Part 4:

Crystal Forms

Twinning

Lecture 11 Crystallography

Crystal FormsHabit: 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.

openform

closed form

Tetragonal Dipyramid

Form Indexes defined by the Miller

index (hkl) of the face in the positive quadrant

enclosed in curly braces {hkl}

a{110}

Tetragonal 4/m 2/m 2/m

a2

c

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

Pyramids and DipyramidsPyramids and Dipyramids

PrismsPrisms

Low Symmetry FormsLow Symmetry Forms

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.

Carlsbad Twin in Orthoclase

Contact Twin in Orthoclase with Braveno Law {021} as twin plane

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 TypesPotential Twin Plane (111)

MirrorReflection

Composition Plane

Contact TwinsContact TwinsComposition planescorrespond to twin planes (mirrors)

Penetration TwinsPenetration TwinsComposition planes are irregular; formed by rotational twin axis operation

TwinAxes

Have a planar composition surface separating 2 individual crystals.

Multiple Twins Formed from 3 or more twinned crystals

Polysynthetic Polysynthetic twinstwins where composition planes are parallel

Cyclic twinsCyclic twins where composition planes are not parallel

Contact twins can also occur as

Albite LawPlagioclase 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 Albite twin law {010} indicates that the twins are the form symmetrical about the mirror plane (010), i.e. perpendicular to the b-axis.

The Pericline law has faces in the zone [010], parallel to the b axis.

Twins in the Triclinic System

Albite Law{010} form twin plane

Albite twins combined with Pericline twinningparallel [010] zone axisresults in “tartan twinning” in microcline (K-feldspar)

Form: refers to a group of faces which have the same relation to the elements of symmetry.

A zone is a set of planes that share one common direction, the zone axis.

Twins in the Monoclinic System

Note that twin planes do not align with mirror planes

Twins in the Orthorhombic Systemcontact & 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

Penetrative Penetrative twins with twins with twin axes twin axes parallel to parallel to rotational rotational axesaxes

Spinel MgAl2O4

Twinning

Aragonite twin

Note atoms in composition plane common to each twin

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

Although aragonite is orthorhombic, the twin looks hexagonal due to the 120o O-C-O angle in the CO3 group

Composition Plane

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 twin3) 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

TwinningMechanisms:1) Growth

Feldspars: Plagioclase: Triclinic Albite-law-striations

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a-ca-c

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a-ca-c

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

TwinningMechanisms:1) Growth

Feldspars: Plagioclase: Triclinic Albite-law-striations

TwinningMechanisms:2) Transformation (secondary twins)

Feldspars: Hi-T K-spar (monoclinic) Lo-T K-spar microcline (triclinic)

MonoclinicMonoclinic(high-T)(high-T)

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a-ca-c TriclinicTriclinic(low-T)(low-T)

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a-ca-c

TwinningMechanisms:2) Transformation (secondary) twins

K-Feldspars: high temperature Sanidine (monoclinic)  transforms to low temperature microcline (triclinic).

“tartan twins” combine

Albite and Pericline twins

TwinningMechanisms: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