Experiment 3: Modeling the Solid State CH3500: Inorganic Chemistry, Plymouth State University

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1 Experiment 3: Modeling the Solid State CH3500: Inorganic Chemistry, Plymouth State University Adapted from Experiment 2. Solid State Structure and Properties, Teaching General Chemistry: A Materials Science Companion, A.B Ellis, M.J. Geselbracht, B.J. Johnson, G.C. Lisensky, W.R. Robinson, American Chemical Society, Washington, D.C (1993). References: 1) 2) 3) "Solid-State Model Kit Instruction Manual, 2 nd edition" GC Lisensky, JC Covert, LA Mayer, Institute for Chemical Education, University of Wisconsin-Madison (1994). Introduction: Crystalline materials in the solid state (including metals, alloys, semiconductors, and ionic compounds) have patterned arrangements of atoms that in principle can extend infinitely in all three dimensions. This extended structure of atoms/ions can be described alternately as layers of stacked spheres or as the three-dimensional repetition of a "unit cell." A large number of identical spheres may be packed in a handful of ways, the most efficient of which is known as close-packed, of which there are two common arrangements: hexagonally close-packed (hcp) and cubic close-packed (ccp). In a pure metal, for example, all the atoms are exactly the same size, so it is no surprise that many (but not all!) metallic elements adopt a ccp or hcp structure. Any scheme involving the packing of spheres will have unoccupied spaces, termed interstitial sites. A useful way to describe the extended structures containing more than one sized atoms (such as ionic compounds or alloys) is to assume that the overall structure is based on a sphere-packing scheme controlled largely by the larger ion, with the smaller ion occupying the interstitial sites (Figure 1). A useful way to describe the basic pattern of an extended structure is to conceive of a threedimensional, six-sided figure having parallel faces (e.g., a box) that encloses a portion of the interior of the extended structure. A cube is one example, but the more general case has neither 90 ᵒ angles nor CN 12 CN 8 CN 6 CN 4 Figure 1: Packing around interstitial sites with coordination numbers 4, 6, 8, and 12. Note the cubicpacking around the site with coordination number 8 and the close-packing around sites with coordination numbers 4, 6, and 12. Copyright Plymouth State University and Jeremiah Duncan. May be distributed freely for education purposes only. 1

2 equal length sides and is called a parallelepiped. A parallelepiped chosen so that, when replicated and moved along its along its edges, it generates the entire structure of the crystal is called a "unit cell." The unit cell is thus the simplest repeating unit of the crystal, the contents of which give the chemical formula for the solid. The simplest systems to consider are the cubic ones, of which there are three types: primitive, body-centered, and face-centered. Figure 2 shows the face-centered cubic unit cell for a compound with a formula of (large ions) 4 (small ions) 4. Notice that there are atoms occupying four different sites in this unit cell, and that each site contains a different fraction of an atom (Table 1). Table 1: Locations and Fraction of Atoms in Figure 2 Site Corners 1/8 Face 1/2 Edge 1/4 Center 1 Fraction of Atom Figure 2: A unit cell with spheres at corners, edges, faces, and the center It is important to be able to describe the contents of a unit cell, including the exact positions of the atoms. This can be cumbersome, especially in 3-D drawings, so a system has been developed for indicating atom positions on a 2-D projection of the 3-D unit cell. Figure 3 shows a body-centered unit cell in three dimensions, with its 2-D projection. Note that axes are labeled 'a,' 'b,' and 'c,' and that atom positions are given as a fraction of the unit cell--in other words, atoms at the edges are either at 0 or 1, and those between edges are a fraction of 1. In the 2-D projection, numbers indicate the position in the 'c' direction; two (or more) numbers in parentheses indicate there are two (or more) atoms in that 'c' axis. (0,1) b c a b a ½ A Figure 3: A) Three-dimensional representation and B) two-dimensional projection of a body-centered cubic unit cell. B Copyright Plymouth State University and Jeremiah Duncan. May be distributed freely for education purposes only. 2

3 In this lab, you will explore the packing arrangements and unit cells of solid state materials with uniform size atoms (e.g. metals) and multiple sizes of atoms (e.g. salts) by constructing portions of extended three-dimensional solids using a solid-state model kit. Your models will be used to determine unit cells, coordination numbers, and empirical formulas. You will then investigate these structures using computer programs that allow you to visualize and manipulate crystal structures. Procedure A. Pre-Lab: Unit Cells on Paper Note: You must perform this part of the procedure in your lab notebook before coming to lab. 1. Draw a cube and fill in the blanks: A cube has corners, edges, and faces. 2. Consult Figure 2, construct, and fill in the following table: Large Ions Large Ions Small Ions Small Ions Site Number of sites Fraction of Atom Number of Atoms 3. In two dimensions, the unit cell is a parallelogram. Repeatedly moving the unit cell in the plane of the paper in the directions of its sides will replicate the entire structure. Structure A (Figure 4) shows this, with the original unit cell as a dark parallelogram and the light parallelograms as the initial repeats. A B C D Figure 4: Two dimensional patterns and unit cells a) Print out Figure 4 (the website contains the file "03-Figure4-for_printing.pdf" with multiple copies of the figure.) In structures B, C, and D, draw the outline of the two-dimensional unit cells. Some helpful notes in determining unit cells are: It must include the circles as well as all the spaces It must have four sides b) Repeat step 'b', on a different copy of Figure 4, but find different until cells. Copyright Plymouth State University and Jeremiah Duncan. May be distributed freely for education purposes only. 3

4 c) By convention, unit cells are designated such that: The corners lie at the center of the atoms It should be as small as possible Determine whether the unit cells you have drawn meet these criteria. If not, draw unit cells meeting these criteria on a third coy of Figure 4. d) Paste your Figure 4's into your notebook. 4. By consulting Figures 3, draw a 2-D projection of the face-centered unit cell in Figure 2. B. Modeling in 3-D In this investigation, you will work with a partner as a team. Two teams will then work together to build and compare different models. 1. Familiarize yourself with the model kit by reading pages 4-5 of the Model Kit Instruction Manual. 2. Practice building a model by following the instructions for the NaCl Example on pg 6-7 of the Instruction Manual. Just build the model, do NOT answer Analysis questions for this structure. 3. Find another Team to work with and decide who will be Team A and who Team B. For each pair of structures listed below, answer the following questions, as well as the specific questions listed for the pair of structures: Analysis Questions a) On the model, identify a unit cell. Sketch this unit cell in your notebook. b) For each atom type, fill out a row in a table such as: Table XX: Appropriately number and label your table Struct ure Atom Anion Cation Number of spheres with centers at the Corners Faces Edges Middle # Corner spheres 1/8 NOTE: some structures only have one atom type. Construct your table appropriately. Atoms in the unit cell # Face spheres 1/2 # Edge spheres 1/4 # Center spheres 1 Total NOTE: Construct table so all the information from all the structures can be collected in one table Copyright Plymouth State University and Jeremiah Duncan. May be distributed freely for education purposes only. 4

5 c) For each atom type, fill out a row in a table such as: Table XX: Appropriately number and label your table Structure Atom Anion Cation Color Number of neighbors touching the sphere in Layer below Same layer Layer above NOTE: some structures only have one atom type. Construct your table appropriately. Coordination number NOTE: Construct table so all the information from all the structures can be collected in one table Note: If the structure has more than one size of spheres, nearest neighbor touching spheres, may be of unequal size. d) Draw a 2-D projection of the unit cell. e) Are the large spheres closest packed? f) How do the two structures of Team A and Team B differ? g) Answer any specific questions asked about each pair. (see below) Structures to Build a) Team A: Primitive cubic (pg 9) Team B: Body-centered cubic (pg 18) Which structure is more efficient at filling space? How would the density of the same element in either of these packing structures compare? b) Team A: CsCl (pg 11) Team B: CsCl, alternate (pg 12) What is the geometric shape of just the large spheres? Of just the small spheres? Are the unit cells the same? If not, how do they differ, and is one wrong? You may wish to build more than just one unit cell to check your answer. c) Team A: Fluorite (CaF 2 ) (pg 14) Team B: Zinc Blende (ZnS, fcc) (pg 41) Which color sphere represents Ca and which represents F? Which color sphere represents Zn and which represents S? Note similarities and differences between these structures, paying particular attention to the stoichiometry. NOTE: After completing structure 'c', move on to Part "C. Using Crystal Structure Display Programs." Come back to structure 'd' only if you have time. d) Team A: Hexagonal close-packed (pg 24) Team B: Cubic close-packed (pg 25) Most of the elemental metals have close packed structures. What is the difference, if any, between the two structures? It may be useful to compare the templates on which the structures are built. Closepacked structures are often described as having layers that repeat as ABAB... or ABCABC... Identify the hcp and ccp structures as either AB or ABC. Note: It is helpful to identify the until cell in these structures by using yellow balls at the corners of the cells. Copyright Plymouth State University and Jeremiah Duncan. May be distributed freely for education purposes only. 5

6 C. Using Crystal Structure Display Programs The programs you will be using run on Linux. You will be provided with a bootable USB drive that can be used to run Linux and the programs on just about any 32-bit PC computer. You may use your own computer or those provided in lab. You will continue working with your lab partner(s) for this portion, though if the computers are available, individual students may each use a computer. 1. Boot into the Linux operating system. (Note: These instructions are for the Dell laptops you will be provided in lab. If you are using your own computer, follow the instructors on your computer's screen to get to the Boot Menu and boot from the USB drive). a) BEFORE turning the computer on, insert the USB drive into a USB port on the computer. b) Turn on the computer and pay close attention. An initial splash screen with the Dell logo will appear. Immediately strike the F12 key a few times to load the Boot Menu. If you are not fast enough, Windows 7 will boot. Allow it to boot fully, then shutdown and try again. c) Chose "USB Storage Device." d) Another boot menu will appear. Chose the first entry "Ubuntu" or just wait a few seconds and it will be chosen automatically. e) Login to the PSU Student account with password "PSUchemistry" 2. Some tips for navigating Ubuntu Linux: a) In the far upper-left corner is an icon of a white mouse (Ubuntu) on a blue globe. This is the Applications menu, which you can use to start a number of programs. b) To the right of the Applications menu is a Places menu, which lists a number of common directories where you can find files. c) In the far upper-right corner will be a button that says "student." Click here to find the Shutdown button. d) If you drag the mouse button to the bottom of the page, a Launcher bar will appear, which can be used to launch several different programs. 3. Create / edit unit cell content files for your structures: a) On the Desktop, you will see the folder "InorgChem Lab 03 Modeling Solid State." In this folder, open the file "03-UnitCell-Generic.cif" with the program "Leafpad" (right-click on the file name to see options of programs to open files). b) Use "Save As" to create and save three new files (with appropriate names), one for each of the structures your group did in Part B. Be sure they all have the extension ".cif" c) One at a time, re-open the.cif files you just saved and edit them. In the second line, change 'Created by J. Duncan' to your group members' names. In the forth line, change 'Generic' to the correct compound formula or crystal name. At the very bottom of the file, you will see an atom list staring with: A These lines include the atom name followed by the a, b, and c coordinates as fractions of the unit cell. Edit them to include the atoms in your unit cell, replacing 'A' and 'B' with the appropriate atomic symbols. Note: Atoms on corners, edges, and faces need only be entered once, as the remaining ones will be symmetry generated by repeating the unit cell. SAVE THE FILES! Copyright Plymouth State University and Jeremiah Duncan. May be distributed freely for education purposes only. 6

7 4. View the unit cells in Gnome Crystal Structure Viewer (gcrystal): a) Open a file: Using either the Applications Menu -> Science, or the Launcher bar, run gcrystal, then open a file with "File -> Open" or the Open file icon Or, right-click the file name and select "Open With Gnome Crystal Structures Viewer" b) Look at your structure. Rotate it around with the left mouse button. Does it look like the 3- D structure you built and does it reflect the 2-D projection you sketched? If not, you have two choices: Go back and edit the.cif file in Leafpad until it does (you will need to close gcrystal and re-run it every time you make an edit). Or, edit the structure within gcrystal: Go to "Crystal -> Atoms" to add, delete, and edit atoms. For every atom you add, make sure you select Type = Van der Waals; Database c) If you make any changes to your file, be sure to save it with "Save As" and using a different file name and a.cif extension. Note: this will write a completely new cif that loses some of the information from your original. Do not overwrite your original file! d) Once the structure looks like it should, you can save the image with File -> Save As Image Save the picture as a.jpg. e) Repeat with all three of your structures. 5. Record the atom lines from your.cif files in your notebook. 6. View the extended structure in GDIS: a) Open a file: Using either the Applications Menu -> Science, or the Launcher bar, run GDIS, then open a file with "File -> Open" or the Open file icon. Then open a.cif file with either "File -> Browse Files" or the open folder icon. Or, right-click the file name and select "Open With GDIS Molecule Modeller" Note: When the file opens, you will likely NOT see all of your atoms. GDIS only displays one atom that appears symmetrically on any corners, faces, or edges. Also, bonds may appear between your atoms. Don't worry--all will be remedied soon. b) Open the Display Properties menu with "Tools -> Display Properties" or the pie chart icon. Set the molecule display mode to CPK c) Generate Unit Cell repeats to extend the structure: In the lower left is a drop-down menu labeled "Model: Content." Click here and chose "Model: Images." In the left column that appears, increase all the "0"s to "1" and observe what happens. d) Investigate your model. The right mouse button can be used to rotate the structure. Change values under the Model: Images menu. The Model: Viewing menu can be used to look at the structure down specific axes. e) Once you have a picture that you believe displays the structure well, capture it with a screenshot. In the upper-right hand corner is an icon that looks like a camera. Click it and take a screenshot. Save the picture as a.jpg. It will probably help if your background is white. In the Display Properties menu, click the "Background Color" tab and set "Color name" to "#FFFFFF". Copyright Plymouth State University and Jeremiah Duncan. May be distributed freely for education purposes only. 7

8 7. Save and copy all your.cif files and images somewhere you can access them. If you do not have a USB memory stick, you can run a web browser to access your . If you have time left, go back, construct structure 'd', and collect the analysis data thereof. Lab Report Your lab report is due by lecture on Wednesday. Your report must be handed in BOTH electronically and in hard copy form. See the document "InorgChem-LabReportGuide.pdf" on the course website for guidelines on writing your report. Questions to be answered in the lab report: 1. Your report should include the images you captured from the computer, as well as the atom lists you developed (last lines of each.cif file). 2. Look up the radii of the ions in your structures b and c. These are available in your book, Resource Section 1: Selected Ionic Radii (pp ). 3. Using the ionic radii and your data on the contents of each unit cell (Part B, Analysis question 'b'), calculate the volumes of the ions (remember the formula for volume of a sphere?!). Collect these results in a a table. 4. Using the ionic radii and your data on the nearest neighboring atoms (Part B, Analysis question 'c') to calculate the dimensions of the unit cells for structures b and c. These should include the lengths of the unit cell axes and the total volume. Collect these results in a a table. 5. Determine the packing efficiency for structures 'b' and 'c' by dividing the volume occupied (Q3, total volume of the spheres in a unit cell) by the volume of the unit cell (Q4). Which structure has the highest packing efficiency? How does this relate to density of the material? 6. Consider the various ways investigated for representing unit cells: 3-D models, 2-D projections, computer programs. Comment on the various benefits and downsides to each. Copyright Plymouth State University and Jeremiah Duncan. May be distributed freely for education purposes only. 8