Boundaries, twin

Twins are intergrown crystals such that the crystallographic directions in one part are related to those in another part by reflection, rotation, or inversion through a center of symmetry across a twin boundary. Twinned crystals are often prized mineralogical specimens. When twins are in contact across a well-defined plane (which is not always so), the boundary is generally called the composition plane. The only twins that are considered here will be reflection twins, where the two related parts of the crystal are mirror images (Fig. 3.22). The mirror plane that relates the two components is called the twin plane. This is frequently, but not always, identical to the plane along which the two mirror-related parts of the crystal join, that is, the composition plane. Repeated parallel composition planes make up a polysynthetic twin (Fig. 3.23). 

Twin geometry may refer to just one set of atoms in the crystal rather than all. This type of twinning is met, for example, in cases where a fraction of octahedral or tetrahedral cation sites in a close-packed array of anions are occupied in an ordered fashion. The close-packed anion array remains unchanged by the twin plane, which applies to the cation array alone (Fig. 3.24). These boundaries are of low energy and are often curved rather than planar. In oxides such as spinel, MgAl204, in which cations are distributed in an ordered fashion over some of the octahedral and tetrahedral sites, boundaries may separate regions that are twinned with respect to the tetrahedral cations only, the octahedral cations only or both. 

There are a number of mechanisms by which twins can form. Growth twins are attributed to a mistake occurring when a crystal is nucleated, so that the orientation 

Twins can also form in perfect crystals by a number of processes. The deformation of a crystal due to the application of a shear stress can result in mechanical twins, which form in order to reduce the strain so produced. The formation of mechanical twins in deformed metals has been extensively investigated, and a number of mechanisms have been proposed to account for the differences that occur between one structure and another. These mechanisms often involve the passage of a sequence 

Mechanical twins that form to reduce internal stress have also been observed in nonmetallic crystals. Mild reduction of vanadium pentoxide at low temperatures produces regions of reduced oxide that induce considerable shear stress in the matrix 

Twins are commonly found or formed in all types of crystals. Their boundaries are of two general types coherent and incoherent. The coherent boundaries are usually also symmetric, so they offer little resistance to dislocation motion. However, the incoherent ones are not symmetric and may resist dislocation motion considerably. 

Ardell, Intermetallics as Precipitates and Dispersoids in High Strength Alloys, Chapter 12 in Intermetallic Compounds vol. 2, Edited by J. H. Westbrook and R. L. Fleischer, J. Wiley Sons, New York, USA (1994). 

Editor, Yield, Flow, and Ftacture of Polycrystals, Applied Science Publishers, London, UK (1983). See R. W. Armstrong, p. 1. 

Brown and R. K. Ham, Dislocaton-Particle Interactions, Chapter 2 in Strenthen-ing Methods in Crystals, Edited by A. Kelly and R. B. Nicholson, Halsted Press Diviion of John Wiley Sons, New York, USA (1971). 

Gilman, and A. K. Head, Dislocation Multipoles and Their Role in Strain-Hardening, J. Appl. Phys., 35(8), 2502 (1964). 

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However, it is not yet clear why the ener es of the SISF and the twin boundary increase with increasing A1 concentration. To find a clue to the problem, it would be needed to make out the effects of the short-range ordering of A1 atoms in excess of the stoichiometric composition of the HAl phase on the energies of planar faults and the stmcture of dislocation cores in the Al-rich HAl phase. 

The importance of twins lies in the existence of a permanent re-entrant corner at the twin boundary for cases a) and b) — and possibly for c) where it is too small to be detected — and therefore a position at the surface where there is no... 

Figure 14. Au nanoparticle on polyaniline support with twin boundary (F. Klasovsky, P. Claus, unpublished results, 2006).

There are two questions that needed to be answered here. (1) How can the ligand access the interiors of big prismatic particles to lead to the smaller particles and (2) Why do the ligands lead to smaller particles at all While it is difficult to conclusively find answers to both the questions, the first step in the digestive ripening procedure offers some leads. (1) The big prismatic particles obtained by the reverse micelle-based synthesis are loaded with defects such as twinning boundaries and stacking faults. 

Other methods for impeding dislocation motion are the introduction of grain boundaries, and/or twin boundaries. While these impediments may increase the hardness, they are also likely to decrease the tensile strength. 

Twin boundaries are frequently encountered in cuprate superconductors. There are a number of ways in which twins might form in a crystal, one of which is... 

Figure 8.12 Basal (001) plane of YBa2Cu307 containing a [110] twin boundary. The projection of the unit cell is outlined. The dopant oxygen atoms run along the b axis in each twin.

Figure 5. HRTEM images (left z = -123 nm, right z = -195 rnn) of Z3 twin boundaries in BaTiOs. The contrast delocalization at the interface is indicated by arrows (Jia et al. 1999).

Single crystal and bulk BaTiOs exhibits a sharp paraelectric-to-ferroelectric transition at 393K. In the presence of submicron grains, the transition becomes diffuse and can be absent for polycrystalline BaTiOs. Twin boundaries along the four crystallographically equivalent 11 planes constitute the main lattice defects. Junctions between such twin boundaries can be frequently observed within a grain. The local atomic arrangement of the core of twin intersections was studied by focal-series reconstruction (Jia etal. 1999). 

Figure 5 shows two high-resolution images representative of a focal series recorded of junctions between twin boundaries in BaTiOs. However,... 

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