Dislocation Loops Research Articles

Modelling of dislocations pile-ups at crack tip. Application to silicon

ABSTRACT The mechanical analysis of plastic zones at crack tip has progressed very little since the publication of the founding BCS model, 60 years ago. This two-dimensional model, and those that followed, consider the plastic zone as a pile-up of dislocations of one sign only. They assume that the crack absorbs the part of the dislocation loop of the opposite sign. Here the real three-dimensional problem is addressed and we demonstrate that the crack front behaves as an obstacle. This change of paradigm requires the plastic zone to be modelled as a two-sign dislocation pile-up. The model fits well with experimental observations in bulk silicon. In addition, the presence of dislocations of opposite signs completely modifies the amplitude of crack shielding. The closer the dislocation is to the crack front, the more significant the effect. Therefore, the increase in toughness observed experimentally is linked to the part of the loop attached to the crack front, and not to the expanding part of the loop. This conclusion is in direct contradiction to that provided by previous models.

Liquid Crystal Ordering in Densely Packed Colloidal Suspensions of Highly Anisotropic Monolayer Nanosheets

Monolayer nanosheets of zirconium phosphate in aqueous suspension exhibit short-range repulsion and long-range attraction, producing, at overall volume fractions larger than about half a percent, phase separation into higher-concentration liquid crystal and lower-concentration isotropic regions. At high concentrations, this phase separation takes the form of an emulsion of condensed, liquid-crystalline droplets, which anneal to form lens-shaped tactoids. These tactoids provide an opportunity to study the liquid crystal ordering of inorganic nanosheets in the limit of large shape anisotropy (diameter/thickness~400) and high packing fraction (volume fraction ≳ 70%). The internal liquid crystal structure of the tactoids remains nematic even under conditions that would usually favor ordering into lamellar smectics. Local lamellar ordering is suggested by short-range, smectic-like layer correlations, but a full transition into a smectic phase appears to be inhibited by the nanosheet edges, which act as a perturbative population of dislocation loops in the system of layers. Under conditions of thermal equilibrium, the nanoplates organize positionally to enable bend deformation of the director, a hallmark of the nematic phase and its principal distinction from the smectic, where bend must be expelled.

Rate theory model of irradiation effects in UO2: Influence of electronic energy losses

To investigate the effect of electronic energy losses on nuclear damage in UO2, we use a simple Rate Theory (RT) model, based on the time evolution of single point defects, governed by their absorption at the surface of TEM lamellae, and by interstitial-type dislocation loops nucleation, solely characterized by their number and average size. We first parametrize the model by fitting six different experimental datasets at various temperatures, ion type and energy (0.39 MeV Xe and 4 MeV Au ion irradiations at 93, 298 and 873 K) where defect evolution in UO2 is dominated by displacement damage caused by nuclear energy losses. The model suggests that dislocation evolution kinetics is driven by monomers diffusion at 873 K. At lower temperature (93 and 298 K) monomer diffusion has little impact and the evolution is governed by the nucleation of loops within the collision cascade. Analysis of four additional experimental datasets at 93 and 298 K where electronic energy losses are strong (single 6 MeV Si and dual simultaneous Xe & Si ion irradiations) required modification of monomer's diffusion coefficients. In the case of single Si ion irradiation, evolution is temperature independent and the enhanced diffusion due to electronic excitations and ionizations are best captured by adding athermal component to the monomer diffusion coefficients. In case of the dual Xe & Si ions irradiation, electronic excitation caused by Si ions impacts the defects pre-generated by Xe ions and enhances defect diffusion by at local heating induced by the thermal spike of Si ions. This effect is best captured by artificially raising the irradiation temperature.

Molecular dynamics simulations on the evolution of irradiation-induced dislocation loops in FeCoNiCrCu high-entropy alloy

High-entropy alloys (HEAs) have received extensive attention due to their excellent irradiation resistance. In this work, the displacement cascade simulations were performed by using the molecular dynamics (MD) method to study the dislocation loop evolution in FeCoNiCrCu HEA. The simulation results showed the dislocation loops evolution in pure Ni were dominated by Frank loops with larger size but lower density, which was caused by the absorption of prismatic dislocation loops by Frank loops. In contrast, prismatic dislocation loops were more prevailing in FeCoNiCrCu HEA with smaller size but higher density, since the interactions between dislocation loops were suppressed in HEA. To figure out the influence of HEA on dislocation loop evolution, the formation energy, interaction energy and mobility were analyzed. It was found that formation energy and interaction energy were basically the same, while the mobility of prismatic dislocation loop in HEA was much lower than that in pure Ni, which was considered as the main reason why the irradiation-induced dislocation loops were more difficult to interact and grow in HEA. The current work provides new insights into understanding the irradiation resistance from micro-mechanism in FeCoNiCrCu HEAs.

Origin and fate of loop punching in Mo-5Re alloy

Loop punching is the basic physical process of lattice expansion due to the introduction of insoluble gas atoms into the crystalline metals leading to the emission of interstitial atoms and even the formation of prismatic dislocations loops, which therefore dominate the degradation of the material. Despite more than half a century of research, experimentally capturing its fundamental process is still lacking, resulting in known mechanisms being speculated and inferred. Here, we reported for the first time the clearest and most direct experimental details of loop punching and proposed a new mechanism. According to the in-situ experiment, the origin and fate of loop punching were detailed into four stages: incubation, loop punching, synergetic growth, and interaction. At temperatures above ∼ 0.4 Tm, the nucleation and growth of dislocation loops became completely induced by bubble growth, which provided direct evidence of loop punching. The critical bubble size window for experimentally detectable loop punching was defined and evaluated, showing that it became wider and increased in average value with increasing temperature, which made that the critical energetics required for loop punching were further quantified. Furthermore, the subsequent fate of punched-out loops involved not only their mutual coalescence to form super-large <111> loops but also interactions with adjacent bubbles, during which the bubbles acted as pinning sites decorating the loop edges and mediating their growth. These results provide a comprehensive new understanding of the loop punching mechanism and promisingly contribute to the development of related theories.

Synergistic regulation of nano-precipitates and reversed austenite in titanium-free maraging steel by low-temperature solution treatment and double aging treatment

To synergistically enhance the strength and toughness of titanium-free maraging steel, a multi-scale characterization method was used to illustrate the effects of low-temperature solution treatment and double aging treatment on the microstructure of titanium-free maraging steel in this paper. After the low-temperature solution treatment and the double aging treatment, the tensile strength of titanium-free maraging steel increased from 1954 MPa to 2160 MPa and the elongation increased by 8.95 %. By the low-temperature solution treatment, the original austenite grain size of the titanium-free maraging steel was refined to 0.69 μm. The double aging treatment promoted the diffusion of Mo and Ni elements, increased the volume fraction of ω phase, Ni3Mo nano-precipitation phase and reversed austenite, and refined the size of ω phase and Ni3Mo by 14.2 % and 7.9 %, respectively. The nanoparticles of titanium-free maraging steel mainly include the ω phase, Ni3Mo and Laves phase. The strengthening mechanism of nanoparticles was quantitatively evaluated from the shear mechanism and Orowan dislocation loop mechanism. The mechanism shows that the ω phase is the main contributor to the overall precipitation strengthening. Therefore, low-temperature solution treatment and double aging treatment provide a potential solution for achieving high strength and high toughness in maraging steel.

Accurate quantification of dislocation loops in complex functional alloys enabled by deep learning image analysis

In-depth statistics of individual defects observed during transmission electron microscopy (TEM) experiments are essential for the thorough characterization of materials. In this study, we aim to quantitatively characterize the population of dislocation loops in ion-irradiated CrFeMnNi alloys. To this end, we propose an efficient guideline to prepare TEM micrographs dataset for deep learning analysis, adapted for accurate characterization of microstructures produced by thousands of overlapping defects, a very common situation in TEM images, unfeasible by previous existing methods. To reduce human effort, we annotate only a few images and complement the database through a two-step process: initially, singular value decomposition to normalize image background, followed by a controlled data augmentation. The performed analysis provides precise quantitative information about the number of loops of different types, as well as their spatial distribution, their size, and the inter-object distances. These characteristics provide insights into the nucleation, mobility, and growth of dislocation loops, as well as the elastic anisotropy of the material. Our results emphasize how accurate analysis of complex microstructures can provide insights into the physical properties of materials and open up many perspectives for attaining quantitative information on materials properties based solely on their image analysis.

Optimal Arrangements and Local Anisotropy of {100} Guinier-Preston (GP) Zones by Parametric Dislocation Dynamics (PDD) Simulations.

Stress-oriented precipitation and the resulting mechanical anisotropy have been widely studied over the decades. However, the local anisotropy of precipitates with specific orientations has been less thoroughly investigated. This study models the interaction between an edge dislocation source and {100} variants of Guinier-Preston (GP) zones in Al-Cu alloys using the parametric dislocation dynamics (PDD) method. Concentric geometrically necessary dislocation (GND) loops were employed to construct a line integral model for thin platelets. The simulations, conducted with our self-developed code based on Green's function method and Eshelby inclusion theory revealed distinct strengthening behavior along the strong and weak directions for 60° GP zones, demonstrating anisotropic strengthening from the perspective of elastic interactions. Furthermore, the optimal inclined arrangement of the GP zone array was determined through elastic energy calculations, and these results were corroborated by TEM observations.

Sink strength of grain boundaries for point defects in irradiated ferritic/martensitic steel

Dislocation-free ferritic/martensitic steel: F82H was prepared by heat-treatment in the appropriate condition in order to investigate the sink strength of grain boundaries for point defects. The size and the areal density of irradiation-induced secondary defects, such as dislocation loops and voids, were investigated in electron-irradiated F82H. The in-situ irradiation experiment resulted in the formation of a defect free zone and the gradient distribution of loop and cavity as a function of distance from boundaries, especially around prior austenite grain boundaries. The atomic density ratio of grain boundary planes is a key parameter in determining the width of defect free zone; a grain boundary with a higher atomic density ratio typically exhibits a wider defect free zone compared to one with a lower ratio. These results clearly indicate that the distribution of irradiation-induced secondary defects in ferritic/martensitic steels is not uniform and is likely controlled by the sink strength, as characterized by the atomic density ratio of grain boundary planes.

Local Strain Effects on Lattice Defect Dynamics and Interstitial Dislocation Loop Formation in Irradiated Tungsten-Molybdenum Alloys: A Molecular Dynamics Study.

In this study, molecular dynamics (MD) simulations were used to investigate how alloying tungsten (W) with molybdenum (Mo) and local strain affect the primary defect formation and interstitial dislocation loops (IDLs) in W-Mo alloys. While the number of Frenkel pairs (FPs) in the W-Mo alloy is similar to pure W, it is half that of pure Mo. The W-20% Mo alloy, chosen for further analysis, showed minimal FP variance after collision cascades induced by primary knock-on atoms (PKAs) at 10 to 80 keV. The research examined hydrostatic strains from -1.4% to 1.6%, finding that higher strains correlated with increased FP counts and cluster formation, including IDLs. The following two types of IDLs were identified: majority ½ <111> loops as well as <100> IDLs that formed within the initial picoseconds of the simulations under higher tensile strain (1.6%) and larger PKA energies (80 keV). The strain effects also correlated with changes in threshold displacement energy (TDE), with higher FP formation under tensile strain. This study highlights the impact of strain and alloying on radiation damage, particularly in low-temperature, high-energy environments.

Co-evolution of M23C6 precipitates and cavities in a boron-free Ni-based alloy GH3617 under high-temperature He ion irradiation: Effects on cavity swelling and mechanical properties

Ni-based alloys are promising materials for advanced nuclear reactors operating at high temperatures due to their exceptional resistance to high temperatures and corrosion. Understanding the synergy of phase stability and helium effects is crucial for assessing the long-term performance and reliability of these alloys in advanced nuclear reactors. This study has investigated the co-evolution behavior of M23C6 precipitates and cavities in a boron-free solid solution strengthened Ni-based alloy GH3617 under high-temperature He ion irradiation, and its impact on alloy swelling and mechanical properties, by He ion irradiation experiments with the highest fluence of 1 × 1017 He/cm2 up to 800 °C. Transmission Electron Microscopy (TEM) and Nanoindentation are employed to investigate microstructural evolution and mechanical properties, respectively. The findings show that at room temperature and 500 °C, cavities and dislocation loops were the dominant irradiation defects, whereas at 800 °C, the density of cavities and dislocations reduced while the formation of M23C6 precipitates increased. These precipitates act as effective trapping sites for He and point defect, leading to cavity formation at the interfaces or within the precipitates. Moreover, increased irradiation fluence accelerates the co-evolution process, resulting in an increase in the density and size of both precipitates and cavities, ultimately leading to enhanced swelling. The {111} planes are favored interfaces between intragranular M23C6 precipitates and the matrix due to their minimal misfit, while the preferred interface planes between cavities with octahedral or cubo-octahedral shapes and the precipitate/matrix are also {111}, owing to their lower surface energy as well. The co-evolution of cavities and precipitates was found to influence mechanical properties, resulting in an irradiation hardening effect at lower fluences, while softening at higher fluences. This study provides novel insights into the degradation mechanisms of Ni-based alloys under coupling effect of He and high-temperature irradiation.

In-situ study on the differential evolution of He bubbles in the multilayer oxide of Fe9Cr1.5W0.4Si F/M steel corroded in lead-bismuth eutectic

The combined effects of corrosion and irradiation on nuclear components have been an important but not yet fully revealed topic. Here, the irradiation behavior of the oxide scale formed on F/M steel after lead-bismuth corrosion was in-situ investigated during He+ irradiation. The results showed that the oxide scale included a Fe3O4 outer oxide layer, a nanograin Fe(FexCr2-x)O4 spinel inner oxide layer, and an internal oxide layer. He bubbles formed in Fe3O4, Fe-Cr spinel and F/M steel were polygon, irregular elongated pores and small spheres, respectively. These differences were attributed to variations in defect generation, migration, and corrosion-induced crystal defects in different oxides. Numerous corrosion-induced nanograin boundaries and vacancies in Fe-Cr spinel exhibited more effective absorption of irradiation-induced defects. Moreover, rhombic perfect dislocation loops were detected in Fe3O4 at the late stage of irradiation, their relative positional relationship with He bubbles indicated a potential interaction between bubbles and loops.

Dislocation evolution in anisotropic deformation of GaN under nanoindentation

The exceptional performance of GaN semiconductors in lasers, wireless communication, and energy storage systems makes them crucial for future multi-functional devices. However, during the polishing of GaN wafers, abrasive particles can induce subsurface damage, compromising device performance. This study investigates dislocation loops in GaN single crystal to understand dislocation nucleation and glide under external stress. Using nanoindentation for compressive stress, we confirmed multiple slip system activation via transmission electron microscopy after pop-in. We also performed molecular dynamics to simulate the nucleation and multiplication of U-shaped dislocation loops. Furthermore, we developed a theoretical model using Peierls–Nabarro stress to quantify GaN's critical shear stress. Raman spectroscopy was also used to analyze shear stress on U-shaped loops, supporting our model. This study provides insights into GaN dislocation dynamics under mechanical stress, aiding in wafer defect evaluation during machining and offering guidance for dislocation evolution.

In-Situ TEM study of microstructural evolution in proton irradiated single crystal UO2 under high-temperature annealing

Understanding microstructural changes in nuclear fuels under different irradiation conditions is important as it directly affects thermal, oxidation and mechanical properties and thereby reactor safety and longevity. This work focuses on the effect of temperature on the evolution of extended defects in uranium dioxide. In-situ transmission electron microscopy (TEM) annealing of proton irradiated UO2 was performed at different temperatures: 900 °C, 1100 °C and 1300 °C, 1 hour for each temperature. Microstructural evolution in terms of dislocation loops and voids were captured using in-situ TEM during annealing at different temperatures. Post-annealing at each temperature, detailed characterization using rel-rod dark field, bright field, and underfocus-overfocus imaging in TEM were used to identify faulted loops, perfect dislocation loops, and voids, respectively. Dislocation loops showed migration, disappearance, coalescence and loop-line interactions which significantly contributed to the recovery process during annealing at temperatures of 1100 °C and 1300 °C. Small voids were observed at 900 °C (diameter ∼ 0.5–1.5 nm) and grew rapidly during 1300 °C annealing (diameter ∼ 1–3 nm). Void growth was attributed to vacancy absorption, Ostwald ripening and void coalescence mechanisms. Extensive void growth was unique to in-situ TEM annealing due to free surface effect as ex-situ annealing confirmed negligible TEM resolvable (> 0.5 nm) voids at 1300 °C. The dislocation loops and voids behavior during in-situ TEM annealing were compared with rate theory and cluster dynamics predictions.

Characterization of irradiation-induced dislocation loops in Vanadium at 25-500 °C

Vanadium-based alloys have emerged as promising candidates for structural materials in fusion applications. However, as its base metal, the response of V to irradiation has received limited attention in prior studies. To gain a fundamental understanding of the irradiation damage in V, its microstructure evolution under 6 MeV Ti ion irradiation at 25–500 °C is investigated in the present study, with the focus on the detailed and comprehensive characterization of the behavior of the irradiation-introduced dislocation loops. Under room temperature irradiation, the “black dot” dislocation loops agglomerate linearly into rafts, during which their Burgers vectors are well aligned. With the temperature increases to 300 °C, the size of rafts increases and the density decreases, while the size of small loops maintains similar to the room temperature irradiation condition. As the irradiation temperature reaches 500 °C, the defects become highly mobile, resulting in the formation of extended dislocation loops or lines with hundreds of nanometers in size, with the rafts vanishing. All the observable loops under this irradiation temperature range exhibit the Burgers vectors of a/2 < 111>. All the loops observed in the displacement region are identified to be interstitial-type, while a small portion of loops observed in the diffusion region under elevated temperatures are vacancy-type.

The evolution of irradiation defects and hardening of CVD-SiC induced by He ions irradiation at 800°C

In this study, 500 keV He ions were used to irradiate CVD-SiC samples at 800 °C. The influence of doses on the microstructural evolution and hardness of the irradiated samples were investigated by TEM, Raman, and nanoindentation. TEM results show that He bubbles and dislocation loops appeared after irradiation, and their number densities increased with doses, resulting in the gradual decrease of the intensity of the TO peak in Raman spectra. Moreover, He platelets with strain field were observed in both stacking faults and matrixes. Nanoindentation results indicated that the irradiation hardening occurred, and the hardening degree was positively correlated with the irradiation dose.

The Influence of Grain Size on Microstructure Evolution in CeO2 under Xenon Ion Irradiation.

Large-grained UO2 is considered a potential accident-tolerant fuel (ATF) due to its superior fission gas retention capabilities. Irradiation experiments for cerium dioxide (CeO2), used as a surrogate fuel, is a common approach for evaluating the performance of UO2. In this work, spark plasma sintered CeO2 pellets with varying grain sizes (145 nm, 353 nm, and 101 μm) and a relative density greater than 93.83% were irradiated with 4 MeV Xe ions at a fluence of 2 × 1015 ions/cm2 at room temperature, followed by annealing at 600 °C for 3 h. Microstructure, including dislocation loops and bubble morphology of the irradiated samples, has been characterized. The average size of dislocation loops increases with increasing grain size. Large-sized dislocation loops are absent near the grain boundary because the boundary absorbs surrounding defects and prevents the dislocation loops from coalescing and expanding. The distribution of bubbles within the grain is uniform, whereas the large-sized and irregularly shaped xenon bubbles observed in the small grain exhibit pipe diffusion along the grain boundaries. The bubble diameter in the large-grained pellet is the smallest. As the grain size increases, the volumetric swelling of the irradiated pellets decreases while the areal density of Xe bubbles increases. Elemental segregation, which tends to occur at dislocation loops and grain boundaries, has been analyzed. Large-grained CeO2 pellet with lower-density grain boundaries exhibits better resistance to volumetric swelling and elemental segregation, suggesting that large-grained UO2 pellets could serve as a potential ATF.

Comparative analysis of irradiation-stimulated hardening in the austenite and ferrite phases of F321 stainless steel

F321 stainless steel is renowned for its outstanding mechanical properties and corrosion resistance, making it a crucial structural material in light water reactors and high-temperature gas reactors. With irradiation (IR), F321 stainless steel undergoes microstructural alterations, such as the formation of IR-stimulated defects (e.g., stacking fault tetrahedrons (SFTs), dislocation loops (DLs), and clusters), resulting in IR hardening. This study compares the IR-stimulated hardening in the austenitic and ferritic phases of F321 stainless steel through both experimental methods and numerical simulations. In the austenitic phase, the size and number density of IR defects (DLs and SFTs) were determined, which were proportional to the IR dose. In the ferritic phase, IR-induced DL parameters were quantified, and the effects of IR on spinodal decomposition were analyzed. The interaction processes and mechanisms between dislocations and IR defects in the austenitic phase were evaluated using molecular dynamics (MD) simulations, leading to the development of a model for IR defect-induced hardening strength. Additionally, an MD data-driven crystal-plasticity-finite-element-model (CPFEM) was established. The nano-indentation hardness of the austenitic and ferritic phases was measured and calculated through both experimental methods and CPFEM simulations. The results show that the nano-indentation hardness of the ferritic phase is reduced compared to the austenitic phase, due to a lower density of IR defects. Understanding these effects provides deeper insights into how IR influences the mechanical and microstructural properties of F321 steel, which is essential for predicting the material's long-term performance and reliability.

Synergistic effects of hydrogen and helium on dislocation loop rafting phenomena and hardening behavior of chromium

Dislocation loop rafts (DLRs), which are ordered arrangements of dislocation loops, are commonly observed in metals under neutron and heavy ion irradiation, yet they have seldom been observed under light ion irradiation. In this study, we reported the formation of DLRs under the synergistic effects of hydrogen and helium in a pure chromium (Cr) coating. Irradiation at room temperature with either single H+or He+ did not result in the formation of DLRs within the Cr coating. Approximately half of the dislocation loops induced by single H+ and He+ irradiation were of the a0〈100〉 type. Nevertheless, DLRs appeared under the combinational irradiation of H+and subsequent He+. The rafts were densely distributed, with lengths of up to 150 nm, and were exclusively composed of 1/2 a0 [11–1] variants along the 〈110〉 crystallographic direction. The emergence of DLRs, affected by the synergistic effect of H and He, results in an enhancement of irradiation hardening.

Enhancing strength and irradiation tolerance of Mg alloy via co-addition of Mn and Ca elements

The Mg alloys with combination of high strength and excellent irradiation resistance are currently required for research reactors. In this work, the novel Mg-3Mn-0.5Ca alloy with a high strength of over 300 MPa has been fabricated via co-addition of Mn and Ca elements. Moreover, the Xe ion implantation (300 °C/4.5 × 1015 ions/cm2) is conducted for pure Mg, Mg-3Mn and Mg-3Mn-0.5Ca alloys. Microstructure characterization shows that the number density of dislocation loops is comparable between Mg-3Mn and pure Mg, while the phase boundary of nano-Mn particles could act as the sink to absorb more Xe atoms, resulting in the abundant formation of Xe bubbles in the matrix of irradiated Mg-3Mn alloy. With further minor addition of Ca element, the formation of Xe bubbles and dislocation loops in Mg-3Mn-0.5Ca alloy has been obviously suppressed, and the abundant grain boundaries (GBs) due to grain refinement then act as the sink region for Xe precipitation. The limited number density of Xe bubbles leads to the extremely low swelling ratio in Mg-3Mn-0.5Ca alloy, ∼0.08 %. The result above suggests that the Mn and Ca co-addition could enhance the mechanical properties and irradiation tolerance of Mg alloys, simultaneously. The present low-alloying strategy would provide a new design reference for novel nuclear materials.