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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Coalescence of GaP on V-Groove Si

With an increase of control over crystalline defects, metallorganic vapor phase epitaxy (MOVPE)-grown III-V-on-Si multijunction solar cells have seen rapid increases in efficiency in recent years, pointing to a promising path to lower cost III-V solar cells. However, the cost of chemo-mechanical polishing the Si wafers to prepare them for epitaxy is high. The use of V-groove nanopatterns enables similar defect reduction to that achieved on planar wafers, but the nanopatterns can be fabricated with a low-cost process. While V-grooves offer advantages over planar Si, they add complexity to the growth process. In particular, coalescence can cause the formation of threading dislocations, and the highly-directional growth conditions required for coalescence are unusual for MOVPE. We have studied the coalescence of GaP films nucleated directly on V-groove Si by MOVPE. We observed that for optimized growth conditions (V/III=5,000 and T=800 C) two growth modes were possible, and the resulting morphology depended on the exact geometry of the SiNx cap used to cover the (0 0 1)-oriented Si at the tops of the grooves. For caps with a width >100 nm, noncoalescing, nano ridge-like growth terminating in f1 1 1g facets was observed. For narrower caps, coalescence with an RMS roughness of 0.2 nm as measured by atomic force microscopy was observed. We will discuss mechanisms responsible for this phenomenon, including the role of Si from the substrate surface. The dislocation dynamics of this system were studied with electron channeling contrast imaging (ECCI) and transmission electron microscopy (TEM). We find that V-grooves do not block dislocation glide; ECCI measurements show misfit dislocations greater than 10 micrometers long observed to continue perpendicularly across neighboring V-grooves. In addition, all threading dislocations appear to lie on f1 1 1g planes, consistent with the GaP relaxing via glided-in glissile dislocations. The dislocation dynamics and morphological evolution of the coalescence of GaP on Si, possible mechanisms behind the observed phenomenons, and further dislocation mitigation strategies for these materials will be presented.

dislocation dynamics↗
DOE OSTI2017

Microstructure of calcite deformed by high-pressure torsion: An X-ray line profile study

Calcite aggregates were deformed to high strain using high-pressure torsion and applying confining pressures of 1–6 GPa and temperatures between room temperature and 450 °C. The run products were characterized by X-ray diffraction, and key microstructural parameters were extracted employing X-ray line profile analysis. The dominant slip system was determined as r {$ 10\bar{1}4 $}⟨$ \bar{2}021 $⟩ with edge dislocation character. The resulting dislocation density and the size of the coherently scattering domains (CSD) exhibit a systematic dependence on the P-T conditions of deformation. While high pressure generally impedes recovery through reducing point defect mobility, the picture is complicated by pressure-induced phase transformations in the CaCO 3 system. Transition from the calcite stability field to those of the high-pressure polymorphs CaCO 3 - II, CaCO 3 - III and CaCO3-IIIb leads to a change of the microstructural evolution with deformation. At 450 °C and pressures within the calcite stability field, dislocation densities and CSD sizes saturate at shear strains exceeding 10 in agreement with earlier studies at lower pressures. In the stability field of CaCO 3 - II, the dislocation density reflects a more complex behavior. Furthermore, at a given strain and strain rate, the dislocation density increases and the CSD size decreases with increasing pressure within the stability fields of either calcite or of the high-pressure polymorphs. There is, in contrast, a jump from high dislocation densities and small CSDs in the upper pressure region of the calcite stability field to lower dislocation densities and larger CSDs in the low-pressure region of the CaCO 3 - II stability field. This jump is more pronounced at higher temperatures and less so at room temperature. The pressure influence on the deformation-induced evolution of dislocation densities implies that pressure variations may change the rheology of carbonate rocks. In particular, a weakening is expected to occur at the transition from the calcite to the CaCO 3 - II stability field, if aragonite does not form.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Structure and energetics of the elbows in the Au(111) herringbone reconstruction

We study the structure of the threading edge dislocations, or “elbows,” which are an essential component of the well-known herringbone reconstruction of the (111) surface of Au. Previous work had shown that these dislocations can be stabilized by long-range elastic relaxations into the bulk. However, the validity of the harmonic spring model that had been used to estimate the energies of the dislocations is uncertain. To enable a more refined model of the dislocation energetics, we have imaged the atomic structure of these dislocations using scanning tunneling microscopy. We find that the harmonic spring model does not adequately reproduce the observed structure. We are able to reproduce the structure, however, with a two-dimensional Frenkel-Kontorova (FK) model that uses a pairwise Morse potential to describe the interactions between the top layer Au atoms on a rigid substrate. The parameters of the potential were obtained by fitting the energy of uniaxially compressed phases, or “stripes”, computed with density functional theory, as a function of surface Au density. Within this model, the formation of the threading dislocations remains unfavorable. However, the large forces on the substrate atoms near the threading-dislocation cores, render the assumption of a completely rigid substrate questionable. Indeed, if the FK parameters are modified to account for the relaxation of just one more atomic layer, threading dislocations can, in principle, become favorable, even without bulk elastic relaxations. Additional evidence for a small elbow energy is that our computed change in the Au(111) surface stress tensor caused by the (√ 3 × 22) reconstruction is considerably smaller than previous estimates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Probing Microplasticity in Small-Scale FCC Crystals via Dynamic Mechanical Analysis

In small-scale metallic systems, collective dislocation activity has been correlated with size effects in strength and with a steplike plastic response under uniaxial compression and tension. Yielding and plastic flow in these samples is often accompanied by the emergence of multiple dislocation avalanches. Dislocations might be active preyield, but their activity typically cannot be discerned because of the inherent instrumental noise in detecting equipment. We apply alternate current load perturbations via dynamic mechanical analysis during quasistatic uniaxial compression experiments on single crystalline Cu nanopillars with diameters of 500 nm and compute dynamic moduli at frequencies 0.1, 0.3, 1, and 10 Hz under progressively higher static loads until yielding. By tracking the collective aspects of the oscillatory stress-strain-time series in multiple samples, we observe an evolving dissipative component of the dislocation network response that signifies the transition from elastic behavior to dislocation avalanches in the globally preyield regime. We postulate that microplasticity, which is associated with the combination of dislocation avalanches and slow viscoplastic relaxations, is the cause of the dependency of dynamic modulus on the driving rate and the quasistatic stress. We construct a continuum mesoscopic dislocation dynamics model to compute the frequency response of stress over strain and obtain a consistent agreement with experimental observations. The results of our experiments and simulations present a pathway to discern and quantify correlated dislocation activity in the preyield regime of deforming crystals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

Fundamental Understanding of Ambient and High-Temperature Plasticity Phenomena in Structural Materials in Advanced Reactors

The goal of this research project is to develop the methods and tools necessary to link unit processes analyzed using atomistic simulations involving interaction of vacancies and interstitials with dislocations, as well as dislocation mediation at sessile junctions and interfaces as affected by radiation, with cooperative influence on higher-length scale behavior of polycrystals. These tools and methods are necessary to design and enhance radiation-induced damage-tolerant alloys. The project will achieve this goal by applying atomistic simulations to characterize unit processes of: 1. Dislocation nucleation, absorption, and desorption at interfaces 2. Vacancy production, radiation-induced segregation of substitutional Cr at defect clusters (point defect sinks) in BCC Fe-Cr ferritic/martensitic steels 3. Investigation of interaction of interstitials and vacancies with impurities (V, Nb, Ta, Mo, W, Al, Si, P, S) 4. Time evolution of swelling (cluster growth) phenomena of irradiated materials 5. Energetics and kinetics of dislocation bypass of defects formed by interstitial clustering and formation of prismatic loops, informing statistical models of continuum character with regard to processes of dislocation glide, vacancy agglomeration and swelling, climb and cross slip This project will consider the Fe, Fe-C, and Fe-Cr ferritic/martensitic material system, accounting for magnetism by choosing appropriate interatomic potentials and validating with first principles calculations. For these alloys, the rate of swelling and creep enhancement is considerably lower than that of face-centered cubic (FCC) alloys and of austenitic Fe-Cr-Mo alloys. The team will confirm mechanisms, validate simulations at various time and length scales, and improve the veracity of computational models. The proposed research's feasibility is supported by recent modeling of radiation effects in metals and alloys, interfacial dislocation transfer reactions in nano-twinned copper, and dislocation reactions at general boundaries, along with extensive modeling cooperative effects of dislocation interactions and migration in crystals and polycrystals using continuum models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

Spontaneous Relaxation through Graphene Suggests an Alternative Strain Relaxation Mechanism in Heteroepitaxy

While conventional epitaxy produces high-quality epitaxial layers, the limited set of commercially available wafers restricts the number of material choice that can be grown through epitaxy. To extend the set of epi-materials, heteroepitaxy has been widely used although the epi-materials have severe lattice mismatch from wafers. The problem of heteroepitaxy of the lattice mismatched systems is that introducing dislocations is unavoidable because of the strain energy built up in epitaxial layers exceeds the threshold energy value to create dislocation. As the dislocations significantly reduce the materials’ properties, people have put intensive effort into finding a new way to resolve this issue. Here, we introduce a new strain relaxation approach which can efficiently engineer the lattice with minimizing dislocation formation. Remote epitaxy allows single-crystalline growths on graphene-coated substrates as atomic potential field guides atomic registry through graphene while weakening binding energy of epilayer to the substrate. We discovered that this weakened interface offers a new pathway for strain relaxation during epitaxy in the lattice mismatched systems. While conventional heteroepitaxy relaxes accumulated strain energy through involving misfit dislocations, heteroepitaxy on graphene-coated substrates spontaneously relaxes its strain minimizing dislocation density. Thus, at the same thickness and misfit strain, the epilayer grown on graphene-coated substrates shows full relaxation with substantially reduced dislocations while that by conventional heteroepitaxy exhibits slight relaxation with full of dislocations. It means that full of strain relaxation at much lower thickness is available through this approach. We strongly believe that our strategy allows broadening range of available semiconductors through epitaxy, which could lead high performance electronic and photonics.

Bae, Sang-Hoon↗
DOE OSTI2022

Coalescence of GaP on V-Groove Si

In recent years, better understanding and control over the formation of crystalline defects during the direct epitaxy of III-V semiconductors on Si substrates via metal organic vapor phase epitaxy (MOVPE) has enabled large gains in III-V-on-Si solar cell efficiency, pointing to pathway to lower-cost, high-performance III-V solar cells. However, such results have only been achieved on costly chemo-mechanically-polished (CMP) Si wafers. The use of V-groove nanopatterned Si substrates has demonstrated similarly high-crystalline-quality III-V-on-Si epitaxy, but also can be combined with lower-cost polishing techniques. Although they offer a potential cost advantage, growth on V-groove substrates adds challenges not present for epitaxy on planar wafers (the III-V material must be coalesced into a thin film after an initial nucleation stage). MOVPE growth conditions that promote highly facet-selective lateral growth needed for coalescence are generally actively avoided for conventional thin fim growth, so growth conditions need to be re-developed for V-groove-based epitaxy. Additionally, coalescence add complexity to the dislocation dynamics related to lattice relaxation, so strategies used to keep threading dislocation density (TDD) low on planar substrates need to be re-tuned for V-grooves. We have studied the morphological evolution and dislocation dynamics of GaP grown on V-groove Si by MOVPE. Growth conditions of V/III=5,000 and Tg=800 degrees C were uniquely found to produce extremely smooth coalesced thin films, with an RMS roughness of 0.2 nm measured by AFM. Additionally, at this growth condition, we identified two regimes of growth determined by the width of the SiNx cap (a remnant of the nanopatterning process) at the top of the V-grooves. For narrow caps, the GaP coalesces into a thin film, and for wide caps, the GaP evolves into {1 1 1}-faceted diamonds that do not coalesce. We suggest the influence of Si from the sidewalls of the V-grooves on the surface reconstruction of the GaP as the mechanism for this effect, with reflection difference spectroscopy (RDS) and Si doping experiments supporting this theory. In addition to morphology, the dislocation dynamics of the system were studied with electron channeling contrast imaging (ECCI) and transmission electron microscopy (TEM). The TDD of the coalesced GaP films was found to be 5 x 10^7 cm^-2 after coalescence via ECCI, a level still too high for high-quality solar cells. However, misfit dislocations crossing multiple grooves greater than 20 micrometers long were observed in ECCI, suggesting that the V-grooves do not block dislocation glide. TEM prior to and after coalescence was used to distinguish between dislocation creation driven by growth conditions and coalescence. Finally, strategies to reduce the dislocation density to levels acceptable for solar cells will be discussed.

GaP↗
DOE OSTI2022

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.

36 MATERIALS SCIENCE↗
DOE OSTI2023

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

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

36 MATERIALS SCIENCE↗
DOE OSTI2025

Phase-field modeling of radiation-induced composition redistribution: An application to additively manufactured austenitic Fe–Cr–Ni

Multicomponent alloys undergoing irradiation damage develop radiation-induced composition redistribution at point defect sinks such as grain boundaries (GBs) and dislocations. Such redistribution results in undesired changes to their mechanical behavior and corrosion resistance. Additively manufactured alloys proposed for future nuclear applications are expected to demonstrate a distinct response to irradiation owing to their unique microstructure with as-solidified dislocation density and chemical microsegregation. To capture the composition redistribution in such systems, we develop a mesoscale model with coupled evolution of atomic and point defect components in the presence of dislocation density, dislocation heterogeneity, and thermodynamic interactions at the GB. The model is parameterized for an FCC Fe–Cr–Ni alloy as a representative system for austenitic stainless steels, and simulations are performed in 1D and 2D as a function of irradiation temperature, dose, dislocation density, and grain size. Radiation-induced segregation (RIS) characterized by Cr depletion and Ni enrichment is predicted at both the GB and the dislocation cell wall, with RIS being lower in magnitude but wider at the cell wall. Strongly biased absorption of self-interstitials by dislocations is found to suppress Ni enrichment but slightly enhance Cr depletion under certain conditions. Thermodynamic segregation at the GB is predicted to be narrower and opposite in sign to RIS for both Cr and Ni. Importantly, non-monotonic segregation is found to occur when both thermodynamic and RIS mechanisms are considered, providing a novel physical interpretation of experimental observations. The model is expected to serve as a key tool in accelerated qualification of irradiated materials.

additively manufactured microstructure↗
DOE OSTI2016

Characterizing the nano-structure and defect structure of nano-scaled non-ferrous structural alloys

The presence and interaction of nanotwins, geometrically necessary dislocations, and grain boundaries play a key role in the mechanical properties of nanostructured crystalline materials. Therefore, it is vital to determine the orientation, width and distance of nanotwins, the angle and axis of grain boundary misorientations as well as the type and the distributions of dislocations in an automatic and statistically meaningful fashion in a relatively large area. In this paper, such details are provided using a transmission electron microscope-based orientation microscopy technique called ASTAR™/precession electron diffraction. The remarkable spatial resolution of this technique (~ 2 nm) enables highly detailed characterization of nanotwins, grain boundaries and the configuration of dislocations. This orientation microscopy technique provides the raw data required for the determination of these parameters. The procedures to post-process the ASTAR™/PED datasets in order to obtain the important (and currently largely hidden) details of nanotwins as well as quantifications of dislocation density distributions are described in this study. - Highlights: • EBSD cannot characterize defects such as dislocations, grain boundaries and nanotwins in severely deformed metals. • TEM based orientation microscopy technique called ASTAR™/PED was used to resolve the problem. • Locations and orientations of nanotwins, dislocation density distribution and grain boundary characters can be resolved. • This work provides the bases for further studies on the interactions between dislocations, grain boundaries and nanotwins. • The computation part is explained sufficiently which helps the readers to post process their own data.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Extended defects in GaAs/GaAs 1-x Sb x /GaAs (001) heterostructures

The atomic-scale structure of extended defects in GaAs/GaAs 1-x Sb x /GaAs (001) heterostructures has been characterized using aberration-corrected scanning transmission electron microscopy. The defect located at the tensile-strained GaAs(cap)/GaAs 0.34 Sb 0.66 interface had no edge component in the projection plane and is identified as either a dissociated screw dislocation or a partial dislocation dipole. The associated intrinsic stacking fault is bounded by two 30° Shockley partial dislocations of opposite sign. Another defect, located at the compressively-strained GaAs 0.91 Sb 0.09 /GaAs(substrate) interface, is identified as a dissociated 90° dislocation. The associated intrinsic stacking fault is bounded by a 30° Shockley partial dislocation and a partial dislocation with a Burgers vector of either or , where a is the lattice constant. Unpaired atomic columns observed at the cores of the 30° Shockley partial dislocations indicate that both defects belong primarily to the glide set.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Anomalous thermal transport in Eshelby twisted van der Waals nanowires

Dislocations in van der Waals (vdW) layered nanomaterials induce strain and structural changes that substantially impact thermal transport. Understanding these effects could enable the manipulation of dislocations for improved thermoelectric and optoelectronic applications, but experimental insights remain limited. Here, in this study, we use synthetic Eshelby twisted vdW GeS nanowires (NWs) with single screw dislocations as a model system to explore the interplay between dislocation-induced structural modifications and lattice thermal conductivity. Our measurements reveal a monoclinic structure stabilized by the dislocation, leading to a substantial drop in thermal conductivity for larger-diameter NWs (70% at room temperature), supported by first-principles calculations. Interestingly, we also find an anomalous enhancement of thermal conductivity with decreasing diameter in twisted NWs, contrary to typical trends in non-twisted GeS NWs. This is attributed to increased conductivity near the NW cores due to compressive strain around the central dislocations, and aligns with a density-functional-theory-informed core–shell model. Our results highlight the critical role of dislocations in thermal conduction, providing fundamental insights for defect and strain engineering in advanced thermal applications.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Defect reduction in Si-doped Al{sub 0.45}Ga{sub 0.55}N films by SiN{sub x} interlayer method

The dislocation density in AlGaN epitaxial layers with Al content as high as 45% grown on sapphire substrates has been effectively reduced by introducing an in-situ deposited SiN{sub x} nanomask layer in this study. By closely monitoring the evolution of numerous material properties, such as surface morphology, dislocation density, photoluminescence, strain states, and electron mobility of the Si-Al{sub 0.45}Ga{sub 0.55}N layers as the functions of SiN{sub x} interlayer growth time, the surface coverage fraction of SiN{sub x} is found to be a crucial factor determining the strain states and dislocation density. The dependence of the strain states and the dislocation density on the surface coverage fraction of SiN{sub x} nanomask supports the very different growth models of Al-rich AlGaN on SiN{sub x} interlayer due to the reduced nucleation selectivity compared with the GaN counterpart. Compared with GaN, which can only nucleate at open pores of SiN{sub x} nanomask, Al-rich AlGaN can simultaneously nucleate at both open pores and SiN{sub x} covered areas. Dislocations will annihilate at the openings due to the 3D growth initiated on the opening area, while 2D growth mode is preserved on SiN{sub x} and the threading dislocations are also preserved. During the following growth process, lateral overgrowth will proceed from the Al{sub 0.45}Ga{sub 0.55}N islands on the openings towards the regions covered by SiN{sub x}, relaxing the compressive strain and bending the dislocations at the same time.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Atomistic tensile deformation mechanisms of Fe with gradient nano-grained structure

Large-scale molecular dynamics (MD) simulations have been performed to investigate the tensile properties and the related atomistic deformation mechanisms of the gradient nano-grained (GNG) structure of bcc Fe (gradient grains with d from 25 nm to 105 nm), and comparisons were made with the uniform nano-grained (NG) structure of bcc Fe (grains with d = 25 nm). The grain size gradient in the nano-scale converts the applied uniaxial stress to multi-axial stresses and promotes the dislocation behaviors in the GNG structure, which results in extra hardening and flow strength. Thus, the GNG structure shows slightly higher flow stress at the early plastic deformation stage when compared to the uniform NG structure (even with smaller grain size). In the GNG structure, the dominant deformation mechanisms are closely related to the grain sizes. For grains with d = 25 nm, the deformation mechanisms are dominated by GB migration, grain rotation and grain coalescence although a few dislocations are observed. For grains with d = 54 nm, dislocation nucleation, propagation and formation of dislocation wall near GBs are observed. Moreover, formation of dislocation wall and dislocation pile-up near GBs are observed for grains with d = 105 nm, which is the first observation by MD simulations to our best knowledge. The strain compatibility among different layers with various grain sizes in the GNG structure should promote the dislocation behaviors and the flow stress of the whole structure, and the present results should provide insights to design the microstructures for developing strong-and-ductile metals.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Deformed Materials: Towards a Theory of Materials Morphology Dynamics

This grant supported work on the response of crystals to external stress. Our primary work described how disordered structural materials break in two (statistical models of fracture in disordered materials), studied models of deformation bursts (avalanches) that mediate deformation on the microscale, and developed continuum dislocation dynamics models for plastic deformation (as when scooping ice cream bends a spoon, Fig. 9). Glass is brittle -- it breaks with almost atomically smooth fracture surfaces. Many metals are ductile -- when they break, the fracture surface is locally sheared and stretched, and it is this damage that makes them hard to break. Bone and seashells are made of brittle material, but they are strong because they are disordered -- lots of little cracks form as they are sheared and near the fracture surface, diluting the external force. We have studied materials like bone and seashells using simulations, mathematical tools, and statistical mechanics models from physics. In particular, we studied the extreme values of fracture strengths (how likely will a beam in a bridge break far below its design strength), and found that the traditional engineering tools could be improved greatly. We also studied fascinating crackling-noise precursors -- systems which formed microcracks of a broad range of sizes before they broke. Ductile metals under stress undergo irreversible plastic deformation -- the planes of atoms must slide across one another (through the motion of dislocations) to change the overall shape in response to the external force. Microscopically, the dislocations in crystals move in bursts of a broad range of sizes (termed 'avalanches' in the statistical mechanics community, whose motion is deemed 'crackling noise'). In this grant period, we resolved a longstanding mystery about the average shape of avalanches of fixed duration (using tools related to an emergent scale invariance), we developed the fundamental theory describing the shapes of avalanches and how they are affected by the edges of the microscope viewing window, we found that slow creep of dislocations can trigger an oscillating response explaining recent experiments, we explained avalanches under external voltage, and we have studied how avalanches in experiments on the microscale relate to deformation of large samples. Inside the crystals forming the metal, the dislocations arrange into mysterious cellular structures, usually ignored in theories of plasticity. Writing a natural continuum theory for dislocation dynamics, we found that it spontaneously formed walls -- much like models of traffic jams and sonic booms. These walls formed rather realistic cellular structures, which we examined in great detail -- our walls formed fractal structures with fascinating scaling properties, related to those found in turbulent fluids. We found, however, that the numerical and mathematical tools available to solve our equations were not flexible enough to incorporate materials-specific information, and our models did not show the dislocation avalanches seen experimentally. In the last year of this grant, we wrote an invited review article, explaining how plastic flow in metals shares features with other stressed materials, and how tools of statistical physics used in these other systems might be crucial for understanding plasticity.

36 MATERIALS SCIENCE↗