In the Classroom
An Inexpensive Kit for Constructing Models of Crystals Michael Laing Department of Chemistry and Applied Chemistry, University of Natal, Durban, South Africa, 4014
Understanding three-dimensional crystal structures is not easy. Many students are unable to picture what is occurring in space by looking at a flat two-dimensional representation on either the blackboard or the page of a book. The best approach is to have the learner construct spatial models of the various important crystal arrangements so that he can perceive three dimensions in his own hands. Over the years many types of models have been described, yet no matter how good they may be, there always seems to be some disadvantage! Close-packing models built of styrofoam spheres are excellent, but they are rigid and opaque and usually the students do not build the models themselves but examine a previously constructed finished product (1). Close-packing models built of transparent spheres are beautiful, but their cost is prohibitive (2). Models consisting of a rigid frame supporting equally spaced sheets of transparent Lucite® or Perspex® with holes to support polystyrene spheres are close to the best compromise (3, 4), but once again the cost is high and the spheres tend to roll out onto the floor. Recently a very elegant system has become available, but the relatively high unit cost puts it beyond the reach of the average chemistry department (5). There is a simple workable compromise: use the very inexpensive commercially available1 square tissue culture Petri dishes (multiwell plates) with 25 compartments. The KubiKit® consists of five of these trays, one lid, and enough glass marbles, white and black (or red), 2 to build the various crystal structures based upon a cubic or tetragonal unit cell. Each atom is represented by one marble, the coordinates of its position in the tray are in quarters (i.e., 0, 1, 2, 3, and 4), and the stack of five trays represents the unit cell of the crystal, with the atoms in each tray having the same coordinate along the third axis, perpendicular to the trays (in quarters again: 0, 1, 2, 3, and 4). The lid is put onto the top tray, a heavy rubber band is put around the stacked model, and the “unit cell” can now be examined from any angle without the marble “atoms” falling out. The components are robust; the trays are transparent. Figures 1 and 2 compare the TiO2 rutile structure made with the Kit with that made with the larger “Purdue” model. A broken down model of the CsCl structure is shown in Figure 3. A set of instructions that is used for a 3-hour sophomore practical exercise is available on request. It describes how to build the various structures (simple cubic, body centered, face centered, diamond, zinc blende, NaCl, CsCl, rutile, CaF2-fluorite, perovskite) and includes questions and calculations about radius ratios, packing densities, and atom–atom distances. The cost is so low, less than $10 per kit, that one can afford to equip a laboratory for 100 students with an individual kit for each student. The KubiKit® was first used in 1989 in a workshop for high-school teachers at the Durban conference of the SA Association for Teachers of Physical Science.
Figure 1. Model of the TiO 2, rutile, structure built with the “Purdue” frame. The unit is approximately 22 cm cubed, with spheres 3 cm in diameter.
Figure 2. Model of the TiO 2, rutile, structure. Black spheres represent oxygen atoms. The model is 10 cm cubed.
Acknowledgments It is a pleasure to thank Derek Davenport and Bill Robinson, Purdue University, for being such generous hosts during the 10th BCCE in July 1988, and for one of the “Purdue” frames from which this KubiKit® was derived. I also thank Garth Buhrman, who in 1988 made 20 copies of the large “Purdue” frame for use in my Sophomore Inorganic Chemistry course.
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In the Classroom
Notes 1. STERILIN Multiwell square petri dish, Catalog No. M.33F25L/F103, Sterilin Ltd., Stone, UK. 2. The KubiKit® and the trays individually or in bulk are available from Somerset Educational, PO Box 281, Somerset East, 5850, South Africa; Fax 27.424.31689.
Literature Cited
Figure 3. A broken-down model of the CsCl structure. The black marble represents the Cs+ cation at 1/2 1/2 1/2; the white marbles represent the Cl { anions at the corners of the unit cell. The edge of each compartment is 2 cm long, and the tray is 2 cm deep.
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1. Sime, R. J. J. Chem. Educ. 1963, 40, 61–62. 2. Gehman, W. G. J. Chem. Educ. 1963, 40, 54–60. 3. Bodner, G. M.; Culter, A.; Greenbowe, T. J.; Robinson, W. R. J. Chem. Educ. 1984, 61, 447–449. 4. Kildahl, N. K.; Berka, L. H.; Bodner, G. M. J. Chem. Educ. 1986, 63, 62–63. 5. Solid State Model Kit, No. 92-004; Institute for Chemical Education, University of Wisconsin, Madison, WI 53706-1396; currently available in two versions at $75 and $110 per kit. This kit is similar to the commercial “Ionic Models” made by Catalin, Waltham Abbey, Essex, England.
