Twin Interface Research Articles

Segregation-driven exceptional twin-boundary strengthening in lean Mg–Zn–Ca alloys

Twinning-mediated plasticity in hexagonal close-packed crystal structures offers great potential for achieving lean Mg-based alloys with high strength and extended ductility. Micropillars from a lean MgZn1 Ca0.3 (ZX10, in wt%) alloy and pure Mg, each comprising one or more pre-existing {101¯2}<1¯011> extension twin boundaries and a parent orientation with its c-axis perpendicular to the loading direction, were subjected to in situ micropillar compression. By means of correlative characterization using transmission electron backscattered diffraction, transmission electron microscopy and nanoscale energy-dispersive X-ray spectroscopy, we assesed the effects of Zn and Ca solutes on micropillar deformation and on the response of pre-existing twin-boundaries to applied stress. In ZX10, both Zn and Ca solutes periodically segregate at the pre-existing extension twin boundaries, giving rise to a strengthening increment by about 300% compared to pure Mg, along with ductility enhancement. Due to segregation, the twin boundaries remain immobile throughout the deformation process, playing a critical role both in non-basal slip and twin-nucleation events. The former is facilitated by the formation of stable I1 stacking faults, while the latter is stimulated by active <c+a> slip across the pinned twin interface. In contrast, the pure Mg micropillars respond by massive twin growth followed by higher-order twinning events and profuse basal slip. In the absence of non-basal slip, pure Mg exhibits an earlier onset to failure due to shear incompatibility at the twin interface. The findings provide new insights into the role of solute Zn and Ca in stabilizing twinned microstructures for achieving synergistic strength-ductility enhancement in lean Mg alloys.

Elasto-Plastic Fatigue Crack Growth Behavior of Extruded Mg Alloy with Deformation Anisotropy Due to Stress Ratio Fluctuation.

Fatigue crack growth (FCG) experiments were performed using a low-temperature extruded magnesium alloy AZ31 with texture. Under a constant maximum stress intensity factor (Kmax), the stress ratio R was changed from 0.1 to −1 during the fatigue crack growth process, and the FCG behavior before and after the R change was investigated. As a result, tensile twins were generated owing to the fatigue load on the compression side of R = −1, and the FCG velocity was accelerated. In addition, when the maximum compressive stress at R = −1 (|(σmin)R = −1|) exceeded the compressive yield strength of the material (σcy), the FCG velocity after R fluctuation greatly accelerated. On the other hand, under the condition |(σmin)R = −1| < σcy, the degree of acceleration of the FCG velocity due to R fluctuation was small. In either case, the degree of acceleration in the FCG increased as the Kmax value increased. The above FCG acceleration mechanism due to the R fluctuation was considered based on the observation of the deformation and twinning states of the fatigue crack tip, the fatigue crack closure behavior, and the cyclic stress–strain curve of the fatigue process. The FCG acceleration mechanism was as follows: First, the driving force of the FCG increased owing to the increase in crack opening displacement due to the generation of tensile twins. Second, the coalescence of the main crack and a plurality of microcracks were generated at the twin interface. The elasto-plastic FCG behavior after the stress ratio fluctuations is defined by the effective J-integral range ΔJeff.

Modeling the dynamic magneto-mechanical response of magnetic shape memory alloys based on Hamilton’s principle: The governing equation system

The governing equation system for modeling the high-frequency dynamic magneto-mechanical response of magnetic shape memory alloys (MSMAs) is formulated based on Hamilton’s principle. First, by taking the single-crystalline Ni-Mn-Ga alloy as a representative member of MSMAs, we introduce some constitutive assumptions and material constants. Then, Hamilton’s action integral is established for a MSMA sample subject to coupled magnetic and mechanical loads. By calculating the variation of Hamilton’s action integral with respect to the independent variables, we derive the Maxwell’s equations, the mechanical dynamic equations and some evolution laws for the internal variables in the effective magnetization. Furthermore, by studying the variation of Hamilton’s action integral with respect to the path of the variant state distribution, the criteria for predicting the motion of twin interfaces in the sample are established. Combining the above equations and the twin interface motion criteria, the governing equation system for modeling the high-frequency dynamic magneto-mechanical response of the MSMA sample is formulated, which lays the foundation for future numerical simulations and underlying mechanism analyses. For convenience of practical application of the current model, we further adopt some simplifications and derive some analytical formulas from the governing equation system, which provide good predictions for the response of the MSMA sample subject to some typical loading conditions.

Digital Twin of Wireless Systems: Overview, Taxonomy, Challenges, and Opportunities

Future wireless services will focus on improving the quality of life by enabling various applications, such as extended reality, brain-computer interaction, and healthcare. These applications will have diverse performance requirements (e.g., user-defined quality of experience metrics, latency, and reliability) which will be challenging to be fulfilled by existing wireless systems. To meet the diverse requirements of the emerging applications, the concept of digital twins has been recently proposed. A digital twin uses a virtual representation along with security-related technologies (e.g., blockchain), communication technologies (e.g., 6G), computing technologies (e.g., edge computing), and machine learning, so as to enable the smart applications. In this tutorial, we present a comprehensive overview on digital twins for wireless systems. First, we present the fundamental concepts (i.e., design aspects, high-level architecture, and frameworks) of digital twins for wireless systems. Second, a comprehensive taxonomy is devised for two aspects, namely, twins for wireless and wireless for twins. For the twins for wireless aspect, we consider issues related to design of twin objects, physical devices, and interface, as well as prototyping, deployment trends, incentive mechanism, isolation of twins, and decoupling. For the wireless for twins aspect, we consider issues related to accessing twin objects, security and privacy, and air interface design are considered. Finally, open research challenges and opportunities are discussed.

Numerical simulations on the high-frequency dynamic mechanical response of single-crystalline Ni–Mn–Ga samples

ABSTRACT In this paper, an efficient numerical scheme is proposed to simulate the high-frequency dynamic mechanical response of single-crystalline Ni–Mn–Ga samples. First, based on a three-dimensional setting, the governing equation system for a single-crystalline Ni–Mn–Ga sample is set up, which is composed of the equation of motion and the twin interface movement criteria. In order to solve the governing system, an iterative numerical algorithm is proposed, in which the finite element method and the NewMark-β method are applied. To demonstrate the efficiency of this numerical scheme, the response of a single-crystalline Ni–Mn–Ga sample under some typical loading conditions are studied. In the numerical simulations, a specific discretisation of the sample is adopted, such that the possible positions of the twin interfaces in the sample can be naturally inherited. With the obtained numerical results, the mechanical behaviours of the sample under the different loading conditions are predicted, which show good consistency with the experimental results. The distribution of variant state and the propagation of twin interfaces in the sample can also be simulated. The numerical scheme proposed in the current work is helpful for the design of novel sensors or actuators based on single-crystalline Ni–Mn–Ga alloys.

Direct Observations of Twin Formation Dynamics in Binary Semiconductors.

With the increased demand for controlled deterministic growth of III-V semiconductors at the nanoscale, the impact and interest of understanding defect formation and crystal structure switching becomes increasingly important. Vapor-liquid-solid (VLS) growth of semiconductor nanocrystals is an important mechanism for controlling and studying the formation of individual crystal layers and stacking defects. Using in situ studies, combining atomic resolution of transmission electron microscopy and controlled VLS crystal growth using metal organic chemical vapor deposition, we investigate the simplest achievable change in atomic layer stacking-single twinned layers formed in GaAs. Using Au-assisted GaAs nanowires of various diameters, we study the formation of individual layers with atomic resolution to reveal the growth difference in forming a twin defect. We determine that the formation of a twinned layer occurs significantly more slowly than that of a normal crystal layer. To understand this, we conduct thermodynamic modeling and determine that the propagation of a twin is limited by the energy cost of forming the twin interface. Finally, we determine that the slower propagation of twinned layers increases the probability of additional layers nucleating, such that multiple layers grow simultaneously. This observation challenges the current understanding that continuous uniform epitaxial growth, especially in the case of liquid-metal assisted nanowires, proceeds one single layer at a time and that its progression is limited by the nucleation rate.

The evolution of local stress during deformation twinning in a Mg-Gd-Y-Zn alloy

In this study, we perform in-situ tensile testing and high-resolution electron backscatter diffraction (HR-EBSD) to monitor the twin local stresses at different stages: (i) before twinning, (ii) twins that have propagated into the parent crystal, and (iii) thickening of the twin lamella. The resolved shear stress (RSS) at the twin interface is calculated during deformation twinning, which indicates that the RSS evolution is a dynamic process. Negative shear stress is observed during the propagation stage, which provides evidence for the twinning shear transformation-induced stress reversal. Furthermore, a local Schmid factor (LSF) is used to evaluate the extent to which the local stress is dominated by the RSS on the identified twin plane. The experimental results indicate that the LSFs evolve with strain and are at their maximum level before twinning. The initiated twins are correlated with the highest LSFs compared with the unactivated variants. In addition, the product of the Luster Morris m′ value times the LSF of the twin variant may reveal a threshold for the slip-induced twinning process.

Diffraction Features from (101¯4) Calcite Twins Mimicking Crystallographic Ordering

During phase transitions the ordering of cations and/or anions along specific crystallographic directions can take place. As a result, extra reflections may occur in diffraction patterns, which can indicate cell doubling and the reduction of the crystallographic symmetry. However, similar features may also arise from twinning. Here the nanostructures of a glendonite, a calcite (CaCO3) pseudomorph after ikaite (CaCO3·6H2O), from Victoria Cave (Russia) were studied using transmission electron microscopy (TEM). This paper demonstrates the occurrence of extra reflections at positions halfway between the Bragg reflections of calcite in 0kl electron diffraction patterns and the doubling of d104 spacings (corresponding to 2∙3.03 Å) in high-resolution TEM images. Interestingly, these diffraction features match with the so-called carbonate c-type reflections, which are associated with Mg and Ca ordering, a phenomenon that cannot occur in pure calcite. TEM and crystallographic analysis suggests that, in fact, (101¯4) calcite twins and the orientation change of CO3 groups across the twin interface are responsible for the extra reflections.

Focus on analytical equipment, spectroscopy, and spectrometry

Focus on analytical equipment, spectroscopy, and spectrometry

Deformation twinning-induced single-variant ω-plates in metastable β-Ti alloys containing athermal ω-precipitates

The ω-phase in metastable β-titanium (Ti) alloys attracts great research interests owing to the metastability and the involved microstructural complexity upon straining, while the fundamental understanding on its formation mechanism is still insufficient. In this study, deformation-induced ω-plates have been systematically investigated using Ti-10 wt% Cr metastable β-Ti alloy containing athermal ω-precipitates. It is found that single-variant ω-plates form either along {332}β twin interfaces or in the twin interiors, which closely depends on twin morphologies. For the acicular β-twin, the ω-plate appears in the twin interiors accompanied by high density of parallel straight dislocations, while for the lenticular twin, the ω-plate attaches to the twin interface without the surrounding dense parallel straight dislocations. These unique formation characteristics result from local stress field induced by the twinning itself and the passive transformation of athermal ω-precipitates. It is further revealed that the passive transformation of athermal ω-precipitates dominates the formation of ω-plates inside the acicular twins, while it is the locally preferential twin thickening that promotes the ω-plates to form along the lenticular twin interfaces. These findings provide new insight into deformation-induced ω-phase transformation and the intricate deformation microstructures in metastable β-Ti alloys.

Nanostructural characteristics-mediated plastic behavior of Cu/Ag polycrystalline multilayered materials

For polycrystalline multilayers materials, the typical nanoscale structural characteristics contain grain, twin and hetero interface, which could make collective and remarkable influence on the mechanical property. In this work, taking Cu/Ag polycrystalline multilayers as an example, the coupling effects of grain boundary, twin boundary and hetero interface on the plastic deformation mechanisms are studied using molecular dynamics simulations. The simulation results show that the dominant plastic deformation mechanisms change from dislocation activities for common multilayer material to hetero interfaces sliding when the ratio of material layer thickness to grain size is small enough, leading to a marked decrease of strength. As for the twin boundary, its strengthening effect follows the conventional Hall-Petch relationship when the grain size is larger than the twin thickness. This twin-related strengthening effect becomes weak with the grain size decreases, indicating a competitive relationship between these two characteristic sizes. These findings will shed light on a more comprehensive understanding of size effects on the underlying mechanisms of plastic deformation of polycrystalline multilayers, which provide crucial guidance for the design of novel materials based on polycrystalline multilayers.

Modeling on the dynamic mechanical response of single-crystalline Ni–Mn–Ga alloys based on Hamilton’s principle

In this paper, a variational approach is proposed to study the dynamic mechanical response of a single-crystalline Ni–Mn–Ga sample. First, some constitutive assumptions are adopted to describe the material properties of single-crystalline Ni–Mn–Ga alloys. Hamilton’s action integral is then formulated for the mechanical system being studied, which depends on the position vector field and the variant state distribution in the sample. By calculating the variation of the action integral with respect to the position vector field, the equation of motion, as well as the boundary condition and the twin interface connection condition, can be obtained. By further calculating the variation of the action integral with respect to the variant state distribution (through twin interface movements), the expression of the driving force on the twin interfaces is derived, based on which the twin interface movement criterion is established. Combining the equation of motion and the twin interface movement criterion, the governing system for modeling the dynamic response of the single-crystalline Ni–Mn–Ga sample can be formulated. To show the validity of the governing system, a simple example is studied and some analytical results are constructed. Especially, the relation between the external mechanical load and the twin interface velocity is revealed, which is consistent with the experimental observations.

Omega transition accompanied by mechanically-induced twinned martensite

We present here an analysis on omega transition process during martensitic transformation. Martensitic transformation occurred during deformation at room temperature, avoiding the influence of auto-tempering on metastable omega phase. Based on the crystallographic relationships of twinned crystals, the twin interface of twinned martensite was characterized by considering the effect of direction of incidence electron beam on diffraction patterns through pole figures. Omega phase only existed at the boundaries of twinned martensite with single variant. It was proposed that lattice invariant twin shear during the dynamic transformation of twinned martensite promoted the formation of omega phase.

On coupled FEM-BEM simulation of the magneto-mechanical behavior of single-crystalline Ni-Mn-Ga alloys

In this paper, a coupled FEM-BEM method is applied to simulate the magneto-mechanical behavior of a single-crystalline Ni-Mn-Ga sample. First, based on some kinematic and constitutive assumptions, the governing system for modeling the response of the Ni-Mn-Ga sample is formulated, which is composed of the magnetic and mechanical field equations, the evolution laws of the internal variables and the twin interface movement criteria. To solve the governing system, an iterative numerical algorithm is proposed. Especially, a coupled FEM-BEM method is adopted in the algorithm to tackle the magnetic field equation. By using this method, one doesn’t need to consider the distribution of the demagnetization field in the surrounding space, thus the number of elements can be reduced significantly. To show the efficiency of the numerical algorithm, some typical examples are studied. It can be found that the numerical results obtained from the coupled FEM-BEM method and the conventional FEM method are in good agreement with each other. The numerical algorithm proposed in the current work would be helpful for the design of novel smart devices made of Ni-Mn-Ga alloys.

A phase field model for the growth and characteristic thickness of deformation-induced twins

Deformation-induced twinning is an important mechanism in metals with a limited number of slip deformation modes. The mechanisms for twin nucleation and growth are not completely understood, and modelling these processes is challenging because of the different length and time scales involved. Twins grow at the speed of sound up to a length of several millimetres and thickness of only a few microns. We present a phase field model for twinning, coupled with a dislocation-density based model for slip, implemented within the crystal plasticity finite element method. Softening of the critical resolved shear stress for twinning is used to reproduce the shear localisation that is typical of twin bands. Two interaction terms are introduced. The first one is a non-local term that models the interaction between residual dislocations at the twin interface and mobile dislocations in untwinned regions. The second is a local term that models the hardening of the twin system due to the presence of dislocations. By introducing these interaction terms, it is possible to reproduce a discrete pattern of twin bands after deformation. These interaction terms and interaction strength parameters determine the nucleation and spatial position of twins, twin thickness and number density of twins as a function of strain. The model is validated by comparing the simulated twin phase field with the dynamic formation of twins in tension, as measured by electron backscatter diffraction experiments on α-uranium. This model sheds light on the mechanism that determines twin growth and twin thickness. Specifically, twins stop thickening after a critical density of residual dislocations at the twin interface is reached. The interaction coefficients are interpreted in terms of the stacking fault energy in order to apply the model to different metals.

Atomic-scale three-dimensional structural characterisation of twin interface in Mg alloys

ABSTRACT Twinning plays important role in plastic deformation of Mg alloys. However, it is difficult to obtain full information on twinning structures through transmission electron microscope observations. Here, we developed a new method to reconstruct the three-dimensional structure of a twin boundary. The {102} twin was observed from three directions, i.e. the [110], [201], and [43] zone axes, in order to establish the atomic model of the boundary. Additionally, we propose that the observed directions for {101} and {103} twins should be [113] & [101] and [21] & [53], respectively.

The Effect of Individual Layer Thickness on Chemical Ordering of Ni-Based Multilayers

The microstructural evolution of magnetron sputtered Ni-based multilayers with different individual layer thicknesses h is investigated. The average grain size of multilayers and formation of chemical ordered Ni3Al phase are dependent on h in annealed Ni-based multilayer system which are disclosed by X-ray diffraction and transmission electron microscopy. Transformation of chemical ordering in the annealed multilayers is facilitated by large grains with lower density of grain boundaries when h ≥ 40 nm. On the contrary, when h &lt; 40 nm, the retained disordered FCC Ni(Al) phase in the annealed Ni-based multilayers is attributed to the twin interface. The ordering mechanism can be explained by interface-controlled formation and migration of vacancies.

Following the Martensitic Configuration Footprints in the Transition Route of Ni-Mn-Ga Magnetic Shape Memory Films: Insight into the Role of Twin Boundaries and Interfaces.

Magnetic shape memory Heuslers have a great potential for their exploitation in next-generation cooling devices and actuating systems, due to their “giant” caloric and thermo/magnetomechanical effects arising from the combination of magnetic order and a martensitic transition. Thermal hysteresis, broad transition range, and twinning stress are among the major obstacles preventing the full exploitation of these materials in applications. Using Ni-Mn-Ga seven-modulated epitaxial thin films as a model system, we investigated the possible links between the phase transition and the details of the twin variants configuration in the martensitic phase. We explored the crystallographic relations between the martensitic variants from the atomic-scale to the micro-scale through high-resolution techniques and combined this information with the direct observation of the evolution of martensitic twin variants vs. temperature. Based on our multiscale investigation, we propose a route for the martensitic phase transition, in which the interfaces between different colonies of twins play the major role of initiators for both the forward and reverse phase transition. Linking the martensitic transition to the martensitic configuration sheds light onto the possible mechanisms influencing the transition and paves the way towards microstructure engineering for the full exploitation of shape memory Heuslers in different applications.

Structural characteristics of {10[formula omitted]1} contraction twin-twin interaction in magnesium

Twin interface characteristics play a crucial role in elucidating twin propagation, twin-twin and twin-dislocation interactions, and then affect their mechanical properties. Herein, focusing on magnesium as a model of a hexagonal close-packed structure, we investigate the structural characteristics of \\{101¯1} contraction twin, depending on crystallographic analysis, molecular dynamics simulations and transmission electron microscopy observations. The geometrical features reveal that it is preferential to form acute twin boundaries during the processes of twin-twin interactions. Subsequently, the dynamics simulations results demonstrate that the propagation process of {101¯1} contraction twin is mainly related to the migration of {101¯3} twin boundaries in twin tip, and its thickening process is dominantly associated with the movement of multiple-layered steps. Additionally, two twin-twin interaction modes- tip-twin boundaries crossing transmission and tip-tip collision-have been successfully constructed, dependent on the preferential acute growth mode of contraction twins. Finally, typically structural characteristics on both free-growth of single contraction twin and twin-twin interactions have been confirmed in the ultrahigh pressure pure magnesium by transmission electron microscopy observations. This work clarifies fundamental physics of {101¯1} contraction twins in hexagonal close-packed metals, which can also be applied to other systems to explain twin strengthening mechanisms.

Practical scheme for predicting twin interface nucleations in single-crystalline Ni-Mn-Ga alloys under coupled magnetic and mechanical loading conditions

In this paper, the phenomenon of twin interface nucleations in single-crystalline Ni-Mn-Ga samples under coupled magnetic and mechanical loading conditions is studied. First, some constitutive assumptions are proposed and the magneto-mechanical governing system for a single-crystalline Ni-Mn-Ga sample is formulated. Then, by analyzing the connection conditions of some physical quantities, the configurational forces on any ‘fictitious twin interfaces’ can be calculated. Further from the twin interface movement criteria in the governing system, a practical scheme for predicting twin interface nucleations at the macroscopic level is proposed, which is integrated into an iterative numerical algorithm for solving the governing system. To show the efficiency of this scheme, some typical examples are studied. Based on the numerical simulation results, the evolution properties of the configurational forces on the fictitious twin interfaces are analyzed. Then, the critical loading states and the preferred positions for the nucleations of twin interfaces can be determined. The predicted magneto-mechanical response of the sample can fit the experimental results well. Furthermore, the configurations of the sample and the distributions of the associated physical quantities in the sample during the different loading stages can be simulated.