Crystals Can Grow
                       Potato Crystallography 
    Cochise College   

   Virtual Geology Museum    Hall of Minerals     
    Geology Home Page               

    Roger Weller, geology instructor ( wellerr@cochise.edu )
    last edited:  10/6/10   copyright 2010-R.Weller

   Part 2-Crystal Systems     
 

   List of Topics for Potato Crystallography Part 2:
    Preparation and Materials
    The Six Crystal Systems
     Isometric System
    Tetragonal System
    Orthorhombic System
    Monoclinic System
    Triclinic System
    Hexagonal/Trigonal System
  
   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.

   

   Isometric System

        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

   Tetragonal system

        Take a potato cube and cut in half.  The resulting shape has a square top and
   short sides.

   

    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


   Orthorhombic System

        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

   Monoclinic System

     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


   Triclinic System

        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
   direction.

   

    Tricinic axes


   

    Copper sulfate produces Triclinic crystals.


   Hexagonal/Trigonal System

        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
   Hexagonal System.

   

    cut potato showing Hexagonal crystallographic axes