions and relative amounts of each of the phases
will change. The compositions of the liquid and a phases will follow the liquidus and
solidus lines, respectively. Furthermore, the fraction of the a phase will increase with
continued cooling. Note that the overall alloy composition (35 wt% Ni–65 wt% Cu)
remains unchanged during cooling even though there is a redistribution of copper and
nickel between the phases.
At 1250 C, point c in Figure 9.4, the compositions of the liquid and a phases are
32 wt% Ni–68 wt% Cu [L(32 Ni)] and 43 wt% Ni–57 wt% Cu [a(43 Ni)], respectively.
The solidification process is virtually complete at about 1220 C, point d; the
composition of the solid a is approximately 35 wt% Ni–65 wt% Cu (the overall al-
loy composition), whereas that of the last remaining liquid is 24 wt% Ni–76 wt% Cu.
Upon crossing the solidus line, this remaining liquid solidifies; the final product then
is a polycrystalline a-phase solid solution that has a uniform 35 wt% Ni–65 wt% Cu
composition (point e, Figure 9.4). Subsequent cooling produces no microstructural or
compositional alterations.

Nonequilibrium Cooling
Conditions of equilibrium solidification and the development of microstructures,
as described in the previous section, are realized only for extremely slow cooling
rates. The reason for this is that with changes in temperature, there must be re-
adjustments in the compositions of the liquid and solid phases in accordance with
the phase diagram (i.e., with the liquidus and solidus lines), as discussed. These
readjustments are accomplished by diffusional processes—that is, diffusion in both
solid and liquid phases and also across the solid–liquid interface. Because diffusion
is a time-dependent phenomenon (Section 5.3), to maintain equilibrium during
cooling, sufficient time must be allowed at each temperature for the appropriate
compositional readjustments. Diffusion rates (i.e., the magnitudes of the diffusion
coefficients) are especially low for the solid phase and, for both phases, decrease
with diminishing temperature. In virtually all practical solidification situations,
cooling rates are much too rapid to allow these compositional readjustments and
maintenance of equilibrium; consequently, microstructures other than those previ-
ously described develop.
Some of the consequences of nonequilibrium solidification for isomorphous al-
loys will now be discussed by considering a 35 wt% Ni–65 wt% Cu alloy, the same
composition that was used for equilibrium cooling in the previous section. The por-
tion of the phase diagram near this composition is shown in Figure 9.5; in addition,
microstructures and associated phase compositions at various temperatures upon
cooling are noted in the circular insets. To simplify this discussion, it will be assumed
that diffusion rates in the liquid phase are sufficiently rapid such that equilibrium is
maintained in the liquid.
Let us begin cooling from a temperature of about 1300 C; this is indicated by point
a¿ in the liquid region. This liquid has a composition of 35 wt% Ni–65 wt% Cu [noted
as L(35 Ni) in the figure], and no changes occur while cooling through the liquid phase
region (moving down vertically from point a¿). At point b¿ (approximately 1260 C),
a-phase particles begin to form, which, from the tie line constructed, have a composition
of 46 wt% Ni–54 wt% Cu [a(46 Ni)].
Upon further cooling to point c¿ (about 1240 C), the liquid composition has shifted
to 29 wt% Ni–71 wt% Cu; furthermore, at this temperature the composition of the a