HOME

TheInfoList



OR:

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. Crystallographers classify twinned crystals by a number of twin laws. These twin laws are specific to the crystal structure. The type of twinning can be a diagnostic tool in mineral identification. Deformation twinning, in which twinning develops in a crystal in response to a
shear stress Shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the ...
, is an important mechanism for permanent shape changes in a crystal.Courtney, Thomas H. (2000) ''Mechanical Behavior of Materials'', 2nd ed. McGraw Hill.


Definition

Twinning 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 In group theory, geometry, representation theory and molecular symmetry, a symmetry operation is a transformation of an object that leaves an object looking the same after it has been carried out. For example, as transformations of an object in spac ...
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.


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 (i.e. ) while rotational twinning is described by the direction of the twin axis (i.e. ). 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 (3-fold, 4-fold, or 6-fold) 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 (twin plane, parallel to an
octahedron In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...
) <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 geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagon ...
. 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 Rutile is an oxide mineral composed of titanium dioxide (TiO2), the most common natural form of TiO2. Rarer polymorphs of TiO2 are known, including anatase, akaogiite, and brookite. Rutile has one of the highest refractive indices at visib ...
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 Aragonite is a carbonate mineral, one of the three most common naturally occurring crystal forms of calcium carbonate, (the other forms being the minerals calcite and vaterite). It is formed by biological and physical processes, including pre ...
,
chrysoberyl The mineral or gemstone chrysoberyl is an aluminate of beryllium with the formula Be Al2 O4. The name chrysoberyl is derived from the Greek words χρυσός ''chrysos'' and βήρυλλος ''beryllos'', meaning "a gold-white spar". Despite ...
, and
cerussite Cerussite (also known as lead carbonate or white lead ore) is a mineral consisting of lead carbonate (PbCO3), and is an important ore of lead. The name is from the Latin ''cerussa'', white lead. ''Cerussa nativa'' was mentioned by Conrad Gessner ...
. In the monoclinic system, twins occur most often on the planes and by the Manebach Law , Carlsbad Law 01 Braveno Law in
orthoclase Orthoclase, or orthoclase feldspar ( endmember formula K Al Si3 O8), is an important tectosilicate mineral which forms igneous rock. The name is from the Ancient Greek for "straight fracture," because its two cleavage planes are at right angles ...
, and the Swallow Tail Twins (Manebach law) in
gypsum Gypsum is a soft sulfate mineral composed of calcium sulfate dihydrate, with the chemical formula . It is widely mined and is used as a fertilizer and as the main constituent in many forms of plaster, blackboard or sidewalk chalk, and drywal ...
. In the triclinic system, the most commonly twinned crystals are the
feldspar Feldspars are a group of rock-forming aluminium tectosilicate minerals, also containing other cations such as sodium, calcium, potassium, or barium. The most common members of the feldspar group are the ''plagioclase'' (sodium-calcium) felds ...
minerals
plagioclase Plagioclase is a series of tectosilicate (framework silicate) minerals within the feldspar group. Rather than referring to a particular mineral with a specific chemical composition, plagioclase is a continuous solid solution series, more pro ...
and
microcline Microcline (KAlSi3O8) is an important igneous rock-forming tectosilicate mineral. It is a potassium-rich alkali feldspar. Microcline typically contains minor amounts of sodium. It is common in granite and pegmatites. Microcline forms during slo ...
. These minerals show the Albite and Pericline Laws. The most common twin operations by
crystal system In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices. Space groups are classified into crystal systems according to their poin ...
are tabulated below. This list is not exhaustive, particularly for the crystal systems of lowest symmetry, such as the triclinic system.


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 Plagioclase is a series of tectosilicate (framework silicate) minerals within the feldspar group. Rather than referring to a particular mineral with a specific chemical composition, plagioclase is a continuous solid solution series, more pro ...
,
quartz Quartz is a hard, crystalline mineral composed of silica ( silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical ...
,
gypsum Gypsum is a soft sulfate mineral composed of calcium sulfate dihydrate, with the chemical formula . It is widely mined and is used as a fertilizer and as the main constituent in many forms of plaster, blackboard or sidewalk chalk, and drywal ...
, 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 Metazeunerite is an arsenate mineral with a chemical formula of Cu(UO2)2(AsO4)2·8H2O. The origin of this mineral is almost always from the natural dehydration process of zeunerite. Named for civil engineer Gustav A. Zeuner who worked at the Sch ...
. Contact twinning characteristically creates reentrant faces where faces of the crystal segments meet on the contact plane at an angle greater than 180°. In ''penetration twins'' the individual crystals have the appearance of ''passing through'' each other in a symmetrical manner.
Orthoclase Orthoclase, or orthoclase feldspar ( endmember formula K Al Si3 O8), is an important tectosilicate mineral which forms igneous rock. The name is from the Ancient Greek for "straight fracture," because its two cleavage planes are at right angles ...
, staurolite,
pyrite The mineral pyrite (), or iron pyrite, also known as fool's gold, is an iron sulfide with the chemical formula Fe S2 (iron (II) disulfide). Pyrite is the most abundant sulfide mineral. Pyrite's metallic luster and pale brass-yellow hue giv ...
, and
fluorite Fluorite (also called fluorspar) is the mineral form of calcium fluoride, CaF2. It belongs to the halide minerals. It crystallizes in isometric cubic habit, although octahedral and more complex isometric forms are not uncommon. The Mohs sca ...
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 Albite is a plagioclase feldspar mineral. It is the sodium endmember of the plagioclase solid solution series. It represents a plagioclase with less than 10% anorthite content. The pure albite endmember has the formula . It is a tectosilicate ...
, calcite, and
pyrite The mineral pyrite (), or iron pyrite, also known as fool's gold, is an iron sulfide with the chemical formula Fe S2 (iron (II) disulfide). Pyrite is the most abundant sulfide mineral. Pyrite's metallic luster and pale brass-yellow hue giv ...
often show polysynthetic twinning. Closely spaced polysynthetic twinning is often observed as
striation Striations means a series of ridges, furrows or linear marks, and is used in several ways: * Glacial striation * Striation (fatigue), in material * Striation (geology), a ''striation'' as a result of a geological fault * Striation Valley, in Ant ...
s or fine parallel lines on the crystal face.
Rutile Rutile is an oxide mineral composed of titanium dioxide (TiO2), the most common natural form of TiO2. Rarer polymorphs of TiO2 are known, including anatase, akaogiite, and brookite. Rutile has one of the highest refractive indices at visib ...
,
aragonite Aragonite is a carbonate mineral, one of the three most common naturally occurring crystal forms of calcium carbonate, (the other forms being the minerals calcite and vaterite). It is formed by biological and physical processes, including pre ...
,
cerussite Cerussite (also known as lead carbonate or white lead ore) is a mineral consisting of lead carbonate (PbCO3), and is an important ore of lead. The name is from the Latin ''cerussa'', white lead. ''Cerussa nativa'' was mentioned by Conrad Gessner ...
, and
chrysoberyl The mineral or gemstone chrysoberyl is an aluminate of beryllium with the formula Be Al2 O4. The name chrysoberyl is derived from the Greek words χρυσός ''chrysos'' and βήρυλλος ''beryllos'', meaning "a gold-white spar". Despite ...
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: :#parallel twinning, when the twin axis and compositional plane lie parallel to each other, :#normal twinning, when the twin plane and compositional plane lie normally, and :#complex twinning, a combination of parallel twinning and normal twinning on one compositional plane.


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 due to a possible deformation from a larger substituting ion. ''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''. ''Parallel growth'' describes a form of crystal growth that produces the appearance of a cluster of aligned crystals. 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.


Growth twinning

Growth twinning likely begins early in crystal growth, since the contact surface usually passes through the center of the crystal. 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.


Transformation twinning

Transformation twinning takes place when a cooling crystal experiences a displacive polymorphic transition. For example,
leucite Leucite is a rock-forming mineral of the feldspathoid group, silica-undersaturated and composed of potassium and aluminium tectosilicate KAlSi2O6. Crystals have the form of cubic icositetrahedra but, as first observed by Sir David Brewster in ...
has an isometric crystal structure above about , but becomes tetragonal below this temperature. Any one of the three original axes of a crystal can become the long axis when this phase change takes place. Twinning results when different parts of the crystal break their isometric symmetry along a different choice of axis. This is typically polysynthetic twinning, which enables the crystal to maintain its isometric shape by averaging out the displacement in each direction. This produces a
pseudomorph In mineralogy, a pseudomorph is a mineral or mineral compound that appears in an atypical form (crystal system), resulting from a substitution process in which the appearance and dimensions remain constant, but the original mineral is replaced b ...
ic crystal that appears to have isometric symmetry. Potassium feldspar likewise experiences polysynthetic twinning as it transforms from a monoclinic structure (
orthoclase Orthoclase, or orthoclase feldspar ( endmember formula K Al Si3 O8), is an important tectosilicate mineral which forms igneous rock. The name is from the Ancient Greek for "straight fracture," because its two cleavage planes are at right angles ...
) to a to triclinic structure (
microcline Microcline (KAlSi3O8) is an important igneous rock-forming tectosilicate mineral. It is a potassium-rich alkali feldspar. Microcline typically contains minor amounts of sodium. It is common in granite and pegmatites. Microcline forms during slo ...
) on slow cooling.


Deformation twinning

Deformation twinning is a response to shear stress. The crystal structure is displaced along successive planes of the crystal, a process also called ''glide''. The twinning is always reflection twinning and the glide plane is also the mirror plane. Deformation twinning can be observed in a calcite cleavage fragment by applying gentle pressure with a knife blade near an edge. This particular glide twinning, , is found almost universally in deformed rock beds containing calcite. Twinning and
slip Slip or SLIP may refer to: Science and technology Biology * Slip (fish), also known as Black Sole * Slip (horticulture), a small cutting of a plant as a specimen or for grafting * Muscle slip, a branching of a muscle, in anatomy Computing and ...
are competitive mechanisms for crystal deformation. Each mechanism is dominant in certain crystal systems and under certain conditions. In fcc metals, slip is almost always dominant because the stress required is far less than twinning stress. Twinning can occur by cooperative displacement of atoms along the face of the twin boundary. This displacement of a large quantity of atoms simultaneously requires significant energy to perform. Therefore, the theoretical stress required to form a twin is quite high. It is believed that twinning is associated with dislocation motion on a coordinated scale, in contrast to slip, which is caused by independent glide at several locations in the
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macro ...
. Compared to slip, twinning produces a deformation pattern that is more heterogeneous in nature. This deformation produces a local gradient across the material and near intersections between twins and grain boundaries. The deformation gradient can lead to fracture along the boundaries, particularly in bcc transition metals at low temperatures. Of the three common crystalline structures bcc,
fcc The Federal Communications Commission (FCC) is an independent agency of the United States federal government that regulates communications by radio, television, wire, satellite, and cable across the United States. The FCC maintains jurisdictio ...
, and hcp, the hcp structure is the most likely to form deformation twins when strained, because they rarely have a sufficient number of slip systems for an arbitrary shape change. High strain rates, low stacking-fault energy and low temperatures facilitate deformation twinning. If a metal with
face-centered cubic In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties of ...
(fcc) structure, like Al, Cu, Ag, Au, etc., is subjected to stress, it will experience twinning. The formation and migration of twin boundaries is partly responsible for
ductility Ductility is a mechanical property commonly described as a material's amenability to drawing (e.g. into wire). In materials science, ductility is defined by the degree to which a material can sustain plastic deformation under tensile str ...
and malleability of fcc metals. Twin boundaries are partly responsible for shock hardening and for many of the changes that occur in
cold work Cold is the presence of low temperature, especially in the atmosphere. In common usage, cold is often a subjective perception. A lower bound to temperature is absolute zero, defined as 0.00K on the Kelvin scale, an absolute thermodynamic ...
of metals with limited slip systems or at very low temperatures. They also occur due to martensitic transformations: the motion of twin boundaries is responsible for the pseudoelastic and shape-memory behavior of
nitinol Nickel titanium, also known as Nitinol, is a metal alloy of nickel and titanium, where the two elements are present in roughly equal atomic percentages. Different alloys are named according to the weight percentage of nickel; e.g., Nitinol 55 and ...
, and their presence is partly responsible for the hardness due to
quench In materials science, quenching is the rapid cooling of a workpiece in water, oil, polymer, air, or other fluids to obtain certain material properties. A type of heat treating, quenching prevents undesired low-temperature processes, such as p ...
ing of steel. In certain types of high strength steels, very fine deformation twins act as primary obstacles against dislocation motion. These steels are referred to as 'TWIP' steels, where TWIP stands for ''twinning-induced plasticity''..


Deformation twin configuration

A deformation twin embryo forms in BCC metal by accumulating stacking faults, with a variant selection governed by the local stress state. Variation of the stress field close to twins inferred from HR-
EBSD Electron backscatter diffraction (EBSD) is a scanning electron microscope–based microstructural-crystallography, crystallographic characterization technique commonly used in the study of crystalline or crystallite, polycrystalline materials. T ...
experimental and crystal plasticity finite element
CPFE
simulation data indicated that twins nucleate on sites with maximum strain energy density and twin resolved
shear stress Shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the ...
; thus, reducing the total elastic energy after formation. This relaxation depends on the twin thickness and is a deciding factor in the spacing between twins. Experimental and three-dimensional analysis has focussed on the (stored) strain energy density measured along a path. This highly localised stress field can provide a sufficient driving force for concurrent twin nucleation and inter/intra-granular crack nucleation. Deformation twin growth can be perceived as a two-step process of i) thickening that is mediated by the interaction between the residual and mobile twin partials at the coherent twin-parent interface, and ii) dislocation mobility along the twin shear direction. The twin propagates when the homogeneous shear
stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
reaches a critical value, and a twin-parent interface advances inside the parent grain 40 The propagating deformation twin generates a stress field due to its confinement by the surrounding parent crystal, and deformation twins develop a 3D oblate spheroid shape (which appears in 2D sections as a bi-convex lens) with a mixed coherent and non-coherent interface (Figure b). Kannan ''et al.'' found, using in-situ ultra-high-speed optical imaging, that twin nucleation in single-crystal
magnesium Magnesium is a chemical element with the symbol Mg and atomic number 12. It is a shiny gray metal having a low density, low melting point and high chemical reactivity. Like the other alkaline earth metals (group 2 of the periodic ta ...
is
stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
-driven accompanied by instantaneous propagation at a speed of 1 km/s (initially) that prioritises volume lateral thickening over forward propagation, past a critical width where growth is then become faster along the shear direction. Barnett also indicated that growth is due to twin tip extension. Furthermore, elastic simulations of the local
stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
field surrounding the ellipsoidal twin tip find that the field can be described using its lens angle (\beta) and that the
stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
field magnitude increases with twin thickness.In practice, plastic accommodation occurs in the parent
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macro ...
; thus, it also depends on the material’s yield stress, the anisotropic elastic stiffness of the parent crystal lattice, and the deformation twinning shear magnitude. This can also be accompanied by long-range diffusion of elements and elemental segregation (e.g., Cr and Co in single crystal Ni-based superalloy MD2), which occurs at the twin boundary to facilitate twin growth by lowering the critical stacking fault energy. A linear variation has been observed between twin thickness, stacking fault energy and grain size, and to a lesser degree, the stress state of the twinning grain ( Schmid Factor). The twin thickness saturated once a critical residual dislocations’ density reached the coherent twin-parent crystal boundary. Significant attention has been paid to the crystallography, morphology and macro mechanical effects of deformation twinning. Although the criterion for deformation twin growth is not entirely understood, it is a tip-controlled phenomenon linked to the interaction between the residual and mobile twin partials at the twin interface; thermodynamically, this involves the elastic energy of the strained lattice, the interface and volume free-energy of the twin, and the dissipated energy of the growth mechanism. To fully understand the interactions between microstructure (i.e., grain size, texture), temperature and strain rate on deformation twinning, it is crucial to characterise the (high) local
stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
and strain field associated with twin thickening and propagation. This is especially important for materials where cleavage fracture can be initiated by twinning (e.g., iron-silicon, the ferrite phase of age-hardened duplex stainless-steel, and single-crystal
magnesium Magnesium is a chemical element with the symbol Mg and atomic number 12. It is a shiny gray metal having a low density, low melting point and high chemical reactivity. Like the other alkaline earth metals (group 2 of the periodic ta ...
) as a stress-relieving mechanism. Early studies of deformation twins arrested within grains of niobium and
iron Iron () is a chemical element with Symbol (chemistry), symbol Fe (from la, Wikt:ferrum, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 element, group 8 of the periodic table. It is, Abundanc ...
visualised the highly local strain concentration at the twin tip using an etch-pit procedure. More recently, high-resolution electron backscatter diffraction (HR-
EBSD Electron backscatter diffraction (EBSD) is a scanning electron microscope–based microstructural-crystallography, crystallographic characterization technique commonly used in the study of crystalline or crystallite, polycrystalline materials. T ...
) has been used to investigate the strain ‘singularity’ ahead of a twin tip in hexagonal close-packed (HCP)
zirconium Zirconium is a chemical element with the symbol Zr and atomic number 40. The name ''zirconium'' is taken from the name of the mineral zircon, the most important source of zirconium. The word is related to Persian '' zargun'' (zircon; ''zar-gun'' ...
alloy. A deformation twin in commercial purity
titanium Titanium is a chemical element with the Symbol (chemistry), symbol Ti and atomic number 22. Found in nature only as an oxide, it can be reduced to produce a lustrous transition metal with a silver color, low density, and high strength, resista ...
was characterised similarly and then quantified using a local Schmid factor (LSF) at the twin tip, as described in equation below. LSF = \sigma:S/, , \sigma, , , Schmid .matrix (S^i_0) = d^i \otimes n^i where  is the maximum principal stress, is the shear direction and  is the plane normal for ''i''th
slip Slip or SLIP may refer to: Science and technology Biology * Slip (fish), also known as Black Sole * Slip (horticulture), a small cutting of a plant as a specimen or for grafting * Muscle slip, a branching of a muscle, in anatomy Computing and ...
system. The authors concluded that conditions at the twin tip control thickening and propagation in a manner analogous to the operation of
dislocation In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to s ...
sources ahead of a crack-tip. In the analysis, a broad region of high LSF ahead of the twin tip favoured propagation, whereas a narrow region of high LSF promoted thickening. Since then, it has been argued that the LSF firmly controls the twin variant selection, as twinning has strong polarity. The LSF novelty – compared to other criteria to describe conditions at the twin – lies in combining a geometrical criterion with the deformation field in the parent grain to provide an approximate indication of the local twin mode (i.e., thickening or propagation). However, the LSF analysis does not take advantage of the available full-field data, relies on global information on the applied
stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
, and does not consider the energy balance that drives twin growth. There have been few in-situ experiments to quantify the strain field ahead of a propagating deformation twin. Such observations might validate geometrical or hybrid geometrical-energy-based criteria for growth. Nanoscale testing (i.e.,
transmission electron microscopy Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The specimen is most often an ultrathin section less than 100 nm thick or a suspension on a g ...
) may not represent the behaviour in bulk samples due to plasticity starvation, i.e., large surface area to volume ratio , so a suitable analysis method is needed. Lloyd described the stress concentration field ahead of the twin tip using a two-dimensional
dislocation In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to s ...
-based model within a single
magnesium Magnesium is a chemical element with the symbol Mg and atomic number 12. It is a shiny gray metal having a low density, low melting point and high chemical reactivity. Like the other alkaline earth metals (group 2 of the periodic ta ...
grain. Wang and Li, who considered microscopic phase-field (MPF) models of cracks, noted that the
stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
fields were similar for
dislocation In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to s ...
s, deformation twinning and
martensitic Martensite is a very hard form of steel crystalline structure. It is named after German metallurgist Adolf Martens. By analogy the term can also refer to any crystal structure that is formed by diffusionless transformation. Properties Marte ...
transformations, with differences only in the traction of the created surface, i.e., there is 100% traction recovery for dislocations and a traction-free surface for a crack. They highlighted that the stress field singularity regulates the advancement of the crack-tip and
dislocation In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to s ...
s. This
stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
concentration can be characterised using a path-independent line integral, as shown by Eshelby for
dislocation In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to s ...
s considering the contribution from the surface traction and ellipsoidal inclusions, and
Rice Rice is the seed of the grass species '' Oryza sativa'' (Asian rice) or less commonly ''Oryza glaberrima'' (African rice). The name wild rice is usually used for species of the genera '' Zizania'' and '' Porteresia'', both wild and domesticat ...
for cracks and stress concentrations with traction-free surfaces. Furthermore, Venables noted that the oblate spheroid shape of the twin tip is the ideal example of an ellipsoid inclusion or a notch.


See also

*
Macle {{no footnotes, date=April 2009 Macle is a term used in crystallography. It is a crystalline form, twin-crystal or double crystal (such as chiastolite). It is crystallographic twin according to the spinel twin law and is seen in octahedral cryst ...
*
Tin cry Tin cry is the characteristic sound heard when a bar made of tin is bent. Variously described as a "screaming" or "crackling" sound, the effect is caused by the crystal twinning in the metal. The sound is not particularly loud, despite terms lik ...
*
Icosahedral twins An icosahedral twin is a nanostructure appearing for atomic clusters and also nanoparticles with some thousands of atoms. These clusters are twenty-faced, made of twenty interlinked tetrahedra crystals, typically joined along triangular (e.g ...
* Slip bands *
Slip (materials science) In materials science, slip is the large displacement of one part of a crystal relative to another part along crystallographic planes and directions. Slip occurs by the passage of dislocations on close/packed planes, which are planes containing ...


References


External links


Slip and twinning mechanism in detail
{{Authority control Crystallography Materials science