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) in a
gold nanoparticle (
electron microscope micrograph). 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. 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 (111) surface facets. In small nanoparticles the decahedral and a more complicated
Icosahedral structure (with twenty units) 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.
Transformation twinning Transformation and
annealing twinning takes place when a cooling crystal experiences a displacive polymorphic transition. For example,
leucite 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
pseudomorphic crystal that appears to have isometric symmetry. Potassium feldspar likewise experiences polysynthetic twinning as it transforms from a monoclinic structure (
orthoclase) to a triclinic structure (
microcline) on slow cooling. 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. 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, 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 (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 and malleability of fcc metals. Twin boundaries are partly responsible for
shock hardening and for many of the changes that occur in
cold work 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, and their presence is partly responsible for the hardness due to
quenching 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 twinning crystallography Twinning is crystallographically defined by its twin plane 𝑲𝟏, the mirror plane in the twin and
parent material, and 𝜼𝟏, which is the twinning shear direction. During twinning, in addition to the twin plane, one more crystallographic plane ( 𝑲2) and a direction (𝜼2) onto that plane remain undistorted but rotated. Deformation twins in Zr are generally lenticular in shape, lengthening in the 𝜼𝟏 direction and thickening along the 𝑲𝟏 plane normal. The twin plane, shear direction, and shear plane form the basis vectors of an orthogonal set. The axis-angle misorientation relationship between the parent and twin is a rotation of angle 𝜉 about the shear plane's normal direction 𝑷. More generally, twinning can be described as a 180° rotation about an axis (𝑲𝟏 for type I twins or 𝜼𝟏 for type II twins normal direction), or a mirror reflection in a plane (𝑲𝟏 or 𝜼𝟏 normal plane). In addition to a homogeneous shear, atomic shuffles are sometimes required to reform the correct crystal structure in the twinned lattice. For each twin variant, a reciprocal twin with swapped 𝑲𝟏 and 𝑲
2, 𝜼𝟏 and 𝜼
2 is possible, but one variant may appear more frequently in reality due to complexities with the required shuffles. there are only two crystallographic planes in a shearing action that do not change their shape and size as a consequence of the shear. The first 𝑲𝟏 is the plane defining the upper and lower surfaces of the sheared volume. This plane contains the shear direction. The other plane, designated C. The shear direction is shown with an arrow and labelled with its customary designation 𝜼𝟏. It follows from the above that there are three ways that a crystal lattice can be sheared while still retaining its crystal structure and symmetry: • When 𝑲𝟏 is a rational plane and 𝜼
2 a rational direction, a twin of the first kind • When 𝑲
2 is a rational plane and 𝜼𝟏 a rational direction, a twin of the second kind, rare • When all four elements 𝑲𝟏
, 𝑲
2, 𝜼𝟏, and 𝜼
2 are rational, a compound twin
Deformation twinning 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 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; 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 reaches a critical value, and a twin-parent interface advances inside the parent grain [240]. 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). found, using in-situ ultra-high-speed optical imaging, that twin nucleation in single-crystal
magnesium is
stress-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 field surrounding the ellipsoidal twin tip find that the field can be described using its lens angle (\beta) and that the
stress field magnitude increases with twin thickness. diode (FSD) image for deformation twins at grain boundary in age-hardened ferrite at I) 18 mm working distance and II) 38 mm working distance. (b) Schematic of a lenticular twin with interface dislocations and (c) Twin band.|376x376px In practice, plastic accommodation occurs in the parent
crystal; 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. 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 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) as a stress-relieving mechanism. Early studies of deformation twins arrested within grains of
niobium and
iron visualised the highly local strain concentration at the twin tip using an etch-pit procedure. More recently, high-resolution electron backscatter diffraction (HR-
EBSD) has been used to investigate the strain 'singularity' ahead of a twin tip in hexagonal close-packed (HCP)
zirconium alloy. A deformation twin in commercial purity
titanium was characterised similarly and then quantified using a local
Schmid factor (LSF) at the twin tip, as described in equation below. \mathrm{LSF} = \frac{\boldsymbol{\sigma} : \boldsymbol{P}^i}{\|\boldsymbol{\sigma}\|}, \quad \boldsymbol{S}^i = \boldsymbol{d}^i \otimes \mathbf{n}^i where
σ is the stress tensor,
Si is the Schmid tensor,
Pi is its symmetric part,
di is the shear direction and
ni is the shear plane normal for
ith
slip system. The authors concluded that conditions at the twin tip control thickening and propagation in a manner analogous to the operation of
dislocation 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 so a suitable analysis method is needed. Lloyd who considered microscopic phase-field (MPF) models of cracks, noted that the
stress fields were similar for
dislocations, deformation twinning and
martensitic 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
dislocations. This
stress concentration can be characterised using a
path-independent line integral, as shown by
Eshelby for
dislocations considering the contribution from the surface traction and ellipsoidal
inclusions, and
Rice 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 ==