Effect of coherency strain on the deformation of In x Ga1− x As superlattices under nanoindentation and bending

It has been shown elsewhere that the room temperature yield pressure of In _x Ga_{1? x} As superlattices measured by nanoindentation, decreases from a high value as the volume averaged strain modulation is increased, while at 500°C under uniaxial compression or tension the yield stress increases from a low value with increasing strain modulation. We have used cross-sectional transmission electron microscopy to examine the deformation mechanisms in these two loading regimes. At room temperature both twinning and dislocation flow was found with the proportion of twinning decreasing with increasing strain modulation. The coherency strain of the superlattice is retained in a twin but partially relaxed by dislocation flow. The strain energy released by the loss of coherency assists dislocation flow and weakens the superlattice. Twins are only nucleated when a critical elastic shear of about 7° is achieved at the surface. The plastic zone dimensions under the indent are finite at the yield point, with a width and depth of approximately 1.3?µm and 1.1?µm respectively. Under uniaxial compression and tension at 500°C the superlattices deform by dislocation flow along {111} planes. The most highly strained samples also partially relax through the formation of misfit dislocations.     

人工水晶-x面上巴西双晶的形成机制

本文以人工水晶-x面上的巴西双晶作为研究对象,在实验的基础上,利用X射线衍射形貌术和电子探针显微分析等手段,研究了双晶的形成机制,同时分析了Kern的双晶成核动力学理论的不足之处。作者提出了双晶界应变能势垒的概念,认为由于晶体的不完整性提高了晶体本身的能量状态,结果相对降低了应变能势垒的高度,使得双晶易于发生。本文结合晶体生长实验和晶体缺陷的测试,分析了双晶形成与籽晶取向、杂质、晶体缺陷的相互关系,着重指出缺陷对双晶形成的影响。本文还以凹入角生长机制讨论了双晶的发育。 关键词：     

Why twins do not grow at the speed of sound all the time

Deformation twinning occurs in various materials including metals, intermetallics, ceramics, superconductors, and even geological systems. The rate of twin growth depends on the material system, but there are no crystallographic models to understand the mechanisms of slow twin growth. The physics of twin growth is presented for bcc-Ti alloys where it is shown that octahedral interstitial sites are not conserved at the twin-matrix interface where oxygen resides. The predicted activation energy for twin growth correlated well with experimental values for the diffusion of oxygen. These models will have a broad application in understanding the twinning process and designing advanced materials.     

Molecular dynamics simulation of twinning in devitrite,Na2Ca3Si6O16

Reports of Type II twins are quite rare for most crystal structures. When they do occur, they are usually one of a number of possible twinning modes observed in a particular material. However, for the triclinic phase devitrite, Na₂Ca₃Si₆O₁₆, which nucleates from commercial soda?lime?silica float glass subjected to suitable heat treatments, the only reported twinning mode to date is a Type II twinning mode. In this study, this Type II twinning mode is first examined by molecular dynamics simulation to determine the lowest energy configuration of perfect twin boundaries for the twin mode. This is then compared with the lowest energy configurations of perfect twin boundaries found for six possible Type I twinning modes for devitrite for which the formal deformation twinning shear is less than 0.6. The most favourable twin plane configuration for the Type II twinning crystallography is shown to produce reasonably low twin boundary energies and sensible predictions for the optimum locations of the twin plane, K ₁, and the [1?0?0] rotation axis, η ₁, about which the 180° Type II twinning operation takes place. By comparison, all the Type I twinning modes were found to have very energetically unstable atomic configurations, and for each of these twinning modes, the lowest energy configurations found all led to high effective K ₁ twin boundary energies relative to perfect crystal. These results therefore provide a rationale for the experimental observation of the particular Type II twinning mode seen in devitrite.     

Energy of a wedge-shaped nanotwin calculated in terms of a dislocation mesoscopic model

The total energy of a wedge-shaped micro- and nanotwin is calculated in terms of a dislocation mesoscopic model. The total energy of the twin is represented as a sum of the elastic energy, energy of interaction between twinning dislocations, and stacking-fault energy of partial dislocations of the wedge-shaped twin. It is found that the evolution of the twin is controlled by the energy of interaction between twinning dislocations: in the case of a microtwin, it is five orders of magnitude higher than the elastic energy and six orders of magnitude higher than the stacking-fault energy. In the case of a nanotwin with the number of twinning dislocations at the twin boundary less than 20, all the three energies listed above are of the same order of magnitude. Therefore, all the components of the total energy contribute to the origination of a wedge-shaped twin. As the length of the twin increases with its width and the number of twinning dislocations at twin boundaries fixed, the total energy modulo grows although the density of twinning dislocations at twin boundaries decreases. This indicates that long-range stress fields due to twinning dislocations play an important part in the evolution of a wedge-shaped twin.     

Anisotropy and twinning in cubic zinc sulfide crystals

The structure of zinc sulfide single crystals grown from the vapor has been studied by a unique combination of X-ray crystallography and thermal conductivity measurements. Weissenberg patterns reveal the face centered cubic structure with rotational twinning in the [111] direction, which could be ascribed to two overlapping lattices. These could be explained by normal stacking faults or by inverted twins. A strong anisotropy in thermal conductivity was measured and interpreted as favoring the inverted twin model.     

Statistical analyses of deformation twinning in magnesium

To extract quantitative and meaningful relationships between material microstructure and deformation twinning in magnesium, we conduct a statistical analysis on large data sets generated by electron backscattering diffraction (EBSD). The analyses show that not all grains of similar orientation and grain size form twins, and twinning does not occur exclusively in grains with high twin Schmid factors or in the relatively large grains of the sample. The number of twins per twinned grain increases with grain area, but twin thickness and the fraction of grains with at least one visible twin are independent of grain area. On the other hand, an analysis of twin pairs joined at a boundary indicates that grain boundary misorientation angle strongly influences twin nucleation and growth. These results question the use of deterministic rules for twin nucleation and Hall–Petch laws for size effects on twinning. Instead, they encourage an examination of the defect structures of grain boundaries and their role in twin nucleation and growth.     

Characterization of twinning in electrodeposited Ni–Mn alloys

Twinning is ubiquitous in electroplated metals. Here, we identify and discuss unique aspects of twinning found in electrodeposited Ni–Mn alloys. Previous reports concluded that the twin boundaries effectively refine the grain size, which enhances mechanical strength. Quantitative measurements from transmission electron microscopy (TEM) images show that the relative boundary length in the as-plated microstructure primarily comprises twin interfaces. Detailed TEM characterization reveals a range of length scales associated with twinning beginning with colonies (～1000?nm) down to the width of individual twins, which is typically <50?nm. We also consider the connection between the crystallographic texture of the electrodeposit and the orientation of the twin planes with respect to the plating direction. The Ni–Mn alloy deposits in this work possess a {110}-fiber texture. While twinning can occur on {111} planes either perpendicular or oblique to the plating direction in {110}-oriented grains, plan-view TEM images show that twins form primarily on those planes parallel to the plating direction. Therefore, grains enclosed by twins and multiply twinned particles are produced. Another important consequence of a high twin density is the formation of large numbers of twin-related junctions. We measure an area density of twin junctions that is comparable to the density of dislocations in a heavily cold-worked metal.     

Twinning in Be-Cu alloys. Part I

Mechanical twinning has been examined for 99.99% beryllium and for alloys of Be with 0.4 at. % and 2.3 at. % Cu. The yield points have been measured for single twins, and also studies have been made of the behavior of the twin boundaries under pulsating and sign-varying loads. The concentration dependence of the yield points for single twins has been used to estimate the interaction energy for the twinning dislocations with impurity atoms. The Bauschinger effect occurs at the boundaries of the mechanical twins, and the characteristics of this are dependent on the angle of the twin wedge, the impurity concentration, and the number of twinning cycles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 104–108, December, 1972.We are indebted to G. F. Tikhinskiy for providing the alloy crystals used here.     

The incorporation of slip dislocations in twins

The conditions for the incorporation of slip dislocations either propagating into a twin or engulfed by a growing twin are studied from the geometrical point of view. The resulting dislocation formed in a twin is independent of the mechanism of the incorporation. Under suitable conditions no stacking faults are formed at the twin boundary. The decomposition of twinning dislocations forming the noncoherent twin boundary is described using complementary partial twinning dislocations. The theory is formulated for both type I and II twins. Compound twins are also briefly treated in the discussion. Using the tensor notation all the formulae are given in the form valid for all crystal structures.The author is greatly indebted to Mr. J. Koík for many helpful comments.     

A disclination model for twinning and de-twinning of nanotwinned copper

The twinning and de-twinning processes within grains of nanotwinned copper (nt-Cu) are schematically demonstrated using the concept of wedge disclination quadrupoles. The stable twin nucleus size and the equilibrium equation of the applied shear stress and twin width during twin growth are obtained. The dependence of the critical resolved shear stress for twinning on the grain size, which conforms to the classic Hall–Petch relationship, is theoretically modelled. Additionally, the disclination quadrupole model for de-twinning is used to interpret the strength softening in nt-Cu. Relative to the classic kinetic and energetic models, this novel approach is more compatible with the experiments.     

Dislocation model for an incoherent nonthin twin

A condition for the equilibrium of a nonthin twin is obtained from a dislocation model using the approximation of a continuous distribution of twinning dislocations at twin boundaries. The model of a nonthin twin is shown to be applicable to the elastic and inelastic stages of twinning. The theory of a thin twin is found to be a particular case of the developed dislocation model of a nonthin twin.     

High resolution transmission electron microscope observation of zero-strain deformation twinning mechanisms in Ag

We have observed a new deformation-twinning mechanism using the high resolution transmission electron microscope in polycrystalline Ag films, zero-strain twinning via nucleation, and the migration of a Σ3{112} incoherent twin boundary (ITB). This twinning mechanism produces a near zero macroscopic strain because the net Burgers vectors either equal zero or are equivalent to a Shockley partial dislocation. This observation provides new insight into the understanding of deformation twinning and confirms a previous hypothesis: detwinning could be accomplished via the nucleation and migration of Σ3{112} ITBs. The zero-strain twinning mechanism may be unique to low staking fault energy metals with implications for their deformation behavior.     

Molecular dynamic studies of the interaction of a/6⟨112⟩ Shockley dislocations with stacking fault tetrahedra in copper. Part II: Intersection of stacking fault tetrahedra by moving twin boundaries

The interactions of moving twin boundaries with stacking fault tetrahedra (SFTs) have been studied by molecular dynamics. The results reveal a spectrum of processes occurring during these interactions. In general, they lead to damage of the parent SFT and formation of new defects in the twin lattice. The character of these defects depends on the nature of the twinning front, the size of the SFT and its orientation with respect to incoming dislocations. Typical structures that may be produced in the twin include product-SFTs, free vacancies, planar stacking faults bounded by partial dislocations, mutually linked stacking faults on non-coplanar {111} _T planes, small {111} _T tetrahedra and their partial forms. Dislocation mechanisms involved in the formation of these defects are being analyzed.     

Modelling of martensite slip and twinning in NiTiHf shape memory alloys

High-temperature shape memory alloy NiTiHf holds considerable promise for structural applications. An important consideration for these advanced alloys is the determination of the magnitude of the twinning stress. Theoretical stresses for twinning and dislocation slip in NiTiHf martensites are determined. The slip and twinning planes are (0?0?1) and (0?1?1) for monoclinic and orthorhombic crystals, respectively. The determination of the slip and twinning stress is achieved with a proposed Peierls–Nabarro-based formulation informed with atomistic simulations. In the case of the twin, multiple dislocations comprising the twin nucleus are considered. The overall energy expression is minimized to obtain the twinning and slip stresses. The magnitude of the predicted twinning stresses is lower than slip stresses which explains why the NiTiHf alloys can undergo reversibility without plastic deformation. In fact, the predicted critical resolved shear stress levels of 433?MPa for slip and 236?MPa for twinning in the case of 12.5% Hf agree very well with the experimental measurements. The high slip resistance confirms that these materials can be very attractive in load-bearing applications.     

Effect of cyclic stresses on the microstructures of hexagonal close packed metals

Slip band extrusions are formed in cadmium, magnesium and titanium, but not in zinc. The extrusions form preferentially in untwinned crystals. Filamentary growths occur at {10¯12} and {11¯21} twin interfaces during cyclic twinning.Possible dislocation interactions at these twin interfaces are described. The dislocation debris produced during cyclic strain in the slip bands and by cyclic twinning is shown to be similar and composed of a high density of dipole loops. It is therefore concluded that the occurrence and distribution of slip band extrusions in metals and the formation of twin boundary filamentary growths can be accounted for by a model based upon the glide of interstitial type dipole loops. Vacancy type loops will then cause crack nucleation in slip bands and deformation twin boundary regions.Twin boundary debris can also cause the observed fragmentation of twins by acting as a barrier to twin boundary movement.The author is grateful to Dr. A. G. Crocker, University of Surrey, for many discussions on the twinning mode in h.c.p. metals and to P. J. E. Forsyth for his interest and encouragement. The paper is published by permission of the Controller, H. M. Stationery Office. Crown copyright is reserved.     

Nonlinear phase field theory for fracture and twinning with analysis of simple shear

A phase field theory for coupled twinning and fracture in single crystal domains is developed. Distinct order parameters denote twinned and fractured domains, finite strains are addressed and elastic nonlinearity is included via a neo-Hookean strain energy potential. The governing equations and boundary conditions are derived; an incremental energy minimization approach is advocated for prediction of equilibrium microstructural morphologies under quasi-static loading protocols. Aspects of the theory are analysed in detail for a material element undergoing simple shear deformation. Exact analytical and/or one-dimensional numerical solutions are obtained in dimensionless form for stress states, stability criteria and order parameter profiles at localized fractures or twinning zones. For sufficient applied strain, the relative likelihood of localized twinning vs. localized fracture is found to depend only on the ratio of twin boundary surface energy to fracture surface energy. Predicted criteria for shear stress-driven fracture or twinning are often found to be in closer agreement with test data for several types of real crystals than those based on the concept of theoretical strength.     

Molecular dynamics simulation of the formation of twin boundaries during agglomeration of nanoparticles

The processes controlling early stages of agglomeration of nanoparticles have been investigated by the molecular dynamics method. It has been established that the formation of boundaries with twin misorientation is the main mechanism of structural relaxation during primary agglomeration of nanoparticles. It has been shown that an increase in the temperature leads to an increase in the number of twin boundaries and that their mutual arrangement depends on the misorientation of the nanoparticles. In the case where twin boundaries are noncoplanar, structure relaxation results in the formation of pentagonal twin boundaries. The role of twinning in the formation of interfaces upon compaction of nanoparticles has been discussed.     

A phase field model of deformation twinning: Nonlinear theory and numerical simulations

A continuum phase field theory and corresponding numerical solution methods are developed to describe deformation twinning in crystalline solids. An order parameter is associated with the magnitude of twinning shear, i.e., the lattice transformation associated with twinning. The general theory addresses the following physics: large deformations, nonlinear anisotropic elastic behavior, and anisotropic phase boundary energy. The theory is applied towards prediction of equilibrium phenomena in the athermal and non-dissipative limit, whereby equilibrium configurations of an externally stressed crystal are obtained via incremental minimization of a free energy functional. Outcomes of such calculations are elastic fields (e.g., displacement, strain, stress, and strain energy density) and the order parameter field that describes the size and shape of energetically stable twin(s). Numerical simulations of homogeneous twin nucleation in magnesium single crystals demonstrate fair agreement between phase field solutions and available analytical elasticity solutions. Results suggest that critical far-field displacement gradients associated with nucleation of a twin embryo of minimum realistic size are 4.5%–5.0%, with particular values of applied shear strain and equilibrium shapes of the twin somewhat sensitive to far-field boundary conditions and anisotropy of twin boundary surface energy.     

Effect of initial orientation on twinning in commercially pure titanium

Abstract

The effect of initial orientation on twinning micro-mechanisms during tensile deformation of commercially pure titanium has been studied using micro focus X-ray diffraction and electron back scatter diffraction (EBSD) in a scanning electron microscope. Three orientations A, B and C obtained from a rolled and annealed block of commercially pure titanium were deformed in uniaxial tension till failure and the tested specimens were characterised with regard to bulk texture, microstructure and crystal orientation mapping using EBSD. Orientation B along the transverse direction in ND-TD plane exhibits higher strength and lower strain hardening compared to orientations A and C along the rolling direction in TD-RD and ND-RD plane, respectively. This is attributed to different texture of sample B compared to samples A and C leading to dissimilar twinning micro-mechanisms and characteristic variation in nature of twinning. It is observed that limited twin nucleation and prominent lateral growth plays a dominant role in orientation B while multiple twin nucleation with significant non-Schmid behaviour is dominant for the other two orientations. It is proposed from this study that conventional factors associated with twin formation like Schmid factor play a main role in twin nucleation and propagation, however, growth or lateral thickening of the twins is explained by elastic stiffness variation across twins and their parent grains.