1. Lecture 11 Crystallography
Part 4:
Crystal Forms
Twinning

2. Crystal Forms
Habit: the general external shape of a crystal (e.g., prismatic, cubic, bladed...)
Form: refers to a group of faces which have the same relation to the elements of symmetry.
Crystals with higher degrees of symmetry tend to generate more form faces.
open
form
closed
form
Tetragonal Dipyramid

3. Form Indexes c
defined by the Miller index (hkl) of the face in the positive quadrant
enclosed in curly braces {hkl}
a {110} a2
Miller indices, in braces, may also be used as a shorthand representation of forms. For example, if the face (110) is present on a tetragonal crystal, three faces that are symmetrically equivalent to (110) by the 4-fold axis should also be present. These are (1,bar-1,0), (bar-1,1,0), and (bar-1,bar-1,0). The set of crystal faces in a crystal class that are symmetrically equivalent are called a form for that class and are designated by braces around the Miller indices of one of the faces. For example, the four faces mentioned above may be represented by the one symbol {110}. This form is called a tetragonal prism
Tetragonal 4/m 2/m 2/m

4. Low Symmetry Forms
Pyramids and Dipyramids
Prisms

5. Trapezohedron, Scalenohedron, Rhombehedron, Disphenoid

6. Isometric Forms

7. Twinning If a crystal is subjected to stress during growth
or temperature/pressure conditions different from those under which it originally formed
two or more intergrown crystals are formed in a symmetrical fashion.
These symmetrical intergrowths of crystals are called twinned crystals.

8. Twinning Mechanism
What happens is that lattice points in one crystal are shared as lattice points in another crystal adding apparent symmetry to the crystal pairs.
Twinning, because it adds symmetry, never occurs in relation to the existing symmetry of the crystal.

9. Twinning defined by symmetry added
Reflection across a mirror plane. The added mirror plane would then be called a twin plane.
Rotation about an axis or line in the crystal.
The added rotation axis would then be
called a twin axis.
Inversion through a point. The added center of symmetry would then be called a twin center.
Contact Twin in Orthoclase with Braveno Law {021} as twin plane
Carlsbad Twin in Orthoclase

10. Twin Laws
Twin laws are expressed as either form symbols to define twin planes (i.e. {hkl}) or zone symbols to define the direction of twin axes (i.e. [hkl]).
The surface along which the lattice points are shared in twinned crystals is called a composition surface.

11. Twin Types Contact Twins Composition planes
Potential
Twin Plane (111)
Composition
Plane
Contact Twins
Composition planes
correspond to twin planes (mirrors)
Mirror
Reflection
Have a planar composition surface separating 2 individual crystals.
Twin
Axes
Penetration Twins
Composition planes are irregular;
formed by rotational twin axis operation

12. Multiple Twins Contact twins can also occur as
Formed from 3 or more twinned crystals
Polysynthetic twins where composition planes are parallel
Cyclic twins where composition planes are not parallel

13. Albite Law
Plagioclase is a solid solution of Anorthite CaAl2Si2O8 to Albite NaAlSi3O8. It very commonly shows Albite polysynthetic twinning. The Albite twin law {010} indicates that the twins make a form, the faces are parallel to the mirror plane (010), i.e. perpendicular to the b-axis.
Albite twinning is so common in plagioclase, that it's presence is a diagnostic property for identification of plagioclase when seen with crossed polarizers.
XPL (crossed polarizers)

14. Pericline Law
- The Pericline law has faces in the zone around [010], so b is the twin axis.
The result of monoclinic Orthoclase or Sanidine transforming to Microcline (all KAlSi3O8).
Pericline twinning usually occurs with Albite twinning in Microcline; then a cross-hatched pattern, called tartan twinning, distinguishes Microcline from the other feldspars under the microscope.
Microcline XPL

15. Microcline: Albite and Pericline Laws
The Pericline law has faces in the zone [010], parallel to the b axis.
The Albite twin law {010} indicates that the twins are the form symmetrical about the mirror plane (010), i.e. perpendicular to the b-axis.

16. Twins in the Triclinic System
Albite twins combined
with Pericline twinning
parallel [010] zone axis
results in “tartan twinning” in microcline (K-feldspar)
A zone is a set of planes that share one common direction, the zone axis.
Albite Law
{010} form twin plane
Form: refers to a group of faces which have the same relation to the elements of symmetry.

17. Twins in the Monoclinic System
Note that twin planes do
not align with mirror planes

18. Twins in the Orthorhombic System
contact & cyclic
twinning
Penetrative

19. Twins in the Tetragonal System

20. Twins in the Hexagonal System
{0112} is most common and may produce single contact or polysynthetic twins
exception:
twin axis || C

21. Twins in the Isometric System
Spinel MgAl2O4
Penetrative twins with twin axes parallel to rotational axes

22. Twinning Aragonite twin
Note atoms in composition plane common to each twin
Although aragonite is orthorhombic, the twin looks hexagonal due to the 120o O-C-O angle in the CO3 group
Composition Plane
Redrawn from Fig of Berry, Mason and Dietrich, Mineralogy, Freeman & Co.

23. Twinning 1) Reflection (twin plane) Example: gypsum “fish-tail”
Twin Operation is the symmetry operation which relates the two (or more) parts (twin mirror, rot. axis)
1) Reflection (twin plane)
Example: gypsum “fish-tail”
2) Rotation (usually 180o) about an axis common to both (twin axis): normal and parallel twins.
Example: carlsbad twin
3) Inversion (twin center)
The twin element cannot be a symmetry element of the individuals. Twin plane can't be a mirror plane of the crystal
Twin Law is a more exact description for a given type (including operation, plane/axis, mineral…)

24. Contact & Penetration twins
Both are simple twins only two parts

25. Multiple twins (> 2 segments repeated by same law)
Cyclic twins - successive planes not parallel
if parallel Polysynthetic twins
Albite Law
in plagioclase

26. Twinning Mechanisms: 1) Growth Feldspars:
Plagioclase: Triclinic Albite-law-striations
If several crystals are aligned by the same twin law they are referred to as multiple twins. If these multiple twins are aligned in parallel they are called polysynthetic twins
a-c
a-c b b

27. Twinning Mechanisms: 1) Growth Feldspars:
Plagioclase: Triclinic Albite-law-striations

28. Twinning Mechanisms: 2) Transformation (secondary twins) Feldspars:
Hi-T K-spar (monoclinic)  Lo-T K-spar microcline (triclinic)
a-c
a-c
Monoclinic
(high-T)
Triclinic
(low-T) b b

29. Twinning Mechanisms: 2) Transformation (secondary) twins
K-Feldspars: high temperature Sanidine (monoclinic)  transforms to low temperature microcline (triclinic).
“tartan twins” combine
Albite and Pericline twins

30. Twinning Mechanisms: 3) Deformation (secondary)
Results from shear stress
greater stress  gliding, and finally rupture Also in feldspars.
Looks like transformation, but the difference in interpretation is tremendous

31. Mechanisms: 3) Deformation (secondary)
Results from shear stress. Plagioclase

32. Mechanisms: 3) Deformation (secondary)
Results from shear stress. Calcite