formal lab 2

Sreyes Kadapala Formal Report #2: Bi-Sn Phase Diagram 1

1.0 INTRODUCTION

A phase diagram is a representation of phases present under equilibrium conditions and the phase compositions at each combination of temperature and overall composition. Sometimes phase diagrams also indicate metastable phases (Askeland, D.R., & Phulé). One type of phase diagram plots temperature against the relative concentrations of two substances in a binary mixture called a binary phase diagram. A binary phase diagram, represented on temperature-composition coordinates, consists of the single-phase regions separated by the two-phase regions. The curves separating of the single-phase regions from two phases represent the compositions of single phases.

In the contemporary engineering world, phase diagrams are used for various applications such as the following: 1) Solidification and casting problems, 2) Thermal analysis of an alloy, 3) Soldering, 4) Brazing, and5) Kirkendahl Voiding.

The preceding applications are mostly for engineering purposes only. However, in the scientific world, a phase diagram is used for even more in analysis of compounds and alloys. Phase diagrams are very important in materials science and engineering because these are tools that define the thermodynamically stable components of a materials' morphology or microstructure. The properties of aluminum, for example, can be dramatically changed if an alloying element is added such that a second phase appears in the microstructure and is distributed throughout the primary aluminum phase (The Sn-Bi Equilibrium Phase Diagram).

The main purpose of this experiment was to determine the phase diagram of tin-bismuth (Sn-Bi) alloy from the experimental data recorded. For the phase diagram to be constructed, different weight percentages of tin and bismuth were air-cooled to room temperature from eight hundred degrees Fahrenheit. The air-cooling of alloys provided the cooling curves for the Sn-Bi alloy. Furthermore, these cooling curves were utilized to create the phase diagram of the Sn-Bi alloy. Multiple teams were assigned by Dr. Lanning for the experiment, and specimens from various teams were examined under the scanning electron microscope (SEM). The energy dispersive X-ray spectroscopy analysis was done on the images obtained from the SEM, and also, the images from the SEM were uploaded in Scandium software. The Scandium software was used to perform phase analysis on the photographs/images obtained from the SEM, and SEM was used also depict the microstructure(s) present.

This report discusses and analyzes the results from the experimental data generated from the lab. The experimental results are compared to published values to check for the percentage differences in between both the experimental and published values. Additionally, the analysis from the EDS and the phase calculations from the Scandium software were verified with the hand calculations (tie-line calculations) done on the experimental phase diagram.


2.0 THEORY

This section discusses the theory required to understand the results and discussion section of the report. First, the required definitions are stated, and then phase diagram and analysis of phase diagrams are discussed. The definitions are taken from the text books — Materials Science for Engineering Students and The Science and Engineering of Materials.

2.1 DEFINITIONS AND BASIC TERMINOLOGY

Phase: is a homogeneous, physically distinct, portion of matter that is present in a non-homogeneous system. A phase may be single component or a mixture. A phase can be defined as any portion, including the whole, of a system that is physically homogeneous within itself and bounded by surface so that it is mechanically separable from any other portions.

Component: is an ingredient of a chemical system

Composition of a Phase: is the relative amount of the components a phase contains.

Binary Phase Diagram: A phase diagram for a system with two components.

Precipitates: are formed when the concentration of a component exceeds the solubility limit.

Eutectic: is an alloy of immiscible components.

Eutectic Point: is the point on the phase diagram where liquid transforms into the eutectic, which consists of two distinct phases. The result is called eutectoid.

Eutectic Line: The eutectic line or, more accurately, the eutectic tie line is the constant temperature line through the eutectic point.

Solidification: the process of becoming hard or solid by cooling or drying or crystallization.

Liquidous: or the liquidous line is the line (or lines) on a phase diagram above which only liquid is present. Technically it is "the locus of temperatures above which only liquid is stable.

Solidus: or the solidus line is the line (or lines) on a phase diagram below which only solid is present. Technically it is "the locus of temperatures below which only solid is stable.

Solvus: or the solvus line on a binary phase diagram (or a surface on a ternary phase diagram) that defines the limit of solid solubility under equilibrium conditions.


2.2 PHASE DIAGRAMS

A phase diagram is a map of the phase or phases stable as a function of different thermodynamic variables such as — temperature, pressure, composition, etc. (The Sn-Bi Equilibrium Phase Diagram). Before going further deeper into phase diagrams, first, other required ideas/concepts are introduced.

A cooling curve illustrates how the temperature of a material changes with time. Cooling curves have horizontal flat parts where the state changes from gas to liquid or from liquid to solid (Heating and Cooling Curves). For example, salol or stearic acid could be used to make a cooling curve. Salol has a melting point of about 45°C and stearic acid has a melting point of about 69°C. They are easily melted in a boiling tube placed in a beaker of hot water. The temperature can be followed using a thermometer or temperature probe connected to a data logger. The liquid may be cooled by putting the boiling tube in a beaker of cold water or just leaving it in the air. Figure 1, below, illustrates the cooling curve for the stearic acid and salol:

Figure 1: Example of a Cooling Curve.(Heating and Cooling Curves)

From the above-illustrated cooling curve, the phase change from liquid to solid could also be depicted. Also, another observation could be made that the melting point of stearic acid and stalol is approximately around forty five degrees Celsius. Figure 2, on the following page illustrates an example of cooling curves for a range of compositions for copper-nickel mixtures, and the corresponding equilibrium phase diagram determined from the cooling curves. As the liquid composition of copper-nickel mixture is cooled,


the slope of time versus temperature changes when a solid starts forming, and the slope again changes when the last of the liquid changes to solid.

Figure 2: Example of a Cooling Curve’s Temperatures for a Phase Diagram.(Lanning, 2009)

A pure substance, that is, in Figure 2, either 100% Copper or 100% Nickel would have only one temperature when both solid and liquids are present, while an impure substance (composition) will have a range of temperatures where both solid and liquid are present.

The cooling curve could be different for metals with different compositions. For example, a metal with an equal percentage of composition of iron and carbon would have a different cooling curve when compared to a metal with twenty-five percent of carbon and seventy-five percent of iron. Figure 3, below, illustrates the cooling curve for an alloy with varying Nickel composition:

Figure 3: Cooling Curve of an Alloy with Varying Composition of Nickel (Fischer, T. (2009)).


From the preceding figure, Figure 3, an observation could be made that the figure is a three dimensional graph (time, temperature and composition as its axis), and as the concentration of Nickel was increased, the phase change was occurring at a much higher temperature. Also, from the preceding figure, an observation could be made that the melting point of pure Nickel was higher than the melting point of pure Copper.

A binary phase diagram depicts the phases formed in differing mixtures of two elements over a range of temperatures. Compositions run from 100% Element A on the left of the diagram, through all possible mixtures, to 100% Element B on the right. An example of a binary phase diagram was depicted in Figure 2. The composition of an alloy is given in the form A – x percentage of B (x %B). For example, Cu – 20 %Al is 80% copper and 20% aluminum. Weight percentages are often used to specify the proportions of the alloying elements, but however, atomic percent may also be used. For example, Cu – 20 wt %Al for weight percentages implies that the weight of copper present is twenty percent of the weight of aluminum, and the similar idea is used for the atomic percentages (Warren, 1997). Figure 4, below, illustrates the axis of a phase diagram:

Figure 4: Axis of a Phase Diagram (Warren, 1997).

In Figure 4, the pure elements (100 % of element A and 100 % of element B) are on the opposite ends of the x-axis, and the temperature on the y-axis. Alloys tend to solidify over a temperature range, rather than at a specific temperature like pure elements. At each end of the phase diagram only one of the elements is present (100% A or 100% B) and therefore a specific melting point exists. Sometimes there is a mixture of the constituent elements that produces solidification at a single temperature like a pure element. This is called the eutectic point. The eutectic point can be found experimentally by plotting cooling rates over ranges of alloy composition in a similar method as depicted in Figure 2. The phase diagrams for some very simple binary alloys do not have eutectic points. This is because the liquid mixture will cool through a solidification region (temperature range) and become a solid solution of the two constituent elements. These simple phase diagrams normally only occur when two very similar elements are being alloyed (Warren, 1997). Figure 5, on the following page, illustrates a simple binary phase diagram like the binary phase depicted in Figure 3 and Figure 2:


Figure 5: Simple Binary Phase Diagram (Warren, 1997).

In the preceding figure, the symbol alpha (α) is the solid phase. By cooling alloys from the liquid state and recording their cooling rates, the temperature at which they start to solidify can be determined and then plotted on the phase diagram. If enough experiments are performed over a range of compositions, a start of solidification curve can be plotted onto the phase diagram. This curve will join the three single solidification points and is called the liquidus line (Warren, 1997). Figure 6 depicts the liquidus line and the eutectic point, which was discussed earlier:

Figure 6: Illustration of a Liquidus Line and Eutectic Point in a Phase Diagram (Warren, 1997).

In the preceding figure, Figure 6, the yellow lines depict the liquidus line, and the yellow dot, that is, the point where both the two liquidus lines meet, is the eutectic point. In the same way that sugar dissolves into hot tea (a liquid solution) it is possible for one element to dissolve in another, whist both remain in the solid state. This is called solid solubility and is characteristically up to a few percent by weight. This solubility limit will normally change with temperature. The extent of the solid solubility region can be plotted onto the phase diagram and labeled appropriately. A solid solution of B in A (i.e. mostly A) is called alpha and a solid solution of A in B (i.e. mostly B) is called beta. It is worthwhile to note that some elements that are alloyed have zero solid solubility; a good example is


Al - Si alloys, where aluminum has zero solid solubility in silicon (Warren, 1997). Figure 7 illustrates the alpha and the beta particles in a phase diagram:

Figure 7: Illustration of the Alpha and Beta Particles in the Phase Diagrams (Warren, 1997).

In the preceding figure, Figure 7, the two yellow lines are the combination of both the solidus and the solvus lines. The bottom two curved lines near the pure composition of the elements are the solvus lines. Whereas, the curved lines on the top portion of the phase diagram are the solidus lines. In Figure 7, the melting points of material A and material B is also depicted. If an alloy's composition does not place it within the small solid solution regions at either side of the phase diagram, the alloy will become fully solid at the eutectic temperature, shown as the eutectic line on the phase diagram in Figure 8, at the bottom of the page. At alloy compositions and temperatures between the start of solidification and the point at which it becomes fully solid (the eutectic temperature) a mushy mix of either alpha or beta will exist as solid lumps with a liquid mixture of A and B (Warren, 1997). These partially solid regions are marked on the phase diagram in Figure 8:

Figure 8: Eutectic line Illustration (Warren, 1997).

In the phase diagram in Figure 8, the region below the eutectic line, and outside the solid

SolidusLine

SolidusLine

SolvusLine

SolvusLine

Melting Point (B)

Melting Point (A)


solution region, will be a solid mixture of alpha and beta, and is labeled to reflect this.

2.3 ANALYSIS OF PHASE DIAGRAMS

The theory for this section has been obtained from the text book, Materials Science for Engineering Students, a class textbook used for ES 320 (Engineering Materials Science Class Section).

2.3.1 Single Phase

In a single phase field (in this or in any other phase diagram) the chemical and physical analysis of what is present in thermodynamic equilibrium is demonstrated in this section. The composition of the material is equal to the overall composition. For example, in Figure 9, below, the 35 wt% Copper alloy is heated to 1400C (state a, in Figure 9). The molten alloy would contain 35 wt% Cu and 65 wt% Ni, and 100% of what is present is liquid. Similarly, if the original alloy is cooled to 1100C (state b, in Figure 9), the phase diagram depicts that the material is all solid and has a composition equal to the overall composition, that is, 35 %wt Cu and 65 wt% Ni .

In any single phase field of any binary equilibrium phase diagrams the rules are the following: i) The chemical composition of the phase is the same as the overall composition

(Co). ii) Physically, the alloy is either 100% homogeneous liquid or 100% homogeneous

solid. iii) Single-phase alloy liquids and solids are generally stable over some range of

compositions and temperature.

Figure 9: Cu-Ni Phase Diagram (Fischer, T. (2009)).


2.3.2 Two Phase Mixture, Tie Line Construction, and Chemical Composition

If the system is in a two-phase (L+S) field, a physical mixture of the two phases exists. The chemical and physical analyses follow different rules from those of the single-phase field. Both analyses center on the construction of a tie line or isotherm; this is a horizontal line (constant temperature) drawn through the state point (C) so that it extends to the left and right until it ends at the single-phase boundaries on either side of the overall composition. Such a line is depicted at 1340C fro the initial 35 wt% Cu-65 wt% Ni alloy. The tie line for the Ni-Cu phase diagram is depicted in Figure 9. However, Figure 10, below, has the enlarged view of the Ni-Cu phase diagram in Figure 9:

Figure 10: Phase Diagram for Ni-Cu Alloy (Fischer, T. (2009)).

Within the L+S field, the composition of the solid (CS) is given by the intersection of the tie line with the solidus curve (read off the horizontal axis). The composition of the liquid (CL) is given by the intersection of the tie line with the liquidus curve. For example, in the 35 wt% Cu-65 wt% alloy at 1340C the following could be calculated — CS = 27 wt% Cu and CL = 40 wt% Cu. This is depicted in the preceding figure, Figure 10. 2.3.3 Two Phase Mixture, Lever Rule, and Relative Phase AmountsIn this section, how the physical composition, namely, the relative proportions or weights of each phase present is determined. The first step is to determine the fraction of the liquid present (fL), and then the fraction of the solid present could be determined by using Equation 1, which stated below:

fS = 1 - fL Equation 1

If the total alloy weighs W grams, the weight of the liquid is calculated by the multiplying the total weight of the alloy and the fraction of the liquid present (W X fL).


Similarly, the weight of the solid is calculated by multiplying the weight of the alloy and the fraction of the solid present (W X fS). The weight of a certain element present could also be determined — the weight of an element in the liquid phase is determined by Equation 2 stated below:

Weight of an element in the liquid phase = W X fL X CL Equation 2

Because no element, that is one of the alloying elements in the alloy, disappears, the total amount of the alloying element in the alloy is the amount of solid plus the amount of the alloying element present in the liquid. The equation avowed below, Equation 3, is the total weight of an alloying element present at a particular instant in the phase diagram:

WCo = W X fL X CL + (W X CS (1 - fL)) Equation 3

From Equation 3, solving for the fL yields the following equations — Equation 4 and Equation 5:

fL = (CS – Co) / (CS – CL) Equation 4

fS = (Co – CS) / (CS – CL) Equation 5

The above two equations, that is, Equation 4 and Equation 5 are known as the lever rule. Note that, in order to obtain the amount of liquid fL, the distance is measured from the overall composition Co to the composition of the solid, and then is divided by the length of the tie line. The phase whose boundary is closest to the initial composition Co is present in the greatest amount. When applied to the 35-wt% Cu-65 wt% Ni at 1340C in Figure 10, the fraction of the solid calculated is .385 ((40 - 35)/(40 - 27)) and that of liquid is .615 ((35 – 27)/(40 – 27)).

In summary, for any two-phase field in binary equilibrium phase diagram the rules are: i) Draw a horizontal tie line corresponding to the chosen temperature, extending to

the left and right phase limits from the overall composition Co. (Tie lines are only draw in two phase fields. They make no sense in a one-phase field.)

ii) The chemical composition of the two phases is given by the ends of the tie line, extended vertically down to, and read off, the horizontal axis.

iii) The weight fraction of each phase within the two-phase mixture is given by the Lever Rule, that is, Equation 4 and Equation 5.


2.4 THE BINARY EUTECTIC PHASE DIAGRAM

The theory for this section has been obtained from the text book, Materials Science for Engineering Students, a class textbook used for ES 320 (Engineering Materials Science Class Section).

Many pairs of elements, for example, Bi-Cd, Sn-Zn, Ag-Cu, Al-Si, etc., do not mix. The bond between the two elements A-B is weaker than the A-A and B-B bond. Each element can dissolve a limited amount of the other. These pairs solidify in a manner similar to Pb-Sn whose eutectic phase diagram is illustrated in Figure 11.

Figure 11: Binary Eutectic Phase Diagram of Pb-Sn (Fischer, T. (2009)).

From the above figure, an observation could be made that the eutectic temperature, that is the temperature at the eutectic point, is 183C, and the eutectic composition, that is, the composition at the eutectic point, is 61.9% Sn or 28.1% Pb. On the left portion of Figure 11, the diagram posses a solid solution designated as the phase, which is lead rich, and on the right side of the diagram, a tin rich solid phase is designated as . The solidus and the solvus lines specify the maximum amount of tin that can be dissolved in the lead at each temperature. The rules of phase analysis in single and two phase fields given previously in Section 2.3 are equally applicable to eutectic systems and are depicted in Figure 12, on the following page:


Figure 12: Tie Line Calculations for the Pb-Sn Phase Diagram (Fischer, T. (2009)).

The preceding figure depicts the following: 1) The weight percentages of Sn and Pb in the alloy,2) The temperatures at which the tie line calculations were made, 3) The phases present at that particular temperature, that is, the temperature at which

the phase analyses were done, 4) The chemical composition of the phases in terms of weight percentage of tin, 5) The amount of each phase present at the interested temperature, and 6) The comment portion of the table in Figure 12, reports the type of structure

present.


The following figure, Figure 13, illustrates the microstructures that could be formed at various compositions of the Sn-Pb alloy when the temperature is decreased slowly from 350C to room temperature of approximately 25C:

Figure 13: Formation of Different Microstructures with Varying Composition of Sn in the Sn-Pb Alloy (Fischer, T. (2009)).

From the preceding figure, at 200C, the α phase contains approximately 18% Sn and the liquid phase 57% Sn. As the temperature approaches 183C, the composition of the liquid approaches the eutectic point and that of the solid changes to 19.2% Sn. Just below 183C, the alloy consists of the proeutectic α phase that was formed at higher temperatures and a solid eutectic (consisting of α with 19.2% Sn and β with 97.5 % Sn). As the alloy cools, the proeutectic α expels tin, following the solvus curve, and becomes almost lead at room temperature. The two phases in the eutectic also become purer lead and tin. A polished and etched section of the alloy is shown in Figure 14, above, on the following page:


Figure 14: Microstructures of Pb-Sn Alloys at Room Temperature (Fischer, T. (2009)).

The following could be visualized, in the above figure, Figure 14:

i) The image on the top right contains the dark proeutectic α phase surrounded by light eutectic for the 50 wt% Sn – 50 wt% Pb.

ii) The image towards the top left consists of dark proeutectic α phase surrounded by eutectic for the 30 wt% Sn – 70 wt% Pb.

iii) The image on the bottom right contains the light proeutectic β phase surrounded by eutectic for the 70 wt% Sn – 30 wt% Pb.

iv) The image towards the bottom left consists of two-phase eutectic microstructure for the 63 wt% Sn – 37 wt% Pb.


2.5 RELATIONSHIP BETWEEN PROPERTIES AND THE PHASE DIAGRAM

The mechanical properties (such as, tensile strength, yield strength, etc.) of an alloy can be related to the phase diagram of that particular alloy. For, example, the following figure, Figure 15, depicts the mechanical properties of a series of copper-nickel alloys related with the phase diagram of copper and nickel:

Figure 15: Relationship Between Mechanical Properties of an Alloy and Phase Diagrams Askeland, D.R., & Phulé, P.P. (2007).

In Figure 15, the strength of copper increases by until about 60 % Nickel is added. Pure Nickel has higher tensile strength that pure copper. However, the maximum strength is obtained for a Cu-60% Ni alloy, known as Monel. Also, as the concentration of zinc increased, the electrical conductivity decreased.

2.6 SCANNING ELECTRON MICROSCOPE AND ENERGY DISPERSIVE X-RAY SPECTROSCOPY

Scanning Electron Microscopy (SEM) is a means of obtaining high-resolution, three dimensional-like images of solid samples. Variations in the surface topography of a material are depicted as variations in gray level of the image. Details as small as 70 angstroms can be resolved on most samples. Dynamic experiments can be documented with the aid of a conventional video recorder.

Energy Dispersive X-Ray Spectroscopy (EDS) extends the usefulness of SEM in that elemental analysis can be performed within regions as small as a few cubic micrometers.


All elements from boron through the periodic table can be detected with sensitivities of approximately a few tenths of one percent.

Modes of Analysis:

1) EDS Spectra: Graphical plot of peaks identifying elements detected within the area analyzed. The area analyzed can be adjusted to encompass sub micrometer or several millimeters. The intensity of peaks (peak height) is related to the elemental concentration.

2) BSE Imaging: Variations in the average atomic weight of the material is depicted as variations in the gray level of the image.

3) Elemental Mapping: Photographic images depicting the distribution of the elements of interest. Variations in gray level of the image are related to variations in the elemental concentration. Images can be obtained for all elements of interest.

4) Concentration Profiles: Graphical plot of the elemental concentration as a function of distance along a given line on the sample.

5) Standardless Semi-Quantitative Analysis: Quick semi-quantitative estimate of elemental concentration (Scanning Electron Microscopy (SEM) & Energy Dispersive X-Ray Spectroscopy (EDS) , 2008).

2.6.1 APPLICATION AND PRINCIPLE OF OPERATION OF EDS

The following are the applications of the EDS:1) Materials evaluation and identification

a) Contaminants, b) Elemental diffusion profiles, c) Glassivation phosphorus content, and d) Multiple spot analyses of areas from 1 micron to 10 cm in diameter.

2) Failure analysis a) Contamination identification, b) Unknowns identification, and c) Stringer location and identification,

3) Quality control screening, a) Material verification, and b) Plating specification and certification.

As the electron beam of the SEM is scanned across the sample surface, it generates X-ray fluorescence from the atoms in its path. The energy of each X-ray photon is characteristic of the element which produced it. The EDS microanalysis system collects the X-rays, sorts and plots them by energy, and automatically identifies and labels the elements responsible for the peaks in this energy distribution (Energy Dispersive X-Ray Spectroscopy (EDS)).

http://www.photometrics.net/images/SEMcontaminant.pdf


3.0 APPARATUS AND PROCEDURES

This section of the report discusses the apparatus and the procedures that were used to conduct the experiment. The experiment was completed by conducting it in two separate lab periods, i.e., on the November 3rd 2009 and November 10th 2009.

3.1 APPARATUS

The following equipment was used for the experiment:

One (1) Pyrex test tube,

One (1) bar of tin,

One (1) cutter as illustrated in the figure below:

Figure 16: A Cutter. Two (2) ring stands,

One weight scale as illustrated below in Figure 17:

Figure 17: Weighing Scale.

One (1) thermocouple,


One (1) striker as illustrated in Figure 18,

One (1) Bunsen burner as illustrated in the figure below:

Figure 18: Bunsen Burner and a Striker.

One (1) stopwatch,

One (1) high-speed cutoff saw as illustrated below in Figure 19:

Figure 19: High-Speed Cutoff Saw.(Source: Lanning, 2005)

One (1) belt grinder polishing machine as illustrated in the figure on the following page:

Bunsen Burner

Striker


Figure 20: Belt Grinder Polishing Machine.(Source: Lanning, 2005)

One (1) 1200 grit SiC (Silicon Carbide) paper,

One (1) hammer,

One (1) scanning electron microscope as illustrated in Figure 21:

Figure 21: Scanning Electron Microscope.

One (1) computer with the Scandium software, and

One (1) jump drive.

3.2 PROCEDURES

This section lists the procedures required for the experiment to be conducted. Even though the experiment was conducted in two different lab periods, the procedures will be written as if the experiment was conducted in a single lab period. The experiment was conducted at the AXFAB building at Embry-Riddle Aeronautical University, Prescott, Arizona. The procedures on the following page were used for the experiment:


1.0 The class was divided into multiple teams with two members per each team, and Dr. Lanning assigned the team numbers.

2.0 Each individual team was asked to obtain a sheet from Dr. Lanning. The sheet comprised of the amount of either tin or bismuth to be added into the test tube.

3.0 The team was asked to measure the appropriate amount of tin that was required to be added into the test tube.

3.1 The measurement of the amount of tin required was done by using a weighing scale, which is depicted in Figure 17.

3.2 When the weight of tin was over or under the required amount, then small amounts of tin were either removed or added respectively.

4.0 Once the appropriate amount of tin was obtained, the team added the tin to the mixture of tin and bismuth from the previous team’s test tube.

5.0 The test tube was then mounted on the ring stand by using the procedures from 5.1 through 5.3:

5.1 The team placed the test tube into the ring stand.

5.2 Since the test tube was not still, that is, the test tube was shaking; the team tightened the crew on the ring stand.

5.3 The team checked whether the ring stand and the test tube were stable. If the ring stand was not stable, then the team went back to procedure 5.2, and then followed on with the remaining procedures.

6.0 The team mounted the thermocouple on a separate ring stand.

7.0 The thermo couple was mounted vertically into the test tube.

8.0 The Bunsen burner was light up with the help of the striker.

9.0 The flame was adjusted until it was fairly small.

10.0 The test tube was placed over the Bunsen burner as illustrated in the figure on the following page:


Figure 22: The Setup of the Experiment.

11.0 The team waited until the mixture completely liquefied.

11.1 During this waiting period, the team was constantly stirred the mixture with the help of the thermocouple.

12.0 Once the mixture was liquefied, the team kept the thermocouple in a constant position inside the liquefied mixture.

12.1 The team ensured that the thermocouple did not touch the sides or bottom of the test tube.

13.0 The stopwatch provided by Dr. Lanning was set to zero (0) seconds.

14.0 Once the mixture had reached a temperature of eight hundred degrees Fahrenheit (800F), the team turned off the Bunsen burner.

15.0 As the Bunsen burner was turned off, the team started the stopwatch to record the temperature.

16.0 The temperature was recorded for every five (5) seconds until the time reached eight (8) minutes.

17.0 The temperature was recorded on the sheet that was provided by Dr. Lanning.

18.0 Once, the timer/stopwatch had reached eight (8) minutes, the team removed the thermocouple.

18.1 To remove the thermocouple, the team lighted the Bunsen burner to liquefy the mixture.

19.0 The temperature recorded on the sheet provided by Dr. Lanning was then put into an Excel file.

20.0 The Excel file was emailed to Dr. Lanning. Later on, Dr. Lanning emailed another Excel sheet with the temperature and time recorded for different configurations of tin-bismuth alloy.


21.0 The Excel file provided by Dr. Lanning was used to create a cooling curve, and then the phase diagram of the Bi-Sn alloy.

22.0 Later on, Dr. Lanning created multiple groups. Each group contained three through four (3-4) members.

23.0 Two (2) groups were assigned a piece of the mixture with composition of 58 % Sn and 42 %Bi.

24.0 Dr. Lanning had asked the two (2) teams to share the specimen of the mixture.

25.0 In order to share the specimen, the team cut the mixture specimen into two (2) different pieces by using the cutter.

26.0 Once the specimen was cut into two (2) different pieces, the two (2) teams picked up one (1) of the two (2) new mixture specimens for polishing.

26.2 One (1) sheet of twelve hundred (1200) grit silicon carbde paper was obtained by the team.

26.1 The specimen was polished using a belt grinder with the twelve hundred (1200) grit paper for approximately five (5) seconds.

27.0 The experiment involving micropscopy was conducted on the specimen.

27.1 First the specimen was placed under the scanning electron mocroscope.

27.2 The evacuate button on the microscope button was pressed to evacuate any particles present in the chamber.

27.3 The cut surface of the specimen was analyzed, and snapshots of the surface were taken at a scale of fifty (50) microns and at twenty (20) kilo volts.

28.0 The images from the SEM were saved on a jump drive, and were uploaded on another computer with the Scandium software.

29.0 The images were uploaded in the Scandium software, and were anayzed.

29.1 The work offline option was chosen as soon as the sofware was started.

29.2 The images from the SEM were cropped to eliminate the black SEM information box from the SEM analysis.

29.2.1 The left mouse button was used to position red crop box and the right mouse button was used to finish the crop.


29.3 The image was selected and then the thresholds were set by selecting the autosettings tab.

29.4 The none option was selected in the background.

29.5 The fixed option was selceted in the Histogram limits group.

29.5.1 The lower limit was set to be zero (0) and the uper limit was set to be two hundred and twenty five (225).

29.6 The number of phases entered was two (2).

29.7 The maual tab was selected to set the color thresholds.

29.8 Since the pictures were not clear, the color bar at the bottom of the picture was manually set, which adjusted the threshold.

29.9 The images were adjusted until all the team members concurred that the images were fine.

29.10 The phase analysis was done.

29.10.1 The measure button was selected.

29.10.2 The amount of each phase by area was the output that was generated.

30.0 The images were loaded on to a jump drive for further analysis.


4.0 RESULTS AND DISCUSSIONS

This section of the report, the data obtained from the two lab experiments is analyzed and discussed. The data for the phase diagram was obtained from the cooling curves of the Bi-Sn alloy at different compositions provided by Dr. Lanning. Figure 23, below, depicts the cooling curve, which was created from Dr. Lanning’s data. The remaining cooling curves’ data is listed in Section 8: Raw Data. The cooling curves were used to plot the phase diagram. The method used to plot the phase diagram was the same method that was discussed in Section 2: Theory.

Figure 23: Cooling Curve of the 100 % Bismuth or 0% Sn.

Whenever the slope of the cooling curve was zero, the temperature at that instant was taken for the phase diagram for a particular configuration. However, in many cases, there were no slopes that were zero. Hence, the instant where the slope changed, the temperature at that instant was recorded for data analysis. The phase diagram was graphed from the data obtained from the experiment and is depicted in Figure 24, on the following page:


0 10 20 30 40 50 60 70 80 90 1000

50

100

150

200

250

300

350

400

450

500

% Sn by weight (tin)

Temperature (Deg. F)

Figure 24: Sn-Bi Phase Diagram from Experimental Data.

In Figure 24, the blue green and red dots depict the experimental temperatures that were recorded for a certain weight percentage of tin. Also, from the above figure, an observation could be made that there were no consistent data points, that is, the there was discrepancy in data from the experiemnt. Hence, the trend lines (the two curved lines) were not intersecting at the eutectic point. However, if the circled blue point had a lower value of temperature, then there could have been a possible intersection of the two curved lines. Another observation that could be made from Figure 24 is that the straight line at the bottom, that is, the eutectic line had consistent data. Also, the liquidus line to the right had consistent data, whereas the liquidus line to the left had inconsistent data. The tie-line calculations cannot be performed on the experimental phase diagrams since there are no solvus lines present. Illustrated in Figure 25, located on top of the following page, is a visual comparison between the experimental results and published results for the Bi-Sn phase diagram experiment:

Liquidus Line

Eutectic Point

Eutectic Line


0 10 20 30 40 50 60 70 80 90 1000

100

200

300

400

500

600

Experimen-tal Data

Polynomial (Experi-mental Data)

Published Value Phase Daigram

% Sn by weight (tin)

Temp. (Deg. F)

Figure 25: Experimental and Published Phase Diagram of Sn-Bi (The Sn-Bi Equilibrium Phase Diagram).

It may be noted at this point that the published results in the preceding figure were obtained from Stevens Institute of Technology (SIT), Hoboken, New Jersey, U.S.A., from their website. The temperature calculations for the published values are depicted in Section 9: Sample Calculations. In Figure 25, the blue lines are the lines that connect all the published values of the phase diagram. An observation could be made that the liquidus line (published) on the left had good correlation with liquidus line (experimental), but this was not true for the liquidus line on the left. Also, the eutectic line was almost same for both the published and the experimental data. However, the eutectic point for the published data was at a lower concentration of Sn than the eutectic point for the experimental data. For a better view of the published results in Figure 25, another published phase diagram is illustrated, on the following page in Figure 26:


Figure 26: Published Phase Diagram from Cambridge University.

As mentioned in the caption of Figure 26, the published Sn-Bi phase diagram was obtained from Cambridge University. While comparing Figure 25 and Figure 26, an observation could be made that the data was almost same for both the published plots. Table 1, below, depicts the percent difference between the published data from SIT and the experimental data from the lab:

Table 1: Comparison of Experimental and Published Data. S.No Composition

(% Sn Weight)

Experimental Temperature

Published Temperature

Percent Difference

1 0 520 520 02 22 480 392 20.53 44 400 285 40.34 62 380 338 12.55 82 425 397 7.166 100 456 449 1.46

In Table 1, the points are not evenly spaced because there was not data at 20 %wt Sn., 40 %wt. Sn, 60 %wt. Sn and 20 %wt. Sn. Hence, the values were taken at 22, 44, 62 and 82 %wt. Sn respectively. From the preceding table, Table 1, an observation could be made that the maximum percent difference was 40.3 percent and was at 44 %wt. Sn, and the minimum percent difference was 0 percent and was at 0%wt. Sn, that is, 100 %wt. Bi. As the % wt. of Sn increased, there was an increase in the percentage difference, and then, there was again a decrease in the percentage difference after a certain point. The increase could be due to the bad


correlation of data between the experimental and the published values on the liquidus line, and the decrease could be due to the fact that the data points on the liquidus line (published) to the right had good correlation to the data points on the liquidus line (experimental). Therefore, moving towards the right in Figure 25, especially after 50 %wt. Sn on the x-axis, the correlation between the experimental and the published values was becoming better. The following inferences may be drawn from Figure 25, Figure 26 and Table 1:

a) The maximum temperatures of the liquidus lines for both the α and β primary phases were found to be within 1.50 percent of the published values at 456 F and 520F, respectively.

b) The eutectic temperature, i.e., the temperature at which the entire solution usually remains all liquid until phase transforms into the lamellar microstructure, was approximated to be an experimental estimate of 275F. The experimental eutectic temperature value was found to within 4 percent of the published value of 284F, thereby depicting excellent agreement.

c) However, the weight percentage at which the eutectic temperature occurs was not depicting excellent agreement. For the experimental data, at the eutectic temperature, the percentage weight of tin was estimated to be 53% wt. Sn. However, for the published data, at the eutectic temperature, the percentage weight of tin was published as 43% wt. Sn. The difference between the published and the experimental values (at the eutectic temperature) for the percentage weight of Sn was calculated to be 18.9.

d) There was not enough experimental data or published data from SIT for the solvus line and the solidus line.

Since both the experimental and published values from SIT did not have either the solvus or the solidus line, another published source was looked at. Figure 27, on the top of the following page, depicts the published value from University of California Davis’ (UCD) college website, and the experimental data for the phase diagram:


0 10 20 30 40 50 60 70 80 90 1000

100

200

300

400

500

600

Exper-imental ResultsLinear (Exper-imental Results)Published Phase Diagram

% Sn by Weight

Temp. (Deg. F)

Figure 27: Experimental and Published (UCD) Phase Diagram (THE BI-SN EQUILIBRIUM PHASE DIAGRAM).

From the preceding figure an observation could be made that Figure 25 and Figure 26 were similar to Figure 27. Table 2, below, depicts the percent difference between the published data from UCD and the experimental data from the lab:

Table 2: Comparison of Experimental and Published Data (UCD). S.No Composition

(% Sn Weight)

Experimental Temperature


Percent Difference

1 0 520 520 02 22 480 389 23.53 44 400 293 36.84 62 380 343 10.95 82 425 398 6.706 100 456 449 1.67

In Table 2, similar to Table 1, the percent difference between the experimental and the published values of UCD was increasing as weight percentage of Sn was increasing in the alloy. However, after a certain point, the percent difference between the experimental and the published values of UCD starts to decrease as the weight percentage of Sn in the alloy increase.


This pattern could be due to the discrepancy in the data from the experiment for the left liquidus line in Figure 24. The discussion for the increase and decrease in percentage difference would be the same for this case as the pervious case since both the published values behaved in a similar fashion. The following inferences may be drawn from Figure 25, Figure 27 and Table 2:

a) The maximum temperatures of the liquidus lines for both the α and β primary phases were found to be within 1.67 percent of the published values at 456 F and 520F, respectively.

b) The eutectic temperature, i.e., the temperature at which the entire solution usually remains all liquid until phase transforms into the lamellar microstructure, was approximated to be an experimental estimate of 275F. The experimental eutectic temperature value was found to within 3 percent of the published value of 281.3 F, thereby depicting excellent agreement.

c) However, the weight percentage at which the eutectic temperature occurs was not depicting excellent agreement. For the experimental data, at the eutectic temperature, the percentage weight of tin was estimated to be 53% wt. Sn. However, for the published data, at the eutectic temperature, the percentage weight of tin was published as 40% wt. Sn. The difference between the published and the experimental values (at the eutectic temperature) for the percentage weight of Sn was calculated to be 24.5.

d) There was not enough experimental data or published data from SIT for the solvus line and the solidus line.

However, the values were slightly different for the both the published values as well, that is, the published values from SIT and UCD. Table 3, below, depicts the differences between the published data that were used for comparison with the experimental data.

Table 3: Comparison of Published Data. S.No Composition

(% Sn Weight)


(SIT)


(UCD)

Percent Difference

1 0 520 520 02 22 392 389 .7653 44 285 293 2.734 62 338 343 1.465 82 397 398 .2516 100 449 449 0

From the preceding table, an observation could be made that the maximum percentage difference between both the published values was 2.73, which indicates that both the published values were in the same vicinity, and that the experiment conducted by the team has a few data points that were incorrect.


From the Table 1, Table 2 and Table 3, and Figure 24 through Figure 27, the following could be observed:

1) Both the published values and the three published diagrams were almost identical. However, for the published data from SIT did not have the solvus and solidus regions.

2) The eutectic temperature from experimental data was within 4 percent of the two published data, depicting an excellent agreement.

3) The weight percentage of Sn at the eutectic temperature was with 20 percent of the two published data, depicting that there was some inconsistent data because the weight percentages of Sn at the eutectic temperature for both the published were within 6.98 percent of each other.

4) The melting points (temperatures) of both the pure elements, that is, the tin and the bismuth, were in the close vicinity for all the three data, the two published and the experimental.

The following reasons could the reason for the inconsistent data:

a) Since the experiment was conducted in a test tube, the Sn-Bi mixture may have been susceptible to both chemical and organic impurities from the environment. Whether or not these impurities may have had a significant impact on the Sn-Bi phase diagram is still unknown.

b) Also, there could have been a misreading of temperature from one of the teams while recording the data during the experiment, which could indicate a slop change much earlier than expected.

c) A possible source for error could have been the frequency of temperature recording while the mixture of Sn and Bi cooled from a temperature of approximately 800 degrees Fahrenheit. An error could only rise from a lack of consistency in the frequency of temperature recordings. All that is required to be noticed is a slope change in the temperature-time plots and these could have been hindered by a lack of consistency in time-temperature recordings.

The experimental melting temperatures of Bi and Sn are compared to the two published melting temperatures of Bi and Sn in Table 4:

Table 4: Melting Points of Sn and Bi.Element Melting Point

(Experimental)Melting Point

(SIT)Melting Point

(UCD)Percent Difference

Sn 520 520 520 0Bi 456 449 449 1.56


From the preceding table, Table 4, an observation could be made that the percent difference between the experimental and the two published values for the melting point of Sn was 0, and the percent difference between the experimental and the two published values for the melting point of Bi was 1.56, indicating excellent agreement between the experimental and the published values.

The following figure, Figure 28 represents the backscatter imaging of a Sn-Bi solid solution of 16 weight percentage of tin, and 84 weight percent of bismuth:

Figure 28: Images of the Specimen from the SEM of the Microstructure.

For the two images in Figure 28, back-scattered electron imaging (BEI) was used. BEI uses high energy elastic electrons to detect differences in atomic (or Z-) number. Higher atomic number elements reflect or highly deflect more electrons along the primary electron axis, where the detector is located. Lower atomic number elements absorb more electrons and appear dark on electron micrographs. Images are the result of Z-number contrast. On flat specimens, this technique may be quite informative, but BEI is sensitive to topography, so this method is suited to specific types of specimens (Morgan). Also in Figure 28, the image to the right is the magnified image of the left.

In Figure 28, the darker regions represent Sn and the lighter regions represent Bi. This is due to the fact that Bi has a higher atomic number than Sn and, therefore, reflects more electrons than the Sn atoms, which was discussed in the preceding paragraph. It may be then concluded that the white lacy structure formed around the dark roundish grains constitutes the Bi-rich α phase, whereas the dark roundish grains represent the Sn-rich β phase. It is evident that the more predominant β phase is the primary phase formed during solidification and that Sn is present at higher weight percentage when compared to Bi within the material.

Another point to be noted is the fact that the white lacy structure is not purely white, that is, this structure, has dark spots. This is because the white region is actually a lamellar microstructure, i.e., a mixture of α and β phases in the form of alternating platelets.


An energy dispersive spectrometry (EDS) measurement on the sample yielded the following results depicted in Table 5:

Table 5: EDS Results on the Bi-Sn Specimen.EDS (wt. % Sn) EDS (wt. % Bi) Calculated (wt.

%Sn)Calculated (wt.

%Bi)Dark Region

(Primary Phase β)91.1 8.90 80 20

Light Region (Lamellar

Microstructure)

33.6 66.4 5 (42) 95 (58)

In order to compare the above results with the published values, first a tie lie was drawn along the 58 weight percent Sn. The vertical line in the Figure R, in the Section 9: Sample Calculations starts at the x-axis where the 58% weight Sn starts and stops just below the eutectic line. At the ends of the tie line, the composition of each phase was noted to be the following:

o For the α phase — 5 percent tin and 95 percent bismuth, ando For the β phase — 80 percent tin and 20 percent bismuth.

In the preceding table, the values in the bracket indicate wt. % Sn and wt. % Bi when the one end of the tie line is assumed at the eutectic point (from the published value). Figure R depicts the ends of the tie line. The complete tie line calculations are depicted in Section 9: Sample Calculations of the report. Table 6, below, compares the calculated weight percentages of the tin and bismuth compared with the values generated from the EDS:

Table 6: Comparison of the EDS Results with Calculated Data.% Difference

(wt. % Sn)% Difference

(wt. % Bi)Dark Region (Primary Phase β) 12.2 55.5

Light Region (Lamellar Microstructure)

85.1 (20) 30.1 (12.7)

In the above table, an observation could be made that when the tie line values ended at the alpha and beta phases, the percentage differences were high. However, when one end the tie lie value was ending at the eutectic point, the percent differences were smaller when compared to the other values for the light region.

As concluded before in this section, the white lacy structure around the dark roundish grains constitutes the Bi-rich α phase, whereas the dark roundish grains represent the Sn-rich β phase. However, when compared to the EDS values, there the percentage differences are really high indicating that the tie line calculation could be wrong. Nevertheless, the when observing the EDS results in Table 5, an observation could be made that —

a) For the dark region, the percentage of tin is higher than the percentage of Bi, which is correct since the dark region is dominated by the tin-rich β phase, but still the percent errors were high for the dark region.


b) For the light region, the percentage of Bi was higher than the percentage of Sn, which is possible since the light region is supposed to be dominated by bismuth, and during the EDS analysis of the dark phase, the white region was chosen for analyzing.

The preceding statements indicate that there was something wrong done during the experiment which generated the huge percent differences. The following reasons could be the cause of error in the experiment:

1. Volume effect: The circle (volume) where electrons interact with the

material varies with a higher magnification, that is, with a large magnification; the small particles’ interaction with the material might be different. In Figure 28, the right image was at a higher magnification than the one on the left one and the resolution is also limited by the size of the interaction volume, or the extent to which the material interacts with the electron beam.

2. Bad scatter: When the primary electron beam interacts with the sample, the electrons lose energy by repeated random scattering and absorption.

3. Black stuff could be something else: The dark region on the image could be a void, a scratch from over polishing in specimen, an air pocket or/and carbide from the silicon carbide paper that was used for polishing.

4. Wrong data recorded: Wrong numbers could have been recorded by the

team while recording the data from the computer.

5. Wrong point selection: While selecting a specific location I the EDS analysis, a wrong location with more number of either dark or light points could have been chosen, which in turn gives huge percent differences.

The scandium software was used to perform a phase analysis on a low-magnification (the left figure in Figure 28) and a high-magnification photograph (the right figure in Figure 28) of the images provided from the SEM. Figure 29 illustrate the images from the scandium software:

Figure 29: Images of the SEM Viewed with Scandium Software of the Microstructure.


The summary of this analysis and its comparison with the calculated tie lie results is summarized on Table 7 and Table 8, below. It is assumed that the weight percent of each phase may be approximated as the area percent of each phase as provided by the scandium software.

Table 7: Scandium Results with Theoretical Estimates for the Low-Magnification SEM Image.

Area % β

Area % α

Weight % β

Weight % α

Difference %β

Difference % α

82.4 17.6 70.7 29.3 14.5 39.9

Table 8: Scandium Results with Theoretical Estimates for the High-Magnification SEM Image.

Area % β

Area % α

Weight % β

Weight % α

Difference %β

Difference % α

79.0 21.0 70.7 29.3 10.5 28.3

From the preceding table, an observation could be made that as the images was zoomed in, the percentage difference between the Scandium results and the theoretical estimates was decreasing. The tie line calculations are depicted in Section 9: Sample Calculations of the report. In Figure 29, the green color represents the white portion in the SEM image, that is, the green color represents the bismuth present. And similarly, the red color represents the dark region, which is the amount of tin present. It may be observed from the above table that there is decent agreement between the experimental and calculated α phase results. However, for the β phase results, the percent difference between the experimental and the calculated values was high. This high difference in the values could be due to the effects mentioned previously for the EDS analysis, and also, when the area percentage is determined, the number of colors chosen was two. Hence only green and red were chose, which would account for everything that is either white or black. As mentioned previously in the EDS analysis, the black spots could not only be the primary phase or the tin rich β phase, but could also be voids, carbide from SiC and etc.

Also, the figure on the left in Figure 29 shows a high percentage of β, which is concurred with the discussion made previously that the tin was β rich, and the figure on the right in Figure 29 depicts a high β concentration as well. However, this is not true since the light region on which the EDS analysis was performed was supposed to be Bi rich. This indicates that when the location for the EDS measurement was chosen, the white or the light location actually had more tin than bismuth, and it just appeared to be the bismuth dominated region.


5.0 CONCLUSIONS AND RECOMMENDATIONS.

5.1 CONCLUSIONS

The following conclusions could be summarized from the Sn-Bi phase diagram experiment:

1) The first portion of the lab helped in creating a cooling curve for the Sn-Bi alloy with varying Sn/Bi compositions.

2) The cooling curves were then used for creating the phase diagram, which was

pretty close to the published phase diagrams.

3) The second portion of the lab helped in determining the elements present in a given specimen with the help EDS. This in turn, allowed the students to learn more details about the SEM’s topics like volume effects and back scatter.

4) New software was introduced to the students, which was known as the Scandium software. This software could do the phase analysis by calculating the area percentage of each phase.

5) However, in both 3 and 4, the method did yield some values that were not expected, and the reasons behind the unexpected values were discussed in Section 4: Results and Discussion.

5.2 RECOMMENDATIONS

The following recommendations could be made for the future labs regarding the Sn-Bi phase diagram experiment:

1) Careful readings of the temperature changes have to be recorded in order to get a valid phase diagram that could be published by the school.

2) During the EDS analysis, proper locations of the light and dark structure have to be picked in order to get less percent differences between the calculated and experimental data.

3) Multiple EDS and Scandium calculations should be done to get an average value for the multiple experiments. This would try to eliminate any inconsistent data.


6.0 REFERENCES

Askeland, D.R., & Phulé, P.P. (2007). The Science and Engineering of Materials: Fifth Edition. Toronto: Thomson.

Energy Dispersive X-Ray Spectroscopy (EDS). (n.d.). Retrieved November 15, 2009, from PhotoMetrics, Inc. : http://www.photometrics.net/eds.html

Fischer, T. (2009). Material Science For Engineering Students: First Edition. Canada: Academic Print of Elsevier (Academic Press).

Heating and Cooling Curves. (n.d.). Retrieved November 12, 2009, from Kentchemistry: http://www.kentchemistry.com/links/Matter/HeatingCurve.htm

Morgan, D. G. (n.d.). Elemental Identification. Retrieved November 16, 2009, from Microscopy: http://www.microscopy.ou.edu/element.shtml

Lanning Jr. D. (2005). Lab Results, Data and Photos. Photos posted on T-drive, under ES321 Folder, and inside Lab Photos Folder archived at T:\ES321\Lab Photos.

Lanning Jr. D. (2006). Lab Results, Data and Photos. Photos posted on T-drive, under ES321 Folder, and inside Lab Photos Folder archived at T:\ES321\Lab Photos.

Lanning Jr. D. (2009). Lab Experiment Sheet #1. Handout Given in Lab/Class on November 3, 2009.

Scanning Electron Microscopy (SEM) & Energy Dispersive X-Ray Spectroscopy (EDS) . (2008). Retrieved November 14, 2009, from Micron Inc. Analytical Service Laboratory: http://www.micronanalytical.com/sem.html

The Sn-Bi Equilibrium Phase Diagram. (n.d.). Retrieved November 14, 2009, from Stevens Institute Of Technology : http://www.stevens.edu/hydrogel/backup/libera/courses/e321/lab_manual/lab_8.pdf

THE BI-SN EQUILIBRIUM PHASE DIAGRAM. (n.d.). Retrieved November 15, 2009, from University Of California Davis: http://chms.engineering.ucdavis.edu/students/undergraduates/labs/files/Experiment-3.pdf

Warren, A. (1997, November 17). Phase Diagrams. Retrieved November 14, 2009, from University of Southampton: http://www.soton.ac.uk/~pasr1/index.htm


7.0 ATTRIBUTIONS

Role PerformerLaboratory Instructor Dr. David Lanning

Experiment of the Sn-Bi Phase Diagram Virat MathurSreyes Kadapala

SEM images and Scandium Images Arpit MehtaVirat Mathur

Sreyes Kadapala


8.0 APPENDIX A: RAW DATA

List of all cooling curves

0 2 4 6 8 10 120

2

4

6

8

10

12main-title

Series1Series3Series5Series7Series9Series11Series13Series15Series17Series19Series21Series23Series25Series27Series29Series31Series33Series35Series37Series39Series41Series43Series45

Time (s)

Tem

pera

ture

(oF)

Published C F 139 282.2

100 231.9 449.4243 139 282.2

100 231.9 449.4279 139 282.2

43 139 282.20 271 519.8

79 139 282.2

0 139 282.2


slope of line 1 = -5.5256x + 519.8

slope of line 2= 2.9337x +

156.05 SIT VALUES % Diff'

0 519.8 5200.03847

6

22398.236

8 480 20.5313

44285.132

8 40040.2855

1

62337.939

4 380 12.4462

82396.613

4 4257.15724

7

100 449.42 4561.46410

9

UCD valuesUCDAVIS EXP %Diff

0 519.8 520 0.03847622 388.58 480 23.5266944 292.46 400 36.7708462 342.68 380 10.8906382 398.3 425 6.70349

100 448.52 456 1.667707

Experimental ValuesBi Sn Temperature

100 0 52096 4 500 27590 10 410 27388 12 490 27584 16 485 27578 22 480 27576 24 470 27572 28 421 27868 32 460 27656 44 400 271


50 50 300 27042 58 355 27538 62 380 27036 64 378 26630 70 386 27126 74 400 26524 76 393 26718 82 425 27014 86 440 26512 88 436

6 94 4502 98 4450 100 456


9.0 APPENDIX B: SAMPLE CALCULATIONS

0 10 20 30 40 50 60 70 80 90 1000

100

200

300

400

500

600

Exper-imental ResultsLinear (Exper-imental Results)Published Phase Diagram

% Sn by Weight

Temp. (Deg. F)

Figure R: Tie Line Calculations

formal lab 2

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