Chemistry for Everyone edited by
Tested Demonstrations
Ed Vitz Kutztown University Kutztown, PA 19530
Paper-and-Glue Unit Cell Models
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submitted by:
James P. Birk* and Ellen J. Yezierski Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ 85287;*
[email protected] checked by:
Michael Laing School of Pure and Applied Chemistry, University of Natal, Dalbridge, Durban 4014, South Africa
The ancient art of Japanese paper folding, known as origami, dates back to the second century. Books on the subject often begin with techniques for paper folding and include instructions for constructing basic geometric shapes (1). At this simple level, it is obvious that origami models shaped like tetrahedrons, octahedrons, and triangular pyramids can serve as useful chemistry models to represent various molecular shapes. A good example of applying origami to molecular models is Molecular Origami by Hanson (2). The book provides a comprehensive and hands-on approach to explore molecular structure and bonding through origami. Additionally, molecular models (3) and coordination polyhedrons (4, 5) can even be constructed by folding paper envelopes. Employing paper models to represent structures in chemistry has been widely used but has been restricted mostly to molecular shapes. In introductory solid-state chemistry, the popular homemade models of unit cells and crystal structures have previously involved materials other than paper. One such model utilizes Styrofoam balls cut into halves, quarters, and eighths glued into a photo cube (6). This model is vivid and useful for small groups of students, but the instructor must construct several of them prior to class. Other models involve templates and clear plastic spheres (7, 8) but suffer from the disadvantage that they cannot be sliced to depict the contents of the unit cell. For students to become familiar with unit cells and crystalline structures, it is advantageous for them to build and keep their own models. This can be accomplished with a
simple technique using inexpensive and widely available materials. To achieve this objective we have created paper-andglue (or tape) templates, shown in Figures 1 and 2, for simple cubic and face-centered cubic unit cell models that students can construct as a brief homework assignment. We offer two designs for a body-centered cubic template, each of which has some shortcomings (Figure 3). The template in Figure 3A uses shading to show that the body-centered atom lies behind the atoms at the corners, but views of two sides at once give the impression that there are multiple atoms in the center. The template in Figure 3B provides one of two halves of a body-centered cubic unit cell. Two of these should be taped together at one corner. This model effectively shows the atom in the center when the unit cell is “opened”. However, it suffers from the deficiency that the center atom cannot be seen on the faces but can be seen only from the dissected view. Upon testing the simple and face-centered cubic unit cell models, we have found that they are useful for students individually and can also be incorporated into a large group activity that demonstrates how unit cells may be built up to illustrate the structure of crystalline solids. If these are to be used together, the templates should be sized differently to mimic the relative atom sizes being modeled. We have also constructed a template for a simple hexagonal unit cell (Figure 4). This unit cell cannot be used for hexagonal close packing since we are unable to show an image of the atom inside the unit cell. However, the model can
Figure 1. Template for a simple cubic unit cell.
Figure 2. Template for a face-centered cubic unit cell.
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Chemistry for Everyone
be used to show the packing in the hexagonal crystal system. Note that the hexagonal unit cell has no 6-fold axis, but 3fold and 2-fold axes are easy to identify from the models. Students can compare the number of unit cells required to make up a full atom in comparison to the cubic systems (6 vs 8 unit cells). Finally, we have constructed a unit cell template for the sodium chloride structure (Figure 5). This unit cell shows the packing pattern very nicely but has a deficiency in that the ion at the body-centered position (1/2, 1/2, 1/2) is not visible. Thus, students cannot use this model to correctly count the number of ions per unit cell. Full-sized versions of the templates, which can be printed on 8.5-in. × 11-in. paper and result in cube sides of about 6 cm, may be found on JCE Online.W Students cut out the figure and fold the paper along each of the lines. The tabs are then glued inside the cube. The unit cells are easy for students to construct and can be used in high school and college chemistry courses. The cubic paper-and-glue templates (Figures 1 and 2) were designed to help students understand the structure of cubic unit cells in the context of a crystalline solids unit of instruction. We have incorporated the models into an intro-
duction to crystalline solids in our general chemistry lecture course. One lecture before introducing solid-state chemistry, we hand out the template sheets to the students. We tell the students to cut them out, to tape or glue them into cubes, and to bring the assembled models to the next lecture (Figure 6). Glue sticks provide the simplest approach to fastening the sides to the tabs during assembly of the models. Most of the students cooperate and arrive with their models in hand. We show microscopic diagrams and animations of various crystalline solids and discuss the structures of the unit cells that comprise these solids. When we introduce the simple cubic and face-centered cubic unit cells, the students bring their models to the front of the lecture hall and add their models to others to build three-dimensional crystalline solids (Figure 7). Even with 200 students, this can be done in 5–10 minutes. Not only is the model effective at showing how the eighths, quarters, and halves make up whole spheres in the crystal, students are also more involved in creating the model. Additionally, students can examine the holes in the structure (white areas) and consider how the structure of the unit cell dictates the shape of a particular hole (cubic, octahedral, or tetrahedral). We then invite the students to take their cubes
A
Figure 4. Template for a hexagonal unit cell.
B
Figure 3. Templates for body-centered cubic unit cell.
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Figure 5. Template for a sodium chloride unit cell.
Journal of Chemical Education • Vol. 80 No. 2 February 2003 • JChemEd.chem.wisc.edu
Chemistry for Everyone
Figure 6. Face-centered and simple cubic unit cell paper-and-glue models.
Figure 7. Model of crystalline solid structure built from face-centered cubic paper-and-glue unit cells.
with them at the end of the class to use as they study the lecture material. We also recommend that they use the models when they study crystalline structures in the laboratory component of the course. The general chemistry students at our university build various solids in the lab using the ICE model kit (7). Based on student responses in their lab reports, the investigation is moderately successful; however, the students still have difficulty visually “slicing” the spheres in the kit in order to identify the type of unit cell in each of the structures. Students report that the paper models from lecture help them to identify unit cells and visualize them when looking at a model of a crystalline solid. We have also used animations designed by members of our research group to show how atoms in crystal structures are “sliced” into unit cells. Assembling the unit cell models to form a model of a crystal enables the students to participate in a large group activity. They also have a personal hands-on model to examine before, during, and after lecture as well as a threedimensional model showing the arrangement of atoms in unit cells.
This work was supported in part by the National Science Foundation under grant no. DUE 9453610 and the U. S. Department of Education under grant no. OPE P336B990064. Opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation or the Department of Education.
Acknowledgments We thank Rachel Morgan of Arizona State University and Michael Laing of the University of Natal for suggestions regarding the dissectable version of the unit cell for the bodycentered cubic unit cell.
WSupplemental
Material
Full-sized versions of the templates, which can be printed on 8.5-in. × 11-in. paper and result in cube sides of about 6 cm, are available on JCE Online. Literature Cited 1. Kasahara, K. Origami Omnibus; Japan Publications, Inc.: Tokyo, 1988. 2. Hanson, R. M. Molecular Origami; University Science Books: California, 1996. 3. Yamana, S. J. Chem. Educ. 1988, 65, 1074. 4. Yamana, S. J. Chem. Educ. 1987, 64, 1033. 5. Yamana, S. J. Chem. Educ. 1987, 6, 1040. 6. Olsen, R.; Tobiason, F. J. Chem. Educ. 1975, 52, 509. 7. Mayer, L.; Lisensky, G. Solid State Model Kit, version 4.0, ICE Publication No. 94-004; Institute for Chemical Education: Madison, Wisconsin, 1994. 8. Laing, M. J. Chem. Educ. 1997, 74, 795.
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