Crystals are divided into seven major systems on the basis of:
- Possible combinations of the elements of symmetry.
- In terms of three or four imaginary lines of reference called the Crystallographic Axes, which pass through the centre of the crystal.
- Crystals are allocated to seven systems according to the number of these axes, their lengths and the angles between them.
There is a conventional notation for the lettering and order of the crystallographic axes.
- In general, the vertical axis is called the “c” axis,
- That running from right to left is the “b” axis,
- That running from front to back is the “a”‘ axis.
- If the horizontal axes are equal in length, they are referred to as a_{1} and a_{2} and the third (vertical) axis is the “c” axis. If all the three axes are equal in length, they are referred to as a_{1}, a_{2} and a_{3} and are interchangeable (as in the cubic system).
Crystallographic axes are not the same as the axes of symmetry. For example: In the Hexagonal, Trigonal and Tetragonal systems, the vertical “c” crystallographic axis coincides with the axis of 6-fold, 3-fold and 4-fold symmetry respectively. In the Orthorhombic system all the three crystallographic axes coincide with the three axes of 2-fold symmetry.
The most characteristic crystallographic elements are used in the following description of the seven crystal systems.
Cubic System (Isometric System) | ||
---|---|---|
No. of Crystal Axes: | 3 | |
Length: | a_{1} = a_{2} = a_{3} | |
Angles: | at 90° | |
Symmetry Elements: | a Center, 9 Planes, 13 Axes (6 of 2-fold, 4 of 3-fold, 3 of 4-fold) | |
Common Forms: | Cube, Octahedron, Do-Decahedron, Tetrahedron etc. | |
Examples: | Diamond, Garnet, Spinel, Fluorite, Pyrite, Lazurite etc. |
Trigonal System | ||
---|---|---|
No. of Crystal Axes: | 4 | |
Length: | a_{1} = a_{2} = a_{3} ≠ c | |
Angles: | at 60°, “c” at 90° to their plane | |
Symmetry Elements: | a Center, 3 Planes, 4 Axes (1 of 3-fold, 3 of 2-fold) | |
Common Forms: | Rhombohedron, Prism, Pyramids, Basal Pinacoid etc. | |
Examples: | Calcite, Quartz, Corundum, Tourmaline etc. |
Tetragonal System | ||
---|---|---|
No. of Crystal Axes: | 3 | |
Length: | a_{1} = a_{2} ≠ c | |
Angles: | at 90° | |
Symmetry Elements: | a Center, 5 Planes, 5 Axes (1 of 4-fold, 4 of 2-fold) | |
Common Forms: | Tetragonal Prism, Bipyramid, Basal Pinacoid etc. | |
Examples: | Zircon, Idocrase, Rutile, Scapolite etc. |
Hexagonal System | ||
---|---|---|
No. of Crystal Axes: | 4 | |
Length: | a_{1} = a_{2} = a_{3} ≠ c | |
Angles: | at 60°, “c” at 90° to their plane | |
Symmetry Elements: | a Center, 7 Planes, 7 Axes (1 of 6-fold, 6 of 2-fold) | |
Common Forms: | Hexagonal Prism, Pyramids, Basal Pinacoid etc. | |
Examples: | Beryl, Apatite, Benitoite etc. |
Orthorhombic System | ||
---|---|---|
No. of Crystal Axes: | 3 | |
Length: | a ≠ b ≠ c | |
Angles: | at 90° | |
Symmetry Elements: | a Center, 3 Planes, 3 Axes (all of 2-fold, 3 of 2 fold) | |
Common Forms: | Prism, Pyramids, Pinacoids, Dome etc. | |
Examples: | Andalusite, Chrysoberyl, Iolite, Peridot, Topaz etc. |
Monoclinic System | ||
---|---|---|
No. of Crystal Axes: | 3 | |
Length: | a ≠ b ≠ c | |
Angles: | “a” axis inclined to the plane containing “band c”, “b and c” at 90° | |
Symmetry Elements: | a Center, 1 Planes, 1 Axes of 2-fold | |
Common Forms: | Prism, Pinacoids, Dome etc. | |
Examples: | Jade, Orthoclase Feldspar, Sphene, Spodumene etc. |
Triclinic System | ||
---|---|---|
No. of Crystal Axes: | 3 | |
Length: | a ≠ b ≠ c | |
Angles: | All inclined | |
Symmetry Elements: | a Center, No Planes, No Axes | |
Common Forms: | Pinacoids, Pedio etc. | |
Examples: | Plagioclase Feldspar, Microcline Feldspar, Kyanite, Turquoise etc. |
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