Department of Mechanical and Mechatronics Engineering

MTE 111 Structure and Properties of Materials

Lab 1 - Crystallography

Prepared for Professor Mayer

Group 102-1

Tomas Gareau Wayne Hoac

Younghwan Jung Umer Kamran Wasee Malik

Tristan Walker

May 16, 2014

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Table of Contents

Abstract ....................................................................................................................................... 2

1. Introduction ................................................................................................................. 2 1.1. Objectives ........................................................................................................................... 2 1.2. Problem Definition ............................................................................................................ 2 1.3. Method for Solution .......................................................................................................... 2

2. Experimental Apparatus and Procedures ................................................................ 3 3. Results .......................................................................................................................... 4 4. Discussion .................................................................................................................... 6

4.1. Results and Observations ................................................................................................. 6 4.1.1. Simple Cubic Structure .................................................................................................. 6 4.1.2. Body Centered Structure ............................................................................................... 6 4.1.3. Face Centered Structure ................................................................................................ 7 4.1.4. Hexagonal Close-Packed Structure .............................................................................. 7 4.1.5. Structure Comparison ................................................................................................... 8 4.1.6. Crystal Defects ................................................................................................................ 9 4.1.7. Materials .......................................................................................................................... 9 4.1.8. Interstitial Crystal Defects ........................................................................................... 10 4.2. Safety of Experiment ....................................................................................................... 10 4.3. External Information ...................................................................................................... 11 4.4. Engineering Tools Used .................................................................................................. 11

5. Conclusions ................................................................................................................ 13 6. References .................................................................................................................. 14 Appendix .......................................................................................................................... 15

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Abstract The purpose of this lab was to gain an understanding of different unit cells and material structures. This was done by stacking Ping-Pong balls on metal pegs to create BCC, FCC and HCP unit cells. The completed models were then compared and analyzed for the stacking sequence of their closest packed planes. The observations of this lab showed that HCP and FCC unit cells are more efficient in terms of empty space within the unit cells of the specific structures, while BCC unit cells are more ductile.

1. Introduction

1.1. Background According to the Atomic Theory as proposed by John Dalton, all matter is made up of discrete units known as atoms [1]. The various arrangements of these small particles with respect to one another is what yields each and every unique material found on the planet. The science of crystallography seeks to examine the structure of solids, and how this affects the associated properties of the molecular object [2]. Auguste Bravais (1811 - 1863) was a French crystallographer who is accredited with identifying the fourteen unique three-dimensional crystal lattices that exist in nature [3]. These provide the foundation for the modern understanding of atomic structure of crystals and are illustrated in Figure A.1 in Appendix A.

1.2. Problem Definition To investigate how various crystalline units are arranged in a three dimensional space, and which of these makes the most efficient use of empty space within the overall structure. Specifically, the body centered cubic unit, the face centered cubic unit, and the hexagonal closed pack unit cells will be examined. Furthermore, a correlation will be sought between this optimization of empty space, and the physical and chemical properties exhibited by materials with the respective structure. In doing so, real world applications of materials consisting of these three crystal lattices will be analyzed to determine how they are best made use of.

1.3. Method for Solution If particles are overlaid together such that the ones in the layer above and below occupy the spaces resulting from the intermediary layer, then the empty spaces will be optimized in such a way as to result in the most compact crystalline structure. If a solid has a structure with minimal free space, then it should have the greatest tensile strength, malleability, and conductivity, but may become less chemically reactive overall. These hypotheses are derived based on observing the properties of known elements with a body centered cubic unit structure (lithium, chromium, and vanadium), with a face centered

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cubic unit structure (aluminum, copper, and gold), and hexagonal closed pack structure (cadmium, magnesium, zinc) [4].

2. Experimental Apparatus and Procedures To acquire a sound understanding of different crystal structures and their respective properties, observations must first be made at a physical level. As such, the apparatus capable of depicting the base unit cell models of different crystal lattices was required. Apparatus 1) Metal rods

2) Wooden Ping-Pong balls 3) Metal base platform

The procedure that was used during the experiment followed the steps outlined for Procedure A in the lab guide. Succinctly described, this involved creating models using cylindrical metal rods and wooden Ping-Pong balls over a metal base platform in the shape of a rectangular prism. Pictures were taken for FCC, BCC, and HCP crystal lattices, and appropriate sketches were made to give a better visualization. The closest packed planes were observed, and empty spaces where interstitial atoms may reside discussed. Procedure B on the lab guide was not a part of the experimental procedure due to technical difficulties with the lab computers. These computers ran the interactive software IMSE, and could not be accessed during the lab exercise. The software would have given a good understanding of the specific orientation and chemical structure of various lattices. To counter this hindrance, additional research was required regarding the orientation of different lattices and the chemical properties that these entail.

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3. Results The results for this experiment reflect the notion that the space between each ping pong ball as the deciding factor to how compact each base unit cell is. Sketches were made on the pictures (refer to Appendix A for pictures) taken for FCC, BCC, and HCP structures.

Figure 1: Sketch reproduction of the FCC structure.

Figure 2: Sketch reproduction of the BCC structure.

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Figure 3: Sketch reproduction of the HCP structure.

Since this experimental procedure involved making physical models of different structures, raw data was gathered for each respective base unit cell. The total number of atoms, coordination number, and atomic packing factor was recorded [3].

Table 1: Number of atoms, coordination number, and atomic packing factor for FCC, BCC, and HCP

Structure Number of atoms Coordination number

Atomic packing factor

FCC 4 12 0.74 BCC 2 8 0.68 HCP 6 12 0.74

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4. Discussion

4.1. Results and Observations

4.1.1. Simple Cubic Structure Though not studied in this investigation, in order to the adequately explain the structures to proceed, it would be very appropriate to explain the simple cubic structure. The simple cubic structure is an arrangement where the atoms are aligned in such a way that any given atom only has adjacent/touching atoms orthogonal to itself. The reason why it is called the simple cubic structure can be seen more clearly when observing its unit cell. A unit cell is the simplest, and least volume consuming structure that can be used to form the rest of the crystal structure [5]. The unit cell of the simple cubic structure looks like a cube, with distances between adjacent atoms being equal and the only atoms that make up the unit cell being the one-eighth atoms on each of the 8 vertices of the cube. Another concept that will become useful in describing the preceding structures is called the atomic packing factor. This is a value representing the ratio between the occupied volumes of the unit cell to the total volume of the unit cell. For example, the calculated packing factor of the simple cubic structure came out to be 0.52 [3].

4.1.2. Body Centered Structure The general sense of the body centered structure can be best described as the unit cell of the simple cubic structure with another atom in the center of the cube [3]. However, due to the fact that an equal sized hard sphere cannot fit in the center of the cube without overlapping with preexisting atom parts, the result of the center sphere causes the overall size of the unit cell to become bigger than seen in the simple cubic structure. As an effect, not only did both the occupied and total volume increase due to the introduction of the new center atom, the atomic packing factor also increased to a value of 0.68. This increase in the atomic packing factor, though simple to determine, provides some valuable information about this specific structure [4]. The low value of the simple cubic structure of the atomic packing factor in tandem with the fact that the alpha form of polonium [6] is the only known example of this lattice supports the notion that materials have a tendency to avoid inefficient or unstable configurations.

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Figure 4: Coordinate, base unit, and mesh visualizations of BCC [4].

4.1.3. Face Centered Structure The face centered structure at first glance may seem quite related to the body centered structure, but the face centered structure has its structural difference. First off, as the name implies, the new atoms appended to the simple cubic structure is in the center of every face as opposed to the center of the entire cubic body. This structure has an atomic packing factor of 0.74, which is even higher than that of the body centered structure. This makes it the most packed cubic structure [3]. These types of structures are thus rightfully named close-packed, this specific one being the cubic close-packed structure [7].

Figure 5: Coordinate, base unit, and mesh visualizations of FCC [4].

4.1.4. Hexagonal Close-Packed Structure The hexagonal close packed structure, similar to the face centered structure is close packed, and thus is one of the most efficiently stacked structures currently known. It also has an atomic packing factor of 0.74.

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Figure 6: Coordinate, base unit, and mesh visualizations of HCP [4].

4.1.5. Structure Comparison In this investigation, three main crystal structures, the body-centered cubic (BCC), the face-centered cubic (FCC) and the hexagonal close packed (HCP) structures were observed. While doing the investigation, it was noted that there are structural similarities and differences to the structures, some more obvious than others and some unexpected. At first glance, the structure of the BCC and the FCC structures seem to have the most in common compared to the HCP structure, the former two sharing the square shaped layers when building them out of the wooden balls and the prongs provided. However, there is a greater structural similarity between the FCC and HCP structure, which can be shown by building the FCC structure on the HCP block by making some minor alterations [8]. The difference between the FCC and HCP structures is but one layer, making the difference between the ABCABC pattern used for making the FCC structure and the ABABAB pattern used for making the HCP structure [3].

Figure 7: Comparison of HCPs ABA orientation and FCCs ABC orientation [3].

This increase in the atomic packing factor, though simple to determine, allows some valuable information about this specific structure. The low value of the simple cubic structures atomic packing factor indicates that it is not a structure that is favored in

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nature because in the natural order of things, two of the most valued properties are efficiency and stability. The higher the number for the atomic packing factor, the more efficient it is, thus making the body centered structure more efficient than simple cubic, but something that can be seen by observing the simple cubic structure is that it is more readily structured to be deformed into another structure like the body centered cubic structure or the face centered structure. As taking the properties that nature values, the correlation between the increase of ductility rising with the atomic packing factor and also with cubic shapes over non-cubic shapes offer valid reasoning. Close packed and cubic structures are both able to shift more readily than other structures, making them less susceptible to breaking when the appropriate force is applied, but rather bending before such consequence takes place [7].

4.1.6. Crystal Defects A crystal defect is defined as a deviation from ideal crystalline patterns. Using the ideal case for each structure allows visualization of these crystal structures and their properties, but in reality it is nearly impossible to create a scale structure that is perfect. However, contrasting its name, crystal defects may have a positive or negative effect depending on what the material was intended for. The existence of these defects inhibits the structures ability to linearly shift, resulting in a less ductile material. If these defects are created due to breakdown of structure due to external causes, natural or artificial, or due to the introduction of another element, because the new structure renders it more difficult for the material to shift into a stable pattern, it is now less ductile, hence stronger [9]. In this investigation, the use of the wooden balls and the prongs allowed for visual observation of the empty spaces in between the atom representations, which resembled tetrahedrons and octahedrons. Tetrahedrons and Octahedrons are the two simplest 3-dimensional shapes that can be formed from faces exclusively made from triangles. Although, the tetrahedral empty spaces were found in all three structures, the octahedral empty space were found in the body centered and face centered cubic structures.

4.1.7. Materials Due to the property of body centered cubic structure not being closely packed, metals that have this structure are usually harder and less ductile seen in metals that are in groups 1A, 2A and some of the early transition metals such as lithium (Li), Sodium (Na), Potassium (K), Chromium (Cr), Barium (Ba), Vanadium (V), Alpha-Iron (a-Fe) and Tungsten (W) or metal alloys that are principally composed of these elements [6]. The face centered cubic structure being the most malleable structure of the three structure mentioned, due to its closely packed nature and cubic shape, it is also rightfully associated with metals that are known for many commercial and industrial uses for their flexible nature [3]. Some metals that have the face centered cubic structure are aluminum (Al), copper (Cu), gold (Au), iridium (Ir), lead (Pb), nickel (Ni), platinum (Pt), and silver (Ag), or alloys where these elements are predominant [4]. Some naturally found metals adopting the hexagonal close packed structure include Beryllium (Be), Cadmium (Cd), Magnesium (Mg), Titanium (Ti), Zinc (Zn), and Zirconium (Zr) [4].

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4.1.8. Interstitial Crystal Defects A crystal defect is defined as a deviation from ideal crystalline patterns. Using the ideal case for each structure allows visualization of these crystal structures and their properties, but in reality it is nearly impossible to create a scale structure that is perfect. However, contrasting its name, crystal defects may have a positive or negative effect depending on what the material was intended for. The existence of these defects inhibits the structures ability to linearly shift, resulting in a less ductile material. If these defects are created due to breakdown of structure due to external causes, natural or artificial, or due to the introduction of another element, because the new structure renders it more difficult for the material to shift into a stable pattern, it is now less ductile, hence stronger [9]. Materials with face centered structures like aluminum are rarely used in their pure forms. Instead, they will be mixed with other metals to create alloys that benefit from face centered cubic structure properties. For example, aluminum can be mixed with metals such as chromium, copper, iron, magnesium, or zinc to create an alloy with higher tensile strength than aluminum in its pure form. Such alloys, being composed primarily of aluminum, will remain lightweight and can be suitable for industrial uses such as aircraft construction [10].

4.2. Safety of Experiment This laboratory exercise, as described in the lab guide, is virtually risk-free. The ping-pong ball models used to visualize the various crystalline structures are constructed from non-hazardous materials (wood and aluminum, specifically). There are no moving parts to account for, and the ping-pong ball models are not large enough to warrant the use of personal protective equipment such as hard-toed footwear. As such, there are very few personal safety considerations to take into account before attempting the exercise. The implementation of the laboratory exercise, however, brings up a few safety considerations. There are certain practices that should be considered due to the relatively small size of the laboratory room. There are a couple potential issues with the size of the room; one issue is that in such a confined space, the propagation of bacteria may be difficult to control. Another is that the crowded orientation of tables and chairs presents a potential safety hazard in the event of an emergency. Frequent use of proper hand washing techniques is important for sick individuals to prevent the transfer of infectious diseases through shared surfaces. This is especially important as multiple groups of students will perform the experiment during the same day, and all are likely to come into contact with the tables and materials that previous groups used. Another issue with the relatively small space in which to work is the spacing of the lab stations. As the room is currently organized, there are many students who end up at the center of a group of tables. These students do not have proper egress space, blocked as they are by other students and backpacks. In the event of an emergency, they may have difficulty in making a timely exit from the room. This sort of overcrowding can be dangerous in the event of a fire, but can easily be addressed by re-organizing the tables

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and chairs in the lab room to provide a wider, clearer space for students to move around in, and by designating a certain corner of the classroom for backpacks and other bags. There are no other significant safety issues specific to this implementation of the lab exercise. There are, however, more general safety procedures that apply to the University of Waterloo. These practices deal with unexpected emergencies, such as fire or first-aid emergencies. The best way to implement these safety practices is by informing students of the universitys emergency response procedures. The website for the University of Waterloos Safety Office is an excellent resource for students [11]. There is building-specific information that should be reviewed prior to commencing any sort of lab work, regardless of the perceived risk (or lack of).

4.3. External Information Two major sources of information used in the discussion section of this report are chemed.chem.purdue.edu and ndt-ed.org. chemed.chem.purdue.edu was a source of information for the crystal lattices studied in this lab exercise. This website is maintained by the Bodner Research Group of Purdue University in Indiana, and serves as a resource for chemistry studies. Information about the effect of the crystal lattices on the materials physical properties, as well as a basic introduction to crystalline structures, can be found here. As a university-provided resource, the information found at this website is considered to be highly reliable. ndt-ed.org is maintained by the Collaboration for Nondestructive Testing, and aims to serve as a resource for the nondestructive testing community. Much of the information relating to nondestructive testing was relevant to the topics covered by this lab report. This is considered a reliable reference due to the support and quality control provided by various US universities and colleges.

4.4. Engineering Tools Used There are two engineering tools designated for use in the visualization of crystalline structures. The first is the ping-pong ball model, the use of which is discussed at length throughout this report. The second is the IMSE software, which will not appear in this report due to technical difficulties experienced during the day of the laboratory exercise. The ping-pong ball model has three main components: balls, rods, and base plates. The balls are constructed from wood and have a hole drilled straight through the centre of the ball. These holes are approximately inch in diameter, and allow the balls to slide onto the aluminum rods. These aluminum rods range in size from approximately 3 to 6 inches, and are held in place by the base plate. The base plates are also constructed from aluminum. They are square plates with hole patterns drilled into the face of the plate. These hole patterns do not pierce through the plate. These holes accommodate the rods. Different base plates are drilled with different hole patterns to build various unit cell models. The three patterns that are used are HCP (Hexagonal Close Packed), FCC (Face Centered Cubic), and BCC (Body Centered Cubic) patterns. The ping-pong ball model is useful for understanding the basic building blocks of crystalline structures. The hands-on approach to this visualization exercise is designed to

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encourage students to step through the structure of crystalline materials in their minds. The end-result of the different packing sequences can be immediately observed in 3 dimensions. A disadvantage of this model is its simplicity when compared to the IMSE software. The IMSE software could process more complex patterns far more quickly than the ping-pong ball model. Unfortunately, technical difficulties prevented the group from exploring structure models with IMSE software.

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5. Conclusions This lab succeeded in demonstrating different unit cells and their relations with material structures. Furthermore, the results of this experiment allowed for a connection to material properties that might be explored later on. After investigating the various crystalline units and their efficiency in terms of unit cell density, HCP and FCC are the most efficient compared to BCC. However, efficient use of the empty space doesnt mean materials with HCP or FCC structures are always better. The different materials have different properties because of their structures. Materials are harder and stronger with a BCC structure which is good for specific purposes but the malleability of HCP and FCC structured materials would be more appropriate in different cases. The empty space in the structures allow for different defects within the structure itself. These defects are also a factor in the properties of a material, and can affect properties such as ductility or density. Specific orientation and chemical structure of various lattices could have been investigated with the interactive IMSE software. This area of investigation is not included in this report due to issues with the software at the time of the lab exercise.

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6. References [1] De Leon, N. Dalton's Atomic Theory. November 2000.

http://www.iun.edu/~cpanhd/C101webnotes/composition/dalton.html (accessed May 15, 2014).

[2] American Crystallographic Association. Careers In Crystallography: Exploring the Structure of Matter. n.d. http://www.amercrystalassn.org/content/pages/main-careers (accessed May 15, 2014).

[3] Shackelford, James F. Materials Science for Engineers, 8th Edition. New Jersey: Prentice Hall, 2014.

[4] Nondestructive Testing Resource Center. Primary Metallic Crystalline Structures. n.d. http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Structure/metallic_structures.htm (accessed May 15, 2014).

[5] Durland, Greg. Unit Cells. n.d. http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch13/unitcell.php (accessed May 15, 2014).

[6] Durland, Greg. The Structure of Metals. n.d. http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch13/structure.php (accessed May 15, 2014).

[7] Nondestructive Testing Resource Center. Solid State Structure. n.d. http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Structure/solidstate.htm (accessed May 15, 2014).

[8] Nondestructive Testing Resource Center. Similarities and Difference Between the FCC and HCP Structure. n.d. http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Structure/fcc_hcp.htm (accessed May 15, 2014).

[9] Nondestructive Testing Resource Center. Crystal Defects. n.d. http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Structure/crystal_defects.htm (accessed May 15, 2014).

[10] Cobden, Rob, Alcan, and Banbury. Aluminum: Physical Properties, Characteristics and Alloys. 1994. http://www.alueurope.eu/talat/lectures/1501.pdf (accessed May 15, 2014).

[11] University of Waterloo Safety Office. Emergency Procedures. n.d. http://www.safetyoffice.uwaterloo.ca/hse/emergency/emergency_intro.html (accessed May 15, 2014).

[12] "Crystallography." In McGraw-Hill Encyclopedia of Science and Technology, by Sybil P Parker. New York: McGraw-Hill Book Company, 1982.

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Appendix A

Figure A-1: The 14 Bravais Lattices, their parameters, and examples [5].

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Figure A-2: Picture of the FCC base unit cell from the experimental procedure.

Figure A-3: Picture of the BCC base unit cell from the experimental procedure.

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Figure A-4: Picture of the HCP base unit cell from the experimental procedure.