Paper-and-Glue Unit Cell Models W

Tested Demonstrations
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
Chemistry for Everyone
Paper-and-Glue Unit Cell Models W
submitted by: James P. Birk* and Ellen J. Yezierski
Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ 85287;*jbirk@asu.edu
checked by: Michael Laing
School of Pure and Applied Chemistry, University of Natal, Dalbridge, Durban 4014, South Africa
Figure 1. Template for a simple cubic unit cell.
edited by
Ed Vitz
Kutztown University
Kutztown, PA 19530
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 2. Template for a face-centered cubic unit cell.
JChemEd.chem.wisc.edu • Vol. 80 No. 2 February 2003 • Journal of Chemical Education 157

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