Twins and Twinning

Twins represent a symmetrical intergrowth of two or more domains of a crystal that have different atomic orientations. The crystal segments are joined along a surface and this is commonly a plane - referred to as the composition plane or surface. Along this plane the crystal segments share a number of atoms and thus twinning can be considered a type of planar structural defect.

Let's define some important terms and concepts so we can discuss twinning:

• The 2 or more individuals of the twinned crystal are related by a symmetry element or Twin operation that is absent in the single untwinned crystal
• Simple twins are comprised of 2 individuals
• Complex twins are composed of more than 2 individuals
• Contact twins appear to have had the 2 (or more) individuals simply glued together along a planar surface
• Penetration twins pass through each other and share a volume of space
• Polysynthetic twins are a special case of contact twins where the 2 orientations repeat back and forth tens or hundreds of times across an entire grain
• Re-entrant angles - the angle between 2 adjoining faces that 'points' toward the interior of a crystal

There are three possible twin operations - reflection, rotation, and inversion.

• The twin law that describes the twin operation specifies the twin operation and the crystallographic plane or axis associated with the twinning.
• Reflection gives enantiomorphic (right and left handed) twin individuals and the mirror plane is identified by its Miller index
  • this plane must not normally be a mirror in the untwinned crystal
  • usually referred to as 'reflection on {hkl}' or 'twins on {hkl}'
• Rotation occurs about an axis that is common to all segments of the final twinned crystal
  • almost always the rotation is 2-fold
  • the axis must not duplicate a rotation axis already present in the crystal however it can 'parallel' an existing axis as long as it has a different 'foldness'; i.e. a 2-fold rotation superimposed along the body diagonal 3-fold axis in the cubic/isometric system
  • refer to this as '2-fold rotation on [uvw]' or simply 'twinning on [uvw]' if the 2-fold rotation can be inferred or presumed
• Inversion can normally be alternatively expressed as reflection twins

So how do these possibilities manifest themselves in the various Crystal Systems?

Triclinic System:

• there are few symmetry restrictions (there is so little symmetry already present)
• feldspars provide the best examples
  • albite law: reflection across {010} twin plane
  • pericline law: rotation about the [010] axis

Monoclinic System:

• Twinning by reflection on the {100} or {001} planes is most common
  • Remember - the {010} plane is the mirror present in the monoclinic system
• Other planes are also possible - see the Baveno twin for orthoclase (K-feldspar)
• The most common Monoclinic rotation twin is the about [001] - the interpenetrating Carlsbad twin (again in orthoclase)
  • The [010] is usually the 2-fold axis so it can't be a twin axis

Orthorhombic System:

• the system is likely to come with 3 2-fold axes and 3 mirror planes so:
  • twin planes, if present, would likely be parallel to a prism face - e.g.{110}
• staurolite is monoclinic but pseudo-orthorhombic with a beta angle of 90°
  • penetration twin on {031}gives a right angle cross
  • penetration twin on {231} gives a 60° cross

Tetragonal System:

• For reasons nearly identical to those that apply to the Orthorhombic system, the most common Tetragonal twins have {011} as the twin plane
  • What does this look like? - Remember the c-axis is the 4-fold

Hexagonal System:

• Twins by reflection parallel to one of the rhombohedron crystal faces {101} or {111}
• In classes with appropriate symmetry, 2-fold rotation on {001} is possible
  • To which classes would this apply??

Isometric System:

• Spinel twins: reflection on {111} - the octahedron faces
• 2-fold rotation on [111]
• 2-fold rotation on [001] in appropriate point group - (Which is????)

Where do twins come from?

1. Growth twins: see Fig. 3.54 (p.167) for an example.
2. Transformation twins: secondary, post formation of the mineral grain
   1. High T to Low T polymorphic transformation via displacive transformation

    

3. Glide or deformation twins
   1. Calcite as an example