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Rotational transition, domain formation, dislocations, and defects in vortex systems with combined sixfold and twelvefold anisotropic interactions
We introduce a phenomenological model for a pairwise repulsive interaction potential of vortices in a type-II superconductor, consisting of superimposed sixfold and twelvefold anisotropies. Using numerical simulations we study how the vortex lattice configuration varies as the magnitudes of the two anisotropic interaction terms change. A triangular lattice appears for all values, and rotates through 30 ° as the ratio of the sixfold and twlevefold anisotropy amplitudes is varied, in agreement with experimental results. The transition causes the vortex lattice to split into domains that have rotated clockwise or counterclockwise, with grain boundaries that are “decorated” by dislocations consisting of fivefold and sevenfold coordinated vortices. We also find intradomain dislocations and defects, and characterize them in terms of their energy cost. We discuss how this model could be generalized to other particle-based systems with anisotropic interactions, such as colloids, and consider the limit of very large anisotropy where it is possible to create cluster crystal states.
In Situ TEM Tensile Testing of Bicrystals with Tailored Misorientation Angles
Grain boundaries have complex structural features that influence strength, ductility and fracture in metals and alloys. Grain boundary misorientation angle has been identified as a key parameter that controls their mechanical behavior, but the effect of misorientation angle has been challenging to isolate in polycrystalline materials. Here, we describe the use of bicrystal Au thin films made using a rapid melt growth process to study deformation at a single grain boundary. Tensile testing is performed on bicrystals with different misorientation angles using in situ TEM, as well as on a single crystalline sample. Plastic deformation is initiated through dislocation nucleation from free surfaces. Grain boundary sliding is not observed, and failure occurs away from the grain boundary through plastic collapse in all cases. The failure behavior in these nanoscale bicrystals does not appear to depend on the misorientation angle or grain boundary energy but instead has a more complex dependence on sample surface structure and dislocation activity.
Origin of dislocation structures in an additively manufactured austenitic stainless steel 316L
In this experiment, the origin of dislocation structures in AM stainless steels was systematically investigated by controlling the effect of thermal stress through geometric constraints for the first time. Stainless steel 316L parts were produced in the form of “1D” rods, “2D” walls, and "3D" rectangular prisms to evaluate the effect of constraints to thermal expansion/shrinkage on the development of defect microstructures and to elucidate the origin of additively manufactured (AM) dislocation microstructures. Dislocation density, organization, chemical micro-segregation, precipitate structures, and misorientations were analyzed as a function of increasing constraints around solidifying material in 1D, 2D, and 3D components built using both directed energy deposition (DED) and powder-bed selective laser melting (SLM). In DED parts, the dislocation density was not dependent on local misorientations or micro-segregation patterns, but evolved from approximately ρ ⊥ = 10 12 m -2 in 1D parts to ρ ⊥ = 10 14 m -2 in 3D parts, indicating that it is primarily thermal distortions that produce AM dislocation structures. In DED 3D parts and SLM parts, dislocation densities were highest (ρ ⊥ ≈ 10 14 m -2 ) and corresponded to the formation of dislocation cells approximately 300-450 nm in diameter. Dislocation cells overlapped with dendrite micro-segregation in some but not all cases. The results illustrate that dendritic micro-segregation, precipitates, or local misorientations influence how the dislocations organize during processing, but are not responsible for producing the organized cell structures. Furthermore, this work shows that AM dislocation structures originate due to thermal distortions during printing, which are primarily dictated by constraints surrounding the melt pool and thermal cycling.
Disclination-dislocation based model for grain boundary stress field evolution due to slip transmission history and influence on subsequent dislocation transmission
This work demonstrates how the structure of a grain boundary (GB) and its evolution due to slip transmission history influences subsequent dislocation transmission. First, a model for the evolution of stress fields within grain boundaries that accounts for the effects of coherent dislocation transmission is introduced. Starting with a disclination-based construct of GBs at minimum energy (equilibrium), the model describes the evolution of the GB stress field to a state characteristic of excess energy (non-equilibrium) due to the incorporation of residual Burgers vector content following sequential slip transmission events. Several essential features of this model are verified via molecular dynamics simulations of lattice dislocation absorption. Second, this model is implemented into a discrete dislocation dynamics (DDD) code and simulations are performed to understand the influence of Non-equilibrium GB stress fields, conditioned by the slip transmission history, on subsequent dislocation transmission. DDD simulations reveal that the critical resolved stress necessary for slip propagation can be reduced by with continued absorption of residual dislocation content. Moreover, DDD simulations prove that a comprehensive consideration of both the binding and driving stresses, and the evolution of the transmission configuration is necessary to quantify the influence of the mechanical state of the GB on slip propagation. In general, this work provides important insights into the role of GB structure evolution, conditioned by prior deformation history, on intergranular plasticity.
Machine Learning Vacancy Formation Energy in Nickel-Based Superalloys
Creep performance plays a key role in nickel-based superalloys for high temeprature applications. Creep behavior depends on many parameters such as strength, dislocations, diffusivity, and microstructural stability in addition to temeprature, applied stress, and oxidation. This work focuses on predicting vacancy formation energy in nickel-based superalloys using machine learning approach. High-throughput density functional theory (DFT) calculations are performed on Ni-based alloys with the addition of various alloying elements to predict the vacancy formation energy and vacancy concentration. Machine learning is performed using various models including graph neural networks.
High-Temperature Creep Behavior of Thin-Walled FeCrAl Alloy Tubes
This report summarizes measured creep properties for FeCrAl alloy C26M measured using subsized specimens machined from prototypic thin-walled tubes. A representative tube fabricated in a previous large batch production effort was machined into dual-gauge axial specimens using electrical-discharge machining. Creep tests, comprising strain-rate jump tests (SRJ), jump stress (JS) and constant-stress (CS) tests, were conducted at temperatures ranging from 600-900ºC to determine creep mechanisms (elucidated from stress exponents) and activation energies to compare with prior data available in the literature at temperatures up to 650ºC. It was found that the results from the SRJ tests indicated that the highest stress exponent of 5.8 occurred at 600ºC, which decreased to the lowest stress exponent of 2.5 at 700ºC. At higher temperatures, the stress exponents increased slightly to a range of 2.9 to 4.3 between 750ºC and 900ºC. The high stress exponent value of 5.8 suggested dislocation glide creep mechanisms dominated creep deformation at 600ºC since high stress values were measured. The low stress exponent of 2.5 at 700ºC suggested diffusional creep mechanisms start to occur that aid in dislocation cross-slip and climb mechanisms. The slightly higher stress exponents of 2.9 to 3.9 may suggest different contributions of creep deformation mechanisms based on diffusional processes associated with Nabarro-Herring and Coble creep and dislocation creep that involve thermally activated cross-slip and climb mechanisms. These deformation mechanisms could have also been affected by the development of recovery and/or recrystallization processes in the microstructure of the C26M2 specimens. From the SJ and single CS tests, two sets of creep activation energies were calculated. The steady state creep values obtained from the SJ tests showed several abnormalities especially with the data at 850ºC. The comparison of the creep activation energies between the data from the SJ and CS tests showed higher creep rates for the SJ tests than the CS tests, indicating microstructure softening occurred in the C26M2 specimens during the SJ tests that led to the higher creep rates at stresses above the initial stress of 10 MPa. For the CS tests, the results showed steady increases in MCR with increasing temperature at each stress. The best linear fit to the MCR values at each stress was with data obtained at 800ºC, 850ºC and 900ºC. The lowest Q c value of 130.8 KJ/mole was observed with the highest stress of 25 MPa. As stress was lowered, the Q c values increased continuously to the highest value of 188.2 KJ/mole at 10 MPa. This trend suggests that the dominant creep mechanism is diffusional based dislocation climb since the decreasing activation energies with increasing stress promotes easier dislocation climb around obstacles. The comparison between the SJ and CS tests indicates that the best type of creep test performed on FeCrAl alloys such as C26M2 is the single CS test.
Bicrystallography-informed Frenkel–Kontorova model for interlayer dislocations in strained 2D heterostructures
In recent years, van der Waals (vdW) heterostructures and homostructures, which consist of stacks of two-dimensional (2D) materials, have risen to prominence due to their association with exotic quantum phenomena originating from correlated electronic states harbored by them. Atomistic scale relaxation effects play an extremely important role in the electronic scale quantum physics of these systems, providing means of manipulation of these materials and allowing them to be tailored for emergent technologies. We investigate such structural relaxation effects in this work using atomistic and mesoscale models, within the context of twisted bilayer graphene — a well-known heterostructure system that features moiré patterns arising from the lattices of the two graphene layers. For small twist angles, atomic relaxation effects in this system are associated with the natural emergence of interface dislocations or strain solitons, which result from the cyclic nature of the generalized stacking fault energy (GSFE), that measures the interface energy based on the relative movement of the two layers. Here, in this work, we first demonstrate using atomistic simulations that atomic reconstruction in bilayer graphene under a large twist also results from interface dislocations, although the Burgers vectors of such dislocations are considerably smaller than those observed in small-twist systems. To reveal the translational invariance of the heterointerface responsible for the formation of such dislocations, we derive the translational symmetry of the GSFE of a 2D heterostructure using the notions of coincident site lattices (CSLs) and displacement shift complete lattices (DSCLs). The workhorse for this exercise is a recently developed Smith normal form bicrystallography framework. Next, we construct a bicrystallography-informed and frame-invariant Frenkel–Kontorova model, which can predict the formation of strain solitons in arbitrary 2D heterostructures, and apply it to study a heterostrained, large-twist bilayer graphene system. Our mesoscale model is found to produce results consistent with atomistic simulations. We anticipate that the model will be invaluable in predicting structural relaxation and for providing insights into various heterostructure systems, especially in cases where the fundamental unit cell is large and therefore, atomistic simulations are computationally expensive.
Helical dislocation in twisted bilayer graphene
Here, we observe helical dislocation network in twisted bilayer graphene (tBLG), which is accompanied by large out-of-plane deformation. By atomistic calculations, we demonstrate two distinct out-of-plane deformation modes, breathing mode with small out-of-plane deformation and bending mode with one order larger corrugation magnitude compared to the breathing mode. The out-of-plane deformation is caused by inhomogeneous interlayer coupling resulting from the periodic stacking order of the tBLG moiré superlattice. Instead of commonly observed screw dislocation in tBLG, we demonstrate a slip-induced helical dislocation network in the bending mode tBLG. We show that bending mode deformation is more stable at low twist angles, as the energy savings due to interface energy exceeds the energy penalty due to the strain energy caused by the large out-of-plane deformation. Our work provides a detailed picture of a new helical dislocation structure in tBLG and establishes a direct connection between the dislocation and deformation. Therefore, understanding the dislocation mechanics of tBLG may open up the possibility to control the corrugation, and reveal an opportunity to tune the intriguing physical properties of twisted bilayer graphene.
An energetic link between order and strength in metals: A nanocrystalline strength limit in high-entropy alloys and intermetallic compounds
The metallurgy and materials communities have long understood and exploited fundamental links between chemical and structural ordering in metallic solids to tailor their mechanical properties. We extend these ideas to include prediction of the nanocrystalline strength limit in high-entropy alloys and intermetallic compounds, where a breakdown occurs in the classical Hall-Petch strengthening behavior. The highest reported strength achievable through alloying has rapidly climbed and given rise to new classifications of materials with extraordinary properties, with a notable case being nanocrystalline metals. High-entropy alloys (chemically disordered, concentrated solid solutions) and intermetallic compounds are two boundary cases of how tailored order can be used to manipulate mechanical behavior. Here, we show that the complex electronic-structure mechanisms governing the peak strength of alloys and pure metals can be reduced to a few physically meaningful parameters based on their atomic arrangements and used – with no fitting parameters – to predict the maximum strength of these materials. This includes a generalized energy-based accounting for the degree of structural and chemical ordering that allows for rapid and reasonably accurate prediction of peak strength (validated in the nanocrystalline limit) as a function of temperature. Predictions of maximum strength based on the activation energy (with all materials properties derived from DFT calculations or experiments) for a stress-driven transition to an amorphous state is shown to accurately describe the breakdown in Hall-Petch behavior at the smallest crystallite sizes for pure metals, intermetallic compounds, high-entropy alloys, and metallic glasses. Further, this activation energy is also shown to be directly proportional to interstitial electronic charge density, which is a good predictor of ductility, stiffness (moduli), and phase stability in high-entropy alloys and solid metals generally. The proposed framework suggests the possibility of coupling ordering and intrinsic strength to mechanisms like dislocation nucleation, hydrogen embrittlement, and transport properties, such as through correlations between the activation energies for amorphization with stacking-fault and grain boundary energies. It additionally opens the prospect for greatly accelerated structural materials design and development to address materials challenges limiting more sustainable and efficient use of energy.
Impact of Irradiation on Microstructure and Mechanical Properties of Materials Produced by Advanced Manufacturing
Advanced non-light water reactor designs, known as Generation IV (Gen IV) reactors, typically operate at higher temperatures and under more extreme radiation conditions than conventional light water reactors. A critical aspect of the successful deployment and advancement of Gen IV reactor designs is the selection of appropriate structural materials for specific applications, which necessitates the timely development of new materials and manufacturing processes. Advanced manufacturing (AM) offers numerous opportunities for innovative designs, enabling the production of high-performance components with potentially shorter development cycles compared to traditional manufacturing methods. However, a significant challenge in deploying AM technologies in the nuclear energy sector is the current lack of data on the irradiation performance of AM-produced components. This presentation will discuss neutron and ion irradiation results of AM materials, including stainless steel 316L, Grade 91, SA508, Inconel 718, and Inconel 625 materials. The materials were manufactured by AM, such as Powder Metallurgy Hot Isostatic Pressing (PM HIP), Laser Powder Bed Fusion (LPBF) and Directed Energy Deposition (DED). The effects of neutron irradiation on microstructure (e.g., dislocations, loops, and nanoclusters), tensile properties (e.g., strength and ductility), and ion irradiation on Irradiation-Assisted Stress Corrosion Cracking (IASCC) will be explored. Results are collected from several projects supported by the Nuclear Science User Facilities (NSUF) program.
Nucleation of Grain Boundary Phases
Here, we derive a theory that describes homogeneous nucleation of grain boundary (GB) phases. Our analysis takes account of the energy resulting from the GB phase junction, the line defect separating two different GB structures, which is necessarily a dislocation as well as an elastic line force due to the jump in GB stresses. The theory provides analytic forms for the elastic interactions and the core energy of the GB phase junction that, along with the change in GB energy, determines the nucleation barrier. We apply the resulting nucleation model to simulations of GB phase transformations in tungsten. Our theory explains why under certain conditions GBs cannot spontaneously change their structure even to a lower energy state.
A data driven approach for cross-slip modelling in continuum dislocation dynamics
Cross-slip is a thermally activated process by which screw dislocation changes its glide plane to another slip plane sharing the same Burgers vector. The rate at which this process happens is determined by a Boltzmann type expression that is a function of the screw segment length and the stress acting on the dislocation. In continuum dislocation dynamics (CDD), the information regarding the length of the screw dislocation segment and local stress state on dislocations are lost due to the coarse-grained representation of the density. Here, in this work, a data driven approach to characterize the lost information by analyzing the discrete dislocation configurations is proposed to enable cross-slip modeling in the CDD framework in terms of the coarse-grained dislocation density and stress fields. The analysis showed that the screw segment length follows an exponential distribution, and the stress fluctuations, defined as the difference between the stress on the dislocations and the mean field stress in CDD, follows a Lorentzian distribution. A novel approach for cross slip implementation in CDD employing the screw segment length and stress fluctuation statistics was proposed and rigorously tested by comparing the CDD cross-slip rates with discrete dislocation dynamics (DDD) rates. This approach has been applied in conjunction with three cross-slip models used in DDD simulations differing mainly in the functional form of cross slip activation energy. It was found that different cross-slip activation energy formulations yielded different cross-slip rates, yet the effect on mechanical stress-strain response and dislocation density evolution was minimal for the [001] type loading.
Prismatic-to-basal plastic slip transition in zirconium
Here, we model three-dimensional dislocation ensembles in Zr pillars using newly developed mobility laws for dislocations on prismatic and basal planes. The effects of the loading orientation and temperature on the micro-scale mechanical response of single crystals are systematically explored. Easy dislocation glide is observed on prismatic planes, while hard glide occurs on basal planes. By selection of sample temperature and loading orientation, we show that the transition from prismatic to basal glide of dislocation ensembles can be controlled. We also show that the presence of dislocation cross-slip strongly promotes prismatic glide as a result of prismatic/basal cross-slip energy asymmetry. Cross-slip does not alter the occurrence of plastic slip transition but only induces a shift towards higher temperatures. The preponderance of plastic slip on basal or prismatic planes is found to be mediated by a transitional dislocation, which is composed of glissile segments on parallel prismatic planes connected by glissile super-jogs on basal planes. These findings provide a mechanistic understanding of experiments and highlight the significance of transitional prismatic-basal dislocations on the macroscopic characteristics of plasticity in HCP crystals.
Mesoscale Investigation of Dislocation-Grain Boundary Interactions in Metals and Alloys [Slides]
GBs have been subject of intense study for several years, including the effects of microstructure on mechanical response. Until recently these have been primarily focused on a limited number of idealized GB structures (i.e, the minimum energy structure). We are specifically focusing on changes in local GB structure and the effect this has on dislocation-grain boundary interactions. This will help us to better understand both (more) realistic and general GB structures.
Effect of grain structure and strain rate on dynamic recrystallization and deformation behavior: A phase field-crystal plasticity model
Herein, a phase field (PF)-crystal plasticity (CP) model has been developed to study the effects of initial grain structures, recrystallized grain orientation, and strain rates on dynamic recrystallization and deformation behavior under stress states typical of the Shear Assisted Processing and Extrusion (ShAPE) process. The model takes the geometrically necessary dislocation density as the nucleation criterion for recrystallization and minimizes the deformation energy as the driving force of recrystallized grain growth. Using this model, the effects of grain orientations and strain rates on dynamic recrystallization and deformation behavior were simulated. The results demonstrate that (1) a polycrystalline structure with the texture observed in ShAPE process has the lowest yield stress under the ShAPE stress conditions, (2) the recrystallized grains with the texture observed in ShAPE process largely soften the materials, and (3) higher shear strain rate or rotation speed results in larger magnitude of material softening.
High-resolution planar electron beam induced current in bulk diodes using high-energy electrons
Understanding the impact of high-energy electron radiation on device characteristics remains critical for the expanding use of semiconductor electronics in space-borne applications and other radiation harsh environments. Here in this paper, we report on in situ measurements of high-energy electron radiation effects on the hole diffusion length in low threading dislocation density homoepitaxial bulk n-GaN Schottky diodes using electron beam induced current (EBIC) in high-voltage scanning electron microscopy mode. Despite the large interaction volume in this system, quantitative EBIC imaging is possible due to the sustained collimation of the incident electron beam. This approach enables direct measurement of electron radiation effects without having to thin the specimen. Using a combination of experimental EBIC measurements and Monte Carlo simulations of electron trajectories, we determine a hole diffusion length of 264 ± 11 nm for n-GaN. Irradiation with 200 kV electron beam with an accumulated dose of 24 × 10 16 electrons cm -2 led to an approximate 35% decrease in the minority carrier diffusion length.
Atomistic determination of Peierls barriers of dislocation glide in nickel
The Peierls barrier measures the lattice resistance to dislocation glide in crystalline solids. We use the nudged elastic band (NEB) method to calculate the Peierls barriers for screw and edge dislocation glide in a face-centered cubic (FCC) metal of Ni. The minimum energy paths (MEPs) across single or sequential Peierls barriers are determined under shear loading. The NEB results show the decreasing Peierls barrier with increasing shear stress, giving the Peierls stress at which the Peierls barrier vanishes. The effects of boundary condition and system size on Peierls barriers are studied by comparing strain- and stress-controlled NEB results. Furthermore, the free-end NEB methods are applied to determine MEPs with improved computational efficiency. The NEB results are also used to evaluate the energetic driving force of dislocation glide, which is consistent with that determined from the Peach-Koehler force. The accuracy of the present NEB results based on an empirical interatomic potential is assessed by comparison with a machine-learning potential. This work demonstrates the robust and efficient quantification of Peierls barriers to dislocation glide in an FCC metal, and it lays a solid foundation for the atomistic determination of Peierls barriers in compositionally complex alloys with the FCC structure in future studies.