Σ3 Boundaries Research Articles

Grain boundary energy control in zinc aluminate nanoceramics

AbstractThis study investigates the grain boundary energy dependence on segregated dopants in nanocrystalline zinc aluminate ceramics. Atomistic simulations of Σ3 and Σ9 grain boundaries showed that trivalent ions of varying ionic radii [Sc3+ (74.5 pm), In3+ (80.0 pm), Y3+ (90.0 pm), and Nd3+ (98.3 pm)] have a tendency to segregate to both interfaces, with Y3+ presenting the highest segregation potentials. The connection between segregation and the reduction of interfacial energies was explored by measuring the grain boundary energy on nanoceramics fabricated via high‐pressure spark plasma sintering (HP‐SPS) using differential scanning calorimetry (DSC). The results revealed that Y3+ doping at 0.5 mol% reduces the grain boundary energy in zinc aluminate nanoceramics from 1.1–1.3 J/m2 to 0.6–0.8 J/m2; the range correlates with the observed size dependence of the excess energy, with higher values observed for the smaller grain sizes (∼17 nm). The noted decrease in interfacial energies for doped samples suggests it is indeed possible to alter the stability of zinc aluminate grain boundaries via dopant segregation.

Annealing Effects on Microstructure and Texture in KOBO-Processed LPBF AlSi10Mg Alloy: Elucidating CSL Boundary Formation

This study introduces a strain-annealing approach to tailor the grain boundary characteristics of additively manufactured AlSi10Mg alloy produced by Laser Powder Bed Fusion (LPBF). By combining KOBO extrusion and subsequent annealing treatments, we aim to increase the proportion of low-Σ coincident site lattice (CSL) grain boundaries, particularly Σ3 boundaries. Through grain boundary engineering (GBE), specifically focused on inducing a high fraction of symmetrical CSL boundaries, our approach allows for the optimization of microstructural features that inhibit defect propagation and improve material stability. Microstructural analysis using electron backscatter diffraction (EBSD) revealed a substantial increase in Σ3 boundaries (60° <111> twin relationship) in the early recrystallization stages of the KOBO-processed LPBF AlSi10Mg alloy, demonstrating the effectiveness of this method. The findings presented in this manuscript highlight a new strategy for advancing the microstructural characteristics of LPBF AlSi10Mg alloy, with promising implications for applications requiring high-performance materials, such as in the aerospace, nuclear, and automotive industries.

The Influence of Microstructure on Corrosion Resistance of B10 Copper Tube

To pinpoint the relationship between the microstructure and corrosion resistance of the B10 copper tube, the copper tubes were annealed at 780°C and 810°C, respectively. Then the simulated seawater full immersion experiment was conducted. The corrosion film, grain size, boundary characteristics, and intragranular microstructure of the alloy were analyzed by OM, SEM, EBSD, and TEM. The results implied that the corrosion rate of the 810°C annealed copper tube is about 0.028 mm/a, which is 1.9 times that of the 780°C annealed copper tube. The average grain size of 810°C annealed copper tube is about 38.85 μm and the low ΣCSL account for 64.8 %, which is 1.5 times and 1.4 times that of 780°C annealed copper tube, respectively. There is a complete spinodal decomposition structure within the grain in an 810°C annealed copper tube, but there is an incomplete spinodal decomposition structure in a 780°C annealed copper tube. Theoretical analysis indicated that the large-sized grain clusters could be formed by numerous low-layer fault energy twin boundaries Σ3, and low ΣCSL combination Σ3, Σ9, Σ27, which can block the large crystal boundaries network, inhibit the phase precipitation and prevent invading of corrosive elements along the large crystal boundaries. The intragranular spinodal decomposition structure can improve the strength and toughness of the B10 copper tube, reduce the initiation of surface microcracks during service, and thus reduce pitting and crevice corrosion.

Unveiling microstructural evolution and its effect on mechanical performance in a Cu-9Ni-6Sn alloy

Cu-9Ni-6Sn alloy exhibits profoundly potential as a new environmental-friendly conductive elastic material. In this work, the formation and growth mechanism of discontinuous precipitation, as well as its effect on mechanical properties of Cu-9Ni-6Sn alloy are systematically studied. The investigation indicated that the discontinuous precipitation does easily initiate from random grain boundaries but showing opposite result for Σ3 boundaries. The lower frequency Σ3 boundaries relatively, the more intense the solute diffusion, resulting in a higher volume fraction of discontinuous precipitation. The increasing aging temperature and time will accelerate the grain boundary discontinuous reaction, and the fine-grained samples exhibit a higher volume fraction of discontinuous precipitates and smaller lamellar spacing due to the more nucleation sites and increased interfacial energy. The strengthening mechanism of Cu-9Ni-6Sn alloy mainly focus on dislocation strengthening and precipitation strengthening, in which the D022 or L12-γ′ phases exhibit more significantly precipitation strengthening effect but is difficult to guarantee ductility. The localized grain boundary discontinuous precipitation detrimentally affect both the tensile strength and ductility.But the nano-lamellar discontinuous precipitation is beneficial to the strength-ductility trade off when it occupies the entirely Cu matrix. This work establishes a robust foundation for the microstructural optimization and multi-component design of Cu-9Ni-6Sn alloy.

Self-diffusion in < 100 > symmetrical tilt grain boundaries in tungsten: Molecular dynamics simulation

The structure and energy of grain boundaries, the energies of point defects formation in them and grain-boundary self-diffusion coefficients in 18 < 100 > symmetrical tilt grain boundaries in tungsten have been determined by atomistic simulation. The dependences of grain boundary energies, defect formation energies in them and activation energy of grain-boundary self-diffusion on the misorientation angle have been calculated. A structural phase transformation has been discovered in Σ5(310) and Σ5(210) boundaries, which affected the diffusion properties of these grain boundaries. The calculations performed are compared with the available experimental data on self-diffusion in grain boundaries of tungsten.

Enhancing mechanical property and corrosion resistance of Al0.3CoCrFeNi1.5 high entropy alloy via grain boundary engineering

In the present study, to improve the performances of Al0.3CoCrFeNi1.5 high entropy alloys (HEAs), grain boundary character distribution (GBCD) of Al0.3CoCrFeNi1.5 HEA has been optimized by an appropriate thermo-mechanical processing. The experiment results showed that the fraction of low-Σ coincidence site lattice (CSL) boundaries could reach approximately 80 % through cold rolling with deformation of 8 % and subsequent annealing at 1050 °C for 5 min. The reason for GBCD optimization could be attributed to sufficient strain-induced boundary migration (SIBM) or grain growth after recrystallization. While recrystallization is not favorable for optimizing GBCD. The mechanical properties and corrosion resistance have been enhanced, with a more pronounced improvement observed in the corrosion resistance. The corrosion current density icorr of the GBEM specimen stands at 0.23 μA∙cm−2, representing a reduction of 66 % in comparison to the BM specimen (0.68 μA∙cm−2). The improvement of corrosion resistance of Al0.3CoCrFeNi1.5 HEA resulted from the discontinuous random grain boundaries (RGBs) broken by the high fraction of low-ΣCSL boundaries, especially Σ3 boundaries suppressed the propagation of corrosion crack.

Determination of five-parameter grain boundary characteristics in nanocrystalline Ni-W by scanning precession electron diffraction tomography

Determining the full five-parameter grain boundary characteristics from experiments is essential for understanding grain boundaries impact on material properties, improving related models, and designing advanced alloys. However, achieving this is generally challenging, in particular at nanoscale, due to their 3D nature. In our study, we successfully determined the grain boundary characteristics of an annealed nickel-tungsten alloy (NiW) nanocrystalline needle-shaped specimen (tip) containing twins using Scanning Precession Electron Diffraction (SPED) Tomography. The presence of annealing twins in this face-centered cubic (fcc) material gives rise to common reflections in the SPED diffraction patterns, which challenges the reconstruction of orientation-specific virtual dark field (VDF) images required for tomographic reconstruction of the 3D grain shapes. To address this, an automated post-processing step identifies and deselects these shared reflections prior to the reconstruction of the VDF images. Combined with appropriate intensity normalization and projection alignment procedures, this approach enables high-fidelity 3D reconstruction of the individual grains contained in the needle-shaped sample volume. To probe the accuracy of the resulting boundary characteristics, the twin boundary surface normal directions were extracted from the 3D voxelated grain boundary map using a 3D Hough transform. For the sub-set of coherent Σ3 boundaries, the expected {111} grain boundary plane normals were obtained with an angular error of <3° for boundary sizes down to 400 nm². This work advances our ability to precisely characterize and understand the complex grain boundaries that govern material properties.

Effects of carbon concentration and transformation temperature on incomplete transformation and crystallography of low-carbon bainitic steel

A close relationship exists between the crystallographic characteristics of a bainitic matrix and formation of martensite/austenite (M/A) constituents. In this work, the isothermal transformation kinetics and crystallographic characteristics of low-carbon bainitic (LCB) steel were investigated to elucidate the formation mechanism of M/A constituents and twin-related V1/V2 variant pairs (Σ3 boundaries). The formation of M/A constituents depends on the bainitic transformation kinetics, which are influenced by the carbon concentration and isothermal temperature. An increase in the carbon concentration or transformation temperature promotes the formation of blocky M/A constituents by increasing the activation energy of the grain boundary and autocatalytic nucleation processes. In addition, increasing the carbon concentration or lowering the transformation temperature increases the strength of the austenite phase and promotes autocatalytic nucleation, thereby producing more twin-related V1/V2 variant pairs. Therefore, the increase in the carbon concentration increases the number of twin-related V1/V2 variant pairs while also causing the formation of blocky M/A constituents. To overcome this limitation, a novel heat treatment process design is proposed that can significantly eliminate blocky M/A constituents and generate high-density twin-related V1/V2 variant pairs.

Origins of twin boundaries in additive manufactured stainless steels

316L and 304L stainless steels and a compositional gradient of both are fabricated using the same processing parameters via laser directed energy deposition additive manufacturing. In those alloys, the increase in chromium-to-nickel ratio is accompanied with grain refinement and formation of a high density of twin boundaries, i.e. Σ3 boundaries. By means of electron microscopy, crystallographic and thermodynamic calculations, we demonstrate that two mechanisms arising from the ferrite-to-austenite solidification mode are at the origin of twin boundary formation and grain refinement: (1) inter-variant boundaries emerging from the encounter of pairs of austenite grains formed from a common ferrite orientation with Kurdjumov–Sachs orientation relationship; (2) icosahedral short-range-ordering-induced (ISRO) nucleation of twin-related γ grains directly from the solidifying liquid. These findings define new routes to achieve grain boundary engineering in a single step in FeCrNi alloys, by tailoring the solidification pathway during the AM process, enabling the design of functionally graded materials with site-specific properties.

A novel surface grain boundary engineering approach to improving corrosion resistance of a high-N and Ni-free austenitic stainless steel

Grain boundary engineering (GBE) can effectively improve the corrosion resistance of materials, but the traditional thermal-mechanical process still exhibits some limitations. In the present work, a novel surface spinning strengthening (3 S) technology followed by heat treatment was applied to modify the microstructure near the surface (∼ 400 μm) of a high-N Ni-free austenitic stainless steel. Under an optimal condition of annealing at 1323 K for 60 min after 3 S, the fraction of special boundaries mainly involving Σ3 boundaries in GBE layer was significantly improved from 48.3 % to 69.1 %, thus achieving excellent resistances to intergranular corrosion and stress corrosion cracking.

Gradient microstructure in Ni-Cr-Mo ultra-heavy steel plate after tempering

This paper studied through-thickness gradient microstructure of an 80mm ultra-heavy steel plate by multi-dimensional characterizations, meanwhile the cause of microstructure variability as well as its effect on strength was analyzed. Results show major lath-structure in the whole steel plate, while lath morphology and grain boundary distribution are different along the thickness direction. During phase transformation, the higher cooling rate in the surface enhances the forming ability of V1/V4 variant pairs and corresponding 5°-10° boundaries, meanwhile the higher cooling rate and smaller original austenite grain contribute to more nucleation sites and stronger strain incompatibility, which is corresponding to more low-angle boundaries, so the surface layer shows higher low-angle boundaries; Compared with the surface layer, the moderate cooling rate is beneficial for V1/V2 variant pairs, and Σ3 boundaries between the pairs are obtained, leading to higher high-angle boundary density with decreased low-angle grain boundary density. This boundary characteristic corresponds to the thinner and longer lath morphology. With respect to the relationship between mechanical properties and microstructure, more low-angle boundaries in the surface layer and more high-angle boundaries in inner layers contribute to stronger dislocation strengthening and grain boundary strengthening respectively, and realizes the coordinated through-thickness property.

Structural transformation behavior of oxide scale during coiling of 0.9 wt% Cr-containing high-strength steel

The phase transformation mechanism of oxide scale on the surfaces of chromium (Cr)-free carbon steel and 0.9 wt% Cr-containing steel at different coiling temperatures and cooling rates was studied using thermal simulation and electron backscattering diffraction experiments. The results showed that the eutectoid transformation of both the steel followed the “C” curve relationship. The Cr-containing steel had a larger eutectoid transformation area fraction than the Cr-free carbon steel. The nose tip temperature of the eutectoid transformation of the oxide scale on the surfaces of Cr-free carbon steel and 0.9 wt% Cr-containing steel were 420∼510 °C and 420–480 °C, respectively. For the 0.9 wt% Cr-containing steel, the proportion of Σ3 and Σ13b grain boundaries in cubic Fe3O4 increased, followed by a decrease, when the coiling temperature decreased from 610 to 410 °C. The Σ3 and Σ13b grain boundaries of the Fe3O4 low-dimensional coincident site lattice had the highest proportion for 510 °C coiling temperature. The low-dimensional coincident site lattice grain boundaries could be used to enhance crack resistance and improve the oxide scale on the steel plate surface.

Novel role of thermomechanical grain boundary engineering in the microstructure evolution of austenitic stainless steel

The effect of special grain boundary development via the grain boundary engineering process (GBE) was explored in a bimodal microstructured 316L austenitic stainless steel with an average grain size of 1.92 μm. The GBE process was carried out by the rolling-annealing method via two routes of low and medium applied strain, followed by a short annealing period in a single-step and iterative manner. The grain boundary character distribution was obtained by Electron Backscatter Diffraction (EBSD) analysis, and the intergranular corrosion resistance and the tensile behavior of the samples were examined. Microstructural characterization showed that applying low strain repetitively increased the coincidence site lattice (CSL) and Σ3 boundaries percentage and created large twin-related domains (TRD). The reduced sensitization was attributed to a high proportion of CSLs and large-sized TRDs by applying a low-strain route. In the early stages of the low-strain route, the grain boundary character distribution showed a high number of primary twin nuclei in coarse grains and a continuous network of single twin nuclei in smaller grains, creating a high percentage of Σ3-grain boundaries. The low applied strain and the absence of the necessary driving force for the recrystallization and GBs migration led to the formation of twin nuclei, which would assist with the reduction of microstructure energy. A high percentage of Σ3 boundaries and an increase in the percentage of triple points consisting of low energy boundaries were found to be influential factors in increasing elongation.

Reversing inverse Hall-Petch and direct computation of Hall-Petch coefficients

A 2D bicrystal atomistic model of dislocation transmission through a Σ11<101>{131} symmetric-tilt grain boundary reveals details of Hall-Petch breakdown in the single dislocation regime in Al, Ni, and Cu. Partly based on a previous study [1], this research determines the stress required for a single dislocation to be transmitted through the Σ11 boundary and finds that single dislocation transmission typically deviates from Hall-Petch behavior because the leading partial dislocation becomes trapped in the boundary and emits glissile grain boundary disconnections that cause boundary sliding deformation at stresses well below boundary transmission stresses. Thus, mechanisms of inverse Hall-Petch, namely grain boundary shear and sliding, are shown to operate in lieu of grain boundary transmission in the single dislocation regime. However, by controlling the applied stresses, inverse Hall-Petch can be reversed and typical Hall-Petch grain boundary transmission regained. This, in turn, allows the direct computation of Hall-Petch coefficients. A second dislocation on the same slip plane preserves typical Hall-Petch behavior for Al and Ni and does not lead to boundary sliding events, thus implying a critical grain size for Hall-Petch breakdown based on the pileup model.

Possible mechanisms of cubic texture generation in heavily rolling face-centered cubic metal due to the annealing twining

Face-centered cubic (FCC) metals were subjected to heavy rolling and two-step recrystallization annealing to form sharp cubic textures. The traditional theory states that the formation of recrystallized cubic-oriented grains originates from rolling cube grains. However, in our study, the Ni8W alloy underwent severe deformation during rolling, forming a typical brass-type rolling texture with almost no cubic-oriented grains. The quasi-3D electron backscatter diffraction results indicated that the newly generated cubic grains were not necessarily adjacent to the rolling cubic grains. Instead of growing from excited rolling cube grains, we found newly oriented recrystallized cubic grains generated from twin growth. Initially, most recrystallized grains undergo grain boundary migration or merging during low-temperature recrystallization annealing. Under such conditions, the initial recrystallized grains maintained the same orientation as the original matrix. However, it is also possible that the initially newly oriented recrystallized grains were generated through twinning. The {221}<122> orientation grains can cause cubic orientation by Σ3 boundaries. This twinning process reveals another pathway for generating initially recrystallized cubic grains in highly deformed FCC alloys. The recrystallized cubic-oriented grains ultimately evolved into cubic textures owing to their growth advantages, as described by the traditional theory. This discovery solves the puzzle of the recrystallization nucleation mechanism for cubic-oriented grains. It can help us better understand the evolution of the recrystallized cubic texture in heavily deformed FCC alloys.

Evolution of recrystallization texture in medium to low stacking fault energy alloys: Experiments and simulations

The present work aims to investigate the evolution of static recrystallization microstructure and texture in medium to low stacking fault energy (SFE) alloys. In these categories of materials, the process of recrystallization becomes complex because of the presence of extensive deformation heterogeneity. Ni-xCo (40 and 60wt.% Co) alloy has been chosen for this purpose, where Ni-40Co belongs to medium SFE, and Ni-60Co belongs to low SFE regimes. The effect of solid solution strengthening and deformed microstructural features on the mechanism of recrystallization are explored. Both the alloys were subjected to 50% cold-rolling reduction followed by isothermal annealing at 600°C. Recrystallization texture of Ni-40Co shows a non-uniform α-fiber having a peak intensity at the Goss component, whereas Ni-60Co shows uniform α-fiber texture. Both the alloys also show rotated cube (Rt C) and rotated Cu (Rt Cu) components after recrystallization. Apart from that Ni-60Co exhibits brass recrystallization (BR) texture component. The differences in the recrystallization texture in both the Ni-Co alloys are attributed to the role of different heterogeneous deformation features in the microstructure and transition from Cu-type to Bs-type as-deformed texture. The recrystallization microstructure is dominated by the formation of substantial annealing twin (Σ3) boundaries, which also produces many new orientations; thereby weaken the recrystallization texture. These experimental findings and the proposed mechanism were used as input to simulate the recrystallization microstructure and texture in the alloy using the parallelized cellular automata (CA) technique. Parallelized CA model has successfully predicted the evolution of recrystallization texture and microstructure through simulation except parallel annealing twin feature.

Pathways of hydrogen atom diffusion at fcc Cu: Σ9 and Σ5 grain boundaries vs single crystal

The diffusion of H-atoms is relevant for innumerous physical–chemical processes in metals. A detailed understanding of diffusion in a polycrystalline material requires the knowledge of the activation energies (ΔEa’s) for diffusion at different defects. Here, we report a study of the diffusion of H-atoms at the Σ9 and Σ5 grain boundaries (GBs) of fcc Cu that are relevant for practical applications of the material. The complete set of possible diffusion pathways was determined for each GB and we compared the ΔEa at bulk fcc Cu with the landscape of ΔEa’s at these defects. We found that while a number of diffusion pathways at the GBs have high tortuosity, there are also many paths with very low tortuosity because of specific structural features of the interstitial GB sites. These data show that the diffusion of H-atoms at these GBs is highly directional but can be fast because at certain paths the ΔEa can be as low as 0.05 eV. The lowest energy paths for diffusion of H-atoms through the whole GB models are ΔEa = 0.05 eV for the Σ9 and ΔEa = 0.20 eV at Σ5 which compare with ΔEa = 0.42 eV for the bulk fcc crystal. This shows that H-atoms will be able to diffuse very fast at these defects. With the Laguerre–Voronoi tessellation method, we studied how the local atomic structure of the interstitial sites of the GBs leads to different ΔEa’s for diffusion of H-atoms. We found that the volume expansions and the coordination numbers alone cannot account for the magnitude of the ΔEa’s. Hence, we developed a symmetry quantifying parameter that measures the deviation of symmetry of the GB sites from that of the bulk octahedral site and hence accounts for the distortion at the GB site. Only when this parameter is introduced together with the volume expansions and the coordination numbers, it is possible to correlate the local structure with the ΔEa’s and to obtain descriptors of diffusion. The complete set of data shows that the extrapolation of diffusion data for H-atoms between different types of GBs is non-trivial and should be done with care.

Σ3 grain boundary dynamics studied by atomistic spherical bicrystal modeling

In this study, we propose an atomistic spherical bicrystal model that employs the synthetic driving force method to investigate the dynamics of curved interfaces. The model allows tracking the migration and faceting of spherical grain boundaries. As a demonstration case, a simulation for a grain boundary with Σ3 misorientation is performed. A subsequent analysis of interface energy and stiffness is performed, whereby it is found that the dynamics of [111] and segments in the Σ3 boundary plane fundamental zone follow energy and stiffness trends, while others, e.g., the segment, do not.

PPB structure elimination, DRX nucleation mechanisms and grain growth behavior of the 3rd-generation PM superalloy for manufacturing aviation components

Previous Particle Boundary (PPB), as the detrimental structure in Powder Metallurgy (PM) components, should be eliminated by subsequent hot process to improve the mechanical properties. The objective is to investigate the Dynamic Recrystallization (DRX) nucleation mechanisms and grain growth behavior of the 3rd-generation PM superalloy with PPB structure. Microstructure observation reveals that PPB decorated with (Ti, Ta, Nb)C carbides belongs to the discontinuous chain-like structure. The elimination of PPB networks can be achieved effectively via hot deformation due to the occurrence of DRX. Four different DRX nucleation mechanisms were proposed and discussed in detail according to the special microstructure characteristics of the PM superalloy. Firstly, local lattice rotations can be detected in the vicinity of (Ti, Ta, Nb)C carbides during hot deformation and thus PPB structure serves as the preferential nucleation sites for DRX grains via Particle-Stimulated Nucleation (PSN). Then, Discontinuous-DRX (DDRX) characterized by grain boundary bulging dominates the microstructure refinement and Continuous-DRX (CDRX) operated by subgrain rotation can be regarded as an important assistant mechanism. At last, the initial Σ3 boundaries would lose their twin characteristics owing to the crystal rotation and then transform into the general High Angle Grain Boundaries (HAGBs). The distorted twins provide additional DRX nucleation sites, viz., twin-assisted nucleation. Particular attention was focused on the grain growth behavior of the PM superalloy in subsequent annealing process. The recrystallization temperature was determined to be about 1110 °C and 1140 °C can be considered as the critical temperature for grain growth. The findings would provide theoretical support for microstructure refinement of the 3rd-generation PM superalloy, which is of pivotal significance for improving the mechanical properties of aviation components.

Hydrogen atom solution and diffusion behaviors at Σ3 and Σ5 grain boundaries of Fe, Ni, Cu and Al: A first-principles study

Understanding the interactions between hydrogen atom and grain boundaries is essential for designing grain boundary structures that can improve the hydrogen embrittlement resistance. In this study, the DFT calculations have been performed to investigate the characteristics of Σ3 and Σ5 grain boundaries of Fe, Ni, Cu and Al and the hydrogen atom solution and diffusion behaviors at these grain boundaries. The calculation results indicate that for the same metallic material, the Σ5 grain boundary has larger grain boundary energy and lower work of separation than that of Σ3 grain boundary. The hydrogen atom solution energies at Σ5 grain boundaries are lower than those at Σ3 grain boundaries. The COHP calculations illustrate that the existence of hydrogen atom will weaken the metallic bond strength at grain boundary no matter in Σ3 or Σ5 grain boundary. With respect to the hydrogen atom diffusion behaviors at the grain boundaries, the hydrogen atom is easier to diffuse at the Σ5 grain boundary compared to that of Σ3 grain boundary for the same metallic material. Thus, increasing the ratio of grain boundaries with lower value of Σ will beneficial to improve the hydrogen embrittlement resistance of metallic polycrystalline materials.