Crystallography

Basic

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

Some solids do not have a structured arrangement of atoms, for instance glass and opal. We refer to these unstructured solids as "amorphous".

A crystal :

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

An amorphous solid has:

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

Ideally, single crystals can be observed with the unaided eye, however, some crystals are so small they cannot be detected without magnification. Often these small crystals bind together to form a solid and this kind of solid is called polycrystalline (poly = many).
Formerly, polycrystalline structures were divided into microcrystalline and cryptocrystalline.

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

Modern microscopes, which can magnify up to 0.3nm, have made the term cryptocrystalline obsolete.

According to observation, we divide crystals into 3 groups and 7 crystal systems.
It should be noted that some gemological institutes (especially USA ones like the GIA) do not consider the trigonal system as a system on its own but 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 each other)
Tetragonal II 5 5 1 3 (a = a ≠ c) (all at 90° to each other)
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 each other)
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 length in all directions of the crystal axes). Gemstones in Group II are uniaxial, and Group III are biaxial.