by Dean J. Campbell, Bradley University, Peoria, Illinois
Many physical models with varying degrees of sophistication are used to illustrate chemical concepts.1-6 Previous posts have described simple, relatively inexpensive models that might be able to be more widely used than more expensive models.3-6 Food packaging trays designed to hold many objects, e.g. egg cartons to hold eggs, are inexpensive and have regular arrays of depressions or dimples. These dimples can hold and spatially organize various objects or even contain chemical reactions.7 In the models described below, trays containing square arrays of dimples can be cut into smaller trays to represent layers of atoms. Colorful markings can be spatially arranged among the tray dimples to designate the locations of the atoms in the layers. Sequences of layers can be used to describe the positions of atoms in unit cells, which are a common way to designate fundamental repeating units for extended solid structures.8
Particularly useful trays for producing unit cell patterns have been used as packaging for mini quiches.9 The mini quiche trays, obtained from a local Costco store, have somewhat shallow, flat-bottomed circular dimples all arranged in a square pattern Figure 1 (TOP). Some time ago, the 24-dimple trays were made of translucent polystyrene.6 Now the trays are made of more transparent polyethylene terephthalate. The trays can be cut into smaller pieces with scissors. The trays can be marked with dry-erase or permanent markers. The marker markings are translucent, so the trays can be stacked over each other, yet still enable viewing of patterns underneath the top layer. For example, Figure 1 (BOTTOM) shows portions of two trays, each containing one unit cell layer, placed partially over one another to show how adjacent unit cells can be placed to produce a larger structure.
Figure 1. (TOP) Mini quiche tray. (BOTTOM) Two quiche trays partially overlapped to show how unit cells can be placed side-by-side to show how an extended structure can be produced by translation of a unit cell.
Since the circular dimples are flat, fractions of atoms or ions (represented by fractions of circles) and annotations can be easily drawn. For example, Figure 2 shows the layer sequence for a face-centered cubic structure. The layers are:
- z = 0 (layer on the bottom face of the unit cell)
- z = ½ (layer positioned halfway up the unit cell)
- z = 1 (layer on the top face of the unit cell, looks the same as the z = 0 layer)
The whole atoms are represented by marker circles around the edges of the circular bottoms of the dimples. The portions of the atoms in each layer that are actually within the boundaries of the unit cell are shaded. The fractions written on each shaded portion describe how much of the atom is within the three-dimensional unit cell. Summing up the atom fractions across the layer sequences gives four atoms per face-centered cubic unit cell.
Figure 2. Layer sequence for face-centered cubic structure
In Figure 2, all of the tray dimples are pointing in the same direction, all up or all down. In this arrangement, the z = 0 and z = 1 trays are essentially the same, and can be replaced with a single z = 0,1 tray. The trays can also be arranged with dimples pointing up or dimples pointing down so that they can more clearly represent fractions of spherical atoms. For example, Figure 3 shows the layer sequence for a rock salt (sodium chloride) structure. As before, the whole atoms are represented by marker circles around the edges of the circular bottoms of the dimples. The portions of the atoms in each layer that are actually within the boundaries of the unit cell are shaded. The fractions written on each shaded portion describe how much of the atom is within the three-dimensional unit cell. In this model, the layers are:
- z = 0 (layer on the bottom face of the unit cell with the tray dimples pointing upward)
- z = ½ (layer positioned halfway up the unit cell, with two trays stacked over each other – a tray with dimples up over a tray with dimples down)
- z = 1 (layer on the top face of the unit cell, looks the same as the z = 0 layer, but with the tray dimples pointing downward)
Summing up the atom fractions across the layer sequences gives four sodium ions and four chloride ions per rock salt unit cell. Although this model makes a somewhat more visually realistic stack of layers, Figure 3, the drawback to this more three-dimensional approach is that these models require more trays than single tray layer models.
Figure 3. (TOP) Layer sequence for rock salt structure. (BOTTOM) Stacked layers for rock salt structure.
The Supporting Information shows the tray layer sequences that can be used to produce the following unit cell structures. Most of these unit cells are of the cubic crystal system (all edges have the same length and intersect at right angles). However, one of the unit cells, that of the YBCO superconductor, is of the tetragonal crystal system (all of the edges intersect at right angles, but the edge length in one direction is different from the other two edge lengths, which are equal).
- simple cubic
- body-centered cubic
- face-centered cubic
- cesium chloride
- rock salt (e.g., NaCl)
- calcium fluoride
- zinc blende (e.g., ZnS)
- rhenium(VI) oxide
- perovskite (e.g., CaTiO3)
- YBCO (YBa2Cu3O7) superconductor
Rather than make one tray for each layer of the unit cell, the layer could be constructed by stacking multiple clear trays with patterns that could be used in other arrangements to produce a variety of layers. Figure 4 shows patterned trays that can act as layer building blocks. For example, to construct the z = 0 layer of the rock salt unit cells in Figure 3, one could stack the first and second tray from the first row and the third tray in the second row of Figure 4. With the ability to mark and erase the clear trays with dry erase markers, these building block trays might have limited utility.
Figure 4. A set of trays that can be used to produce many of the layers in the layer sequences in the models described in this post.
As noted above, at one point the mini quiche trays were made of polystyrene. Sections of some of these trays were marked with permanent marker, and placed on aluminum foil in a toaster oven. The heat in the oven raised the polystyrene above its glass transition temperature, causing the trays to flatten and shrink.6 The marker patterns on the bottoms of the dimples shrank but stayed essentially circular and in a square arrangement. These heat-shrunken layers were arranged in order on strings (holes must be punched in the polystyrene trays before heat shrinking). Figure 5 shows models of the layers of face-centered cubic (TOP) and rock salt (BOTTOM) unit cells. Other dimpled polystyrene trays might also work for these purposes, but it should be noted that the trays do not always shrink uniformly in all directions. Therefore, an image produced from heat-shrinking polystyrene might be significantly distorted.
Figure 5. Heat-shrunken models of the layers of face-centered cubic (TOP) and rock salt (BOTTOM) unit cells.
Finally, if the transparent mini quiche trays are not available, there are other options. Various other trays with square arrays of dimples can be found, most notably egg cartons. Figure 6 shows examples of models that can be made with 18-count polystyrene foam egg carton trays. Many of the layers of the unit cells described in this post can be built with three-dimple by three-dimple tray sections, which can be made simply by cutting the 18-count egg carton tray in half, Figure 6 (LEFT). When flipped dimple side up, each dimple represents an atom. Four of the nine dimples are pushed in the tray section, each representing the absence of an atom. Figure 6 (MIDDLE) shows a stack of three egg carton-based trays with some dimples pushed in, all representing a face-centered cubic structure. The stack is supported by skewering the foam trays on two wooden chopsticks. The egg cartons can be patterned with colors to represent different atoms. Figure 6 (RIGHT) shows two egg carton-based trays with dimples colored with dry-erase markers, all representing layers in a rock salt structure.
Figure 6. (LEFT) Eighteen-count egg carton and a three-dimple tray section that can be made from the carton. Four of the nine dimples are pushed in, each representing the absence of an atom. (MIDDLE) Stack of three egg carton-based trays with some pushed in, all representing a face-centered cubic structure. (RIGHT) Two egg carton-based trays with dimples colored with dry-erase markers, all representing layers in a rock salt structure.
Many of the simple structures likely to be used in an introductory chemistry setting have been described here in this post. As part of a recent assignment in my Materials Chemistry course, I divided my class into small groups. Each group was given a few dry-erase markers and a few empty portions of mini quiche trays and were instructed to draw layer sequences for their assigned structure. Most groups successfully submitted the assignment with the correct tray markings. Layers for these sequences and for other structures are shown in the Supporting Information.
Safety Sharper scissors cut more easily through layers of plastic, but they also cut skin more easily. Consider the hand-eye coordination of individuals being asked to cut the plastic. Precautions, including proper personal protective equipment such as goggles, should be used when shrinking polystyrene trays. Toaster ovens can have parts that are hot to the touch. Polystyrene that has been heated to above its glass transition temperature (over 100°C) is also hot to the touch. Tongs are recommended. Polystyrene can also melt, off-gas obnoxious fumes, or even burn when heated. It is recommended that the polystyrene is heated on a sheet of aluminum foil rather than directly on the shelf of the toaster oven.
Acknowledgements Thanks to the students in my Materials Chemistry course, especially Bezawit Legesse, for putting together some of the layer sequence models. Thanks to Wayne Bosma for supplying many mini quiche trays over the years. This work was supported by Bradley University and the Mund-Lagowski Department of Chemistry and Biochemistry with additional support from the Illinois Heartland Section of the American Chemical Society. The material contained in this document is based upon work supported by a National Aeronautics and Space Administration (NASA) grant or cooperative agreement. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of NASA. This work was supported through a NASA grant awarded to the Illinois/NASA Space Grant Consortium.
1. Campbell, D. J.; Miller, J. D.; Bannon, S. J.; Obermaier, L. M. “An Exploration of the Nanoworld with LEGO® Bricks.” J. Chem. Educ., 2011, 88, 602-606.
2. Campbell, D. J.; Brewer, E. R.; Martinez, K. A.; Fitzjarrald, T. J. "Using Beads and Divided Containers to Study Kinetic and Equilibrium Isotope Effects in the Laboratory and in the Classroom." J. Chem. Educ., 2017, 94, 1118-1123.
3. Campbell, D.; Kahila, T. “Plastic Beverage Bottles and More as Orbital Models.” ChemEd Exchange. https://www.chemedx.org/blog/plastic-beverage-bottles-and-more-orbital-m... (accessed Sep 2023).
4. Campbell, D. J. “Hatching Ideas to use Egg Cartons to Represent Electron Arrangements.” ChemEd Exchange. https://www.chemedx.org/blog/hatching-ideas-use-egg-cartons-represent-el... (accessed Sep 2023).
5. Campbell, D. J.; Walls, K.; Steres, C. “Paper Snowflakes to Model Flat Symmetrical Molecules.” ChemEd Exchange. https://www.chemedx.org/blog/paper-snowflakes-model-flat-symmetrical-mol... (accessed Sep 2023).
6. Campbell, D. J. “A Polystyrene Model of Polystyrene Tacticity.” ChemEd Exchange. https://www.chemedx.org/blog/polystyrene-model-polystyrene-tacticity (accessed Sep 2023).
7. Campbell, D. J. "Letter to the Editor ‘An Alternative Thermochemical Container.’” J. Chem. Educ., 2004, 81, 1421.
8. Ellis, A. B.; Geselbracht, M. J.; Johnson, B. J.; Lisensky, G. C.; Robinson, W. R. Teaching General Chemistry: A Materials Science Companion; American Chemical Society: Washington, DC, 1993.
9. Cuisine Adventures. Mini Quiche. https://cuisineadventuresfoods.com/products/mini-quiche-kosher-costco-us/(accessed Sep 2023).
For Laboratory Work: Please refer to the ACS Guidelines for Chemical Laboratory Safety in Secondary Schools (2016).
For Demonstrations: Please refer to the ACS Division of Chemical Education Safety Guidelines for Chemical Demonstrations.
Other Safety resources
RAMP: Recognize hazards; Assess the risks of hazards; Minimize the risks of hazards; Prepare for emergencies