Dislocation Behavior Research Articles

Cooperative dislocations for pressure-dependent sequential deformation of multi-principal element alloys under shock loading

Multi-principal element alloys (MPEAs) are promising materials for structural applications under extreme conditions. Their outstanding mechanical properties are closely related to the activation of multiple deformation modes of dislocation gliding, twinning, and phase transformation that appear in sequence during deformation at low temperatures, high pressures, or high strain rates. However, the inherent correlations among these deformation modes and, thus, underlying deformation mechanisms of MPEAs remain largely unknown. We report soft-recovery plate impact experiments of face-centered-cubic (FCC) CrCoNi MPEAs, demonstrating pressure-dependent deformation modes from low-pressure stacking faults to medium-pressure twinning and high-pressure FCC to hexagonal-close-packed (HCP) phase transformation. Atomic-scale characterizations unveil that the sequential deformation is manipulated by the cooperation of 90° and 30° Shockley partial dislocations at deformation fronts, which is facilitated by low stacking fault energy and pressure-dependent phase stability of the MPEAs. Moreover, the cooperative dislocation behavior can also be observed at twin fronts of shock-loaded CrMnFeCoNi MPEA, validating the universality of the cooperative deformation mode in FCC alloys with a low stacking fault energy. Theoretical analyses suggest that the distinctive cooperative dislocation behavior results in the self-compensation of dislocation strain fields and the minimization of interfacial elastic energy at incoherent twin and FCC/HCP interfaces.

Microstructural evolution, mechanical behavior, and deformation mechanisms of a lightweight Ti–Nb–Cr–V refractory high-entropy alloy at room and elevated temperatures

Refractory high-entropy alloys (RHEAs) have emerged as promising candidates for high-temperature applications owing to their distinctive mechanical properties. However, their limited tensile ductility and high density pose hurdles for further engineering utilization. In this study, we introduce a novel RHEA composition, Ti45Nb30Cr15V10 (at.%), distinguished by its reduced density (∼6.2 g/cm3), achieved through the assistance of CALPHAD (CALculation of PHAse Diagrams) modeling. The as-cast RHEA exhibits a single body-centered cubic (BCC) structure, demonstrating a tensile yield strength of ∼904 MPa along with a total elongation of ∼9.7 %. By employing cold rolling followed by recrystallized annealing (designated as the CRRA sample), we achieve notable enhancements in both strength and ductility. Specifically, the CRRA sample manifests an impressive tensile yield strength of ∼1010 MPa and a total elongation of ∼20.6 % at room temperature. Remarkably, even at an elevated temperature of 700 °C, the CRRA sample maintains notable strength, displaying a yield strength of ∼695 MPa. The observed dislocation behavior, transitioning from dual-system slip to multi-system slip, along with the intricate interactions of dislocation substructures (e.g., loops, tangles, networks, bands, and cells) and kink bands, are identified as the principal deformation mechanisms contributing to the exceptional tensile properties of the CRRA sample at room temperature. At 700 °C, the presence of wavy-slipping dislocations, induced by the strong pinning effect of component fluctuations, predominantly contributes to the strength of the CRRA sample. However, the emergence of Cr2(Ti, Nb, V) Laves phase at grain boundaries results in premature fracture. The extraordinary tensile properties exhibited by the CRRA sample at both room and elevated temperatures underscore its potential for advanced engineering applications.

Dislocation penetration in basal-to-prismatic slip transfer in Mg: A fracture mechanics criterion

Understanding the transition mechanism from microscopic to macroscopic yielding is crucial for developing high-strength metallic materials. Basal-to-prismatic slip transfer at grain boundaries (GBs) of Mg alloys is known to trigger macroscopic yielding. Here, the penetration behavior of pileup dislocations at a simple basal–prismatic (BP) boundary was analyzed using molecular dynamics simulations. Edge dislocation penetration creates a step in the BP boundary at the intersection with the slip plane, widened via subsequent penetration of dislocations. Many GBs, including the BP boundary, have a regular GB dislocation network that corresponds to a coincidence site lattice. Dislocation penetrations must gradually destroy the initial GB dislocation network, requiring increasing driving force for subsequent dislocation penetrations; thus, slip transfer at the boundary occurs sporadically and stably via the penetration of individual lattice dislocations. As the width of the step created by dislocation penetration increases, a GB dislocation network can be formed in the step, which can stabilize the energy of the step with specific widths. When the energy of step decreases with increasing step width, a smaller driving force is required for the subsequent penetration of dislocations, and thus slip transfer occurs unstably via the penetration of several sequential lattice dislocations. Once the step has a low energy at a specific width, it strongly obstructs dislocation penetration. This formation and disruption of the GB dislocation network cause intermittent penetration of dislocations. Finally, dislocation penetration at the BP boundary is discussed based on a fracture mechanics approach, which well-reproduces the transition between penetration behaviors and the macroscopic yield stress.

Dislocation motion induced by pulse current in Ti/Al bimetal composite observed by in-situ TEM

The in-situ transmission electron microscopy (TEM) was applied to investigate the effect of pulse current on the dislocation evolution of Ti/Al bimetal composite sheet. By comparison of electrical in-situ and thermal in-situ experiment, the dislocation moving along the electron wind direction were observed in the Al matrix and interface region. The results revealed that the dislocation behavior of the Al matrix and interface were affected not only by Joule heating effect, but also by non-thermal effect. In contrast, the dislocation motion of the Ti matrix was more significantly affected by Joule heating effect. The effect of the pulse current on dislocation evolution can be divided into three stages. When the current was <0.8 mA, the current has little effect on the dislocation of Ti/Al bimetal composite sheet. When the current was between 0.8 mA and 2.2 mA, the dislocation motion appeared to be enhanced by current. But the effect was confined, and the dislocation pile up did not improve. When the current is >2.4 mA, the dislocation motion was promoted significantly due to the pulse current, and the dislocation entanglements were facilitated to open. The dislocation density of Ti/Al bimetal composite sheet decreased.

Superplasticity induced by cyclic phase transitions in nanosystems: An atomic study

Three samples, namely, iron (Fe) bulk, nanowire (NW) and nanotube (NT) with the initial body centered cubic (bcc) structure were designed and constructed. Using molecular dynamics simulation, tensile experiments were performed on the three samples. The results show that the NT exhibits the highest plasticity followed by the NW and bulk. Cyclical phase transitions were observed in the NW and NT, releasing the accumulated stress and allowing the samples to achieve the superplasticity. Focusing on nucleation and growth, the phase transitions were analyzed in detail and it could be concluded that the higher surface-volume ratio and the surface roughness induced by grain reorientation are the main reasons for the highest plasticity in the NT. In addition, the dislocation behaviors in the three samples were investigated. The results of this work might be helpful to understand the mechanism of phase transition induced superplasticity and provide some new ideas for the material design with high plasticity requirement.

Cluster mediated high strength and large ductility in a strip casting micro-alloyed steel

Exhibiting exceptional mechanical properties and formability, high strength low alloy steels characterized by a single ferrite microstructure with finely dispersed nano-precipitates (ferritic HSLA steel) have garnered notable attention in the automotive industry. Nevertheless, to maximally utilize the precipitation hardening effect, these steels necessitate substantial additions of carbide-forming elements, unavoidably narrowing the process window and escalating the cost. Strip casting, featuring a streamlined process chain and high energy efficiency, has emerged as a promising technique for developing ferritic HSLA steels. In this work, leveraging the process characteristics of strip casting, we report that a novel single ferrite microstructure with multi-atomic layered clusters distributed in both interphase-precipitation and random fashions was engineered in a low Nb micro-alloyed ferritic HSLAs via raising the coiling temperature to 650 ℃. The multi-atomic layered clusters play a pivotal role in tailoring dislocation behaviors, facilitating local double cross-slips, contributing to dislocation multiplication and homogeneous distribution. These mechanisms collectively sustain mild work hardening to higher strains, leading to combined strength and ductility increments. In comparison to their cluster-free bainitic counterparts coiled at 480 ℃, the results demonstrate significant mechanical improvements with an increase in ultimate strength (630 MPa to 670 MPa) and a 90 % rise in plasticity (10.3 % to 19.1 %), signifying an alternative pathway for advancing the utilization of strip casting technology in designing and processing novel low-cost, high-performance HSLAs.

Dislocation random walk under cyclic deformation.

Dislocation motion under cyclic loading is of great interest from theoretical and practical viewpoints. In this paper, we develop a random walk model for the purpose of evaluating the diffusion coefficient of dislocation under cyclic loading condition. The dislocation behavior was modeled as a series of binomial stochastic processes (one-dimensional random walk), where dislocations are randomly driven by the external load. The probability distribution of dislocation motion and the diffusion coefficient per cycle were analytically derived from the random-walk description as a function of the loading condition and the microscopic material properties. The derived equationwas validated by comparing the predicted diffusion coefficient with the molecular dynamics simulation result copper under cyclic deformation. As a result, we confirmed fairly good agreement between the random walk model and the molecular dynamics simulation results.

Effect of phase boundary on the critical resolved shear stress and dislocation behavior of dual-phase titanium alloy

Interphase boundary plays a dominant role in the mechanical properties of dual-phase titanium alloys, and therefore mechanistic understandings of the effect of phase boundary on the plasticity is significant to tailor the microstructure for desired performance. In this study, compression tests were conducted on the Ti-6Al-4V micro-pillars with a dual-phase lamellar structure and designated crystallographic orientation of pillars and the number of interphase boundaries in the pillars were achieved by elaborate processing, to reveal the interphase boundary and its quantity on the dislocation behavior and critical resolved shear stress (CRSS) of the alloy. Transmission electron microscopy was employed to characterize the dislocations and their interplay with interphase boundaries during compression. It is found that in the pillars oriented for prismatic 〈a3〉 slip, which represents the hard mode for dislocation transmission through the α/β phase boundary, the strain distribution in the pillars was significantly delocalized by introducing interphase boundaries. More dislocation slip bands are generated owing to the strengthening effect from the interphase boundaries during compression, which results in a more homogeneous strain distribution. Moreover, quantitative analyses of the contribution of interphase boundaries on the CRSS were performed, and the interphase strength for prismatic 〈a3〉 slip was experimentally determined to be ∼ 50 MPa. The effect of pillar size on the CRSS value was also assessed. Although the CRSS of the pillars increases when their size decreases, the size dependency becomes much less pronounced when more interphase boundaries are introduced into the pillars. The underlying mechanisms for these phenomena were discussed based on the experimental results and finite element modeling. These results provide some new insights into the plasticity and strengthening mechanism of Ti-6Al-4V alloy, which are also applicable to other dual-phase titanium alloys.

Microstructure evolution and mechanical properties of additively manufactured Ni-based GH4099 superalloy via hot isostatic pressing and heat treatment

In this study, GH4099 alloys with over 99.99 % density were produced by laser powder bed fusion (LPBF) and followed by hot isostatic pressing (HIP) and heat treatment (HT). The effects of HIP and HT on the microstructure evolution and mechanical properties of the additively manufactured GH4099 superalloy were examined systematically. The as-deposited columnar crystals were effectively transformed into equiaxed crystals via HIP and HT. During HIP, the elimination of defects and elemental segregation in the deposited samples occurs. However, uneven precipitation of the γ′ phase within grains causes the emergence of minor gaps in the γ matrix, which adversely affects mechanical properties. The microstructure resulting from HIP + solution treatment (ST) consists entirely of equiaxed recrystallized grains. The presence of twin and long-period stacking-ordered (LPSO) phases at twin boundaries strongly hinders dislocation behavior, and the remelting of precipitates and carbides greatly improves plasticity. Moreover, during the loading process at 900 °C, γ′ phase and carbides were re-precipitated, and the strain concentration was minimized during the precipitation process, resulting in the highest high-temperature strength. Conversely, in the HIP + solution and aging treatment (SAT) process, the progression of γ′ phase precipitation, condensation, annexation, and growth contributes to a reduction in strength. Coupled with an increase in the plasticity of the LPBF GH4099 alloy.

Wear behaviors and plastic deformation mechanisms induced by nano-grinding of indium-doped gallium nitride single crystal

The wear behaviors and plastic deformation mechanisms of indium (In)-doped gallium nitride (GaN) induced by nano-grinding are investigated in this work, which is of great significance for improving the quality and precision of the machined surface of the nitride semiconductor, as well as for elucidating their mechanical properties during the nano-grinding process. A numerical simulation approach based on molecular dynamics (MD) is used to carry out a comparative analysis of the nano-grinding process for the undoped and In-doped GaN by analyzing the machined surface morphology, formation mechanisms of the subsurface damage (SSD) layer, dislocation behaviors, and residual stress. In addition, the effects of material temperature and grinding speed on the nano-grinding process of the In-doped GaN are investigated. Compared to the undoped GaN, indium doping increases the pile-ups and chips on both sides of the abrasive, the roughness of the machined surface, and the coefficient of friction. Moreover, it reduces the thickness of the SSD layer and restricts the occurrence of phase transformations. Indium doping also weakens the dislocation interactions and reduces the generation of dislocation entanglements as well as wall-like dislocations. Furthermore, it decreases the maximum value of the residual stress and increases the area of high residual stress regions. The wear behaviors and plastic deformation mechanisms of In-doped GaN are quite sensitive to material temperature, but not much influenced by grinding speed.

Shock compression of single-crystal stainless steel

We studied the orientation-dependent dynamic properties and plastic deformation mechanisms in single-crystal austenitic FeCr18Ni12.5 stainless steel shocked to peak stresses ranging 3.8-12.0 GPa. The 〈110〉 and 〈111〉 principal Hugoniots generally match that of polycrystalline 304L stainless steel, but the 〈100〉 Hugoniot exhibits lower shock velocities and comprises two distinct regions. The Hugoniot elastic limits (HELs) and spallation strengths range 0.5-1.2 GPa and 2.2-3.8 GPa, respectively, and exhibit trends previously observed in polycrystalline steels. We generally observed the largest HELs along 〈100〉 and the largest spallation strengths along 〈111〉. Microscopy revealed larger twin and martensite fractions in the 〈100〉 samples, correlations in twinning and martensite prevalence with dynamic response, and orientation-dependent differences in dislocation behavior near the spallation plane.

Room and cryogenic deformation behavior of AZ61 and AZ61-xCaO (x = 0.5, 1 wt.%) alloy

This study investigates the influence of CaO (0.5, 1 (wt.%)) alloying on the microstructural evolution, texture development and deformation behavior of AZ61 magnesium alloy. The uniaxial tension tests at room (RT) and cryogenic (CT, -150 °C) temperature were performed to investigate the twinability and dislocation behavior and its consequent effect on flow stress, ductility and strain hardening rate. The results showed that the AZ61-1CaO exhibited superior strength/ductility synergy at RT with a yield strength (YS) of 223 MPa and a ductility of 23% as compared to AZ61 (178 MPa, 18.5%) and AZ61-0.5CaO (198 MPa, 21%). Similar trend was witnessed for all the samples during CT deformation, where increase in the YS and decrease in ductility were observed. The Mtex tools based in-grain misorientation axis (IGMA) analysis of RT deformed samples revealed the higher activities of prismatic <a> slip in AZ61-CaO, which led to superior ductility. Moreover, subsequent EBSD analysis of CT deformed samples showed the increased fraction of fine {10-12} tension twins and nucleation of multiple {10-12} twin variants caused by higher local stress concentration at the grain boundaries, which imposed the strengthening by twin-twin interaction. Lastly, the detailed investigations on strengthening contributors showed that the dislocation strengthening has the highest contribution towards strength in all samples.

Numerical study on the influence of excavation slope on the structural behavior of ground penetrating shield tunnels

The ground penetrating shield technology (GPST) is a fast shield tunnelling method, wherein the shield is launched and received at the ground surface without constructing deep and large working shafts. With regard to the notable sloping excavation characteristics of the GPST, this study established a three-dimensional numerical model to analyze the impact of the excavation slope on the structural response of the tunnel lining based on the South Longshui Road Cross-river Tunnel project in Shanghai. The results indicate that the circumferential earth pressure acting on the lining is determined by both the buried depth and decomposition angle induced by the change in the excavation slope. The distribution of the earth pressure along the longitudinal direction may be affected by the excavation slope, and this subsequently affects convergence deformation of the tunnel. An increase in the excavation slope equalized the distributed force acting on the lining. In addition, the existence of circumferential joints exaggerates the impact of the excavation slope on the differential convergence between adjacent rings. A larger excavation slope resulted in a decrease in the proportion of convergence deformation caused by the longitudinal joints. These findings can provide important guidance for controlling the ovalization and dislocation behaviors of GPST.

Mechanism of solute hardening and dislocation debris-mediated ductilization in Nb-Si alloy

Niobium (Nb) is sensitive to even minute quantities of silicon (Si) solutes, which are known to induce pronounced hardening. However, the underlying mechanism for hardening remains elusive since the effect of Si solutes on dislocation behavior is unclear. Here, using tensile testing, in-situ microscopy and nanomechanical testing, the behavior of dislocations in dilute Nb-Si alloys, containing from 0 at.% to 0.8 at.% Si, is investigated. We show that the hardness, strength and strain hardening rate increase from two to four times, while the uniform elongation in tension only reduces 50 % as the Si content increases. Dislocations evolve from complex entangled patterns in Nb to parallel long-straight screw dislocation-dominated structures in Nb-Si alloys. In-situ indentation reveals that the origins of the marked hardening in Nb-Si alloy are the reduction of dislocation mobility and cross-slip propensity. Large densities of dislocation debris-superjogs and loops introduced throughout the sample during warm rolling and annealing are found to provide active internal dislocation sources, which explain the minimal ductility loss seen in these Nb-Si alloys. These findings can help guide the alloy design of high-performance refractory materials for extreme temperature applications.

Multiscale modeling of dislocation-mediated plasticity of refractory high entropy alloys

Refractory high entropy alloys (RHEAs) have drawn growing attention due to their remarkable strength retention at high temperatures. Understanding dislocation mobility is vital for optimizing high-temperature properties and ambient temperature ductility of RHEAs. Nevertheless, fundamental questions persist regarding the variability of dislocation motion in the rugged energy landscape and the effective activation barrier for specific mechanisms, such as kink-pair nucleation and kink migration. Here we perform systematic atomistic simulations and conduct statistical analysis to obtain the effective activation barriers for the mechanisms underlying various types of dislocation motion in a typical RHEA, NbMoTaW. Moreover, a stochastic line tension model is developed to calculate the activation barrier with substantially reduced computational costs. By incorporating the effective activation barriers into the crystal plasticity model, a multiscale simulation framework for predicting the mechanical properties of RHEAs is established. The ambient temperature yield strength of NbMoTaW is well-predicted by the kink-pair nucleation mechanism of screw dislocations, while the strengthening originating from screw dislocations does not predominate at high temperatures. Our work provides a robust foundation for atomistic studies of effective dislocation behaviors in random solution solids, elucidating the intricate relationship between microscopic mechanisms and macroscopic properties.

Couple-stress elasticity of intrinsic and extrinsic dislocations in three-dimensional multilayered materials

This work investigates the influence of couple stresses on intrinsic and extrinsic dislocations within three-dimensional heterogeneous multilayered structures. The materials consist of orthotropic and dissimilar layers with different elastic properties, incorporating the microstructural lengths from a special version of the anisotropic couple-stress elasticity. Double Fourier series expansions are used to describe extended displacements and tractions, considering rotation and couple-stress components and accounting for arbitrary displacement and rotation discontinuities associated with dislocation and disclination loops as well as periodic dislocation and disclination networks at semi-coherent interfaces. The dual-variable and position technique is used to recursively determine the field responses at any point in the multilayered laminate. The application examples focus on dislocation problems with couple stresses, revealing the effects of the core-spreading dislocation technique, free surfaces, anisotropic elasticity, and couple stresses on the field solutions. The analysis also uncovers pressure and von Mises stress amplitudes, non-zero rotation, and non-symmetric stress profiles due to couple stresses in copper/niobium bimaterials. Changes in the sign and magnitude of the Peach-Koehler forces are observed when couple stresses are introduced, which deviate from the classical theory of dislocations. The investigation finds a significant 29% reduction in energy per unit area at a semi-coherent interface between copper and niobium influenced by couple stresses. These results deepen our understanding of how couple stresses affect dislocation behavior in multilayered materials, and provide prospects for future discrete dislocation and disclination dynamics simulations with engineering applications in various nano- and micro-structured materials.

Investigating the Microstructural and Mechanical Characteristics of Laser Additive‐Manufactured AlSi10Mg Specimens Through Experimental and Phase‐Field Modeling Approaches

Metal‐based additive manufacturing can make complicated parts that are complex or expensive to cast and process. Rapid cooling rates increase laser powder bed fusion (LPBF's) mechanical properties during manufacturing. The objective of this study is to examine the impact of process parameters in the L‐PBF technique on the characteristics of microstructure and mechanical properties, specifically, on the nanohardness influenced by Si segregation. The microstructures of the produced specimens are examined using field‐emission scanning electron microscopy and the analysis identifies the existence of bimodal equiaxed α‐Al grains, accompanied by Si phases located within their grain boundaries. In addition, the solidified sample exhibits the segregation of secondary precipitates, particularly Mg2Si, which results in enhanced mechanical properties. Both cellular walls and Si precipitates impede the motion and generation of dislocations, thereby influencing the overall behavior of dislocations. The examination of segregation at the top layer is conducted in a comprehensive manner, subsequently using energy‐dispersive X‐ray spectroscopy for analysis. The presence of Mg2Si, Al2MgSi2, and other phases in all samples is confirmed through X‐ray diffraction. The as‐built samples’ residual stress under different process conditions is also investigated. Additionally, the obtained microstructure is compared to a phase‐field model to forecast the evolution of the microstructure.

The mechanism for annealing-induced ductile to brittle transition in a high-temperature titanium alloy and its mitigation

By investigating the relation between microstructure evolution and tensile responses of a BTi6431S alloy at room temperature and 700 °C, this study finds an annealing-induced ductile-to-brittle transition phenomenon in the near-α titanium alloy. The high strength of the as-received BTi6431S alloy is rooted in the high dislocation density and collective dislocation behavior in the α phase. However, after annealing at 650 °C, the alloy exhibits brittle fracture at room temperature. Using multiscale characterization methods, we attribute this phenomenon to the presence of brittle precipitates and the change of dislocation structures near the surface of BTi6431S titanium alloy. Silicides are generated in the vicinity of the surface region due to the relatively high dislocation density on the surface after the rolling process. The room temperature ductility can be restored by removing the near-surface area. When the alloy is tested at 700 °C, most of the near-surface brittle silicides and dislocations can be eliminated, because the deformation is mainly affected by dislocation behavior and dynamic recrystallization at high temperature. The findings in this study can advance the understanding of alloying effects on the mechanical behavior of high-temperature titanium alloy. The results suggest that inhibiting silicide formation and controlling the environmental temperature during service are potential approaches for maintaining the mechanical performance of this near-α titanium alloy.

Unveiling deformation behavior and damage mechanism of irradiated high entropy alloys

The oxide dispersion strengthening (ODS) high entropy alloy (HEA) exhibits the high elevated temperature performance and radiation resistance due to severe atomic lattice distortion and oxide particles dispersed in matrix, which is expected to become the most promising structural material in the next generation of nuclear energy systems. However, microstructure and damage evolution of irradiated ODS HEA under loading remain elusive at submicron scale using the existing simulations owing to a lack of atomic-lattice-distortion information from a micromechanics description. Here, the random field theory informed discrete dislocation dynamics simulations based on the results of high-resolution transmission electron microscopy are developed to study the dislocation behavior and damage evolution in ODS HEA considering the influence of severe lattice distortion and nanoscale oxide particle. Noteworthy, the damage behavior shows an unusual trend of the decreasing-to-increasing transition with the continuous loading process. There are two main types of damage micromechanics generated in irradiated ODS HEA: the dislocation loop damage in which the damage is controlled by irradiation-induced dislocation loops and their evolution, the strain localization damage in which the damage comes from the dislocation multiplication in the local plastic region. The oxide particle hinders the dislocation movement in the main slip plane, and the lattice distortion induces the dislocation sliding to the secondary slip plane, which promotes the dislocation cross-slip and dislocation loop annihilation, and thus reduces the material damage in the elastic damage stage. These findings can deeply understand atomic-scale damage mechanism and guide the design of ODS HEA with high radiation resistance.

Nano-indentation study of dislocation evolution in GaN-based laser diodes

The slip systems and motion behavior of dislocations induced by nano-indentation technique in GaN-based LDs were investigated. Dislocations with burgers vector of b = 1/3 <112¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{2}$$\\end{document}3> were introduced on either {112¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{2}$$\\end{document}2} <112¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{2}$$\\end{document}3>, or {11¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{1}$$\\end{document}01} <112¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{2}$$\\end{document}3> pyramidal slip systems in the upper p-GaN layer. Besides, {0001} <112¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{2}$$\\end{document}0> basal slip system was also activated. The AlGaN/InGaN multi-layers in device can provide mismatch stresses to prevent dislocations from slipping through. It was observed that the density of dislocations induced by the indenter significantly decreased from the upper to the lower regions of the multi-layers. The a + c dislocations on pyramidal slip planes were mostly blocked by the strained layers.