Experiment No. 5
UNIT CELL MODELS (Dry Lab)
ABRIDGMENT
BACKGROUND
The Origami can be used to represent the structures in chemistry which
have been widely used but have been restricted mostly to molecular shapes.
James P. Birk and Ellen J. Yezierski from the Department of Chemistry and
Biochemistry, Arizona State University devised simple, body-centered, and
face-centered cubic, hexagonal, and sodium chloride unit cell models for
teaching about crystalline solids, which students can build from paper templates
and glue. These constructed individual unit cells can be combined to create a
large model of a crystalline solid. Not only does this activity provide each
student with personal models, but the students can also participate in a large
group activity as the large crystal structures are assembled (Birk, 2003)
Unit Cell
A unit cell is the most basic and least volume consuming repeating
structure of any solid. The unit cell is used to visually simplify the crystalline
patterns solid arrangement. The repeated unit cell is called the lattice (Petrucci,
2007).
In the early 19th century, Auguste Bravais’ work revealed that there are
only fourteen lattice structures, also known as the Bravais lattice. These
fourteen different structures are derived from seven crystal systems, that
indicates the different shapes of a unit cell and four types of lattice, that tells
that the atom is arranged within unit.
The method X-ray diffraction is used to determine the arrangement of
the crystals, it is consist of X-ray beam being fired at a solid, and from the
diffraction of the beams calculated by Bragg’s Equation the configuration can
be determined.
n = 2d sin T
Packing Efficiency, it is the percentage of total space filled by the
constituent particles in the unit cells.
𝑉𝑜𝑙𝑢𝑚𝑒 𝑂𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝑏𝑦 𝐴𝑡𝑜𝑚
𝑥 100 =
𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑈𝑛𝑖𝑡 𝐶𝑒𝑙𝑙
Note: For all unit cells except hexagonal, atoms on the faces
contribute 1/2 atom to each unit cell, atoms on the edges contribute 1/4 atom
to each unit cell, and atoms on the corners contribute 1/8 atom to each unit cell.
Figure 1: The 14 Bravais unit cells
Origami in Chemistry
The Origami is an ancient art of Japanese paper folding, that dates back
to the second century. Based on the Origami Omnibus of (Kasahara, 1988),
paper folding techniques can be included in the instructions for constructing
basic geometric shapes.
Geometry is one of the most important concepts to be considered in
chemistry and the origami models can be used as a good example to represent
various geometric shapes and molecular shapes, shaped like tetrahedrons,
octahedrons, and triangular pyramids (Hanson, 1996).
The origami models used in chemistry is vivid and useful for small groups
of students, for students to become familiar with unit cells and crystalline
structures, it is advantageous for them to build and keep their own models.
Figure 2:Template
for Simple Cubic
Unit Cell
Figure 3 :Template
for face-centered
Cubic Unit Cell
Figure 4: Template for Body-centered Cubic
Unit Cell
Figure 5: Template
for Hexagonal Unit
Cell
Figure 6: Template
for sodium chloride
unit cell
Figure 7: Facecentered and simple
cubic unit cell model
Figure 8: Model of
crystalline solid
structure
OBJECTIVES
1. To be familiarized with the basic crystalline structures.
2. To create unit cell models of different crystalline structures.
3. To calculate crystal packing efficiency of the different crystalline
structures.
MATERIALS AND EQUIPMENTS
EQUIPMENT/S
Printed Template
Scissors
Glue/Paste
Box/ container
Ruler
REAGENT/S
None in Particular
PROCEDURE
The templates developed by James P. Birk and Ellen J. Yezierski, will be
used for the construction of the unit cell models (see attachment).
1. Cut edges of the template assigned.
2. Fold the side of the template to paste and form the one-unit cell.
3. Construct 8 unit cells for each template but construct 9 unit cells for
hexagonal unit to form solid structure.
4. Make a box/ container that the solid structure can fit.
5. Calculate for the packing efficiency of each crystalline structures
Experiment No. 5
UNIT CELL MODELS
PRE-LAB
Score:
Date:
Group No.:
PRECAUTIONS
MATERIALS
OBJECTIVES
Name:
Program:
Yr & Sec.:
PROCEDURE
Construct a schematic diagram of the procedure in a separate sheet of bond
paper and attach it here.
ADVANCE QUESTION
1. What is a unit cell?
2. Draw the following unit cells.
Simple cubic centered unit cell
Basic cubic centered unit cell
Face centered unit cell
Hexagonal unit cell
Sodium Chloride
Experiment No. 5
UNIT CELL MODELS
POST-LAB
Name:
Program:
Yr & Sec.:
Score:
Date:
Group No.:
DATA AND RESULTS
Table 1. Basic crystalline structures
Volume
Unit Cell
Occupied by
atom
Simple centered
cell
Body centered
cell
Model 1
Body centered
cell
Model 2
Volume
Occupied by
unit cell
Face centered
Hexagonal unit
cell
Sodium
Chloride
ANALYSIS OF RESULTS
1. Calculate the packing efficiency for each unit cell.
Packing
efficiency
2. Compare the packing efficiencies of the unit cells and discuss its
differences.
QUESTIONS
1. What are the coordination numbers for each unit cells used in this
activity? Illustrate