Crystallography of Gemstones: The Crystal System
Crystalline (Crystal Lattice) Structures
Crystallography is the science of determining the arrangement of atoms within any solid structure, including, but not limited to gemstones. All gemstones are crystalline structures made from a mixture of different elemental compounds, and the shape of a crystal is based on the atomic structure of these elemental building blocks. Atoms within a mineral are arranged in an ordered geometric pattern called a "motif" which determines its "crystal structure." A gem's crystal structure will determine a its symmetry, optical properties, cleavage planes, and overall geometric shape. The recipe, or mixture of these compounds becomes the blueprint for how the crystal will grow. A crystal's growth pattern is referred to as its "Crystal Habit."
The crystal system is a grouping of crystal structures that are categorized according to the axial system used to describe their atomic "lattice" structure. A crystal's lattice is a three dimensional network of atoms that are arranged in a symmetrical pattern.
Each crystal system consists of a set of three crystallographic axes (a, b, and c) in a particular geometrical arrangement. The seven unique crystal systems, listed in order of decreasing symmetry, are: 1. Isometric System, 2. Hexagonal System, 3. Tetragonal System, 4. Rhombohedric (Trigonal) System, 5. Orthorhombic System, 6. Monoclinic System, 7. Triclinic System.
Bravais lattices describe the geometric arrangement of the individual lattice points within each of the seven crystal systems. There are fourteen Bravais lattices which are distinct from one another in the translational symmetry they contain, and all crystalline minerals fit in one of these unique fourteen arrangements.
The "unit cell" is the smallest divisible unit of a given mineral with symmetrical characteristics that are unique to its crystalline structure. A structure's unit-cell is a spatial arrangement of atoms (motifs) which are "tiled" in a three-dimensional space to form the crystal. The unit-cell's form is determined by its unique "lattice" parameters, the length of the cell edges, and the angles between them. The positions of the atoms inside the unit-cell are described by the set of atomic positions (xi,yi,zi) measured from a given lattice point.
The Seven Crystal Systems
The cubic crystal system is also known as the "isometric" system. The cubic (Isometric) crystal system is characterized by its total symmetry. The Cubic system has three crystallographic axes that are all perpendicular to each other, and equal in length. The cubic system has one lattice point on each of the cube's four corners.
The hexagonal crystal system has four crystallographic axes consisting of three equal horizontal or equatorial (a, b, and d) axes at 120¼, and one vertical (c) axis that is perpendicular to the other three. The (c) axis can be shorter, or longer than the horizontal axes.
A tetragonal crystal is a simple cubic shape that is stretched along its (c) axis to form a rectangular prism. The tetragonal crystal will have a square base and top, but a height which is taller. By continuing to stretch the "body-centered" cubic, one more Bravais lattice of the tetragonal system is constructed.
A rhombohedron (aka trigonal system) has a three-dimensional shape that is similar to a cube, but it has been skewed or inclined to one side making it oblique. Its form is considered "prismatic" because all six crystal faces are parallel to each other. Any faces that are not squared at right angels are called "rhombi." A rhombohedral crystal has six faces, 12 edges, and 8 vertices. If all of the non-obtuse internal angles of the faces are equal (flat sample, below), it can be called a trigonal-trapezohedron.
Minerals that form in the orthorhombic (aka rhombic) crystal system have three mutually perpendicular axes, all with different, or unequal lengths.
Crystals that form in the monoclinic system have three unequal axes. The (a) and (c) crystallographic axes are inclined toward each other at an oblique angle, and the (b) axis is perpendicular to a and c. The (b) crystallographic axis is called the "ortho" axis.
Crystals that form in the triclinic system have three unequal crystallographic axes, all of which intersect at oblique angles. Triclinic crystals have a 1-fold symmetry axis with virtually no discernible symmetry, and no mirrored or prismatic planes.
Any grouping of crystal faces or facets that are arranged in the same symmetry is called a "form." There are approximately 48 crystal forms broken down into "open" or "closed" categories. There are 30 "closed" and 18 "open" crystal forms. "Closed Forms" are those groupings of facets that are related by symmetry and completely enclose a volume of space.
Although a crystal structure is an orderly arrangement of atoms on a lattice-like structure, the order may be different along different directions or axes in the crystal.
Certain properties of a particular crystal can depend on direction. These variable properties are called "vectorial properties," which are divided into two categories: "continuous" and "discontinuous." An example of a "continuous property" is a crystal's hardness. An example of a "discontinuous property" would be cleavage.
Bibliography on Crystal Lattice Structures
1. University of Wisconsin, The 48 Special Crystal Forms . www.uwgb.edu
2. Web Mineral, Crystallography and Minerals by Crystal Form . webmineral.com
3. Tulane University, External Symmetry of Crystals . www.tulane.edu
4. Rockhounds, Introduction to Crystallography . www.rockhounds.com
5. MathWorld, Solid Geometry . mathworld.wolfram.com
6. W. S. MacKenzie, A. E. Adams, Color Atlas of Rocks and Minerals . John Wiley & Sons
7. Judith Crowe, The Jeweler's Directory of Gemstones . DK Publishing
8. Walter Schumann, Gemstones of the World . NAG Press; 2Rev Ed edition
9. Paul R. Shaffer, Herbert S. Zim, Raymond Perlman, Rocks, Gems and Minerals . Martin's Press