Figure 1. Half and half solder (Pb-50Sn), slowly solidified.

The
microstructure consists of dark grains of the lead-rich phase in a lamellar
eutectic matrix consisting of dark lead-rich regions and light tin-rich
regions. Magnification: approximately 550X [1].
THE BI-SN EQUILIBRIUM PHASE DIAGRAM
Introduction
Equilibrium phase diagrams are one of the single most useful tools of a materials scientist and
engineer. As maps of the temperature ranges and solubility limits of each known phase in the alloy
system, including compounds, they are obviously useful to metal casters, heat treaters and
ceramicists and are an invaluable tool in alloy design, in the development of high-temperature
superconductors and in investigations of practically any temperature dependent property. To one
who is familiar with how these diagrams are generated and especially to those who calculate phase
diagrams they are also representations of a number of basic thermodynamic properties and in
themselves contribute to a better understanding of engineering materials.
There are a number of methods available for establishing a phase diagram. One is x-ray diffraction.
This technique allows one to make direct measurements of the changes in phase at temperature,
allowing one to determine the transformation temperatures, identify the products of these
transformations, and to study the details of the crystallographic aspects of phase transformations.
Electron diffraction, done using a transmission electron microscope, can be used to obtain similar
results, though it is limited to the analysis of very small regions of a specimen and elevated
temperature electron microscopy can be very difficult and expensive. But the most commonly used
methods are based on thermal analysis. These include differential scanning calorimetry (DSC)
which measures the heat energy expelled or adsorbed by the sample as it undergoes phase
transformations and differential thermal analysis (DTA) which carefully measures changes in
heating or cooling behavior as compared to a reference material. Both of these can also be used to
measure fundamental thermodynamic quantities such as heat capacity, enthalpy and entropy.
Dilatometry is another thermal analysis technique which is widely used to measure the coefficient
of thermal expansion but can also determine a transformation temperature by detecting the rapid
change in volume which accompanies a phase transformation. In general, one can devise any
number of bulk and microanalytical methods for establishing a phase diagram by measuring any
change in the sample which accompanies a phase transformation. In practice, the results of a number
of techniques published by many authors are collected and carefully evaluated by the scientific
community before they are made available for more general use and even then you may find
differences in phase diagrams for the same system (compare figures 2 and 3).
The Bi-Sn system is a classic binary eutectic system and is a good example of a system which
exhibits limited solid solubility and no intermediate compounds. Its phase diagram is very similar
to that of the well known Pb/Sn system which provides us with a number of solders, including the
40/60 solder which is widely used in electrical applications. The simplicity of this type of system
combined with the lower melting temperatures and lower toxicity of the Bi/Sn system makes it an
ideal candidate for classroom experiments. As a low melting alloy Bi/Sn alloys are used in
temperature overload devices and as solders in cases where the Pb/Sn solders are not suitable. For
example, they may be used in wave soldering operations where surface mount components make
direct contact with the molten metal, when the heat treatment of the metals being joined can be
altered, when soldering other low melting point alloys such as pewter and when nearby solder joints
might be compromised [2].
Objective
In this experiment the cooling curve method (similar to but simpler than DTA in that it does not
employ a reference) is employed to determine the transformation temperatures for a set of Bi/Sn
samples. These results are then used to construct an equilibrium phase diagram and this phase
diagram is then used to determine the composition of a sample whose composition is unknown.
Preparation
Before actually starting the experiment you should stop to consider the suitability and performance
of the instrumentation, certain aspects of the experimental procedure and to try to anticipate the
experimental results. This will help ensure that the experiment goes well the first time. The
following questions should get you started.
1. Sketch the equilibrium phase diagram for the Bi-Sn system.
2. What are the highest and lowest transformation temperatures you expect to measure when
working with the 0, 10, 30, 50 and 100 weight percent Sn samples?
3. Estimate the value of Seebecks coefficient for a K-type thermocouple for temperatures
between room temperature and 300C? Compare this to Seebecks coefficient for a J-type
thermocouple.
4. Combining questions 2 and 3, what are the lowest and highest voltages you will be
measuring? What voltage resolution will you need to be able to resolve 1C? What is the
voltage resolution of your system?
5. When you put the thermocouple into the molten Bi/Sn mixture the thermocouple will cause
the liquid to cool, possibly solidifying some of it before you can start measuring its cooling
behavior. How do you plan to deal with this?
6. If your reference junction is not working properly, for instance if it is off or if the battery has
died, how much error would you expect to see in your temperature measurements?
7. The molten samples will cool somewhat while you are transferring them from the heater to
the insulated beaker where you will record its cooling behavior. How do you plan to deal
with this?
8. Assuming you have done everything perfectly and the thermocouple is your only source of
error, how large might this temperature error be?
9. If you dont weigh out your Bi and Sn perfectly you would expect the transformation
temperatures you measure to differ from those in the established phase diagrams. How much
error in weighing do you expect to see and how do you plan to deal with this error?
10. Indicate on your sketch (question 1) the sample compositions and transformation
temperatures which will not be effected by errors in weighing out the Bi and Sn for your
samples?
11. Assume your unknown sample has transformation temperatures of 139 and 195C.
Referring to your equilibrium phase diagram you can see that this fits two compositions.
How would you determine the composition of this sample?
Materials
The raw materials you will be using to make your samples are generally reagent grade pure metals
which are in either a granular or shot form. Note the type of metals used, their manufacturers,
purities, form and part numbers.
Equipment
The following is a generic list of the types equipment that may be used in this experiment. Please
make sure you have everything you need before starting the experiment and note exactly what type
of equipment you will be using.
1. A heater capable of heating the test tubes to 400C
2. Test tubes to hold the samples and tongs for handling the hot test tubes
3. Electronic balance with 0.01 gram sensitivity, weigh boats and two spoons
4. Insulated beakers (600 ml beakers filled with glass or ceramic wool)
5. Thermocouples with extension wires and reference junctions
6. Chart recorders or a DMM/scanner connected to a computer or another type of data
acquisition system capable of measuring temperature using thermocouples
7. Containers for disposing of the samples and the test tubes
Safety
This experiment presents minor hazards for all students in the laboratory. Test tubes occasionally
shatter so safety glasses should be worn from the moment the first specimen is heated until the last
one is cool. The specimen materials themselves pose minor hazards due to their toxicity. These
should be handled carefully and disposed of properly. (MSDSs for each chemical are available in
the laboratory.) The most serious hazard is the possibility of being burned by the heater and the hot
test tubes. The ceramic tubes which hold the test tubes are heated to nearly 400C and the test tubes
are often heated to above 300C.
Chemical Hazards There is a hazard associated with the minor toxicity of Sn and Bi.
These materials should not be ingested and proper disposal methods
should be used. Refer to the MSDS for each material.
Physical Hazards Serious burns are possible. The ceramic heater tubes and the
specimens in the test tubes are heated close to 400C. The hot parts
of the heater are labeled accordingly. Test tube clamps should be
used when handling the hot specimens.
The glass test tubes often break and spill the molten metal, especially
when being reheated to remove the thermocouple. Safety glasses and
closed toe shoes must be worn at all times.
Biohazards None.
Radiation Hazards None.
Protective Equipment Recommended: laboratory aprons and long pants.
Required: safety glasses or goggles. Normal eye-glasses are not
acceptable. Open toed shoes will not be allowed.
Procedure
Examine the setup of the experimental equipment. Find out what each part does and how each part
works. Make sure everything is working properly and if possible try a couple of dry runs of the
experiment.
Weigh and mix the pure components to make samples of the specified compositions and the
specified total weight. Transfer the pure components to a test tube and then cover and shake the test
tube to thoroughly mix them. Finally, label each sample immediately to avoid mixing them up.
Note that it might not be possible to weigh out these granular materials as precisely as youd like
so make sure you record the actual composition of each sample.
Carefully and gently melt each sample. Be careful to not overheat them or to heat them for too long
as you might oxidize the sample or damage the test tube. On the other hand, make sure the sample
has completely melted before removing it from the heater and while you dont want to overheat the
sample you should heat it high enough above its liquidus that it doesnt start to solidify before you
can start recording the cooling behavior.
Transfer the test tubes containing the melted samples to the insulated beakers and start recording the
cooling behavior as soon as possible. Continue recording until you are sure that no additional phase
transformations are expected. (Consult an established Bi/Sn phase diagram.) When done remelt the
sample so that you can remove the thermocouple. Clean the thermocouple and dispose of the sample
properly.
Results
A good way to start your analysis of the results is to make a brief qualitative review of the cooling
curves. Which features do they all have in common, which ones are unique and what is the
significance of each of these features? Are there different types of cooling curves and if so what
type is the cooling curve for the unknown sample?
Moving on to the quantitative part of this section of the report, you will have to devise the best
method for reliably and consistently determining the transformation temperatures. Perform this
analysis, organize these results in a table and then plot these data points on an existing phase
diagram. Note the similarities and differences and note the character and the magnitude of the
experimental errors.
Once your own phase diagram is complete you should be able to determine the composition of the
unknown. In your report you will have to explain exactly how you did this and how much error
you think there might be in your result.
Record any other interesting observations you may have made. These notes can be very helpful
when writing your report.
Discussion
This experiment is straightforward and is essentially a duplication of the work of others. Your
discussion will probably start out comparing your phase diagram to established phase diagrams (see
figures 2 and 3) and you may even be able to say which phase diagram youd put more stock in.
Next, you may revisit the issue of experimental error before finally reviewing how the composition
of the unknown was determined and telling the reader how confident he/she can be that your
determination is correct. In general, you will have to convince the reader that you have done a good
set of experiments, constructed a good equilibrium phase diagram and have demonstrated its
usefulness by determining the composition of the unknown sample.
Conclusion
Formulate your own conclusions regarding the quality and utility of the phase diagram you have
constructed. You may have also made other observations which merit a final comment. This is a
good opportunity to make these comments.
References and Other Resources
1. ASM Metals Handbook, Metallography and Microstructures, 9
th
edition, ASM International,
Metals Park, OH, vol.9, p.422, (1986).
2. ASM Metals Handbook, Properties and Selection: Nonferrous and Special-Purpose
Materials, 10
th
edition, ASM International, Metals Park, OH, vol.2, pp.753-757, (1992).
3. ASM Metals Handbook, Alloy Phase Diagrams, 10
th
edition, ASM International, Metals
Park, OH, vol.3, p.106, (1992).
4. Eric Brandes, ed., Smithells Metals Reference, 6
th
edition, Butterworths, London, p11-139
(1983).
5. J.F.Shackelford, Introduction to Materials Science for Engineers, 4
th
edition, Prentice-Hall,
Inc., New Jersey, pp.123-126 (1996).
6. W.D.Callister, Materials Science and Engineering, An Introduction, John Wiley and Sons,
Inc., New York, 3
rd
edition, Chapter 9, (1994).
7. D.R.Askeland, The Science and Engineering of Materials, PWS Publishing Co., Boston,
chapters 9, 10 and 11, (1994).
8. Journal of Phase Equilibrium, ASM International.
Figure 2. ASM Metals Handbooks equilibrium phase diagram for the Bi-Sn system [3].
Figure 3. Smithells Metals References equilibrium phase diagram for the Bi-Sn system
[4].