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Part 2-Crystal Systems
List of Topics
for Potato Crystallography Part 2:
Preparation and Materials
The Six Crystal Systems
Preparation and Materials
Materials needed: Several large potatoes, a large sharp knife, a small paring knife,
and a bunch of round toothpicks.
It is much easier to demonstrate crystal shapes if you start with big potatoes
(Russet). Peel several potatoes and cut the largest cubes that you can from each
potato. You will probably need at least twelve cubes. Try to be as accurate as
possible to make perfect cubes, all the sides of equal length and at right angles.
It might take a little practice.
The Six Crystal Systems
Naturally occurring crystals have studied for over two hundred years and all of
the shapes can be sorted out and placed into 6 families (or systems) of symmetry.
Five of the systems of symmetry can be each defined by the orientation of 3
imaginary lines called axes that describe the type of symmetry along each axis;
the sixth system (#8 in the figure below) requires four axes.
The Isometric system is best described by a simple cube.
cut potato showing basic form of the Isometric system
This system is described by 3 axes oriented at right angles to the other two.
Each of these axes has four-fold symmetry and has the same length. The best
example is a cube. A toothpick stuck into the middle of any cube face will act as
an axis and will show show four-fold symmetry. This system has the greatest
amount of symmetry of the six crystal systems.
cut potato model with toothpicks representing crystallographic axes
wooden model of cube
Take a potato cube and cut in half. The resulting shape has a square top and
potato-flattened Tetragonal form
The tetragonal basic form can also be elongated in one direction
cut potato illustrating elongated central axis
comparison between a cube (Isometric) and an elongated Tetragonal form
A toothpick stuck in the middle of the square face and then rotated shows that
this is an axis of four-fold symmetry. A toothpick inserted into the middle of any
of the short sides will only be an axis of two-fold symmetry. The Tetragonal
System is defined by three axes at right angles to each other; one axis has
four-fold symmetry and the other two axes only have two-fold symmetry. The two
axes of two-fold symmetry have the same length, while the four-fold axis is either
longer or shorter than the other two.
cut potato with elongated central axis
wooden model of simple tetragonal form
Take the leftover half of the potato cube that you created when you made to
Tetragonal form and cut off a small sliver parallel to one of the small faces. You
should have a rectangular blow where the length, width, and height are all different.
cut potato model of basic orthorhombic form
A toothpick stuck in the middle of any one of the 6 faces will turn out to be an
axis of two-fold symmetry. The Orthorhombic System is defined by three axes at
right angles to each other and each axis only has two-fold symmetry. All three
axes are of unequal length. The simplest Orthorhombic crystal is similar to the
shape of a breakfast cereal box.
cut potato model showing relationship of Orthorhombic crystallographic axes
wooden model of basic Orthorhombic shape
Cutting the potato is now going to become more difficult. First cut the potato
into an Orthorhombic shape, a box-like shape where the length, width, and height
are all different. Follow the diagram below and cut an inclined slice off two
opposing sides so that the final form looks like a box leaning over in one direction.
cut potato model of basic Monoclinic shape
wooden model of basic Monoclinic shape
The leaning in one direction is where this crystal gets its name. "Mono" means
one and "cline" means to lean. The Monoclinic System is defined by three axes of
unequal length and where two axes are at right angles to each other and the third
is at an angle other than 90 degrees.
cut potato model showing relationship of Monoclinic crystallographic axes
Cut another potato into a monoclinic shape of a box leaning in one direction.
Following the diagram below, cut inclined slices off two opposing sides that
were at right angles to the box. You should now now have a shape that looks
like a box leaning in two directions.
cut potato model of basic Triclinic shape
wooden model of basic Triclinic shape
Even though the box looks like it is leaning in two directions, the name for this
type of symmetry is Triclinic. The reasoning behind this name is that the Triclinic
system is described by three axes of unequal length where none of the axes makes
a right angle with the other two. In other words, all three axes are leaning in some
Copper sulfate produces Triclinic crystals.
For this crystal system, do not start out by making a cube. The simplest way of
describing the shape you need to create is a hexagonal column. Carefully study
the diagram below. The six sides should be parallel to each other and of equal
length. The top and bottom of the column should be flat.
cut potato model showing basic Hexagonal shape
wooden model of basic Hexagonal shape
The axes that describe the Hexagonal system consist of one axis with six-fold
symmetry at right angles to the axes of equal length oriented at 60 degree angles
to their neighboring axes. In the Trigonal System the main axis has three-fold
symmetry instead of six-fold symmetry. Some crystallographers treat the Trigonal
System as a separate system, while others consider it a sub-category of the
cut potato showing Hexagonal crystallographic axes