Crystal twinning

Crystal twinning occurs when two or more adjacent crystals of the same mineral are oriented so that they share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals that are tightly bonded to each other. The surface along which the lattice points are shared in twinned crystals is called a composition surface or twin plane.
In crystallography twinned crystals are described by a number of twin laws, which are specific to the crystal structure. The type of twinning can be a diagnostic tool in mineral identification. There are three main types of twinning. The first is [|growth twinning] which can occur both in very large and very small particles. The second is [|transformation twinning], where there is a change in the crystal structure. The third is deformation twinning, in which twinning develops in a crystal in response to a shear stress, and is an important mechanism for permanent shape changes in a crystal.

Definition

Twinning, a version of macle, is a form of symmetrical intergrowth between two or more adjacent crystals of the same mineral. It differs from the ordinary random intergrowth of mineral grains in a mineral deposit, because the relative orientations of the two crystal segments show a fixed relationship that is characteristic of the mineral structure. The relationship is defined by a symmetry operation called a twin operation.
The twin operation is not one of the normal symmetry operations of the untwinned crystal structure. For example, the twin operation may be reflection across a plane that is not a symmetry plane of the single crystal.
On the microscopic level, the twin boundary is characterized by a set of atomic positions in the crystal lattice that are shared between the two orientations. These shared lattice points give the junction between the crystal segments much greater strength than that between randomly oriented grains, so that the twinned crystals do not easily break apart.
Parallel growth describes a form of crystal growth that produces the appearance of a cluster of aligned crystals which could be mistaken for twins. Close examination reveals that the cluster is actually a single crystal. This is not twinning, since the crystal lattice is continuous throughout the cluster. Parallel growth likely takes place because it reduces system energy.

Twin laws

Twin laws are symmetry operations that define the orientation between twin crystal segments. These are as characteristic of the mineral as are its crystal face angles. For example, crystals of staurolite show twinning at angles of almost precisely 90 degrees or 30 degrees. A twin law is not a symmetry operation of the full set of basis points.
Twin laws include reflection operations, rotation operations, and the inversion operation. Reflection twinning is described by the Miller indices of the twin plane while rotational twinning is described by the direction of the twin axis. Inversion twinning is typically equivalent to a reflection or rotation symmetry.
Rotational twin laws are almost always 2-fold rotations, though any other permitted rotation symmetry is possible. The twin axis will be perpendicular to a lattice plane. It is possible for a rotational twin law to share the same axis as a rotational symmetry of the individual crystal if the twin law is a 2-fold rotation and the symmetry operation is a 3-fold rotation. This is the case for spinel law twinning on <111>: The spinel structure has a 3-fold rotational symmetry on <111> and spinel is commonly twinned by 2-fold rotation on <111>.
The boundary between crystal segments is called a composition surface or, if it is planar, a composition plane. The composition plane is often, though not always, parallel to the twin law plane of a reflection law. If this is the case, the twin plane is always parallel to a possible crystal face.

Common twin laws

In the isometric system, the most common types of twins are the Spinel Law <111>, where the twin axis is perpendicular to an octahedral face, and the Iron Cross <001>, which is the interpenetration of two pyritohedrons, a subtype of dodecahedron.
In the hexagonal system, calcite shows the contact twin laws and. Quartz shows the Brazil Law, and Dauphiné Law <0001>, which are penetration twins caused by transformation, and Japan Law, which is often caused by accidents during growth.
In the tetragonal system, cyclical contact twins are the most commonly observed type of twin, such as in rutile titanium dioxide and cassiterite tin oxide.
In the orthorhombic system, crystals usually twin on planes parallel to the prism face, where the most common is a twin, which produces cyclical twins, such as in aragonite, chrysoberyl, and cerussite.
In the monoclinic system, twins occur most often on the planes and by the Manebach Law, Carlsbad Law , Baveno Law in orthoclase, and the Swallow Tail Twins in gypsum.
In the triclinic system, the most commonly twinned crystals are the feldspar minerals plagioclase and microcline. These minerals show the Albite and Pericline Laws.
The most common twin operations by crystal system are tabulated below. This list is not exhaustive, particularly for the crystal systems of lowest symmetry, such as the triclinic system.

System	Law	Operation	Examples
Triclinic	Albite law Pericline law Carlsbad law Baveno law Manebach law	<010> <001>	Plagioclase
Monoclinic	Carlsbad law Baveno law Manebach law	<001> <031> <231>	Orthoclase Gypsum Staurolite
Orthorhombic			Aragonite, cerrusite; often cyclic
Tetragonal			Cassiterite, rutile
Hexagonal	Brazil law Dauphine law Japan law	<0001>	Calcite Quartz
Isometric	Spinel law Iron cross law	<111> <001>	Spinel Pyrite

Types of twinning

Simple twinned crystals may be contact twins or penetration twins. Contact twins meet on a single composition plane, often appearing as mirror images across the boundary. Plagioclase, quartz, gypsum, and spinel often exhibit contact twinning. Merohedral twinning occurs when the lattices of the contact twins superimpose in three dimensions, such as by relative rotation of one twin from the other. An example is metazeunerite. Contact twinning characteristically creates reentrant faces where faces of the crystal segments meet on the contact plane at an angle greater than 180°.
A type of twinning involving 180° relationships is called hemitropism or hemitropy.
In penetration twins the individual crystals have the appearance of passing through each other in a symmetrical manner. Orthoclase, staurolite, pyrite, and fluorite often show penetration twinning. The composition surface in penetration twins is usually irregular and extends to the center of the crystal.
Contact twinning can arise from either reflection or rotation, whereas penetration twinning is usually produced by rotation.
If several twin crystal parts are aligned by the same twin law they are referred to as multiple or repeated twins. If these multiple twins are aligned in parallel they are called polysynthetic twins. When the multiple twins are not parallel they are cyclic twins. Albite, calcite, and pyrite often show polysynthetic twinning. Closely spaced polysynthetic twinning is often observed as striations or fine parallel lines on the crystal face. Cyclic twins are caused by repeated twinning around a rotation axis. This type of twinning occurs around three, four, five, six, or eight-fold axes, the corresponding patterns are called threelings, fourlings, fivelings, sixlings, and eightlings. Sixlings are common in aragonite. Rutile, aragonite, cerussite, and chrysoberyl often exhibit cyclic twinning, typically in a radiating pattern.
For rotational twinning the relationship between the twin axis and twin plane falls into one of three types:

Modes of formation

There are three modes of formation of twinned crystals.

Growth twins are the result of an interruption or change in the lattice during formation or growth. This may be due to a larger substituting ion, statistics as the energy difference to nucleate a new plane of atoms in a twin orientation is small, or because the twins lead to a lower energy structure.
Annealing or transformation twins are the result of a change in crystal system during cooling as one form becomes unstable and the crystal structure must re-organize or transform into another more stable form.
Deformation or gliding twins are the result of stress on the crystal after the crystal has formed. Because growth twins are formed during the initial growth of the crystal, they are described as primary, whereas transformation or deformation twins are formed in an existing crystal and are described as secondary.
Growth twinning (nanotwinning)

There are two types of twinning that can occur during growth, accidental and ones where the twinned structure has lower energy.
In accidental growth twinning an atom joins a crystal face in a less than ideal position, forming a seed for growth of a twin. The original crystal and its twin then grow together and closely resemble each other. This is characteristic enough of certain minerals to suggest that it is thermodynamically or kinetically favored under conditions of rapid growth.
Different from these are twins found in nanoparticles such as the image here, these fivefold or decahedral nanoparticles being one of the most common. These cyclic twins occur as they are lower in energy at small sizes. For the five-fold case shown, there is a disclination along the common axis which leads to an additional strain energy. Balancing this there is a reduction in the surface free energy, in large part due to more surface facets. In small nanoparticles the decahedral and a more complicated Icosahedral structure are lower energy, but at larger energies single crystals become lower energy. However, they do not have to transform into single crystals and can grow very large, and are known as fivelings, documented as early as 1831 by Gustav Rose; further drawings are available in the Atlas der Kristallformen, and see also the article on fivelings.