Twinning

When two or more crystalline domains of identical composition merge in a strict geometric alignment, the resulting structured intergrowth is called a twin. ^[1] The key word is symmetrical - twinning is not the random jumbling of grains that inevitably occurs in any rock or mineral deposit, but a geometrically precise relationship between segments in which one segment is related to the other by a specific symmetry operation. Because the segments are joined along a surface, twinning can be treated as a variety of planar structural defect. In practice it ranges from large, visually striking intergrowths - such as the cross-shaped staurolite twins familiar in museum collections - to ultrafine polysynthetic lamellae visible only under the microscope. ^[1]

Quick Revision

• Twin operation: the symmetry operation (reflection, rotation, inversion) that relates two twin segments ^[1]
• Twin law: specifies the operation and the crystallographic plane or axis involved ^[1]
• Composition surface: the surface along which twin segments are joined; rational planar version = composition plane ^[1]
• Contact twin: flat composition plane, segments not visually intergrown ^[1]
• Penetration twin: irregular surface, segments appear intergrown ^[1]
• Polysynthetic twin: multiple segments on repeated parallel planes (e.g. plagioclase albite twins) ^[1]
• Cyclic twin: multiple segments on non-parallel planes (e.g. rutile) ^[1]
• Growth twinning: established during nucleation; twin geometry may be lower energy ^[1]
• Transformation twinning: produced by displacive polymorphic transition (e.g. leucite) ^[1]
• Deformation twinning: shear stress drives coordinated lattice displacement; always mirror twins ^[1]

Twin Operations and Twin Laws

Every twinned crystal has its segments related by a twin operation - a symmetry operation that converts one segment into the other. There are three possible twin operations: reflection, rotation, and inversion. ^[1] The twin law that describes the twinning combines the identity of the operation with the crystallographic plane or axis to which it is referenced.

Reflection twinning produces two segments related by a mirror plane parallel to a crystallographic plane that is common to both segments. Critically, the mirror must not be a plane that already exists as a symmetry element in the untwinned crystal - introducing it as a twin operation creates a new relationship that does not merely duplicate the existing symmetry. The twin law is expressed as “reflection on {hkl}” or “twins on {hkl}”, where {hkl} is the form symbol of the mirror plane. ^[1]

Rotation twinning produces two or more segments related by rotation about a crystallographic axis common to all segments. The rotation is almost always 2-fold (180°), though other rational rotations are possible. The rotation used for twinning must not duplicate a rotation axis already present in the untwinned crystal, although a twin axis can be parallel to a symmetry axis provided the rotation required for twinning is different. The isometric [111] body diagonal is normally a 3-fold rotation axis; 2-fold rotation on [111] is therefore a valid twin operation because it uses that axis but with a different rotation. The twin law for 2-fold rotation is expressed as “2-fold rotation on [uvw]” or simply “twinning on [uvw].” If the twin axis is defined as perpendicular to a crystal plane (hkl), it is expressed as “2-fold rotation ⊥ (hkl)”. ^[1]

Inversion twinning relates two segments by inversion through the centre of the crystal. In most practical cases, however, the same twin can be expressed equivalently using rotation or reflection, so inversion twinning is rarely the uniquely necessary description. ^[1]

Composition Surfaces and Twin Types

The surface along which two twin segments are joined is the composition surface. It may be irregular, or it may follow a rational crystallographic plane that can be given a Miller index. When the composition surface is a smooth rational plane it is called the composition plane. If twinning is produced by reflection, the twin plane and the composition plane are the same surface. Rotation twins may produce either a rational composition plane or an irregular composition surface, depending on the geometry. ^[1]

Contact twins are joined on a rational composition plane. The twin segments do not appear intergrown - they sit on either side of a flat surface. Contact twins may be produced by either reflection or rotation. ^[1]

Penetration twins appear intergrown - the two segments interpenetrate each other irregularly, and the composition surface between them is correspondingly irregular. Penetration twins are typically produced by rotation twinning. ^[1]

Simple twins consist of exactly two segments. Multiple twins consist of three or more segments all related by the same twin law. When the segments are joined along successive parallel composition planes the result is polysynthetic twinning - thin lamellae alternating in orientation throughout the crystal. When successive composition planes are not parallel, the result is a cyclic twin in which the segments wrap around in a ring. ^[1]

Plagioclase is the mineralogical benchmark for polysynthetic twinning. Because plagioclase is triclinic, reflection on {010} is repeated over and over, producing thin lamellae in one orientation alternating with lamellae in the reflected orientation. The striations on plagioclase cleavage surfaces that introductory geology students learn to use as an identification feature are the direct expression of this polysynthetic twinning - each striation is the edge of one lamella exposed on the cleavage surface. Rutile, by contrast, displays cyclic twinning by repeated reflection on {011}, building a ring of segments around a central axis. ^[1]

Recognising Twinning

Distinguishing twinning from random grain intergrowths is not always straightforward. Several observable features can indicate its presence. Reentrants - places where crystal faces meet at an inward-pointing angle rather than the outward-pointing angles typical of a single crystal - are a characteristic feature. Cleavage striations - straight parallel lines on a cleavage surface - can record polysynthetic twinning. A systematic intergrowth pattern that appears consistently in multiple samples of the same mineral strongly suggests twinning rather than coincidence. Under a polarising microscope, different twin segments on the same grain often show different optical orientations - they extinguish or change colour at different angles as the stage is rotated - making even fine lamellae detectable in thin section. ^[1]

Twinning by Crystal System

Common twin laws vary systematically with crystal system because the symmetry restrictions on what constitutes a valid twin operation differ between systems. ^[1]

Triclinic: Very few symmetry restrictions exist, so a wide variety of twin laws is possible. Albite twins in plagioclase - polysynthetic reflection on {010} - are the key example. ^[1]

Monoclinic: Reflection on {001} and {100} is common, though almost any plane except {010} is possible. Because [010] is normally a 2-fold axis, twins on that axis are not found - they would duplicate an existing symmetry element. Carlsbad twins in K-feldspar, produced by 2-fold rotation on the c axis, are the named example for this system. ^[1]

Orthorhombic: Minerals in this system frequently exhibit reflection twinning across prism faces (e.g., {110}). ^[1]

Tetragonal: Reflection across pyramidal planes, commonly {011}, dominates this system, generating the distinctive “elbow” morphology famously displayed by rutile. ^[1]

Hexagonal: Reflection parallel to a rhombohedral face {101} or {111} is common. Reflection on {001} or 2-fold rotation on {001} may also occur in classes with appropriate symmetry, as seen in calcite. ^[1]

Isometric: Reflection on octahedral faces defines the spinel law, named because this twin is common in the spinel mineral group. Two-fold rotation on the [111] or [001] axes may also occur; the iron-cross penetration twin in pyrite is produced by 90° rotation on [001]. ^[1]

Mechanisms of Twin Formation

Growth Twinning

Many penetration twins and contact twins were clearly established at or very soon after the initiation of crystal growth, because the twin segments are continuous from the crystal’s exterior all the way to its centre - there is no untwinned core surrounded by a later-added twinned rim. The mechanisms that favour twinned growth over untwinned growth are not well understood, but the consistent development of specific twins in certain minerals suggests that the twinned geometry may represent either a lower-energy configuration or a kinetically favoured pathway at the conditions of crystallisation. ^[1]

Transformation Twinning

Transformation twinning is produced as a consequence of a displacive polymorphic transition. Leucite (KAlSi₂O₆), a mineral common in certain K-rich mafic lavas, provides the best-studied example. At the conditions of crystallisation in lava, leucite forms trapezohedra with isometric symmetry and a cubic unit cell in which a = b = c. When temperature falls below about 665°C the leucite undergoes a displacive transition to tetragonal symmetry, and the unit cell dimensions change so that a = b ≠ c. ^[1]

The critical complication is that in the original isometric structure all three axes a, b, and c are identical, so any one of them has an equal probability of becoming the tetragonal c axis after the transition. If the entire crystal converted to a single tetragonal orientation, its external dimensions would change - but the crystal is constrained by the surrounding solid rock. Instead, different parts of the crystal independently choose different orientations for the new c axis, producing three sets of lamellae with three different crystallographic orientations. Because the dimensional changes in each orientation are complementary, they average out and the macroscopic shape of the leucite crystal is preserved unchanged. ^[1]

Microcline, the triclinic polymorph of K-feldspar (KAlSi₃O₈), provides a second important example of transformation twinning. As microcline cools slowly and Al³⁺-Si⁴⁺ ordering proceeds, the symmetry changes from monoclinic to triclinic, and polysynthetic twins develop simultaneously in two directions - the characteristic cross-hatched or grid pattern visible in thin section that is diagnostic of microcline. ^[1]

Deformation Twinning

Deformation twins are produced when an appropriate shear stress is applied to a crystal. In response, the crystal lattice is distorted to a new orientation by coordinated displacement along successive crystallographic planes - a process sometimes called glide. The plane on which displacement occurs is the glide plane. Deformation twins are always mirror twins, and the glide plane serves as the mirror - reflecting the lattice across the glide plane is precisely the operation that produces the new orientation. ^[1]

Calcite is among the easiest minerals to twin by deformation. The stress needed is so small that pressing a knife blade along the edge of a calcite cleavage rhomb in the hand is sufficient to produce visible deformation twins. In deformed rocks, calcite grains typically display twin lamellae formed by glide on the {102} crystallographic planes. The abundance and orientation of these calcite deformation twins in a rock can be used to reconstruct the stress conditions under which the rock was deformed - an application in structural geology known as calcite twinning palaeopiezometry. ^[1]

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