Crystal Forms

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Lecture 11 Crystallography

• Part 4
• Crystal Forms
• Twinning

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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
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Unique Attributes of Crystal Forms
Anthophyllite
Pyrite
Quartz
NaCl
Faces of particular forms commonly share unique
physical or chemical attributes
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Form Indexes
c

• defined by the Miller index (hkl) of the face in
  the positive quadrant
• enclosed in brackets hkl
• a 100, r 111, c 001

a2
a1
Tetragonal 4/m 2/m 2/m
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Low Symmetry Forms
Pyramids and Dipyramids
Prisms
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Trapezohedron, Scalehedron, Rhombehedron,
Disphenoid
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Isometric Forms
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Twinning

• Symmetrical intergrowth of two or more crystals
  related to a symmetry operation (twin element)
  that is otherwise absent in a single crystal.
• Twin elements includes mirrors, rotation axes
  (usually 2-fold) and roto-inversion that usually
  do not align with symmetry elements in the
  crystal.
• Twin Laws define the twin element and its
  crystallographic orientation (twin planes are
  identified by a Miller index (hkl), twin axes are
  defined by a zone symbol hkl).

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Twin Types
Potential Twin Plane (111)
Composition Plane
Contact Twins Composition planes correspond to
twin planes (mirrors)
Mirror Reflection
Twin Axes
Penetration Twins Composition planes are
irregular formed by rotational twin axis
operation
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Multiple Twins

• Formed from 3 or more twinned crystals
• Polysynthetic twins where composition planes are
  parallel
• Cyclic twins where composition planes are not
  parallel

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Twins in the Triclinic System
Albite combined with Pericline 010 twin
axis results in tartan twinning in microcline
(K-feldspar)
Albite Law 010 twin plane
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Twins in the Monoclinic System
Note that twin planes do not align with mirror
planes
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Twins in the Orthorhombic System
contact cyclic twinning
Penetrative
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Twins in the Tetragonal System
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Twins in the Hexagonal System
0112 is most common and may produce single
contact or polysynthetic twins
exception twin axis C
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Twins in the Isometric System
Penetrative twins with twin axes parallel to
rotational axes
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Twinning

• Rational symmetrically-related intergrowth
• Lattices of each orientation have definite
  crystallographic relation to each other

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Twinning

• Aragonite twin
• Note zone at twin plane which is common to each
  part

Although aragonite is orthorhombic, the twin
looks hexagonal due to the 120o O-C-O angle in
the CO3 group
Redrawn from Fig 2-69 of Berry, Mason and
Dietrich, Mineralogy, Freeman Co.
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Twinning

• 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)

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• Contact Penetration twins
• Both are simple twins only two parts

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• Multiple twins (gt 2 segments repeated by same
  law)
• Cyclic twins - successive planes not
  parallel

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Twinning
http//www.tulane.edu/sanelson/eens211/twinning.h
tm

• Mechanisms
• 1) Growth
• Growth increment cluster adds w/ twin orientation
• Epitaxial more stable than random
• Not all epitaxis (growth of one composition on
  another) ? twins
• Usually simple penetration

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Twinning

• Mechanisms
• 1) Growth
• Feldspars
• Plagioclase Triclinic Albite-law-striations

a-c
a-c
b
b
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Twinning

• Mechanisms
• 1) Growth
• Feldspars
• Plagioclase Triclinic Albite-law-striations

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Twinning
cyclic twinning in inverted low quartz

• Mechanisms
• 2) Transformation (secondary)
• SiO2 High T is higher symmetry

High Quartz P6222
Low Quartz P3221
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Twinning

• Mechanisms
• 2) Transformation (secondary twins)
• Feldspars
• Orthoclase (monoclinic) ? microcline (triclinic)

a-c
a-c
Triclinic (low-T)
Monoclinic (high-T)
b
b
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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
• Interpretation wrt petrology!

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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

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

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

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Next Lecture

• 2-D Internal Symmetry