The Use of Cooling Curves in the Determination of the Phase Diagram for a Lead-Tin System
Department of Mining, Metallurgical and Materials Engineering University of the Philippines, Diliman
This paper discusses the use of the cooling curves in the determination of the phase diagram of a Lead-Tin system. The inflection points of these cooling curves were obtained by melting a series of mixtures of lead and tin at varying compositions. These critical points were used on a temperature versus percent tin plot, thus obtaining the experimental phase diagram. Comparing the theoretical critical temperatures to the experimental data, percent deviations that ranged from 0.04% to 19.15% were calculated. This large difference in error was due to many factors on the way the experiment was conducted. Errors contributed by the instruments used and the difficulty in determining inflection points from the cooling curves, were all considered. It was analyzed that the reconsideration of such errors could prevent some of the erroneous readings and a better phase diagram can be obtained.
A phase diagram is a graphical representation of
chemical equilibrium. Since chemical equilibrium
is dependent on the composition of the system, the
pressure, and the temperature, a phase diagram
should be able to tell us what phases are in
equilibrium for any composition at any temperature
and pressure of the system .
In the phase diagrams of eutectic systems, the
first addition of either component metal to the other
causes lowering of the melting point, so that the
liquidus curve passes through a temperature
minimum known as the eutectic point .
Three two-phase regions are designated in the
figure above namely, L + α, L + β and α + β. The
three two-phase regions meet at a special kind of
tie-line that is common to all the regions and that
joins the compositions of three conjugate phases
that coexist at the eutectic temperature, the eutectic
reaction isotherm .
This experiment illustrates the use of cooling
curves to establish the phase diagram of a binary
system, lead and tin. The temperature at which
solid phases appear upon cooling various solutions
of the two components are detected by observation
of the changes in slope of the plot of temperature
This experiment also aims to illustrate the use of
cooling curves to establish the phase diagram for a
Figure 1. Lead-Tin Phase Diagram 
For binary systems, two solid phases α and β, are
to be distinguished. These phases may have
identical crystal structures but usually do not; each,
of course, has the crystal structure of the
component with which it is associated .
Figure 2. Cooling curve inflection points 
Using the inflection points from the cooling
curves, position points in the phase diagram can be
determined. These inflection points are called
Tabell, Victor Oliver. Determination of the Phase Diagram for a Lead-Tin System. Page 1 of 4
critical temperatures. Putting together all of the
critical temperatures from each composition of
metal mixture, will result to the construction of
Ten-gram lead-tin samples of different amounts
were weighed. The composition of each sample is
listed in Table 1.
Table 1. Composition of samples
Pb, %Comp Sn, %Comp
Amount of Pb
Amount of Sn
The figures below show the cooling curves of the
eleven different metal mixtures. The curves were
divided into two figures, as showing all the curves
in one graph would create overlapping...
References: New York: McGraw-Hill, 1956. Print.
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