Line-integral representations for extended displacements, stresses,and interaction energy of arbitrary dislocation loops in transversely isotropic magneto-electro-elastic bimaterials

In addition to the hexagonal crystals of class 6 mm, many piezoelectric materials （e.g., BaTiO3）, piezomagnetic materials （e.g., CoFe2O4）, and multiferroic com-posite materials （e.g., BaTiO3-CoFe2O4 composites） also exhibit symmetry of transverse isotropy after poling, with the isotropic plane perpendicular to the poling direction. In this paper, simple and elegant line-integral expressions are derived for extended displace-ments, extended stresses, self-energy, and interaction energy of arbitrarily shaped, three-dimensional （3D） dislocation loops with a constant extended Burgers vector in trans-versely isotropic magneto-electro-elastic （MEE） bimaterials （i.e., joined half-spaces）. The derived solutions can also be simply reduced to those expressions for piezoelectric, piezo-magnetic, or purely elastic materials. Several numerical examples are given to show both the multi-field coupling effect and the interface/surface effect in transversely isotropic MEE materials.

The Strain/Stress Fields of a Subsurface Rectangular Dislocation Loop Parallel to the Surface of a Half Medium: Analytical Solution with Verification

The strain and stress fields of a rectangular dislocation loop in an isotropic solid that is a semi-infinite medium (half medium) are developed here for a Volterra-type dislocation. Specifically, the loop is parallel to the free surface of the solid. The elastic fields of the dislocation loop are developed by integrating the displacement equation of infinitesimals dislocation loops over a finite rectangular loop area below the free surface. The strains and stress then follow from the small strain tensor and Hooke’s law for isotropic materials, respectively. In this paper, analytical verification and numerical verification for the elastic fields are both demonstrated. Equilibrium equations and strain compatibility equations are applied in the verification. Also, a comparison with a newly-developed numerical method for dislocations near a free surface is performed as well. The developed solution is a function of the loop depth beneath the surface and can be used as a fundamental solution to solve elasticity, plasticity or dislocation problems.

Effect of dose rate on the characteristics of dislocation loops in palladium:In-situ TEM analysis during 30 keV H_(2)^(+)irradiation

Ion irradiation is usually used to simulate neutron irradiation to accelerate the evaluation of the irradia-tion behavior of reactor materials.However,the validity of using a high damage rate of ion irradiation to simulate a low damage rate of neutron irradiation has always been a controversial topic.Here,the effect of two dose rates(2.94×10^(-6) and 7.35×10^(-5) dpa s^(-1))on the characteristics and evolution of dislo-cation loops in palladium was studied in situ during 30 keV H2+irradiation using transmission electron microscopy.The dose rate obviously affected the nucleation rate and growth rate of dislocation loops,the types(Frank loops or perfect loops)of dislocation loops,and the irradiation hardening and total damage obtained from the product of average loop size and loop density.At the same irradiation dose,a high dose rate would lead to high loop density,small average loop size,low loop growth rate,and low irra-diation hardening and damage induced by loops in pure Pd.Meanwhile,it was found for the first time that a high dose rate was beneficial to the generation of perfect dislocation loops.The effect of dose rate was attributed to the different dynamic equilibrium results between the effective generation rate of point defects and their absorption rate by existing sinks.The present results show that the effect of dose rate should be considered when using ion irradiation to simulate neutron irradiation to evaluate the irradiation damage to materials.

In-situ TEM investigation on the evolution of He bubbles and dislocation loops in Ni-based alloy irradiated by H_(2)^(+)&He^(+)dual-beam ions

The synergistic evolution mechanisms of He bubbles and dislocation loops under 30 keV H_(2)^(+)&He^(+)dual-beam ions irradiation at 650℃ in the Ni-based alloy GH3535,which is the most promising candidate structure material for molten salt reactors(MSRs),were revealed via in-situ TEM.The nucleation,merg-ing,and change in the size of the dislocation loops and He bubbles were characterized in detail to study the influences of irradiation fluence and pre-existing dislocation loops on their evolutions.The number density of both the He bubbles and dislocation loops increases rapidly and subsequently saturates,whereas their size continuously increases with the increasing ion fluence.Pre-existing dislocation loops with strong absorption characteristics grow preferentially and suppress the nucleation of dislocation loops during the dual-beam ions irradiation.Moreover,the bubbles tend to nucleate within the dislocation loops to form bubble-loop complexes,and then decrease in their number density.The details of the un-faulting processes of the Frank loops were discussed,where the energy difference between the two types of loops as well as the evolution of the inside Shockley dislocation loops dominates the unfaulting be-havior.The several evolution stages of the loop-punching mechanism are revealed,and the emitted loops can directly form perfect loops as well as unfault the neighboring Frank loops.The He bubbles inside the loops provide corresponding stress for the formation of rhombic loops,which can achieve rapid growth and sweep ability by merging with the neighboring loops.Additionally,its dissociation to Shockley dis-location can unfault the Frank loops along their slip direction.Among the four Frank loop variations,the edge-on Frank loop variations have the highest growth rate,followed by the perfect loop.The related mechanisms based on in-situ experimental observation are discussed in depth.

In-situ TEM observation of the evolution of helium bubbles & dislocation loops and their interaction in Pd during He^(+) irradiation

The microstructural evolution of purity Pd under 30 keV He^(+)irradiation at 573 K was investigated by in-situ transmission electron microscopy.The nucleation,growth,merging,annihilation,size change,number density variation,and types of dislocation loops were analyzed under the influence of irradiation fluence and sample thickness.Both perfect dislocation loops with b=1/2<110>and faulted dislocation loops with b=1/3<111>were formed.However,at low irradiation fluence,most of the loops were 1/3<111>loops.The thickness of TEM foil obviously affected the ratio of 1/3<111>loop variants,the size and number density of dislocation loops,and the characteristics of bubble-loop complexes.With the increase of irradiation fluence,the size of dislocation loops increased,but loop volume number density remained almost constant until dislocation loops merged and evolved into dislocation network.There was an obvious interaction between dislocation loops and bubbles,indicating that 1/3<111>loop was first formed at the initial stage of irradiation,and when the loop grew to a certain size,obvious helium bubbles appeared inside its region.

Evolution of Dislocation Loops in AL-6XN Stainless Steels Irradiated by Hydrogen Ions

AL-6XN stainless steels, one of the candidate structure materials for supercritical water-cooled reactor, were irradiated from 0.5 to 5 dpa using 100 keV H2＋ ions at 290 and 380 ℃. Microstructures were characterized by transmission electron microscopy （TEM）. Dislocation loops were the dominant radiation-induced defects. All the dislocation loops had 1/3 〈111〉 type Burgers vector. Number density and size of the loops have been measured. Nucleation and evolution of dislocation loops were also investigated. Voids were observed only in the condition of 5 dpa at 380 ℃. Different evolution mechanisms of the radiation-induced dislocation loops were discussed. Effects of hydrogen and elevated temperature on the microstructural evolution were also investigated. Besides, the formed voids have a further effect on the evolution of dislocation loops.

In-situ TEM investigation of dislocation loop reaction and irradiation hardening in H_(2)^(+)-He^(+) dual-beam irradiated Mo

Through in-situ TEM observation during 30 keV H_(2)^(+)-He^(+) dual-beam irradiation at 723 K,the reaction and transformation of dislocation loops in pure Mo were investigated,especially for<100>loops.Irradiation could directly cause the formation of 1/2<111>loops and<100>loops,but 1/2<111>loops were dominant.In-situ observation confirmed the formation mechanism of<100>loops,including direct irradiation induced mechanism,1/2<111>loop direct conversion mechanism,and reaction mechanism of two 1/2<111>loops.Meanwhile,the reaction of two 1/2<111>loops to produce<100>loop should not require the strict size similarity condition.The reaction between 1/2<111>loops could also produce 1/2<111>loop,which was essentially a process in which one loop absorbed another one.The yield strength increment caused by irradiation-induced loops was analyzed,and its saturation value reached0.48 GPa at 0.06 dpa.Compared with single He+irradiation,the number density and average diameter of loops increased significantly and more serious damage was caused under the synergistic effect of hydrogen and helium.The mechanism based on in-situ experimental observation was discussed in depth.

Anisotropic interaction between self-interstitial atoms and 1/2<111> dislocation loops in tungsten

We investigate the interaction between <111> self-interstitial atoms(SIAs) and 1/2<111> self-interstitial dislocation loops in tungsten(W) via atomistic simulations. We explore the variation of the anisotropic distribution of binding energies with the shapes and sizes of the 1/2[111] loop and the nonequivalent configurations of <111> SIAs. For an arbitrarily shaped loop, SIA can be more easily trapped in the concave region of the loop than the convex region, which forms a loop whose curvature is closer to that of a circular loop. The direction of SIAs can largely affect the interaction behaviors with the loop. The capture distance of an SIA by the edge of a circular-shaped 1/2[111] loop is clearly elongated along the direction of the SIA;however, it weakly depends on the size of the loop. Then, we analyze the slanted ring-like capture volume of <111> SIAs formed by the circular loop based on their generated anisotropic stress fields. Furthermore, the binding energies obtained from the elastic theory and atomistic simulations are compared. The results provide a reasonable interpretation of the growth mechanism of the loop and the anisotropic interaction that induces irregular-shaped capture volume, affording an insight into the numerical and Object Kinetic Monte Carlo simulations to evaluate the long-term and large-scale microstructural evolution and mechanical properties of W.

Efficient and Reliable Nanoindentation Simulation by Dislocation Loop Erasing Method

Nanoindentation is a useful technique to measure material properties at microscopic level.However,the intrinsically multiscale nature makes it challenging for large-scale simulations to be carried out.It is shown that in molecular statics simulations of nanoindentation,the separated dislocation loops(SDLs)are trapped in simulation box which detrimentally affects the plastic behavior in the plastic zone(PZ);and the long-distance propagation of SDLs consumes much computational cost yet with little contribution to the variation of tip force.To tackle the problem,the dislocation loop erasing(DLE)method is proposed in the work to alleviate the influence of artificial boundary conditions on the SDL–PZ interaction and improve simulation efficiency.Simulation results indicate that the force–depth curves obtained from simulations with and without DLE are consistent with each other,while the method with DLE yields more reasonable results of microstructural evolution and shows better efficiency.The new method provides an alternative approach for large-scale molecular simulation of nanoindentation with reliable results and higher efficiency and also sheds lights on improving existing multiscale methods.

Transmission electron microscopy characterization of dislocation loops in irradiated zirconium

Characterization of irradiation defects is of great importanceto mitigate irradiation damage,reduce irradiation growth and tune mechanical properties in Zr alloys.Here,we describe a practical method to characterize the dislocation loops in irradiated Zr using conventional transmission electron microscopy(TEM).Vacancy or interstitial nature of dislocation loops is determined using the inside and outside contrast method.The habit plane of dislocation loops is determined by tilting the sample to multiple zone axes and judged based on the projected loop shape.The size ofloops is measured by tilting the sample to an edge-on position and the loop number is counted under a weak-beam dark-field TEM condition.<c>loops have a line contrast under viewing direction of a-axis and a circular shape under viewing direction of c-axis.In addition,a large number of triangle-shaped vacancy platelets(TVPs)were formed on the basal plane.With increasing the irradiation damage from 0.5 to 1.5 dpa,the number density ofloops keeps constant,while the number density of TVPs increased significantly,owing to the anisotropic diffusion and accumulation of point defects within basal plane.The methods introduced here are easy to follow and extend into other related investigations.

Correlation between the Cyclic Stress Behavior and Microstructure in 316LN based on the Analysis of Hysteresis Loops

Total strain controlled cyclic test was performed on 316 LN under uniaxial loadings. Through the partitioning of hysteresis loops, the evolution of two components of cyclic flow stress, the internal and effective stresses, was reported. The former one determines the cyclic stress response. Based on the transmission electron microscopic（TEM） observation on specimens loaded with scheduled cycles, it is found that planar dislocation structures prevail during the entire cyclic process at low strain amplitude, while a remarkable dislocation rearrangement from planar structures to heterogeneous spatial distributions is companied by a cyclic softening behavior at high strain amplitude. The competition between the evolution of the intergranular and the intragranular components of the internal stress caused by the transition of slip mode induces the cyclic hardening and softening at high strain levels. The intergranular internal stress represents the most part of the internal stress at low strain level.

Spherical nanoindentation stress–strain responses of SIMP steel to synergistic effects of irradiation by H and He ions

A novel Fe-10Cr ferritic/martensitic steel called SIMP was chosen to investigate synergistic effects of H and He on the mechanical properties of structural materials for innovative nuclear energy systems. Sequential and separate irradiation experiments on SIMP steel specimens at room temperature using H and He ions with various energy levels were conducted to produce an ion deposition plateau at 300-650 nm. The indentation stress-strain responses were examined using spherical nanoindentation tests after the irradiation experiments. It was found that the sequential irradiation by He and H produced a higher indentation yield stress than separate irradiation, indicating that the hardening was enhanced by the synergy of the H and He irradiation. The micro-mechanism responsible for enhancing the hardening of the SIMP steel through the H and He synergy was investigated using Doppler broadening spectroscopy detection and transmission electron spectroscopy observations.

Boron implanted emitter for n-type silicon solar cell

The effects of ion doses on the properties of boron implanted Si for n-type solar cell application were investigated with doses ranging from 5×10^14cm^-2 to 2×10^15cm^-2 and a subsequent two-step annealing process in a tube furnace.With the help of the TCAD process simulation tool, knowledge on diffusion kinetics of dopants and damage evolution was obtained by fitting SIMS measured boron profiles. Due to insufficient elimination of the residual damage, the implanted emitter was found to have a higher saturation current density（J0e） and a poorer crystallographic quality. Consistent with this observation, V oc, J sc, and the efficiency of the all-implanted p^＋–n–n^＋solar cells followed a decreasing trend with an increase of the implantation dose. The obtained maximum efficiency was 19.59% at a low dose of 5×10^14cm^-2. The main efficiency loss under high doses came not only from increased recombination of carriers in the space charge region revealed by double-diode parameters of dark I–V curves, but also from the degraded minority carrier diffusion length in the emitter and base evidenced by IQE data. These experimental results indicated that clusters and dislocation loops had appeared at high implantation doses, which acted as effective recombination centers for photogenerated carriers.

Achieving high strength and ductility in high-entropy alloys via spinodal decomposition-induced compositional heterogeneity

The compositional heterogeneity in high-entropy alloys(HEAs)has been reported to be an inherent en-tity,which significantly alters the mechanical properties of materials by tuning the variation of lattice resistance for dislocation motion.However,since the body-centered cubic(BCC)structure is not close-packed,the change of lattice resistance is less sensitive to the normal concentration wave compared to that in face-centered cubic(FCC)structured materials.In this work,we selected a refractory bcc HEAs TiZrNbTa for the matrix and added a small amount of Al to facilitate the special spinodal decomposition structure.In particular,(TiZrNbTa)98.5 Al 1.5 displayed a typical basket-weave fabric morphology of spinodal decomposition structure with a characteristic periodicity of∼8 nm and had an optimal combination of strength and ductility(the yield strength of 1123±9 MPa and ductility of∼20.7%±0.6%).It was de-termined that by doing in situ TEM mechanical testing,the plastic deformation was dominated by the formation and operation of dislocation loops which provided both edge and screw components of dislo-cations.The synergetic effect of the remarkable chemical heterogeneity created by the spinodal decompo-sition and the spreading lattice distortion in high entropy alloys is quite effective in tuning the mobility of different types of dislocations and facilitates dislocation interactions,enabling the combination of high strength and ductility.

Effect of Post-irradiation Annealing on Microstructure Evolution and Hardening in GH3535 Alloy Irradiated by Au Ions

The Au ion-irradiation experiments of GH3535 alloy,a candidate alloy structural material for molten salt reactor,was carried out in this study.Herein,isochronous annealing experiments were conducted from 200 to 850 ℃ to clarify the evolution behavior of damage defects with increasing temperature.The coarsening of dislocation loops and formation and dissolution of precipitates with increasing annealing temperature were characterized by transmission electron microscopy.Nanoindentation was performed to measure the variation of hardness caused by irradiation.Additionally,the relationship between irradiation hardening and microstructure evolution was established.This study lays a foundation for the evaluation of irradiation damage properties of GH3535 alloy at different annealing temperatures.

Effect of niobium content on irradiation microstructure and hardening in FeCrAl-based alloys

Iron-chromium-aluminum(FeCrAl)alloys with different content of niobium(Nb)—0,0.4 wt%,0.8 wt%,and 1.2 wt%—were designed and prepared.All samples were then irradiated with 2.4 MeV Fe^(2+)ion to the dose of 1 and 15 displacements per atom(dpa)at 400℃.The formations of dislocation loops induced by self-ion irradiation in these alloys were investigated by transmission electron microscopy(TEM).Nano-indentation tests were used to assess the hardness and irradiation hardening of samples.For the samples before irradiation,the(Fe,Cr)_(2)(Nb,Mo)Laves phases density and the nano-indentation hardness increased with increasing Nb content of the samples.After irradiation to 1 and 15 dpa,both of a/2<111>and a<100>dislocation loops were produced but no voids orα’phase were found in all samples.With increasing Nb content of the samples,the size of dislocation loops increased first and then decreased,while the total volume number density decreased and then increased.The fraction of a<100>dislocation loops increased first and then decreased with increasing Nb content,and increased with increasing irradiation dose.Dislocation networks and the amorphization of the Laves phases were observed in the samples with irradiation dose of 15 dpa.Irradiation hardening of Nb free samples was two to four times that of Nb containing samples,and the irradiation hardening increased with increasing Nb content of Nb containing samples.The experimental results indicate that the increase of Nb content in Fe Cr Al alloys can increase the density of Laves phases,leading to the decrease of Mo content and increase of Cr content in the matrix.The competition between the two types of solutes affects the nucleation and growth of the dislocation loops.

In-situ study of initiation and extension of nano-thick defect-free channels in irradiated nickel

Radiation defects-induced plastic flow localization is the origin of loss of ductility in irradiated metals.Defect-free channels(DFCs)are a typical form of strain localization that lead to crack initiation and premature failure.A comprehensive understanding of the DFC dynamics is key to managing radiation boosted property degradation.Despite great research efforts,a clear mechanism of DFC remains unknown.Here,our in-situ tests on irradiated Ni pillars provide a real-time observation of the dynamics of DFCs,including DFC initiation,extension and thickening.The merging and spreading of dislocation loops serve as an alternative mechanism of dislocation sources that emit massive dislocations and initiate nano-thick DFCs inside the grain.Nano-thick DFCs were formed through chopping up or sweeping away of loops by mobile dislocations.Annihilation of opposite loops and interactions between loops and vacancies accelerate DFC extension.Activation of multiple dislocation sources and dislocation cross-slips are the mechanisms for DFC thickening.