Twin Laws in Gemmology

A crystal twin is an intergrowth of two or more crystal individuals of the same species that
share some lattice points but have different crystallographic orientations. The geometric
relationship between the parts is defined by the twin law – a symmetry operation
(reflection across a twin plane, or rotation about a twin axis) that is not a symmetry
element of the point group of the untwinned crystal.

Types of twin by geometry:

• Contact twin: individuals joined at a flat, planar composition surface (the twin plane).
  The boundary is visible as a straight line on the crystal face.
• Penetration twin: individuals interpenetrate; no single planar boundary. The composition
  surface is irregular or concave.
• Polysynthetic (lamellar) twin: repeated alternating thin lamellae, each related by the
  same twin law. Produces parallel striations on crystal faces or cleavage surfaces.
• Cyclic twin: more than two individuals, each related by the same twin operation, arranged
  around a common axis; may produce cross-, star-, or ring-shaped habits.

The twin plane or axis is described in Miller index notation of the host crystal system.

Source: Read, P. Gemmology, 3rd ed. DOI: 10.4324/9780080507224 [VERIFIED]

The spinel law is the defining twin law of the cubic system, operating on the {111} octahedral
planes.

• System: Cubic
• Twin element: {111} twin plane
• Type: Contact twin (occasionally polysynthetic as "contact polysynthetic")
• Recognition feature: Produces flat, triangular "macle" – an octahedron that appears
  compressed perpendicular to the {111} plane. The contact face shows a re-entrant notch
  (triangular depression) where the two individuals meet at the composition surface.
• Gem species:
  • Spinel: flat triangular octahedra ("spinels" in the geological sense); the macle habit
    is diagnostic for rough spinel in alluvial deposits.
  • Diamond: flat triangular macles ("macle diamonds"), characteristic of some alluvial
    diamond rough. The triangular table and re-entrant notch are recognisable sight-holder
    features.

Three named twin laws apply to monoclinic feldspars (orthoclase, sanidine), distinguished
by their twin element and the geometry of the resulting composition surface.

Plagioclase feldspars (albite, oligoclase, labradorite, bytownite, anorthite) are triclinic
and characteristically show two simultaneous polysynthetic twin laws that produce the
diagnostic striations used to distinguish plagioclase from orthoclase.

• System: Trigonal
• Twin element: {11̄20} twin plane – polysynthetic penetration twin
• Type: Polysynthetic penetration twin
• Recognition: Sectors of opposite optical handedness (left-handed and right-handed
  quartz) are intergrown within a single crystal. There is no external morphological
  distinction between the two sectors – the twin is invisible optically by normal
  transmitted light. Detection requires:
  • Etch figures: acid etching of the r-face produces triangular etch pits of opposite
    orientation in left- vs. right-handed sectors.
  • X-ray diffraction: Laue photographs show the handedness.
• Effect on properties: Brazil-law twins cancel piezoelectric response in alternating
  sectors. This is why natural quartz must be checked for Brazil twinning before use in
  precision frequency applications; only single-handed quartz is useful. Gem-quality natural
  quartz for piezoelectric use must be twin-free.
• Gem species: All varieties of quartz (amethyst, citrine, rock crystal, smoky quartz).

• System: Trigonal
• Twin element: c-axis (rotation of 60° or 180°) – penetration twin
• Type: Penetration twin
• Recognition: Dauphiné-law twins are crystallographically rotated by 60° about the
  c-axis, but this operation is equivalent to a 180° rotation in the point group 32 (the
  quartz class). They are indistinguishable externally: no striations, no colour
  difference, and no change in RI or birefringence.
  • Under the polariscope, Dauphiné twinning causes sector-by-sector anomalous extinction;
    different sectors extinguish at slightly different angles, producing an irregular
    "flashing" pattern under crossed polars. This can confuse the gemmologist if not
    recognised.
  • The twin does NOT change the optical handedness of the quartz (unlike Brazil law),
    so it has no effect on optical rotation.
  • Electrical twin: Dauphiné twinning reverses the direction of the a-axes. In sectors
    separated by the twin, the piezoelectric polarity is reversed. This is the origin of the
    term "electrical twin."
• Gem species: Quartz (common; many quartz crystals contain Dauphiné domains).

• System: Trigonal
• Twin element: {11̄22} twin plane – contact twin
• Type: Contact twin
• Recognition: Produces a heart-shaped or V-shaped contact twin. The two prism faces of
  the two individuals meet at a re-entrant angle of approximately 84°, giving the
  characteristic heart ("macle") shape. The composition surface is a flat plane coinciding
  with the {11̄22} face.
• Named for: Specimens from Yamanashi prefecture, Japan, where this twin habit is
  particularly well developed. Also found in Brazilian and Alpine quartz.
• Gem species: Quartz.

Corundum (ruby and sapphire) has no true cleavage. Instead, it commonly shows parting on
two planes that arise from polysynthetic twinning on those planes. This is a classic
examination trap: the Diploma requires candidates to know that corundum has no cleavage,
only parting.

Twin plane: {10-11} (rhombohedral plane, trigonal four-index notation).

Repeated polysynthetic twinning on {10-11} produces closely spaced lamellae of alternating
orientation. The composition planes between twin individuals are slightly weaker than the
bulk crystal, producing the {10-11} parting.

Additionally, corundum shows {0001} basal parting (c-parting) from polysynthetic twinning
on the basal pinacoid plane.

Source: Pignatelli, Nespolo & Pardieu, Mineralogy and Petrology, 2024.
DOI: 10.1007/s00710-024-00858-1 [VERIFIED]

Named twin laws appear at multiple points in gemmological identification:

• Spinel macle / diamond macle: sight-holder feature for alluvial rough; flat triangular
  habit with re-entrant notch is immediately recognisable.
• Albite striations on plagioclase cleavage: fastest loupe test to distinguish plagioclase
  from orthoclase without instruments; decisive when RI values overlap.
• Dauphiné twinning in quartz: explains anomalous extinction patterns under the polariscope;
  without this knowledge a gemmologist might mistake the stone for biaxial.
• Brazil twinning: explains why some quartz shows alternating optical effects; relevant
  when evaluating quartz for piezoelectric use.
• Corundum parting vs cleavage: stating "corundum has perfect basal cleavage" is a
  Diploma-level examination error. The correct answer is parting along {0001} and {10-11}.
• Labradorescence: the polysynthetic albite and pericline twinning lamellae in labradorite
  create the thin-film interference responsible for labradorescence – twinning is directly
  linked to the phenomenon.

• Read, P. Gemmology, 3rd ed. Routledge, 2012. DOI: 10.4324/9780080507224. [VERIFIED]
• Pignatelli, I.; Nespolo, M.; Pardieu, V. et al. "Basal twinning of Greenland corundum."
  Mineralogy and Petrology, 2024. DOI: 10.1007/s00710-024-00858-1. [VERIFIED]
• Gem-A Diploma syllabus §3.1: twinning types and named twin laws.