Crystallography

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Basic

Tradionally crystallography is the study of crystals and describing them according to geometrical observations. This involves the measurement of the crystal faces in relation to the imaginary crystal axes, with the use of a goniometer, and symmetry.
In modern times crystallography is the study of atom arrangements in solids through x-ray diffraction photography.

Some solids do not have a structured arrangement of atoms and we name them "amorphous", like for instance glass and opal.

A crystal is a:

  • geometrical solid bound by flat surfaces
  • it has a regular and symmetrical pattern of atoms ('crystal lattice')
  • physical and optical properties may vary with direction

An amorphous solid has:

  • no definite shape ('not crystalline')
  • physical and optical properties remain the same in every direction

Ideally single crystals can be observed with the unaided eye, some crystals however are so small they can not be detected without magnification. Often these small crystals bind together to form a solid and we name them polycrystalline (poly = many).
Tradition divided polycrystalline structures into microcrystalline and cryptocrystalline.

  • Microcrystalline bodies are composed of small crystals that can be individualy observed with magnification (as a microscope).
  • Cryptocrystalline substances are made up of such small crystals that the microscope can not distinguish individual crystals.

With modern microscopes, that can magnify upto 0.3nm, the term cryptocrystalline has become obsolete.

According observations we devide crystals in 3 groups and 7 crystal systems.
It should be noted that some gemological institutes (as the GIA) do not consider the trigonal system as a system on its own, rather they classify it as a subgroup of the hexagonal system.


Crystal system Group Axes of symmetry Planes of symmetry Center of symmetry Crystal axes (with dimensions and angles)
Cubic (isometric) I 13 9 1 3 (a = a = a) (all at 90° to eachother)
Tetragonal II 5 5 1 3 (a = a ≠ c) (all at 90° to eachother)
Hexagonal II 7 7 1 4 (a = a = a ≠ c) (3 at 120°, c-axis at 90° to them)
Trigonal II 4 3 1 4 (a = a = a ≠ c) (3 at 120°, c-axis at 90° to them)
Orthorhombic III 3 3 1 3 (a ≠ b ≠ c) (all at 90° to eachother)
Monoclinic III 1 1 1 3 (a ≠ b ≠ c) (a inclining to c, b at 90° to them)
Triclinic III none none 1 3 (a ≠ b ≠ c) (all inclining)

The above mentioned 7 crystal systems are further divided into 32 classes. These classes have different levels of symmetry within each system. The symmetries given above are the highest levels of symmetry within each system.
For example, the trigonal mineral tourmaline has different terminations on the prism ends (due to hemimorphism) and thus will miss one plane of symmetry.

Gemstones in group I are isometric (same distances in all directions of the crystal axes), those in group II are biaxial and the ones in group III are biaxial gemstones.

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