Bismuth Crystals: Preparation and Measurement of Thermal andElectrical PropertiesGianna Aleman Milan,* Brian Millier, Andrew Ritchie, Craig Bryan, Sarah Vinette, Bjorn Wielens,and Mary Anne White
Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada
*S Supporting Information
ABSTRACT: We describe a laboratory experiment that serves as an introduction tosolid-state and materials science, a topic that requires additional attention in theundergraduate chemistry laboratory curriculum. The experiment illustrates the long-range translational order, crystal growth, and the macroscopic manifestations of thatorder. This is demonstrated through the preparation and characterization of large,well-formed bismuth crystals, an aesthetically pleasing product. The characterization ofthe grown bismuth crystals involves determination of melting point and enthalpy offusion via differential scanning calorimetry. The temperature dependence of theelectrical resistance of grown bismuth crystals is also measured. Students areencouraged to consider the effect of metallic bonding interactions on the melting ofthe crystal samples and on their ability to conduct electricity. Students also analyzehow the impurities influence the melting point and the electrical properties. Theexperiment is suitable for use in the third- or fourth-year undergraduate laboratory and is performed by students in one four-hoursession. The experiment could be adapted to two laboratory sessions, with the first two-hour session covering crystal growth, andthe second two-hour session focused on thermal and electrical characterization.
High-quality single crystals have been integral in theevolution of many of the electronic technologies we now
take for granted, from radios1 to computers.2 Despite theimportance of crystals in our lives, students usually are notaware that the “crystal” we use for fine drinking glasses is not acrystalline solid nor, perhaps more importantly, that opaquematerials such as metals often are crystalline. In the early 1990s,there was a campaign to highlight the importance of solidmaterials as a fundamental part of the undergraduatecurriculum.3 Since then, despite the accelerated importance ofmaterials research in academia and industry, only a fewexperiments illustrating the principles of crystal growthprocesses have found their way into the chemistry curriculumliterature.4−6
The experiment described here is an integral component of athird-year undergraduate materials science course in theDepartment of Chemistry at Dalhousie University, givenconcurrently as an undergraduate-level physics course. Suchan experiment also could be carried out in upper-year physicalchemistry or inorganic chemistry laboratories. This experimentintroduces students to the principles of crystal growth andcharacterization. It is divided into three parts: (i) bismuthcrystal growth, (ii) thermal characterization, and (iii) electricalcharacterization. In the first part, students observe crystalformations developing from a melt, a rarity for samplepreparation.7 Students can qualitatively determine whichconditions promote the formation of large single crystals.
The concepts of oxide layers on metals and colors resultingfrom thin-layer interference effects are also introduced. In thesecond part, students analyze their crystals using differentialscanning calorimetry (DSC). The use of DSC in theundergraduate lab for the determination of thermodynamicproperties and other characterization studies, including puritydetermination, has been previously reported.8−10 In the presentexperiment, students determine the enthalpy change andmelting temperature of their crystals. The concept of meltingpoint depression is discussed and used to assess the purity ofthe samples. In the final part, students measure the temperaturedependence of the electrical resistance of the grown crystals, anaspect of the chemistry curriculum that, although previouslyreported in this Journal,11 requires further attention. The fullexperiment is carried out in one four-hour laboratory session.Students work in pairs. The experiment is suitable for third- orfourth-year undergraduate students, with a background inphysical chemistry and physics.
■ PREPARATION OF BISMUTH CRYSTALS
Experimental Procedure
The procedure was carried out in air, behind a splash shield formaximum protection. In the preliminary step approximately100 g of solid bismuth shot (Aldrich, 4−30 mesh, 99.9% purity)
was melted, behind the splash shield, in a ceramic crucible usinga hot plate. Molten bismuth was poured into a siliconecontainer that was placed on a metal base behind the splashshield. Seed crystals (Figure 1) of different sizes were pulled
from the molten bismuth using constantan wire. The end of thewire was submerged below the surface of the bismuth pool.Once a small cubelike solid with an edge of the desired size wasobserved, the wire was removed and placed on the metal basebehind the splash shield, and the seed was allowed to cool. Thisprocess was repeated to obtain several seed crystals. Theremaining bismuth was transferred back to the ceramic crucibleand remelted on the hot plate.In the second (growth) step, which immediately followed the
production of the seed crystal, the molten bismuth was pouredback into the silicone container that had been placed in thecenter of a glass wool nest, inside a commercial aluminumbaking pan (Figure 2). The aluminum vessel was then placed
on a flexible heating mantle sitting on an adjustable laboratoryjack. A constantan wire containing a seed crystal was clampedto a rod and suspended above the silicone container. Thelaboratory jack was raised to submerge the seed crystal justbelow the surface of the molten bismuth. The molten bismuthwas allowed to cool until a thin “skin” of solid was observed atits surface. The ability of solid bismuth to float atop a pool of itsliquid, resulting in this thin “skin” of solid, allowed for theconvenient surveillance of crystal development as they werepulled from the liquid. The laboratory jack was then lowered ata rate of about 1 mm every 10 or 15 s. When the growingcrystal attained a width nearly as wide as the molten bismuthpool, or the pool solidified to the point where the crystal was indanger of fusing to the pool, the jack was lowered to fullyremove the crystal. The crystal was then allowed to cool inplace to room temperature, during which time color developedas a layer of Bi2O3 formed.
Results
Bismuth crystals pulled from the melt exhibited distinct stair-step morphologies, as shown in Figure 3. Once pulled from the
liquid, the solid bismuth quickly develops an oxide layer, Bi2O3.The thin-film oxide layer gives rise to color, based onconstructive interference of the light reflected from the frontand back surfaces of the layer.12 The iridescence adds to theaesthetic appeal of the crystals. A thin film of bismuth oxidealso forms atop the melt while on the hot plate, and one canobserve the surface color change as the layer thickens.Discussion
The step formations of a bismuth crystal, forming what isknown as a hopper crystal, are the result of differences in therates of facial and edge growth7 where the edges of the crystaltend to grow faster than the faces. The size of the crystals canbe influenced by controlling and altering several parameters.The variables investigated included cooling rate (slower ratesresulted in larger crystals) and seed size and shape (smallerseeds gave crystals with fewer crystal domains; larger moreirregular seeds resulted in more numerous crystal domainsgrown into each other).The Bi2O3 layer is a result of rapid reaction of the metal at
elevated temperature with atmospheric O2. If the solid is cooledquickly (e.g., in water) or in the absence of O2, this layer doesnot form and the crystal displays a lustrous silver color.
■ THERMAL PROPERTIES OF LAB-GROWN BISMUTHCRYSTALS
Experimental Procedure
Samples of the grown bismuth crystals and the commercialbismuth shot used to grow the crystals were analyzed using alow-cost DSC built in-house. Details concerning the con-struction of DSC are given in the Supporting Information. Theexperiment could be conducted in a commercial DSC. Indiumwire (Aldrich, 1.0 mm diameter, 99.99% purity) was used tocalibrate the instrument. A piece of one of the grown crystals ofapproximately the same size as the bismuth shot was cut outusing a utility knife. Samples were massed on an analyticalbalance and placed in an aluminum DSC pan on the sample
Figure 1. Example of seed crystals. Seed crystals exhibiting jaggedprotrusions as seen on the seed to the right were found to result inlarger crystals with better defined hopper structures.
Figure 2. Schematic view of the experimental apparatus for crystalgrowth.
Figure 3. Example of a bismuth crystal produced in the lab from amelt. Image of the bottom view of the crystal, looking up toward theseed crystal and the constantan wire.
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cell. A thermal baseline was established by running emptysample pans on the reference cell. The experiment was carriedover a temperature range from 100 to 325 °C, heated at 20 °Cmin−1. The temperature of fusion and enthalpy change weredetermined from the DSC thermograms. A detailed descriptionof the experimental procedure is available in the SupportingInformation.Data Analysis
The peak area in the DSC thermogram is proportional to theamount of material undergoing the phase transition, and alsospecific to each instrument. In order to calculate the amount ofenergy required to melt the bismuth samples, a calibration ratiowas established,
=E E( )
(peak area)( )
(peak area)fus In
In
fus Bi
Bi (1)
where the energy required for the fusion of indium, (Efus)In, isdetermined from the known molar enthalpy of fusion,13
(ΔfusH)In, and the number of moles of indium in the sample,nIn, according to
= ΔE H n( ) ( )fus In fus In In (2)
An equation analogous to eq 2 for bismuth gives (ΔfusH)Bi.The presence of impurities in a sample often decreases the
melting point and results in broader endotherms.8 Under theassumption that the impurity forms an ideal solution in themelt, the mole fraction of impurity in the sample, ximpurity, isgiven by
=Δ °
−⎡⎣⎢⎢
⎤⎦⎥⎥x
HR T T
1 1impurity
fus
imp p (3)
where ΔfusH° is the standard molar enthalpy of fusion of thepure sample (pure bismuth here), assumed to be independentof temperature over the range, Timp and Tp are the meltingtemperature of the impure sample (the grown crystals and thebismuth shot) and the melting temperature of pure bismuth,respectively, and R is the gas constant. Students are asked tocompare the experimentally determined temperatures andenthalpies of fusion to the values for pure bismuth,14 tocalculate the amount of impurity present in each sample, and torationalize their results.Results
DSC thermograms for indium and two bismuth samples areshown in Figure 4. The rapid change in slope of the differencein power between the sample and reference, ΔQ, represents thebeginning of the melting process. The melting temperature,Tonset, is determined by the intersection point between thebaseline prior to the thermal event and the tangent at the peak’ssteepest slope. The enthalpy of fusion is determined from thepeak area and the calibration data using eqs 1 and 2. Studentresults are shown in Table 1.Discussion
Students are able to make the following observations: (i) themelting point of the bismuth shot is lower than that of thegrown crystal and (ii) both bismuth samples have meltingpoints below the reported melting point of pure bismuth(271.41 °C).14 The calculation of the percent impurityindicates that the higher the percent impurity in the sample,the lower the melting temperature. Students are generallypuzzled by the first observation as they normally expect the
“pure” bismuth shot to have fewer impurities than the finalproduct. However, there are two factors at play. One is thatthey carry out the DSC experiment on an interior piece of thelab-grown crystal, which has little surface oxide. The moreimportant factor is the impurity separation inherent to thecrystal growth process, due to differences in melting points anddensities of bismuth and impurities in the shot, and differencesin impurity levels in the melt compared with the solid. Bykeeping the temperature of the hot plate slightly above themelting point of bismuth, bismuth oxide floats on the surface.As the crystal is pulled from the melt, some impurities are leftbehind, and hence the melting point of the crystal is higherthan that of the shot (Figure 4). Students are able to explain theobserved trend based on these two factors.In general, the determination of ΔfusH by DSC depends on
several factors including sample preparation (cutting, weighing,thermal contact), method (heating rate), measurement(calibration), and evaluation (baseline, integration limits).15
Good agreement is found between the values of theexperimentally determined ΔfusH for bismuth and the literaturevalue (11.1 ± 0.02 kJ mol−1).14
■ ELECTRICAL PROPERTIES OF LAB-GROWNBISMUTH CRYSTALS
Experimental Procedure
Electrical resistance measurements in the temperature rangefrom 250 to 180 K were carried out using the 4-wire Ohmmeasurement technique. Samples approximately 1−2 cm ineach dimension were cut from the lab-grown crystals using autility knife. Measurement leads (standard tinned copper wire)were embedded into each end of the sample by melting thebismuth using a clean soldering iron with a prefluxed tip.During the resistance experiment, the temperature of thesample was determined using a T type thermocouple that wasembedded in the sample using the same procedure. The samplewas mounted, via its four measurement wires, to the bottom ofa Dewar cover, as shown in Figure 5. The Dewar was filled withliquid nitrogen to a depth of about 5 cm. A 10 W power
Figure 4. DSC thermograms for the melting of indium (solid line),commercial bismuth shot (long dashed line), and lab-grown bismuthcrystal (dotted line). The melting (onset) temperatures of the samplesare TIn = 153.4 °C, TBi(shot) = 255.8 °C and TBi(crystal) = 269.3 °C. Peakareas ABC, DEF, and GHI scale to the enthalpy of fusion of indium,the bismuth shot, and the lab-grown bismuth crystal sample,respectively.
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resistor, which acted as a liquid nitrogen boil-off heater, wasimmersed in the liquid. The sample was then suspended abovethe liquid nitrogen, avoiding direct contact between the sampleand the liquid nitrogen, and it was cooled by the nitrogen boil-off vapor. A custom-built controller unit was used to monitorthe bismuth resistance and the temperature and to control thecooling rate (Figure 6). The data set was written to a USBmemory stick and imported into an Excel spreadsheet for dataprocessing. Details on the construction of the apparatus aregiven in the Supporting Information.Data Analysis
The electrical resistance, R, of a material depends on thedimensions, as well as on the nature of the material andtemperature. (Note that R is also used in eq 3 for the gasconstant. Both uses of R are according to the IUPACrecommendations,16 but their meaning here should be distinct.)The dependence of the electrical properties on dimensions isgiven by
ρ= ⎜ ⎟⎛⎝
⎞⎠R
LA (4)
where L and A are the length and the cross-sectional area of thematerial, respectively, and ρ is the electrical resistivity, which is
an intrinsic property of the material. The temperaturedependence of the electrical resistance is determined by thetemperature dependence of the electrical resistivity, which for ametal increases with temperature, and this increase is essentiallylinear except at the lowest temperatures.12 The relationbetween resistance and temperature is described by
α= + −R R T T[1 ( )]0 0 (5)
where R0 is the resistance at a reference temperature T0, R isthe resistance at any temperature T, and α is the temperaturecoefficient of resistance.17 The temperature coefficient ofresistance for the temperature interval ΔT can be calculatedby eq 6,17
α =Δ
= ΔΔ
Δ⎜ ⎟⎛⎝
⎞⎠
TR
R T
RR
avg
avg
(6)
where Ravg is the average resistance in the temperature intervalΔT and ΔR/ΔT is the slope of a graph of R versus T.Results
The experimentally determined temperature dependence of theelectrical resistance for several bismuth samples is shown inFigure 7. Reference samples, prepared by the instructor, wereused by the students to validate their results. The electricalresistance increased linearly with temperature. Temperaturecoefficients were calculated using eq 6. The value of the slope
aThe uncertainties in Tonset and ΔfusH were estimated to be ±4.1 °C and ±4.8%, respectively. Details are given in the Supporting Information.
Figure 5. Illustration of sample mounting for electrical resistancemeasurements: (A) bottom view of sample mounting cover; (B) sideview of sample mounting cover.
Figure 6. Experimental apparatus for electrical resistance measure-ments.
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and its standard error for each run were determined usingregression analysis. Student results are shown in Table 2.Discussion
The observed linear dependence of electrical resistance ontemperature is evidence of the metallic character of the bismuthcrystals.11,12,18,19 As the temperature is increased, the thermalmotion of the atoms on their lattice sites increases, and thismotion adds additional resistance to the conduction ofelectrons.The differences in resistances for different samples are due to
different geometries. The average temperature coefficient ofresistance was determined to be 0.0034 ± 0.0001 K−1. Thisresult is in excellent agreement with the value of thetemperature coefficient reported by Pietenpol and Miley,17
0.003 K−1, which is quite good considering that the accuracy ofthe results can be affected by the presence of impurities orimperfections in the lattice structure. Nonlinearity of thetemperature dependence of the resistance measurements, seenin some experiments, was usually the result of poor wireconnections, in which case the connections should be redone.
■ HAZARDSThe Material Safety Data Sheet for bismuth19 indicates that thisproduct has an oral acute toxicity of category 5. Thisclassification is given to a chemical which is of relatively lowacute toxicity but which, under certain circumstances, may pose
a hazard to vulnerable populations. However, the toxicologicalinformation shows that very little is known about the toxiceffects of the element. The use of bismuth in a number ofcommercial applications including pewter and over-the-counterupset stomach remedies such as Pepto Bismol is evidence thatthe body can handle it fairly well in small doses. However, ifexposure to bismuth is significant, a number of health issuesmay arise.The main hazard associated with this experimental laboratory
procedure is heat. While students rarely have a problem dealingwith the responsibility of a hot plate, there could be a strongimpulse to reach out and grab newly produced crystals whilethey are still hot. In addition, there is a danger of individualsbeing burned by spilled molten bismuth. Bismuth crystals mustbe grown behind a splash shield, and heat-resistant gloves mustbe worn when handling the molten bismuth and the growncrystals. Safety glasses, a lab coat, and closed-toe footwearshould be worn to limit the exposed areas. Based on the lowvapor pressure of bismuth at its melting point, 2.63 × 10−13
atm,20 it is exceptionally unlikely that bismuth fumes will begenerated during this experiment. To prevent the ingestion ofbismuth, hands should be washed with soap and plenty of waterafter finishing the procedure.Sharp objects must be handled with care. Cut resistant gloves
must be worn when using a utility knife to avoid getting cut.Samples must always be cut away from the body and face;several passes must be made when cutting thicker samples.Knives should be kept capped when not in use.Liquid nitrogen can cause frostbite on prolonged dermal
contact or if splashed into the eyes. Loose fitting thermalinsulated or leather gloves, safety glasses, a lab coat, and closed-toe footwear must be worn when handling the cryogenic liquid.Indium is flammable, and hazardous in case of ingestion.
Handling of the constantan wire should not cause any ill healtheffects. However, individuals who may have had allergicreaction or sensitivity to metals such as copper and nickelmay encounter skin rash or dermatitis if skin contact with thisproduct occurs.
■ SUMMARY
Students were introduced to a method for crystal growth that istypically unknown to undergraduates. The attractive nature ofthe products gives this experiment a strong novelty thatstrengthens its impact on students and provides an excitingintroduction to the world of materials. The experimentprovides an illustration of color formation from the interactionsof light with bulk matter. Students were given the opportunityto explore the relationship between crystal structure andmetallic bonding interactions that leads to properties observedat the macroscopic scale. The production of bismuth crystals is
Figure 7. Electrical resistance, R, as a function of temperature and linesof best fit for seven different grown bismuth crystals.
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relatively straightforward, and the effects of a wide variety ofconditions can be studied in this experiment. Advancedexamples include the influence of cooling methods on color,or the effects of using different (nonbismuth) seeds.
■ ASSOCIATED CONTENT*S Supporting Information
Instructions for students, notes for the instructor, and a detaileddescription of the custom-built instruments used in thisexperiment. This material is available via the Internet athttp://pubs.acs.org.
B.M.: Computer Interface Consultants, 31 Three Brooks Drive,Hubley, Nova Scotia, B3Z 1A3, Canada.A.R.: Department of Chemistry, University of Saskatchewan,Saskatoon, Saskatchewan, S7N 5C9, Canada.C.B.: School of Electrical Engineering and Computer Science(EECS), University of Ottawa, Ottawa, Ontario, K1N6N5,Canada.S.V.: Foothills Medical Centre, Seaman Family MR ResearchCentre, 1403 29th Street N.W., Calgary, Alberta, T2N 2T9,Canada.
Notes
The authors declare no competing financial interest.
■ ACKNOWLEDGMENTSWe acknowledge the Dalhousie University Integrated ScienceProgram (DISP) for providing the opportunity for the threefirst-year students (C.B., S.V., B.W.) to have a researchexperience in developing the crystal growth of bismuth. Wethank the students of the CHEM 3305 Materials Science coursefor their feedback on this experiment. The financial support ofDalhousie University also is gratefully acknowledged.
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