Lecture 11 Crystallography Part 4: Crystal Forms Twinning

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

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

Low Symmetry Forms Pyramids and Dipyramids Prisms

Trapezohedron, Scalenohedron, Rhombehedron, Disphenoid

Isometric Forms

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.

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.

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

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.

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

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

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)

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

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.

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.

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

Twins in the Orthorhombic System contact & cyclic twinning Penetrative

Twins in the Tetragonal System

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

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

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 2-69 of Berry, Mason and Dietrich, Mineralogy, Freeman & Co.

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…)

Contact & Penetration twins Both are simple twins only two parts

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

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

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

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

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

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

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

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