Paper-and-Glue Unit Cell Models W

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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- A B Figure 3. Templates for body-centered cubic unit cell. 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 Figure 4. Template for a hexagonal unit cell. Figure 5. Template for a sodium chloride unit cell. 158 Journal of Chemical Education • Vol. 80 No. 2 February 2003 • JChemEd.chem.wisc.edu
Figure 6. Face-centered and simple cubic unit cell paper-and-glue models. 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. 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. Chemistry for Everyone Figure 7. Model of crystalline solid structure built from face-centered cubic paper-and-glue 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. W Supplemental 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. JChemEd.chem.wisc.edu • Vol. 80 No. 2 February 2003 • Journal of Chemical Education 159
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