LAB REPORT ON LEAD-TIN PHASE EQUILIBIRUMHarsh Menon

The purpose of this lab was to study lead-tin phase equilibrium. This was accomplished by mixing different amounts of lead and tin, heating them to about 800˚F and then letting them cool exposed to air. Once the cooling process had begun, the temperature was recorded every 5 seconds, until the temperature went below 200˚F. The data was then used to generate cooling curves for the different composition alloys. The temperatures at which the slopes of the cooling curves changed were then plotted on the phase-equilibrium diagram.

The different compositions tested in the lab were:

1. Pure Lead2. 10% Tin3. 20% Tin4. 40% Tin5. Eutectic (61.9% Tin)6. 80% Tin7. Pure Tin

The table below lists the different weights of lead and tin used to make the compositions listed above:

Table 1: Weights of lead and tin used in the experiment.

Composition Weight of Lead Weight of TinComposition of

LeadComposition of

Tin  (g) (g) % %

Pure Lead 10 0 100 010% Tin 10 1.11 90 1020% Tin 10 2.5 80 2040% Tin 10 6.67 60 40

61.9% Tin 10 16.25 38.1 61.980% Tin 2.5 10 20 80Pure Tin 0 10 0 100

The table above lists the weights of lead and tin required to make the necessary compositions. However, since we did not restart the experiment every time (i.e., once we had heated and cooled pure lead, we added 1.11g of tin and continued the experiment), we had to ensure that we added the right amount of tin to the specimen. For example, for the 20% tin specimen, since we already had the 10% Tin specimen, we just had to add 1.39 g to the 10% tin specimen to get the required weight of 2.5g.

The lead-tin phase-equilibrium diagram is shown on the next page.

Figure 1: Lead-tin equilibrium phase diagram(Chung, 2002).

The figure above can be used to predict the form of the cooling curves of the different compositions of tin. In the figure above, the alloys with different compositions of tin will show changes in their slopes whenever they cross one of the blue boundaries – which physically represents a change in the phase of the alloy. A change in slope occurs at the liquidus as primary alpha microstructure begins to form. The formation and growth of primary alpha results in the evolution of latent heat of fusion which in turn slows the cooling rate. Therefore, the slope decreases across the liquidus. At the eutectic temperature, a thermal arrest takes place. This happens because the eutectic reaction (which converts the liquid to alpha and beta) takes place at a constant temperature of 183˚C or 361.4˚F. Thus we can predict that both hypoeutectic and hypereutectic alloys will have a change in slope at the liquidus, and the new slope will be followed by an invariant temperature region and then followed by another change in slope. The eutectic alloy’s cooling curve will have a decrease in slope with temperature, followed by the eutectic invariant temperature and then followed by another change in slope.

Pure lead and tin will also have an invariant temperature region. However, for pure lead and pure tin, the invariant temperature region corresponds to a melting region. The corresponding temperature is the melting temperature. Consider the cooling curves of pure tin and pure lead shown on the next page.

Figure 2: Cooling curves for pure lead and pure tin.

The melting temperatures of pure lead and pure tin are determined from investigating the invariant temperature region in the figure above. For pure lead, the melting temperature was determined to be 611˚F and for pure tin, the melting temperature was determined to be 447˚F. In the pure tin cooling curve, there appears to be an initial change in slope at around 658˚F. However, this change in slope is probably an inflexion in the data.

The cooling curve for the 10% alloy is shown below:

Figure 3: Cooling Curve for 10% Tin alloy.

We know that the 10% alloy starts off in a liquid phase, goes to a liquid + alpha mixture, then to an alpha phase and finally to an alpha + beta mixture. Thus, there should be four separate slopes in the figure above, but there are five. This could imply an inflexion in the data at the 350˚F region, since the 10% alloy does not undergo the eutectic reaction (which takes place at 361.4˚F). If this was so, then the first line would represent the liquid phase, the next the liquid + alpha mixture, the third long region would represent the pure alpha phase and the last slope would represent the alpha + beta phase. The experimentally determined transition temperatures are listed below and compared with book values from Askeland & Phulé (2006):

Table 2: Experimental temperatures versus book temperatures for 10% tin alloy.

Experimental Temperature (F)

Book Temperature (F) Percent Difference (%)

Liquid to Alpha + Liquid

611 644 5.1

Alpha + Liquid to Alpha

611 554 10.3

Alpha to Alpha + Beta

352 284 23.9

The table above shows that the experimentally determined values are close to the book values with a maximum percent difference of 23.9%. Possible reasons for deviations from the book values could be due to experimental errors in mixing the lead and tin and uneven heating and cooling.

Consider the cooling curves for the 20% alloy and the 40% alloy shown below:

Figure 4: (a) Cooling Curve for 20% alloy and 40% alloy

The figures above show the same general behavior. Both alloys, start from the liquid phase, and continue in that phase till about 600˚F for the 20% alloy and 480˚F for the 40% alloy. Some of the liquid then precipitates into alpha and the alloys enter an alpha + liquid mixture. The decrease in slope is due to the evolution of latent heat due to the formation and growth of primary alpha microstructure. This continues until the eutectic temperature, which is about 350˚F for both alloys. At this temperature, two solid solutions - alpha and beta, begin to form from the liquid. This continues till all the liquid has been transformed into a mixture of alpha and beta. In terms of microstructure, at the end of the eutectic reaction, there exists primary alpha and the eutectic. The experimentally determined transition temperatures are listed below and compared with book values from Askeland & Phulé (2006):

Table 3: Experimental temperatures versus book temperatures for 20% and 40% tin alloy.

20% alloy Transition

Temperature (F)

20% alloy Book

value (F)

Percent Difference

(%)

40% alloy Transition

Temperature (F)

40% alloy Book

value (F)

Percent Difference

(%)

Liquid to Liquid +

Alpha

600 554 8.3 480 464 3.4

Liquid + Alpha to Eutectic

350 361.4 3.1 350 361.4 3.1

Eutectic to Alpha + Beta

350 361.4 3.1 350 361.4 3.1

The table above shows that for both hypoeutectic alloys, the transition temperatures are close to the book temperatures with a maximum percent difference of 8.3%. The eutectic temperature of 350˚F is also very close to the book value of 361.4˚F.

Now consider the eutectic alloy with 61.9% tin. The cooling curve of the eutectic alloy is shown below:

Figure 5: Cooling curve for eutectic alloy.

The cooling curve of the eutectic alloy should be similar to that of a pure metal since eutectics freeze or melt at a single temperature (as can be seen from Figure 1). The figure above shows a few inflexion regions in the eutectic cooling curve. However, the general form of the curve is similar to that of a metal. There is an initial decline, followed by a region of almost constant temperature, followed by another region of decline. The first region corresponds to the pure liquid phase, the second to the eutectic temperature where all the liquid solidifies to alpha and beta, and the third corresponds to the mixture of alpha and beta. The eutectic temperature determined from the above cooling curve ranges between 410˚F and 350˚F. An average temperature would be 380˚F, which is a 5.1% difference from the book value of 361.4˚F. The inflexions exist at 612˚F, 378˚F, 361˚F and 350˚F.

Finally, consider the cooling curve for the hypereutectic alloy with 80% tin as shown below:

Figure 5: Cooling curve for 80% tin alloy.

The hypoeutectic alloy goes from a liquid phase to a beta + liquid phase, then undergoes the eutectic reaction and turns into a mixture of alpha and beta. There is a gradual change in the first slope of the cooling curve at around 390˚F, followed by an inflexion point and a much lower slope. The first slope corresponds to the liquid phase. This slope is a composite of two slopes with a transition temperature of 607˚F. However, this change in slope is gradual and is probably an inflexion point. The next smaller slope is due to the beta + liquid phase. Right after the beta + liquid slope is the nearly horizontal line corresponding to the eutectic reaction. The final slope is that of the alpha + beta mixture. The experimentally determined transition temperatures are listed on the next page and compared with book values from Askeland & Phulé (2006).

Table 4: Experimental temperatures versus book temperatures for 80% tin alloy.

Experimental Temperature (F)

Book Temperature (F) Percent Difference (%)

Liquid to Beta + Liquid

378 410 7.8

Beta+ Liquid to Eutectic

361 361.4 0.1

Eutectic to Alpha + Beta

350 361.4 3.1

The table above shows that the experimental values are close to the book values with a maximum percent difference of 7.8%.

The transition temperatures from all the different compositions of lead-tin alloys were then plotted on the lead-tin phase equilibrium diagram as shown below:

Figure 6: Transition temperatures on the lead-tin phase equilibrium diagram.

The figure above shows the different transition temperatures and their locations on the phase diagram. Ideally, the data points would lie exactly on the green lines. However, the data points are shifted either forward or back of the green lines. The 10% alloy points (in blue) are ahead of the green curves. In case of the 20% and 40% specimen, the initial data point is ahead of the liquidus, but the second data point is almost on the eutectic temperature line. The eutectic composition has some anomalous data points as well as a data point very close to the eutectic. The hypereutectic alloy has most of its data points in between the green lines, which is unlike those of the other alloys. The pure lead and tin have melting temperatures which match the temperatures on the phase diagram. Some possible reasons for the deviations from the green lines could be incorrect measurement techniques, contamination of specimen, variation of slope with altitude, or a combination of the three.

Further analysis was done on the 40% tin, eutectic and 80% tin alloys by observing them under a scanning electron microscope. The surface of the 40% tin alloy is shown below as seen from the scanning electron microscope:

Figure 6: 40% tin alloy under a scanning electron microscope.

The image above shows certain bright regions that stand out from the rest. The brighter regions represent regions of higher atomic mass, and therefore, represent the lead-rich phase, or the alpha phase. In terms of microstructure, the 40% alloy has primary alpha and eutectic (lamellar) microstructure. Lamellar microstructure is formed by plates of alpha and beta stacked on top of one another. The bright spotted regions represent regions of lamellar microstructure. However, not much can be discerned from this picture.

An image of the eutectic under the microscope did not reveal any useful results either. It can be seen on the next page.

Figure 7: Eutectic alloy under a scanning electron microscope.

The eutectic alloy should have shown the dominant lamellar microstructure formed after undergoing the eutectic reaction. However, none can be seen in the figure above. The 80% tin alloy showed a few bright regions, where lamellar microstructure might have existed. The image can be seen below:

Figure 8: 80% tin alloy under a scanning electron microscope.

The figure above shows certain bright regions. However, the dominant feature of the image appears to be holes or sandpaper particles deposited on the surface of the alloy during grinding.

The 40% tin and 80% tin images were then analyzed to determine the percentage of alpha and beta present in them. Prior to the experiment, calculations were done using the tie line rule on the lead-tin equilibrium phase diagram. The theoretically determined percentages of the alpha and beta in the two specimen are tabulated below:

Table 5: Calculated percentages for 40% and 80% tin alloys.

40% tin alloy 80% tin alloyPercentage of alpha 73.2% 22.3%Percentage of beta 26.8% 77.7%

The images were then analyzed using a software program called SCANDIUM to determine the percent area that each phase occupied in the image. In the case of the 40% tin alloy, the image was cut and reduced to the small region where the spots were the brightest. The figures below show the spotted region of Figure 6 in green and yellow – green representing beta and yellow representing alpha:

(a) (b)Figure 9: (a) 40% tin alloy with original color scheme (b) with tweaked color scheme

The figure to the left shows the alloy with the intensity levels adjusted so that there was a sharp difference between the alpha phase and the beta phase and so that the colors accurately represented the two phases. However, the percentage of alpha and beta obtained from that image were not consistent with the data shown in Table 5. The percentages obtained were 41.3% alpha and 58.70% beta. Therefore, readjustments in the intensity levels were made until the percentages were the same as those in Table 5. The result of this is shown in the figure to the right. The figure to the right has a lot more dark spaces in it than the figure to the left, and this might be a plausible reason why the percentages did not meet up in figure (a).

The same process was repeated for the 80% tin alloy. The images obtained are shown on the next page.

(a) (b)Figure 9: (a) 80% tin alloy with original color scheme (b) with tweaked color scheme

The figure to the left represents the original color scheme, with the team eyeballing what they thought was the best way to adjust the intensity levels so that the two colors accurately represented the phases. However, this yielded an alpha percentage of 13.2% and a beta percentage of 86.8%. The percentages were then tweaked to obtain the same as those in Table 5. The difference appears to be in intensity threshold levels. The image to the right has a few brighter regions than the image to the left. However, trying to adjust the intensity levels and not take the holes in the background is quite a challenge.

References

Chung, D.L. (2002). Retrieved from the State University of New York at Buffalo, Mechanical and Aerospace Engineering website: http://www.mae.buffalo.edu/courses/mae381/lecturenotes/