The Effects of Thermal Conductivity on Bismuth Crystal Size

Introduction and Review of Literature

Bismuth crystals are extremely rare to find in nature. These natural crystals are dull gray in color and are typically very small. Most bismuth crystals available to collectors are artificially grown. Artificial growing produces strange hopper crystals with all the colors of the spectrum. They are truly a beautiful sight. This topic area was discovered while observing a rock and mineral collection. The tag on the specimen in the collection read, “BISMUTH GROWN IN W. GERMANY.” The idea that the crystals had to be synthetically grown sparked curiosity. Further research was done to find out the difficulty of growing these crystals. The findings showed that these crystals could be quickly grown without the need for special equipment. This experiment was chosen because of the simplicity at which the crystals could be grown and an interest in rocks and mineral. This topic is significant because its findings can be applied to the commercial production of bismuth crystals for use by jewelers and collectors. This research was done to determine how thermal conductivity affects the size to which bismuth crystals grow.

Due to the uniqueness of this experiment, no other experiments like this one were found through research. Also, because of the money involved with bismuth crystals in the commercial collector/jeweler industry, even the procedures for growing bismuth crystals were hard to come by.

Bismuth (Bi), element number 83, forms hopper crystals with perfect cleavage (Behner). Hopper crystals develop because their outer edges grow more quickly than their faces (Skerlec). These crystals also form a thin layer of bismuth oxide on their surface which is very colorful (Behner). The size and color intensity of these crystals depends on the purity of the bismuth (Behner). In order to achieve good results, at least 99.99% pure bismuth should be used (Gray 2003). Although purity is important, cooling speed is another major variable in bismuth crystal growth.

The slower the bismuth cools, the larger the crystals will be because they have more time to grow (Gray 2003). The opposite is also true; the faster the bismuth cools, the smaller the crystals will be (Gray 2003). Cooling time is directly related to thermal conductivity. “Thermal conductivity is defined as the rate at which heat flows through a certain area of a body” (Beginner’s). In other words, it measures the power a material has to pull heat away from another material. Thermal conductivity is measured, using the SI system, in watts per meter-Kelvin, or W∙m^-1∙K^-1 (Thermal). Using this formula, watts are the unit for power, meters are the unit for distance, and Kelvin is the unit for temperature (Thermal). The higher a material’s thermal conductivity is, the more quickly it will pull away heat from another material.

The materials used in this experiment were aluminum, copper, and zinc. Aluminum has a thermal conductivity of 235 W∙m^-1∙K^-1 (Winter Aluminum), copper of 400 W∙m^-1∙K^-1 (Winter Copper), and zinc of 120 W∙m^-1∙K^-1 (Winter Zinc). Using this information, it was deduced that because zinc had the lowest thermal conductivity, it would allow the bismuth crystals to grow slowest, and would yield the largest bismuth crystals when used as a cooling surface. The next largest crystals would form when using aluminum, and the smallest would form when using copper. This inverse correlation between thermal conductivity and bismuth crystal size will expand the knowledge of bismuth crystal growing.

Hypothesis

If the thermal conductivity of the cooling surface is increased, then the size of the bismuth crystals will decrease.

Methods and Materials

This experiment was performed by altering the independent variable, thermal conductivity, to determine the change in bismuth crystal size, the dependent variable. The thermal conductivity was altered by changing the surfaces on which the bismuth was cooled. The crystal size was measured in millimeters, using a caliper. The controlled variables in this experiment were that the same mass of bismuth was used for all trials, the same sized measuring cups were used for all trials, the room temperature was maintained at 72°F for all trials, and the same amount of cooling time was used for all trials.

The materials used were two stainless steel ¼ cup measuring cups; 150, 10g pellets of 99.99% pure bismuth from www.rare-earth-magnets.com; a heat source that reached at least 520.5°F such as a Bunsen burner or a gas/electric stove; a timer or stopwatch; a 12” x 12” x .04” sheet of each aluminum (Al), copper (Cu), and zinc (Zn); a caliper able to measure up to .05mm; heat resistant gloves; safety goggles; and a lab apron.

At all times, the safety goggles, heat resistant gloves, and lab apron were worn. The first task performed was dividing the 150 bismuth pellets into five 30 pellet (300g) experimental groups. Next, one of the 300g groups of bismuth was placed in one of the ¼ cup measuring cups and over the flame of a stove to be melted. Once all of the bismuth had melted, the measuring cup was removed and placed on the sheet of aluminum for 2 minutes to cool. After the time was up, the bismuth in the measuring cup that remained liquid was poured into the other measuring cup. Left behind in the first cup were the bismuth crystals. The length and width of three crystals were measured using the caliper and recorded in the research notebook. After measuring, the bismuth that was poured into the second measuring cup was removed and placed back into the first measuring cup. Then, all the bismuth was remelted and the procedures were repeated using copper next and then aluminum. After all three metals had been tested with the first 300g experimental group, this bismuth parcel was removed from the measuring cups and placed to the side. Next, the second 300g experimental group of bismuth was used following the same procedures as before except the cooling surfaces would be first the copper, second the zinc, and third the aluminum. Then, the third 300g experimental group of bismuth was used following the same procedures as before except the cooling surfaces would be first the zinc, second the aluminum, and third the copper. Next, the fourth 300g experimental group of bismuth was used following the exact same procedures as before. Finally, the fifth 300g experimental group of bismuth was used following the same procedures as before except the cooling surfaces would be first the copper, second the zinc, and third the aluminum.

Data and Results

Statistical Error Analysis:

The error range for uncertainty in recorded data was ± 0.025mm.

Sample Calculation:

The following is a sample calculation of the area of the top of a bismuth crystal using the dimensions of Crystal #1 cooled on aluminum:

A = l ∙ w where: A = area, l = length, and w = width

A = 5.65mm ∙ 3.65mm using data found in Table 1

A = 20.6mm²

The remaining values of area were calculated in a similar manner.

Table 1
Dimensions of Bismuth Crystals When Cooled on Aluminum
Crystal #	Dimensions (mm)
1	3.65 x 5.65
2	2.60 x 2.70
3	8.55 x 6.55
4	3.80 x 3.40
5	2.30 x 2.15
6	5.60 x 3.10
7	2.45 x 2.85
8	6.65 x 4.70
9	10.10 x 5.80
10	6.75 x 4.85
11	5.10 x 4.95
12	5.40 x 4.60
13	5.75 x 4.55
14	4.35 x 4.55
15	5.10 x 3.50

This table contains the dimensions of the bismuth crystals cooled on aluminum.

Table 2
Area of Bismuth Crystals When Cooled on Aluminum
Crystal #	Area (mm²)
1	20.6
2	7.02
3	56.0
4	12.9
5	4.95
6	17.4
7	6.98
8	31.3
9	58.6
10	32.7
11	25.2
12	24.8
13	26.2
14	19.8
15	17.9
Mean	24.2

This table contains the areas of the bismuth crystals cooled on aluminum. The areas were calculated using the dimensions from Table 1. These crystals were the second largest on average compared to the copper and zinc.

Table 3
Deviations in Data When Cooled on Aluminum
Crystal #	Absolute Deviations
1	3.6
2	17.18
3	31.8
4	11.3
5	19.25
6	6.8
7	17.22
8	7.1
9	34.4
10	8.5
11	1
12	.6
13	2
14	4.4
15	6.3
Mean	11.4
Percent Deviation: 47.1%

This table contains the absolute deviations that were calculated using the area data from Table 2.

Table 4
Dimensions of Bismuth Crystals When Cooled on Copper
Crystal #	Dimensions (mm)
1	6.60 x 3.80
2	3.30 x 4.60
3	4.65 x 2.90
4	2.30 x 2.05
5	1.30 x 1.75
6	4.50 x 3.00
7	3.45 x 2.15
8	3.20 x 2.65
9	4.75 x 4.10
10	3.30 x 2.70
11	6.15 x 4.55
12	2.55 x 2.05
13	6.55 x 7.75
14	4.00 x 3.75
15	2.45 x 1.90

This table contains the dimensions of the bismuth crystals cooled on copper.

Table 5
Area of Bismuth Crystals When Cooled on Copper
Crystal #	Area (mm²)
1	25.1
2	15.2
3	13.5
4	4.72
5	2.28
6	13.5
7	7.42
8	8.48
9	19.5
10	8.91
11	28.0
12	5.23
13	50.8
14	15.0
15	4.66
Mean	14.8

This table contains the areas of the bismuth crystals cooled on copper. The areas were calculated using the dimensions from Table 4. These crystals were the smallest on average compared to the aluminum and zinc.

Table 6
Deviations in Data When Cooled on Copper
Crystal #	Absolute Deviations
1	10.3
2	.4
3	1.3
4	10.08
5	12.52
6	1.3
7	7.38
8	6.32
9	4.7
10	5.89
11	13.2
12	9.57
13	36
14	.2
15	10.14
Mean	8.62
Percent Deviation: 58.2%

This table contains the absolute deviations that were calculated using the area data from Table 5.

Table 7
Dimensions of Bismuth Crystals When Cooled on Zinc
Crystal #	Dimensions (mm)
1	1.95 x 2.40
2	6.50 x 3.25
3	3.70 x 3.80
4	3.05 x 2.45
5	4.30 x 4.50
6	3.75 x 4.00
7	3.85 x 3.00
8	7.50 x 5.25
9	5.70 x 6.20
10	6.55 x 4.85
11	7.70 x 7.20
12	6.45 x 6.30
13	6.10 x 6.30
14	4.55 x 3.60
15	9.50 x 6.80

This table contains the dimensions of the bismuth crystals cooled on zinc.

Table 8
Area of Bismuth Crystals When Cooled on Zinc
Crystal #	Area (mm²)
1	4.68
2	21.1
3	14.1
4	7.47
5	19.4
6	15.0
7	11.6
8	39.4
9	35.3
10	31.8
11	55.4
12	40.6
13	38.4
14	16.4
15	64.6
Mean	27.7

This table contains the areas of the bismuth crystals cooled on zinc. The areas were calculated using the dimensions from Table 7. These crystals were the largest on average compared to the aluminum and copper.

Table 9
Deviations in Data When Cooled on Zinc
Crystal #	Absolute Deviations
1	23.02
2	6.6
3	13.6
4	20.23
5	8.3
6	12.7
7	16.1
8	11.7
9	7.6
10	4.1
11	27.7
12	12.9
13	10.7
14	11.3
15	36.9
Mean	14.9
Percent Deviation: 53.8%

This table contains the absolute deviations that were calculated using the area data from Table 8.

Discussion and Analysis

The results of this experiment showed that there was an inverse correlation between thermal conductivity and bismuth crystal size. These results were similar to the information already known about this subject. Despite this, the percent deviation for all the metals was very high, indicating how “scattered” the data was. Although there were very high percent deviations, these findings did not occur by chance and were supported by the research.

Originally, lead was to also be used as a cooling surface, but during the first trials, it melted. Because the lead melted and because lead’s melting is 56.2°C higher than that of bismuth’s, the bismuth was being heated to above its melting point to uncontrolled temperatures. Another source of error was that a layer of bismuth oxide formed on the surface of the bismuth while melting. This layer of oxide often interfered with the crystal growth and with the ability to measure crystals underneath it. Because the oxide caused some crystals to be immeasurable since they were hidden by it, this limited the number of measurable crystals and may be an explanation for the high percent deviation. Another factor that impacted the number of measurable crystals was measuring cup size. If a larger one were used, all the crystals would have been larger, making them easier to measure. Another source of error included not being able to control vibrations and movements that would affect the crystal growth while cooling.

Despite the high percent deviation and sources of error, the results of this experiment did not occur by chance. The data was all backed up by the research.

Conclusion

In conclusion, when the thermal conductivity of the cooling surface was increased, then the size of the bismuth crystals were decreased. The hypothesis of this experiment was supported by both the research and the results of the experiment. The hypothesis and research sources both showed that there was an inverse correlation between thermal conductivity and bismuth crystal size, and this was backed up further by the results in data which supported it. In this experiment, it was discovered that copper, the metal cooling surface with the highest thermal conductivity, produced the smallest crystals. Also, the aluminum, which had the second highest thermal conductivity, produced the second smallest crystals. Finally, the zinc, which had the lowest thermal conductivity, produced the largest crystals. These results both support the hypothesis, and demonstrate the findings of the research.

Applications and Extensions

The information on growing bismuth crystals obtained from this experiment could be used to most efficiently grow these crystals for use in jewelry. The vibrant colors and strange hopper crystals are traits favorable to mineral collectors also. The knowledge gained from this project could be used to create the largest possible crystals so they can be sold to collectors.

There are many improvements that may be done to next time better this experiment. One may be finding a way to control exactly how high the temperature gets while melting the bismuth. Another improvement could be limiting all movements and vibrations in the location the bismuth is being cooled as not to disturb the crystal growth. Furthermore, more crystals should have been measured to limit the percent deviations. This could have been done by using more bismuth so all the crystals would be bigger and more measurable or by eliminating the oxide that formed on the surface and hindered the ability to measure the crystals. Eliminating the oxide is probably only possible by physically removing it with a spoon at a point time in the cooling process. Also, finding a way to automatically time and pour out the bismuth would eliminate human judgment errors. A possible further investigation would be to investigate the procedures for producing “free” crystals compare to the ones in this experiment that had their bases attached to the leftover bismuth in the measuring cup.

Literature Cited

“Beginner’s Guide to Measuring Thermal Conductivity.” National Physical Laboratory. 31 Dec. 2003 <http://www.npl.co.uk/thermal/stuff/guide2.html>

Behner, Udo. “Bismuth Crystals” 29 Sept. 2003 <http://www.crystalgrowing.com/bismut h/bismuth1.htm>

Gray, Theodore. (theodore@wolfram.com). “Re: growing bismuth crystals.” E-mail to Jon Smith (jsmitty2005@hotmail.com). 30 Sept. 2003.

Skerlec, Jeff. "Everything You Ever Wanted to Know About Bismuth." 14 Oct. 2003 <htt p://www.webcosmos.com/design/tech_wr/bismuth/ >

“Thermal Conductivity.” 31 Dec. 2003 <http://en.wikipedia.org/wiki/Thermal_conductivi ty>

Winter, Mark. “Aluminum Thermal Properties and Temperatures.” WebElements The University of Sheffield. 03 Jan. 2004 <http://www.webelements.com/webelement s/elements/print/Al/heat.html>

Winter, Mark. “Copper Thermal Properties and Temperatures.” WebElements The University of Sheffield. 03 Jan. 2004 <http://www.webelements.com/webelement s/elements/print/Cu/heat.html>

Winter, Mark. “Zinc Thermal Properties and Temperatures.” WebElements The University of Sheffield. 03 Jan. 2004 <http://www.webelements.com/webelement s/elements/print/Zn/heat.html>

Acknowledgements

This science project on the effects of thermal conductivity on bismuth crystals was accomplished with the help of Erica Wildasin, Mr. Theodore Gray, Ms. Diane Kinney, James Smith, Laura Smith, and Rachael Smith. Project inspired by a bismuth specimen in Dave Wildasin’s collection and backboard title inspired by Dixie Wildasin.