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.     

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.     

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.     

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.     

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.     

Strengthening and softening in gradient nanotwinned FCC metallic multilayers

Plastic-deformation behaviors of gradient nanotwinned (GNT) metallic multilayers are investigated in nanoscale via molecular dynamics simulation. The evolution law of deformation behaviors of GNT metallic multilayers with different stacking fault energies (SFEs) during nanoindentation is revealed. The deformation behavior transforms from the dislocation dynamics to the twinning/detwinning in the GNT Ag, Cu, to Al with SFE increasing. In addition, it is found that the GNT Ag and GNT Cu strengthen in the case of a larger twin gradient based on more significant twin boundary (TB) strengthening and dislocation strengthening, while the GNT Al softens due to more TB migration and dislocation nucleation from TB at a larger twin gradient. The softening mechanism is further analyzed theoretically. These results not only provide an atomic insight into the plastic-deformation behaviors of certain GNT metallic multilayers with different SFEs, but also give a guideline to design the GNT metallic multilayers with required mechanical properties.     

Discovery,characterization and modelling of novel shape memory behaviour of fcc metal nanowires

Novel shape memory behaviour was discovered recently in single-crystalline fcc nanowires of Cu, Ni and Au with lateral dimensions below 5?nm. Under proper thermomechanical conditions, these wires can recover elongations up to 50%. This phenomenon only exists at the nanoscale and is associated with reversible lattice reorientations within the fcc lattice structure driven by surface stresses. Whereas the propagation of partial dislocations and twin planes specific to fcc metals are the required mechanism, only materials with higher propensities for twinning (e.g. Cu and Ni) show this behaviour and those with lower propensities for twinning (e.g. Al) do not. This paper provides an overview of this novel behaviour with a focus on the transformation mechanism, driving force, reversible strain, size and temperature effects and energy dissipation. A mechanism-based micromechanical continuum model for the tensile behaviour is developed. This model uses a decomposition of the lattice reorientation process into a reversible, smooth transition between a series of phase-equilibrium states and a superimposed irreversible, dissipative propagation of a twin boundary. The reversible part is associated with strain energy functions with multiple local minima and quantifies the energy conversion process between the twinning phases. The irreversible part is due to the ruggedness of the strain energy landscape, associated with dislocation nucleation, gliding and annihilation, and characterizes the dissipation during the transformation. This model captures all major characteristics of the behaviour, quantifies the size and temperature effects and yields results which are in excellent agreement with data from molecular dynamics simulations.     

Distribution of dislocations and twins in copper and 18Cr-10Ni-Ti steel under shock-wave loading

The distribution of dislocations and twins over the cross section of shock-loaded copper and 18Cr-10Ni-Ti steel specimens is investigated experimentally and numerically. It is found that the volume fraction of twins near the loaded surface and a spall crack is an order of magnitude higher than their fraction at the center of the target. The features of twins arising in different parts of the target are discussed. A model of a twinning mechanism in coarse-grained metals is proposed and used for numerical simulation of the dislocation and twin depth distribution in shock-loaded targets. It is shown that in thin targets (less than 1 mm thick), the distribution of twins can be even more uniform than the distribution of the dislocations density.     

Effect of dislocation distribution in twin boundaries on the nucleation of microcracks at the twin tip

The effect of dislocation distribution in the boundaries of an arrested twin on the nucleation of microcracks at its tip is investigated. The twin is simulated by a double step pileup (cluster) of twinning dislocations located in adjacent slip planes. The equilibrium equations for dislocations are solved numerically. Clusters with different total numbers of dislocations and with different ratios of the numbers of dislocations at the upper and lower twin boundaries are considered. The formation of microcracks as a result of coalescence of head dislocations according to the force and thermally activated mechanisms is analyzed. The equilibrium configurations of a single twin boundary and of the twin are calculated. It is found that the condition for microcrack formation at the twin tip considerably depends on the ratio of the numbers of dislocations in twin boundaries. In the limit, this condition coincides with the condition of crack formation at the tip of a single twin boundary with the same total number of dislocations. It is shown that thermally activated formation of a microrack corresponds to lower values of the critical stress.     

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.     

Change in the Bauschinger effect during the relaxation of twinned crystals

Changes taking place in the quantitative characteristics of the Bauschinger effect in wedge-shaped twins are studied in relation to the period for which these are held before untwinning. All the measurements are made in the cleavage plane of single-crystal zinc and Zn-Cu alloys. The Bauschinger displacement of the twin boundaries first increases slightly and then starts diminishing during the delay period. In the course of untwinning, the region of easy untwinning on the (b) relationship diminishes with time in the softened zone; the extent of the softened zone remains constant during the relaxation of the crystals. The suppression of the Bauschinger effect takes place more intensively if the crystal is held under load before untwinning. The change in the quantitative characteristics of the Bauschinger effect may be explained by the diffusion of impurities to the twinning dislocations and dislocation sources and the consequent blocking of these, and also by the relaxation of stresses in the twin boundaries as a result of plastic shears and dislocation reactions between complete and twinning dislocations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 113–117, April, 1971.     

Stress field around a high speed screw dislocation

Using a simple lattice model, the stress field around a high speed screw dislocation is calculated. On the basis of the results, a possible pattern of “breakdown” which was discovered by Earmme and Weiner in a one-dimensional dislocation model is discussed and a new model of twinning is proposed. Mid-ribs in b.c.c, twins can be explained on the basis of this model.     

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.     

Surface nanocrystallization mechanism of a rare earth magnesium alloy induced by HVOF supersonic microparticles bombarding

A nanostructured surface layer with a thickness up to 60 μm was produced on a rare earth Mg-Gd-Y magnesium alloy using a new process named HVOF-SMB (high velocity oxygen-fuel flame supersonic microparticles bombarding). The microstructural features of the treated surface at various depth of the deformed layer were characterized by optical microscopy (OM), transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM) with an aim to reveal the formation mechanism. Results showed that three steps during grain refinement process were found, i.e., twinning dominates the plastic deformation and divides the coarse grains into finer twin platelets at the initial stage, stacking faults are generated and a number of dislocation slip systems are activated leading to the cross slips with increasing strain and strain rate, eventually high-density dislocation networks, dislocation cells and dislocation arrays are formed, which further subdivides the twin platelets and residual microbands into sub-microstructures. As a result, homogeneous nanostructure with a grain size of about 10-20 nm is formed through dynamic recrystallization in the topmost surface layer. Based on the experimental observations, a grain refinement mechanism induced by plastic deformation with higher strain rate during the HVOF-SMB treatment in the rare earth Mg-Gd-Y alloy was proposed.     

Crack-stimulated generation of deformation twins in nanocrystalline metals and ceramics

A theoretical model is proposed that describes the generation of deformation twins near brittle cracks of mixed I and II modes in nanocrystalline metals and ceramics. In the framework of the model, a deformation twin nucleates through stress-driven emission of twinning dislocations from a grain boundary distant from the crack tip. The emission is driven by both the external stress concentrated by the pre-existent crack and the stress field of a neighbouring extrinsic grain boundary dislocation. The ranges of the key parameters, the external shear stress, τ, and the crack length, L, are calculated within which the deformation-twin formation near pre-existent cracks is energetically favourable in a typical nanocrystalline metal (Al) and ceramic (3C-SiC). The results of the proposed model account for experimental data on observation of deformation twins in nanocrystalline materials reported in the literature. The deformation-twin formation is treated as a toughening mechanism effectively operating in nanocrystalline metals and ceramics.     

Formation and thickness evolution of periodic twin domains in manganite films grown on SrTiO3(001) substrates

We present an extended synchrotron x-ray scattering study of the structure of thin manganite films grown on SrTiO3(001) substrates and reveal a new kind of misfit strain relaxation process which exploits twinning to adjust lattice mismatch. We show that this relaxation mechanism emerges in thin films as one-dimensional twinning waves which freeze out into a twin domain pattern as the manganite film continues to grow. A quantitative microscopic model which uses a matrix formalism is able to reproduce all x-ray features and provides a detailed insight into this novel relaxation mechanism. We further demonstrate how this twin angle pattern affects the transport properties in these functional films.     

The effect of a dislocation network on plastic strain in Fe-Si

The paper describes the way a dislocation network affects the course of plastic strain in Fe-Si. It is found that the dislocation network causes a decrease in elongation, a faster — relative to strain in recrystallized material — growth of the density of dislocations, and susceptibility to twinning.On the basis of experimental evidence, an attempt is made to establish a relation between the dislocation network, the dislocation barrier of Friedel, and twinning.     

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.     

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：     

Recent advances in understanding the origin of martensite aging phenomena in shape memory alloys

The martensite aging phenomena (martensite stabilization and rubber-like behavior) found in many shape memory alloys have puzzled material scientists for over 60 years without a definite answer. In this article we critically reviewed previous models to understand the aging phenomena, which include pseudotwin-type model, LRO model, SRO model, twinning dislocation model, and domain (twin) boundary pinning model. We showed that these models failed to meet generality criterion, although being able to explain the phenomena to some extent. Then we focused on a very recent general model (Ren and Otsuka, Nature, 389, 579–582, 1997) which makes use of only two common features of martensitic transformation and aging, i.e., diffusionless symmetry change during martensitic transformation and diffusion during aging. This model appears to be able to explain all of the available experimental observations on the aging phenomena. In view of recent development in this field, we have reason to believe that we are approaching the final solution to the aging problem.