Goniometer Click to enlarge image
The emergence of crystallography (study of crystals) as an independent science was directly related to the development of optical instruments. Once the angles between crystal faces could be accurately measured then minerals could be described. The instrument developed to measure these interfacial angles became known as a goniometer. A reflecting goniometer measures angles “based on the physical laws of the reflection of light from a plane mirror with equal angels of incidence and reflection: the incident light is reflected from smooth crystal faces.” Image: Stuart Humphreys
© Australian Museum

Up until about the 1950s, most minerals were identified according to their chemical composition (made by wet chemical analysis) and external crystallography (e.g. detailed measurement of crystal faces, lengths of faces, and angles between faces). However, these days we use electron microprobe analysis (based on the property of each element to emit distinctive spectra when bombarded by electrons) and X-ray crystallography (based on the property of each mineral to reflect X-rays at distinct and unique angles specific to that mineral).

The seven crystal systems

There are seven main crystal groups or systems:

  1. Cubic (cub): (also known as Isometric) where the length of all axes are equal and the angle between each axis is 90°.
  2. Tetragonal (tet): where horizontal (a) and (b) axes are of equal length and angles between each axis are 90°. The vertical (c) axis can be longer or shorter than the horizontal axes.
  3. Hexagonal (hex): where the horizontal (a) and (b) axes are of equal length but the angles between the horizontal axes are 60°/120°. There is a six-fold rotation axis.
  4. Trigonal (rhombohedral): Sometimes included in Hexagonal. The horizontal (a) and (b) axes are of equal length but the angles between the axes are different. There is a three-fold rotation axis.
  5. Orthorhombic (orth): where each axis is of different length but the angle between each axis is 90°. (25% of known minerals).
  6. Monoclinic (mon): where each axis is of a different length but the angle between two of the axes is 90°. (50% of known minerals).
  7. Triclinic (tric): where each axis is of a different length and all angles between axes are not 90 °. (15% of known minerals).

Elements of symmetry in crystals

  • Centre of symmetry: All the faces of a crystal are arranged in parallel pairs on opposite sides of a point at the centre of the crystal.
  • Axis of symmetry: When the crystal has the same appearance after being rotated through 60, 90, 120 or 180 degrees.
  • Plane of symmetry: When a crystal can be divided into two exact mirror halves by a plane. This plane is called the plane of symmetry.

Twinning in crystals

Occurs when two crystals of the same mineral occur in direct contact with each other along a specified plane or axis. Twins include:

  • Contact Twins: where two crystals occur together along the same flat surface.
  • Penetration Twins: where two crystals are associated internally or through each other.
  • Repeated Twins: where two or more crystals of the same mineral have a regular contact between them.

Structure and chemistry

  • Polymorphism: minerals with the same chemical composition but different structural state (e.g. silica SiO2 : occurs in a number of different polymorphs with each polymorph being stable under particular conditions of temperature and pressure). Normal quartz is low-T alpha-quartz. Quartz formed in volcanic environments is commonly beta-quartz (very similar structure to alpha-quartz though commonly occurring as equant-shaped crystals), and tridymite or cristobalite (the most common variety of silica in obsidian). Coesite occurs in some very high pressure metamorphic rocks and both coesite and stishovite occur in quartz grains which have been affected by meteorite impact (extreme pressure conditions but relatively low temperature).
  • Isomorphism: is where minerals of differing chemistry have the same structure (e.g. halite (NaCl) and galena (PbS).)
  • Pseudomorphism: is where one mineral of a certain crystal system replaces a mineral of another crystal system. The replacement mineral will usually have a different chemical composition (e.g. goethite pseudomorphs after pyrite cubes).


  • Crystal: any solid object bounded by naturally flat, smooth surfaces (faces).
  • Edge: an edge is formed by the intersection of any two adjacent faces.
  • Face: crystals are bounded by a number of surfaces (usually flat) which we call faces.
  • Solid Angle: a solid angle is formed by the intersection of three or more faces.