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Cluster dynamics modeling of Mn-Ni-Si precipitates coupled with radiation-induced segregation in low-Cu reactor pressure vessel steels
Formation of precipitates enhanced or induced by irradiation causes hardening and embrittlement of nuclear structural materials. Post-irradiation microstructure characterization of reactor pressure vessel (RPV) steels has shown that precipitation can be strongly associated with radiation-induced segregation (RIS) of solutes on dislocations. However, RIS and precipitation have not been coupled in previous precipitation modeling of RPV steels. Here in this study, a new hybrid and spatially-dependent precipitation model is developed that couples cluster dynamics with RIS, providing an unique way to account for concurrent evolution of heterogeneous cluster densities as well as solute and point defect concentration profiles. The model is applied to study the segregation of Mn, Ni, and Si on dislocations and heterogeneous nucleation of Mn-Ni-Si rich precipitates (MNSPs) in a low-Cu RPV steel. The result shows that the onset of MNSP nucleation on dislocations occurs at the fluence of 2 x 10 23 n.m -2 . The number density and mean radius can reach ~ 10 24 m -3 and 1-2 nm at high fluence, respectively. These observations suggest that the role of RIS and heterogeneous nucleation can be significant for RPV steels under a high fluence of irradiation. Results of simulations adopting various dose rates and dislocation densities show an increased fraction of MNSPs on dislocations at the condition of low dose rate, high dislocation density, and high fluence.
Molecular-Dynamics Analysis of the Mechanical Behavior of Plasma-Facing Tungsten
We report a systematic computational analysis of the mechanical behavior of plasma-facing component (PFC) tungsten focusing on the impact of void and helium (He) bubble defects on the mechanical response beyond the elastic regime. Specifically, we explore the effects of porosity and He atomic fraction on the mechanical properties and structural response of PFC tungsten, at varying temperature and bubble size. We find that the Young modulus of defective tungsten undergoes substantial softening that follows an exponential scaling relation as a function of matrix porosity and He atomic content. Beyond the elastic regime, our high strain rate simulations reveal that the presence of nanoscale spherical defects (empty voids and He bubbles) reduces the yield strength of tungsten in a monotonically decreasing fashion, obeying an exponential scaling relation as a function of tungsten matrix porosity and He concentration. Our detailed analysis of the structural response of PFC tungsten near the yield point reveals that yielding is initiated by emission of dislocation loops from bubble/matrix interfaces, mainly 1/2<111> shear loops, followed by gliding and growth of these loops and reactions to form <100> dislocations. Furthermore, dislocation gliding on the <111>{211} twin systems nucleates 1/6<111> twin regions in the tungsten matrix. These dynamical processes reduce the stress in the matrix substantially. Subsequent dislocation interactions and depletion of the twin phases via nucleation and propagation of detwinning partials lead the tungsten matrix to a next deformation stage characterized by stress increase during applied straining. Furthermore, our structural analysis reveals that the depletion of twin boundaries (areal defects) is strongly impacted by the density of He bubbles at higher porosities. After the initial stress relief upon yielding, increase in the dislocation density in conjunction with decrease in the areal defect density facilitates the initiation of dislocation-driven deformation mechanisms in the PFC crystal.
Probing the limits of metal plasticity with molecular dynamics simulations
Ordinarily, the strength and plasticity properties of a metal are defined by dislocations—line defects in the crystal lattice whose motion results in material slippage along lattice planes. Dislocation dynamics models are usually used as mesoscale proxies for true atomistic dynamics, which are computationally expensive to perform routinely. However, atomistic simulations accurately capture every possible mechanism of material response, resolving every “jiggle and wiggle” of atomic motion, whereas dislocation dynamics models do not. We present fully dynamic atomistic simulations of bulk single-crystal plasticity in the body-centred-cubic metal tantalum. Our goal is to quantify the conditions under which the limits of dislocation-mediated plasticity are reached and to understand what happens to the metal beyond any such limit. In our simulations, the metal is compressed at ultrahigh strain rates along its [001] crystal axis under conditions of constant pressure, temperature and strain rate. To address the complexity of crystal plasticity processes on the length scales (85–340 nm) and timescales (1 ns–1μs) that we examine, we use recently developed methods of in situ computational microscopy to recast the enormous amount of transient trajectory data generated in our simulations into a form that can be analysed by a human. Our simulations predict that, on reaching certain limiting conditions of strain, dislocations alone can no longer relieve mechanical loads; instead, another mechanism, known as deformation twinning (the sudden re-orientation of the crystal lattice), takes over as the dominant mode of dynamic response. Below this limit, the metal assumes a strain-path-independent steady state of plastic flow in which the flow stress and the dislocation density remain constant as long as the conditions of straining thereafter remain unchanged. In this distinct state, tantalum flows like a viscous fluid while retaining its crystal lattice and remaining a strong and stiff metal.
Characterization of mechanical deformation in aluminum by optical second harmonic generation
Second harmonic generation (SHG), a laser-based surface technique, was used to characterize near-surface defect evolution associated with mechanical deformation in 2024-T3 aluminum due to tensile loads. Electron backscatter diffraction (EBSD) measurements were also performed to determine the geometrically necessary dislocation density before and after tensile deformation. Comparison of the EBSD and SHG results found that dislocation density and SHG signal are inversely proportional; tensile deformation in the plastic regime led to an increase in dislocation density and a decrease in SHG response. A similar trend was seen in the SHG results on as-received (unpolished) Al samples; SHG response decreases with extent of plastic deformation. Furthermore, this study suggests that SHG has potential as a nondestructive evaluation technique.
Hierarchical top-down bottom-up calibration with consideration for uncertainty and inter-scale discrepancy of Peierls stress of bcc Fe
A hierarchical multiscale model of plasticity in single crystal bcc Fe, framed at the mesoscale pertaining to a statistically representative set of dislocations for each slip system, relies on specification of a set of parameters which are informed using both bottom-up (BU) (atomistic) and top-down (TD) (experimental) information. We term this specification process a 'connection' between BU and TD pathways to inform the mesoscale model. The connection is considered in the presence of error, uncertainty, and discrepancy between the models. Furthermore, we expand upon a previously developed reconciled TD and BU calibration method to account for anticipated discrepancy between information from different length scales. The results of a previously formulated likelihood-based connection test of the multiscale model suggest a 'missing link' may be responsible for part of the inter-scale discrepancy. In this case, this link is assumed to be a relation between the unit-process (single dislocation line) of coordinated kink-pair nucleation on a screw dislocation segment and the many-body dislocation process which manifests in the onset of experimentally observed plastic deformation in a single crystal. A physics-informed discrepancy layer is formulated to improve the connection in the presence of additional persistent uncertainties. This physics-informed hypothesis testing is demonstrated as an alternative to fully data-driven search methods, particularly applicable to datasets of limited size that are often encountered in such multiscale material modeling applications. Discrete dislocation dynamics simulations are used to investigate the effect of the Peierls stress on straight screw dislocations and in the operation of Frank–Read sources. Discussion concerns the critical role of uncertainty quantification in providing a basis for this form of incremental hypothesis testing.
Progress report on the incorporation of lower lengthscales into polycrystal plasticity models - Part 2
Creep is the time-dependent, irreversible deformation that occurs at a low rate, at stresses below the ultimate stress of the material. Non-hydrostatic stresses (i.e. shear stresses) are required for creep. The kinds of creep relevant in cladding materials are (1) thermal creep, and (2) irradiation creep. These deformation processes require elevated temperatures, and applied stresses. Both processes are mediated by the motion of dislocations. Dislocations preferentially absorb either vacancies or interstitials, causing them to climb over obstacles. In thermal creep, the higher temperature causes high mobility of point defects, leading to a significant absorption rate of point defects by dislocations, leading to dislocation motion. In irradiation creep, the high radiation flux causes a supersaturation of point defects, that in turn leads to point defect absorption, and consequently dislocation motion. Irradiation growth is defined as the irradiation induced dimensional changes that take place in the absence of applied stresses, and is caused by the partitioning of vacancies and interstitials among two or more kinds of sinks. Each kind of sink produces strain in a different crystallographic direction, such that the final deformation is anisotropic, and is volume conserved. In this phenomenon, the high radiation flux causes the supersaturation of point defects. These point defects then tend to aggregate into dislocation loops (either interstitial of vacancy). These loops then absorb more point defects, thereby growing in size, and leading to macroscopic strain. The two phenomena of creep and growth become coupled in polycrystalline materials. Growth in a single grain is opposed by stresses caused by interaction of the growing grain with its neighbors (that are also growing, but it in different directions). These stresses initiate and/or potentiate irradiation creep. In extreme cases, such as accident scenarios, thermal creep becomes important. Internal stresses in turn affect the diffusive characteristics of point defects within a grain, and consequently affecting the phenomenon of growth. In this report, we examine the coupling between creep and growth in a polycrystalline materials, and also look at the atomistic mechanisms that contribute to these phenomena.
High purith low defect FZ silicon
The most common intrinsic defects in dislocation-free float zone (FZ) silicon crystals are the A- and B-type swirl defects. The mechanisms of their formation and annihilation have been extensively studied. Another type of defect in dislocation-free FZ crystals is referred to as a D-type defect. Concentrations of these defects can be minimized by optimizing the growth conditions, and the residual swirls can be reduced by the post-growth extrinsic gettering process. Czochralski (Cz) silicon wafers are known to exhibit higher resistance to slip and warpage due to thermal stress than do FZ wafers. The Cz crystals containing dislocations are more resistant to dislocation movement than dislocated FZ crystals because of the locking of dislocations by oxygen atoms present in the Cz crystals. Recently a transverse magnetic field was applied during the FZ growth of extrinsic silicon. Resultant flow patterns, as revealed by striation etching and spreading resistance in Ga-doped silicon crystals, indicate strong effects of the transverse magnetic field on the circulation within the melt. At fields of 5500 gauss, the fluid flow in the melt volume is so altered as to affect the morphology of the growing crystal.
Microstructural Development of Directionally Solidified Hg(1-x)Zn(x)Se Alloys
Hg(1-x)Zn(x)Se alloys have been studied as an alternative to HgCdTe for the detection of electromagnetic radiation, because the shorter ZnSe and HgSe bonds were predicted to improve lattice stability. Previous studies showed that optical properties were stable with time and that the microhardness was higher than for HgTe based alloys. However, for this material to be commercially viable, compositional variations must be reduced, and the distribution of defects induced by the growth process must be understood. The basic structural properties of bulk materials were characterized, and dislocation etch pit densities were measured to determine whether the addition of Zn to the HgSe lattice reduced the potential for dislocation formation. Hg(0.9)Zn(0.1)Se alloys were directionally solidified using a modified Bridgman-Stockbarger method and in an applied magnetic field. Radial compositional variations were greatly reduced when solidification occurred in an applied magnetic field. The combination of a convex liquid-solid interface shape and a method for reduced wetting produced boules that were a single crystal after reaching full diameter. Observed surface features indicated ampoule wetting could be eliminated using a graphite getter. Microstructural characteristics were greatly improved over HgCdTe alloys, In six boules, a total of only one twin was observed, and no inclusions were found. A method for polishing and producing dislocation etch pits was developed for these alloys, revealing dislocation etch pit densities one to two orders of magnitude less than HgTe based alloys. A kink in the thermal profile during processing of one boule generated more dislocations than did lattice mismatch due to compositional variations. The results of this investigation indicate this alloy has improved microstructural properties and resistance to dislocation formation compared with similar II-VI alloys, and should be further investigated for the detection of electromagnetic radiation.
InGaSb Defect Filter Layer to Improve Performance of GaSb Solar Cells Grown on GaAs Substrates
The reduction of the threading dislocation density in metamorphic GaSb grown on GaAs substrates through the use of InGaSb defect filter layers has been investigated. More specifically, we study the effects of strain and thickness on the ability of a InGaSb defect filter layer to reduce threading dislocations in GaSb solar cells grown on GaAs substrates. The strain between the GaSb metamorphic layer on GaAs substrate (99.5% relaxed) and the InGaSb defect filter layer is varied by changing the indium composition in the InGaSb layer. Here, it is demonstrated that an InGaSb defect filter layer with 0.6% strain is more effective for blocking threading dislocations compared with higher-strain layers, resulting in improved short-circuit current (J sc ) and open-circuit voltage (V oc ) for the metamorphic GaSb solar cell. The optimization of the defect filter layer involves varying the thickness of the layer to achieve the lowest possible threading dislocation density. This also takes into account the critical thickness of the InGaSb layer on GaSb to avoid generation of threading dislocations from the InGaSb layer itself. It is shown that adding an In 0.11 Ga 0.89 Sb defect filter layer with thickness of 250 nm and 0.6% strain beneath a GaSb solar cell grown on a GaAs substrate improves V oc from 0.1 V to 0.16 V and J sc from 19.7 mA/cm 2 to 24.7 mA/cm 2 .
Plastic deformation in nanoindentation of tantalum: A new mechanism for prismatic loop formation
Here, the mechanisms of deformation under a nanoindentation in tantalum, chosen as a model body-centered cubic (bcc) metal, are identified and quantified. Molecular dynamics (MD) simulations and indentation experiments are conducted for [1 0 0], [1 1 0] and [1 1 1] normals to surface orientations. The simulated plastic deformation proceeds by the formation of nanotwins, which rapidly evolve into shear dislocation loops. It is shown through a dislocation analysis that an elementary twin (three layers) is energetically favorable for a diameter below ~7 nm, at which point a shear loop comprising a perfect dislocation is formed. MD simulations show that shear loops expand into the material by the advancement of their edge components. Simultaneously with this advancement, screw components of the loop cross-slip and generate a cylindrical surface. When opposite segments approach, they eventually cancel by virtue of the attraction between them, forming a quasi-circular prismatic loop composed of edge dislocation segments. This “lasso”-like mechanism by which a shear loop transitions to a prismatic loop is identified for both [0 0 1] and [1 1 1] indentations. The prismatic loops advance into the material along $\langle$1 1 1$\rangle$ directions, transporting material away from the nucleation site. Analytical calculations supplement MD and experimental observations, and provide a framework for the improved understanding of the evolution of plastic deformation under a nanoindenter. Dislocation densities under the indenter are estimated experimentally (~1.2 × 10 15 m -2 ), by MD (~7 × 10 15 m -2 ) and through an analytical calculation (2.6–19 × 10 15 m -2 ). Considering the assumptions and simplifications, this agreement is considered satisfactory. MD simulations also show expected changes in pile-up symmetry after unloading, compatible with crystal plasticity.
Nanocompression of 20 nm Silver Nanoparticles: In situ Aberration‐Corrected TEM and Atomistic Simulations
Single‐crystalline nanoparticles play an increasingly important role in a wide variety of fields including pharmaceuticals, advanced materials, catalysts for fuel cells, energy materials, as well as environmental detection and monitoring. Yet, the deformation mechanisms of very small nanoparticles are still poorly understood, in particular the role played by single dislocations and their interaction with surfaces. Here, in this work, silver nanoparticles with particularly small dimensions (≈20 nanometers in diameter) are compressed in situ in an aberration‐corrected transmission electron microscopy (TEM) and molecular dynamics (MD) simulations. During compression, the emergence of both dislocations and nanotwins are observed. However, these defects prove to be unstable and disappear upon removal of the indenter. Atomistic simulations confirm the role played by image stresses associated with the nearby surfaces and the reduction in dislocation line length as it approaches the free surface, thereby supporting the experimental observations. These results provide justification for the frequent observation of the absence of dislocations in nanoparticles of a few nanometers in size during in situ experiments, even after significant deformation. This phenomenon contributes to the self‐healing of samples through dislocation ejection toward the surfaces.
Micromechanism of High-Temperature Tensile Deformation Behavior of a Directionally Solidified Nickel Base Superalloy
High-temperature tensile deformation behavior of directionally solidified nickel base superalloy CM 247 DS is studied by conducting tensile tests in temperature range RT-955 °C employing a constant strain rate of 10{sup −3} s{sup −1} and carrying out extensive electron microscopic examinations to understand the concomitant substructural evolution. The alloy exhibits yield strength anomaly (YSA) behavior like many other superalloys, and the yield strength maxima occur at 750 °C. However, unlike in most of the superalloys, ductility continuously increases with temperature. The deformation behavior of the alloy changes significantly with temperature. Transmission electron microscopic examination confirmed that at lower temperature (≤ 750 °C), γ′ shearing is the dominant deformation mechanism; whereas at temperatures above 750 °C, thermally activated dislocation looping around γ′ precipitate is dominant. Substructures evolved during deformation at 750 °C consists mainly of superlattice stacking faults (SSFs) inside γ′ precipitates, whereas at 850 °C uniform dislocation tangles are observed in γ matrix. Superlattice stacking faults result from shearing of γ′ precipitate by a/3〈112〉 dislocations, which arise from the decomposition of a/2〈110〉 matrix dislocations. YSA in this alloy is attributed to dislocation interactions inside γ′; however, the enhanced ductility even at 750 °C is due to formation of SSFs.
Neutron irradiation effects in Fe and Fe-Cr at 300 °C
Not Available
A generalized O-element approach for analyzing interface structures
A correct description of interfacial dislocations is critical to the understanding of physical and mechanical properties of the interfaces and their impact on phase transformation and deformation mechanisms. The O-lattice theory provides a general theoretical framework for determining interfacial dislocation structures. However, for systems having an invariant line (IL) or an invariant plane, the O-elements do not always exist in the three-dimensional (3D) space, which impedes the capability of the O-lattice theory to the interfaces in these systems. To determine the dislocation structures in interfaces for which the O-elements do not extend in the 3D space, we introduce a generalized O-element approach by employing the Moore-Penrose pseudoinverse. The generalized O-elements, as the least square solutions to the O-lattice, play a parallel role as that of the ideal O-elements and extend the candidate locations for the coherent regions between dislocations. Worked examples for dislocation structures in both homo-phase and hetero-phase systems are presented. The predicted interface structures are in good agreement with experimental observations and molecular statics (MS)/molecular dynamics (MD) simulations.
On the distribution of stacking faults at dissociated medium-angle grain boundaries: Crystallographic geometry and metastability
Grain boundaries in FCC metals with low stacking-fault energy can form in dissociated configurations of stacking faults. Perhaps the most studied example is 9R stacking at boundaries near Σ3{112}, where the distribution of stacking faults is related to the emission of Shockley partial dislocations. Here, we combine atomic-resolution electron microscopy, atomistic simulations, and dislocation theory to demonstrate that boundaries vicinal to Σ33a support the stabilization of dissociated 9R stacking within a narrow range of inclinations. This boundary is interesting since its misorientation (20.05°) lies in the medium-angle regime, just past the upper misorientation limit for low-angle boundaries, motivating questions for how best to describe it in terms of dislocations. Our HAADF-STEM observations of thin film bicrystals, supported by atomistic modeling, reveal that this inclination dependence arises from specific geometric constraints on the arrangement of Shockley partial dislocations at the interface. Quantification of stacking-fault distributions across multiple boundaries indicates that the density and spacing of faults closely follow the ideal 9R motif, with subtle variations reflecting the complex energy landscape of these boundaries. Through energetic analysis, we establish the presence of competing metastable states enabled by variations in stacking sequences, emphasizing the significant role of crystallographic geometry. We generalize our analysis as a function of misorientation, showing how 9R at the Σ33a boundary is related to previous observations and calculations of HCP at a 29.7° boundary. This study provides a crystallographically grounded framework connecting dislocation structures, stacking-fault distributions, and metastability at grain boundaries in FCC metals.
Multiscale Concurrent Atomistic-Continuum (CAC) modeling of multicomponent alloys
We report strengthening in complex multicomponent systems such as solid solution alloys is controlled primarily by the dynamic interactions between dislocation lines and heterogeneously distributed solute species. Modeling of extended defect length scales in such multicomponent systems becomes prohibitively expensive, motivating the development of reduced order approaches. This work explores the application of the Concurrent Atomistic-Continuum (CAC) method to model dislocation mobility in random alloys at extended length scales. By employing recently developed average-atom interatomic potentials, the average “bulk” material response in coarse-grained regions interacts with true random solute species in the atomistic-scale domain. We demonstrate that spurious stresses in domain resolution transition regions are eliminated entirely due to the CAC formulation. Simultaneously, the key details of local stress fluctuation due to randomness in the dislocation core region are captured, and fluctuating stress smoothly decays to the long-range dislocation stress field response. Dislocation mobility calculations, for line lengths over 400 nm, are computed as a function of alloy composition in the model FeNiCr system and compared to full molecular dynamics (MD). The results capture the composition-dependent trends, while reducing degrees of freedom by nearly 40%. This approach can be readily extended to any system described by an EAM potential and facilitates the study of large-scale defect dynamics in complex solute environments to support computational alloy design.
Comparative analysis of plasticity-based GND density estimation methods in crystal plasticity finite element models
In crystal plasticity finite element (CPFE) simulations, accurately quantifying geometrically necessary dislocations (GNDs) is critical for capturing strain gradients in polycrystals. We compare different methods for quantifying GNDs, all of which originate from the Nye tensor, which is computed as the curl of the plastic deformation gradient. The projection technique directly decomposes the Nye tensor onto individual screw and edge dislocation components to compute GNDs. This approach requires converting a nine-component Nye tensor into densities for a larger number of dislocation systems, a fundamentally underdetermined (non-unique) process, which is resolved using L2 minimization. In contrast, when employing CPFE analysis, one could directly compute dislocation densities on each slip system using shear gradients. Projection and slip gradient methods are compared with respect to their prediction of GNDs with changing grain size, strain, and grain neighborhoods, including multigrain junctions. Although these techniques match analytical GND densities for single slip, single crystal deformation, and are consistent with anticipated overall GND trends, we find that the GND densities from projection techniques are significantly lower than those predicted from CPFE-based slip gradients in polycrystals. A suggested improvement of only using the active dislocation systems in the projection technique almost entirely resolved this mismatch.