Unit Cell: The smallest unit of a crystal that still retains all the physical, chemical and crystallographic properties of the mineral.

The 4 pure symmetry operations (which are operations that leave one point in the crystal unmoved) include:

1. Rotation Axis - An axis through the object, around which the object is rotated such that the original "motif"
                                 (or appearance) is repeated a specific number of times during 360 degrees

   Fold of Rotation	1	2	3	4	6
   Shorthand Notation		1A2	1A3	1A4	1A6
   Stereonet Symbol
   Amount of Rotation Needed to Repeat Image	360°	180°	120°	90°	60°

   
   
   
2. Mirror plane: plane passed through object such that the images on opposite sides of the plane
                               are mirror images of one another
   
   

   Shorthand Notation	1m
   Stereonet Symbols	vertical mirror	solid line
   	horizontal mirror	solid primitive circle
   	tilted mirror	solid great circle line

3. Roto-inversion axis: first a rotation (the amount of this rotation determines the fold of the axis),
                               then an 180° inversion around the center point of the crystal

   Shorthand Notation (x=fold of rotation)
   Stereonet Symbol

4. Center of symmetry : is present if two lines of equal length can be extended from the center of a
                               crystal in opposite directions, and reach equivalent elements on the crystal's surface.

   Shorthand Notation	i
   Stereonet Symbol	none

   
   

   ---

   
   There are 32 possible combinations of the 4 pure symmetry elements that exist in nature.
   These make up the 32 Crystal Classes.
   Crystal classes are grouped into 6 Crystal Systems based on shared symmetry.

   Crystal systems:

   System Name	Shared Symmetry	Axial Lengths	Angles
   Triclinic	i or none	a ≠ b ≠ c	α ≠ β ≠ γ   no angle = 90°
   Monoclinic	1A2 and/or 1m	a ≠ b ≠ c	β ≠ α = γ = 90°
   Orthorhombic	3A2 and/or 1A22m	a ≠ b ≠ c	α = β = γ = 90°
   Tetragonal	1A4	a1 = a2 ≠ c	α = β = γ = 90°
   Hexagonal	hex/hex:1A6	a1 = a2 = a3 ≠ c	β1 = β2 = β3 = 90° γ1 = γ2 = γ3 = 120°
   	hex/rhomb:1A3	a1 = a2 = a3 = c
   Isometric	4A3	a = b = c	α = β = γ = 90°

   
   
   
   • Most minerals are monoclinic or orthorhombic - 75%
   • Isometric minerals = 12.2%
   
   
   * Note: Most minerals form in the classes with the highest symmetry in each system.
     These are called "holohedral classes or holosymetric" classes.
   
   The holohedral classes for each system are:
   the Pinacoidal Class for the Triclinic System
   the Prismatic Class for the Monoclinic System
   the Rhombic Dipyramidal Class for the Orthorhombic System
   the Ditetragonal Dipyramidal Class for the Tetragonal System
   the Hexagonal Scalenohedral Class for the Hex/Rhombohedral System
   the Dihexagonal Dipyramidal Class for the Hex/Hexagonal System
   and the Hexoctahedral Class for the Isometric System.

   ---

   
   5 Planar Nets (2-dimensional atomic arrangements)

   Oblique t1 < t2	Rectangular t1 < t2
   Square t1 = t2	Rhombic t1 = t2
   Centered Rectangular is formed by connecting the shared corners & centers                                                             of two adjacent rectangles. i.e.,

   
   

   ---

   
   14 Bravais Lattices (3-dimensional atomic arrangements)

   Formed by extending planar nets into 3rd dimension. Atom positions within Bravais Lattices can occur as follows:

   • P - primitive: atoms only at corners
   • F - face-centered: atoms at center of each face
   • C - 2-face-centered: atoms at two opposite faces
   • I(R) - body centered: atom at very center
   
   

   ---

   
   Steno's Law of the Constancy of Interfacial Angles: The angles between equivalent faces of crystals of the same substance, measured at the same temperature, are consistently the same.

   Zone: Faces of a crystal that intercept such that their edges run parallel to each other make up a "zone."

   Form: Faces that share the same relationship to the symmetry that is present in a crystal are grouped together as a "form."

   ---

   http://classes.colgate.edu/rapril/geol201/ Questions to: rapril@mail.colgate.edu Copyright 1997 © Colgate University.

   Mineralogy Home page