The Phase Diagram Of Sn Bi System Engineering Essay

Published: Last Edited:

This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.

Soldering is a method where the solder is melted with low temperature in order to connect two pieces of metal. It is very different from welding and brazing process in terms of temperature since it uses much lower temperature compared to both processes. It is used widely in the electronic industry such as in manufacturing electronic devices[ ].This was one of the most important processes back then in late 1980's as it has been used to solder copper water supply pipes. A problem arose when the water supply was contaminated with the lead due to the lead-tin alloys soldering used for to solder copper pipes. As a result, this was very harmful to human as they were relying on the water supply as drinking water. This problem has initiated the study of different composition of alloys that will be used for soldering. SEM or Scanning Electron Microscope has been introduced to this study and this experiment will determine the chemistry of solders and their phases at certain temperature. The captured images from the SEM were analyzed in order to determine the composition of two phases of alloys that are used in soldering.

Materials and Methods

Soldering Process

A propane blow-torch, a wire brush, a flux, a solder, a bucket of water, a spark, a copper pipe, and a solder consists of 90wt%Sn: 10wt%Bi were prepared for this experiment. To ensure that there is no debris, large oxides on the pipe and it fits into the connector, the two surfaces of pipe were cleaned using the wire brush. After that, a small amount flux was brushed on both surfaces to ensure that the flux would wet the copper and it would prevent oxidation to occur. The copper pipe was connected into the connector and both parts were twisted several times in order to prevent oxidation from occurring on the joint. Then, the propane blow-torch was held in the right hand while the solder was held in the left hand. The flame was applied on the thickest section of the joint until the flux was melt. Next, the solder was held on the joint interface and it was left to melt as it touched the heated copper. A small pressure was applied on the solder during this process and as a result from the capillary forces, the solder was drawn into the joint. The solder was left to melt until it displaced all the molten flux and wetted the entire surfaces of interface. After the heating process was completed, the blow-torch was quickly removed and the joint was cooled down ensure that the solder was completely solidified. The joint was also soaked into a bucket of water as another repetition process to cool down the joint. Then, the soldered copper pipes were tested with high water pressure in order to examine whether the soldering was successful or not. To achieve this, the copper pipes were observed if there was any leaking on it.

Scanning Electron Microscope

SEM is one of the microscopic techniques to determine the surface of a certain component using the concept of energy dispersive X-ray [ ]. An electron beam was scattered onto the surface of tin-bismuth alloys of three different compositions: hypoeutectic, hypereutectic, eutectic, and the chemical composition of solder at the room temperature. After the electrons hit the surface, it was bounced back by the surface to the cathode ray tube 1. The function of cathode ray tube was to collect all the electrons and at the same time display the image of the surface of tin-bismuth alloy. All pictures were saved to be analyzed


The volume fraction of a component in a binary system is given by equation 1.


Where VA and VB are the volume fraction A-phase and B-phase, while A and B are the density of each component.

The average density of two components in a binary system is given by equation 2.


Where C1 and C2 are the weight percentage of each component, while 1 and 2 are the density of the pure elements.

The amount of each phase in terms of wt % in a binary system is given by equation 3.


Where Ca is a tie line drawn to phase α, is a tie line drawn to phase β, C1 is the overall composition.


Where C1 and C2 are the composition of two different phases while A1 and A2 are the atomic percentage of two different components.


Figure 1: Sn - Bi Phase Diagram

Estimation of the area fraction:

= 123 / 225 x 100%

Volume fraction = 54.7 %

Figure 2: 30 wt % Sn, 70 wt% Bi

Estimation of area fraction

= 79 / 225 x 100%

Volume fraction = 35.1 %

Figure 3: 43 wt % Sn, 57wt% Bi

Estimation of area fraction

= 33 / 225 x 100%

Volume fraction = 14.67 %

Figure 4: 80 wt % Sn, 20 wt% Bi

Estimation of area fraction

= 7 / 225 x 100%

Volume fraction = 3.1 %

Figure 5: 90 wt % Sn, 10 wt% Bi

Table 1:





Overall composition from

EDS [wt% Bi]

4.88 wt%

67.65 wt%

47.28 wt%

19.55 wt%

Composition of primary phase from EDS

[wt% B i]


92.31 wt%


96.67 wt%

Area fraction of primary

phase, calculated from SEM micrograph [%]





Weight fraction of primary phase calculated from area fraction [wt%]


67.42 wt%


68.84 wt%

Weight fraction of primary phase calculated from tie line drawn on phase diagram [wt%]


34.2 wt%


100 wt%

Composition of Sn-rich phase from EDS

[wt% Bi]

3.50 wt%

15.82 wt%

15.71 wt%

5.12 wt%

Composition of Sn-rich phase as determined from phase diagram [wt% Bi]

3.0 wt%

3.0 wt%

3.0 wt%

3.0 wt%

Weight fraction of total Sn-rich phase calculated from tie line drawn on phase diagram [wt%]

91.8 wt%

29.9 wt%

43.3 wt%

81.4 wt%

Composition of Bi-rich phase from EDS

[wt% Bi]

98.28 wt%

92.31 wt%

95.16 wt%

96.67 wt%

Composition of Bi-rich phase as determined from phase diagram [wt% Bi]

99.0 wt%

99.0 wt%

99.0 wt%

99.0 wt%

Weight fraction of total Bi-rich phase calculated from tie line drawn on phase diagram [wt%]

8.25 wt%

70.10 wt%

56.70 wt%

18.56 wt%


The phase diagram of Sn-Bi system is determined from the slight changes in the cooling curves of each component. First, the freezing point of each component can be determined from the first slight change occurs on the cooling curve. A freezing point takes place when the heat is released to completely solidify the liquid and it also shows the separation of liquid and solid phase. The composition of 60,50,40,30, and 20 wt% tin have the lowest freezing point which is around 138oC compared to other compositions. For other compositions, each of them has different freezing point at different time. The cooling curves are not demonstrated for every single composition of the mixture, however, the rest can be predicted easily as they have a similar pattern. As the composition of tin decreases while the composition of bismuth increases, the freezing point of the alloy is decreasing. However, the freezing point suddenly increases again when the composition is fully dominated by bismuth. From these freezing points, a liquidus line can be constructed in the phase diagram. In addition, the eutectic isotherm can be deduced between the compositions of 20 wt% to 60 wt% tin at 138oC because at this temperature, the (alpha + liquid) phase and (beta + liquid) phase are solidified. As a result, both phases change to one phase of (alpha + beta) and no more liquid phase exist at this point.

The cooling curves do not show the accurate eutectic temperature of the Sn-Bi system. However, it is very close to phase diagram where it indicates that the eutectic temperature is at 138oC while the eutectic temperature based on the phase diagram is at 141oC. The same thing happens to the highest melting point of Bismuth and Tin where the temperature shown by the cooling curves is also close to the phase diagram value. In cooling curves, the highest melting point for Bismuth is around 270oC while the temperature in phase diagram is 275oC. For tin, the highest melting point in cooling curves is 230oC while in the phase diagram is 240oC.

In soldering process, it requires a low temperature to melt the solder compared to other processes such as welding and brazing. Different solder would have different lowest freezing point in the phase diagrams. So, the discovery of eutectic temperature in the phase diagram is essential as it requires the lowest temperature to melt the solder. Yet, the strength of the solder is maintained even though it requires less heat to melt the solder. In a large industrial scale, this feature is very beneficial as it would lessen the cost on natural gas. As a consequence, the amount of natural gas that has to be consumed to generate flame is lowered as well and a low usage of gas would also contribute to reduce negative impacts to the environment.