The Equilibrium Condition of a Non-Thin Screw Wedge-Shaped Twin Located in the Distance from the Surface of an Undeformed Crystal

The equilibrium condition for a non-thin helical wedge-shaped twin located far from the surface of the crystal is obtained. The case of an undeformed solid is considered. It is established that under such conditions a helical twin can not twin can not exist under such conditions. The result is in full conformity with generally known results for dislocation walls from helical dislocations. An approximation for continuous distribution of twinning dislocations at twin boundaries has been used in methodology for deriving an equilibrium condition. The shape of the twin boundaries has been described by functions that depend on density of the twinning dislocations at the twin boundaries. It has been assumed that the forces acting on the twin boundaries from the side of the twin dislocations are equal to zero. One degree of freedom along a twinning direction has been presupposed for twinning dislocations. Dislocation creeping effects have been excluded in the model. A calculation of stress fields for a twin has been carried out within the framework of an elasticity theory. In this case a superposition of stresses from each twin boundary has been considered. The solution of equations has been sought in the form of a polynomial. A linear approximation of such solution is considered in detail. The ем resulting equilibrium condition is satisfied for two values equal to zero that is a twin length and its width at the mouth. The result is important in the field of mechanics for twinning materials, shape memory materials, and in the development of techniques for predicting destruction and functioning of twinning materials.

Analysis on the Twinning of FCC Metals by EBSD

For the technology of EBSD, the twinning of metals was described in the form of rotation angle combined with rotation axis, while the twinning of metals was usually described in the form of twinning plane combined with twinning direction. In this report, the corresponding relationship between the two description forms of twinning of face-centered cubic (FCC) metals has been built, based on this relationship, the twinning plane and twinning direction of FCC metals can be determined by EBSD. As the practical application of this relationship above, the twinning variants of two kinds of Ni based superalloys were analyzed.

Calculation Methods to Determine Crystallographic Elements Based on Electron Diffraction Orientation Measurements by SEM/EBSD or TEM

In the present work, we summarized two calculation methods to determine some specific crystallographic elements based on electron diffraction orientation measurements by SEM/EBSD or TEM. The first one is to determine the twin type and twinning elements of crystal twins based on the minimum shear criterion, using the experimentally determined twinning plane for Type I twin and compound twin or twinning direction for Type II twin as initial input. The method is valid for any crystal structure. The second one is one to determine the plane indices of the faceted interfaces where the orientation relationships (ORs) between the adjacent crystals are reproducible. The method requires one prepared sample surface instead of two perpendicular surfaces. These methods are expected to facilitate the related microstructural characterizations.

A general method to determine twinning elements

The fundamental theory of crystal twinning has been long established, leading to a significant advance in understanding the nature of this physical phenomenon. However, there remains a substantial gap between the elaborate theory and the practical determination of twinning elements. This paper proposes a direct and simple method – valid for any crystal structure and based on the minimum shear criterion – to calculate various twinning elements from the experimentally determined twinning plane for Type I twins or the twinning direction for Type II twins. Without additional efforts, it is generally applicable to identify and predict possible twinning modes occurring in a variety of crystalline solids. Therefore, the present method is a promising tool to characterize twinning elements, especially for those materials with complex crystal structure.

Rhombohedral Twin Structure in Hematite (α-Fe2O3)

Electron optical imaging of the structure of haematite ( α-Fe2O3) in two projections has allowed the microscopic twinning elements of rhombohedral twins to be determined. A systematic analysis of alternative structural models, using computer-simulation and image-matching considerations, as well as crystallochemical arguments, is presented. The twin has a screw operation consisting of a pure rotation of 180� about [0111], the twinning direction, combined with a parallel translation of (1/22) [0111]. The twinning plane (0112) forms a coherent interface, consisting of face-and edge-shared octahedra , with no change in the normal nearest-neighbour coordination.

Electron Microscopy Study Of Mocvd-Grown Tio2Thin Films and Tio2/Al203 Interfaces

ABSTRACTTiO2 thin films grown on (1120) sapphire at 800°C by the MOCVD technique have been characterized by transmission electron microscopy. The TiO2 thin films are single crystalline and have the rutile structure. The epitaxial orientation relationship between the TiO2 thin films (R) and the substrate (S) has been foundto be: (101)[010]R║(1l20)[0001]s. Growth twins in the films are commonly observed with the twin plane{101} and twinning direction <011>. Detailed atomic structures of the twin boundaries and TiO2/α-Al203 interfaces have been investigated by highresolution electron microscopy (HREM).When the interfaces are viewed in the direction of [010]R/[000l]S, the interfaces are found to be structurally coherent in the direction of [1Ol]R/[1100]s,in which the lattice mismatch at the interfaces is about 0.5%.

Influence of Shear Stress on Screw Dislocations in a Model Sodium Lattice

The behavior of the screw dislocation core in the presence of an external shear stress has been examined for the body-centered cubic and hexagonal close-packed phases of a model sodium lattice, using an effective ion–ion potential calculated from first principles. The Peierls stress for screw dislocations in the b.c.c. lattice at 0 °K is dependent on the orientation of the applied shear stress, and has a minimum value of 0.0105G, where G is the shear modulus, for slip in the twinning direction on {112} planes. The Peierls stress in the h.c.p. lattice is at least 25 times smaller. Dislocation movement in the model b.c.c. lattice takes place by unit translations on {110} planes, with the selection rule that no two consecutive translations can take place on the same slip plane.

Orientation and temperature dependence of plastic deformation processes in 3·25% silicon iron

Single crystals of a 3·25 % silicon iron were deformed in tension between 20 and 293 °K. The orientation was varied systematically between [010] and [110], to determine the orientation dependence of slip and twinning. The operative slip and twinning systems were measured by two surface analysis. At 20 °K all specimens twinned and fractured; at 77 °K crystals within 11° of [010] twinned and fractured and the remainder yielded before fracture; at 195 and 293 °K all specimens yielded. Yielding occurred by the formation and propagation of slip bands along the specimen. At 77 °K slip was confined to {011} planes but at higher temperatures slip occurred on the plane containing the <111> slip direction with the maximum resolved shear stress independent of whether or not it was a low index plane. The yield propagation stress varied with orientation in close agreement with that expected for slip on an {011} <111> system at all temperatures. Twinning occurred on those systems with the maximum resolved shear stress on the twin plane in the twinning direction and the results support a critical resolved shear stress law.