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DOE OSTI2015

Displacement Fields and Self-Energies of Circular and Polygonal Dislocation Loops in Homogeneous and Layered Anisotropic Solids

There are large classes of materials problems that involve the solutions of stress, displacement, and strain energy of dislocation loops in elastically anisotropic solids, including increasingly detailed investigations of the generation and evolution of irradiation induced defect clusters ranging in sizes from the micro- to meso-scopic length scales. Based on a two-dimensional Fourier transform and Stroh formalism that are ideal for homogeneous and layered anisotropic solids, we have developed robust and computationally efficient methods to calculate the displacement fields for circular and polygonal dislocation loops. Using the homogeneous nature of the Green tensor of order -1, we have shown that the displacement and stress fields of dislocation loops can be obtained by numerical quadrature of a line integral. In addition, it is shown that the sextuple integrals associated with the strain energy of loops can be represented by the product of a pre-factor containing elastic anisotropy effects and a universal term that is singular and equal to that for elastic isotropic case. Furthermore, we have found that the self-energy pre-factor of prismatic loops is identical to the effective modulus of normal contact, and the pre-factor of shear loops differs from the effective indentation modulus in shear by only a few percent. These results provide a convenient method for examining dislocation reaction energetic and efficient procedures for numerical computation of local displacements and stresses of dislocation loops, both of which play integral roles in quantitative defect analyses within combined experimental–theoretical investigations.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Automated Quantitative Analysis of Extended Irradiation Defects - Dislocations, Voids and Precipitates in Neutron Irradiated HT-9 Steel

Structural alloys that make up the core components of nuclear reactors are exposed to radiation that can substantially alter the microstructure and mechanical properties of the material. Irradiation can cause the formation of extended defects including dislocation line and loops, voids and various types of precipitates. To understand the irradiation effects, it is critical to characterize these defects individually and collectively to quantify how they evolve throughout irradiation stages. Transmission electron microscopy (TEM) is a standard tool for providing extensive size, number density and spatial distribution of extended irradiation defects, however, manual measurement of defect size and number density requires time-intensive effort to analyze enough defects that provide a statistically meaningful result and are prone to errors of subjectivity. In this work, we developed a set of MATLAB algorithms offering robust and automated identification and quantification of extended irradiation defects like dislocation lines, voids and precipitates commonly observed in neutron irradiated cladding alloys [1]. Using a neutron-irradiated HT-9 martensitic alloy irradiated at 412°C to 111.8 dpa, we demonstrate the capability of these algorithms for quantitative defect analysis. Figure 1 presents defect images of the HT-9 using an advanced diffraction contrast imaging scanning transmission electron microscopy (DCI STEM) that suppresses bend contours and provides better defect contrast compared to conventional TEM [2]. The first step of defect analysis is defect identification, a process that can be digitally achieved by contrast thresholding (for simple defect contrast) and by machine learning computer vision for defect semantic segmentation [3]. Here, labeled binary defect images (Figures 2a and 2c) were used. For dislocation density quantification, we employed an optimized circular-grid intersection method first introduced by Dr. John Steeds [4]. This method is shown in Figures 2a and 2b, where the number of intersections of dislocation lines with circular traces was measured. This produces an unbiased sampling of dislocation lines, regardless of their orientation. This process was optimized with automated digital intersection number and grid length registration. Interestingly, it was found that a relatively large number of circles in a set circular gird is was needed to produce an invariant result (Figure 2b), with a low systematic measurement error. This demonstrates the main advantage of computer-based defect analysis, in performing repetitive operations quickly with a reduced systematic error. For the quantitative analysis of voids and precipitates a challenge encountered with automated defect analysis is feature overlap, particularly when the density of voids/precipitates is high. To mitigate this problem, as shown in Figure 2d, we modified the popular circular Hough transformation and treated ‘circular shape’ as the particle descriptor for voids/precipitates, efficiently resolving the overlapping particles. In summary, this automated digital quantification together with machine learning enabled defect identification [3] opens new opportunities for standardizing the characterization workflow for quantitative analysis of extended irradiation defects.

Sainju, Rajat↗

DOE OSTI2017

Three-dimensional imaging of dislocation dynamics during the hydriding phase transformation

Crystallographic imperfections can significantly alter material properties and responses to external stimuli, including solute induced phase transformations and crystal growth and dissolution . Despite recent progress in imaging defects using both electron and x-ray techniques, in situ three-dimensional imaging studies of defect dynamics, necessary to understand and engineer nanoscale processes, remains challenging. Here, we report in situ three-dimensional imaging of defect dynamics during the hydriding phase transformation of individual palladium nanocrystals by Bragg Coherent Diffractive Imaging (BCDI) . During constant pressure experiments, we observed that the phase transformation begins after the nucleation of dislocations in large (300 nm) particles. The 3D dislocation network shows that dislocations are close to the phase boundary. The 3D phase morphology resolved by BCDI suggests that the hydrogen-rich phase is more similar to a spherical cap on the hydrogen-poor phase than the core-shell model commonly assumed. We substantiate this conclusion using 3D phase field modeling and demonstrate how phase morphology affects the critical size for dislocation nucleation. We determine the size dependence of the transformation pressure for large (150-300 nm) palladium nanocrystals using variable pressure experiments. Our results reveal a pathway for solute induced structural phase transformations in nanocrystals and demonstrate BCDI as a novel method for understanding dislocation dynamics in phase transforming systems at the nanoscale.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Mild-to-wild plastic transition is governed by athermal screw dislocation slip in bcc Nb

Plastic deformation in crystals is mediated by the motion of line defects known as dislocations. For decades, dislocation activity has been treated as a homogeneous, smooth continuous process. However, it is now recognized that plasticity can be determined by long-range correlated and intermittent collective dislocation processes, known as avalanches. Here we demonstrate in body-centered cubic Nb how the long-range and scale-free dynamics at room temperature are progressively quenched out with decreasing temperature, eventually revealing intermittency with a characteristic length scale that approaches the Burgers vector itself. Plasticity is shown to be bimodal across the studied temperature regime, with conventional thermally-activated smooth plastic flow (‘mild’) coexisting with sporadic bursts (‘wild’) controlled by athermal screw dislocation activity, thereby violating the classical notion of temperature-dependent screw dislocation motion at low temperatures. An abrupt increase of the athermal avalanche component is identified at the critical temperature of the material. Our results indicate that plasticity at any scale can be understood in terms of the coexistence of these mild and wild modes of deformation, which could help design better alloys by suppressing one of the two modes in desired temperature windows.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Multi-scale investigation of short-range order and dislocation glide in MoNbTi and TaNbTi multi-principal element alloys

Refractory multi-principal element alloys (RMPEAs) are promising materials for high-temperature structural applications. Here, we investigate the role of short-range ordering (SRO) on dislocation glide in the MoNbTi and TaNbTi RMPEAs using a multi-scale modeling approach. Monte carlo/molecular dynamics simulations with a moment tensor potential show that MoNbTi exhibits a much greater degree of SRO than TaNbTi and the local composition has a direct effect on the unstable stacking fault energies (USFEs). From mesoscale phase-field dislocation dynamics simulations, we find that increasing SRO leads to higher mean USFEs and stress required for dislocation glide. The gliding dislocations experience significant hardening due to pinning and depinning caused by random compositional fluctuations, with higher SRO decreasing the degree of USFE dispersion and hence, amount of hardening. Finally, we show how the morphology of an expanding dislocation loop is affected by the applied stress.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Differences in Outcomes between Patellar Dislocations Managed in Emergent versus Non-Emergent Care Settings

Abstract Patellar dislocations occur at a much higher rate in military than civilian populations. Past population-level studies have shown that surgical management is as good as or superior to conservative care and may reduce future reoccurrences. Although in acute cases and in civilian clinics, patellar dislocations are usually managed first in an emergent care setting, previous work suggests this can lead to increased costs. This study compared differences in downstream care type and intensity of services based on whether initial care occurred in emergent or non-emergent care settings. In our sample of 1,523 Military Health System (MHS) beneficiaries with patellar dislocation and 2-year follow-up, we found non-significant differences in costs, intensity of services, and rates of surgical repair regardless of whether the patient was initially seen in an emergent versus non-emergent care setting. Although we found significant increases in the use of imaging, patellar dislocation-related medical visits, and frequency of closed treatment approaches in emergent care settings, these values were very small and likely not clinically significant. These findings, which included all the patellar dislocations reported across the entire MHS in a 24-month period, suggest that neither emergent nor non-emergent care settings are likely to influence the long-term care received by the individual.

Orthopedics↗

DOE OSTI2025

Spatial description of dislocation nucleation in the shock response of single-crystal aluminum

Nonequilibrium molecular dynamics simulations of shock loaded single-crystal Al in the $\langle$100$\rangle$, $\langle$110$\rangle$, $\langle$111$\rangle$, and $\langle$123$\rangle$ orientations are conducted to study elastic and plastic shockwave formation and details associated with dislocation activity. A computer vision-based approach is implemented to capture the presence of dislocations and describe their spatial characteristics in the zone of nucleation behind the propagating shockwave. The methodology developed relies on the sequences of images extracted during shock loading that show dislocation activity within a cross section of the sample. Results reveal that the spacing between activated slip systems is orientation dependent and exhibits a modest reduction for the $\langle$100$\rangle$ and $\langle$111$\rangle$ orientations as shock pressure increases. Comparisons are made to existing theoretical models. Such relationships between shock pressure and dislocation activity, extracted from molecular dynamics simulations, can be used to inform higher length scale simulations or modeling of dislocation-based plasticity during shock.

36 MATERIALS SCIENCE↗

DOE OSTI2012

Dislocation vs. production bias revisited with account of radiation-induced emission bias I. Void swelling under electron and light ion irradiation

Early experimental data on void swelling in electron-irradiated materials disagree with the dislocation bias models based on the dislocation-point defect elastic interactions. Later this became one of the reasons that prompted the development of models based on production bias (PBM) as the main driver for swelling, which assumed that the dislocation bias was much lower than that predicted by theory. However, the PBM in its present form fails to account for important and common observations: the indefinite void growth often observed under cascade irradiation and the swelling saturation observed under high dose irradiation and in void lattices. In this paper we show that these contradictions can be naturally resolved in the framework of the rate theory modified with account of the radiation-induced vacancy emission from extended defects, such as voids, dislocations and grain boundaries. The modified rate theory agrees well with the experimental data, which proves that original dislocation bias should be used in rate theory models in different irradiation. The modified theory predictions include (but not limited to) the radiation-induced annealing of voids, swelling saturation under high dose irradiation, generally, and in void lattices, in particular.

Dubinko, Volodymyr↗

DOE OSTI2016

An electron microscopy study of dislocation structures in Mg single crystals compressed along [0 0 0 1] at room temperature

We compressed Mg single crystals along [0 0 0 1] at room temperature to various stress levels (40, 80, 120, 160 and 320 MPa) and the evolution of dislocation structure with stress increment was investigated by TEM slip is confirmed to be the dominant deformation mode; the predominance of edge dislocation debris lying along the <1 0 $\bar{1}$ 0> implies that screw dislocations are more mobile than their edge counterpart. The edge dislocation may dissociate into and dislocations, and the latter can extend further on the basal plane and bound a basal-stacking fault.

36 MATERIALS SCIENCE↗

DOE OSTI2016

The discrete-continuum connection in dislocation dynamics: I. Time coarse graining of cross slip

A recent continuum dislocation dynamics formalism (Xia and El-Azab 2015 Model. Simul. Mater. Sci. Eng. 23 055009) has been enriched by incorporating an improved cross slip model. 3D discrete dislocation dynamics simulations were used to collect cross slip rate data in the form of time series that were analysed to estimate the correlation time for cross slip, which was subsequently used as a time scale for local window averaging of the collected cross slip rate data. This time averaging filters out the cross slip rate fluctuations over time intervals less than the correlation time, thus resulting in relatively smoother time series for the cross slip rates. The coarse grained series were further cast in the form of smooth trends with superposed fluctuations and implemented in continuum dislocation dynamics simulations using a Monte Carlo scheme. Here, this approach resulted in a significant improvement of the predicted stress–strain response and a more realistic dislocation cell structure evolution. The similitude law for the average cell size evolution with inverse of stress, however, remains unaffected by the cross slip rates used in continuum dislocation dynamics.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Phase-field modeling of stored-energy-driven grain growth with intra-granular variation in dislocation density

Abstract We present a phase-field (PF) model to simulate the microstructure evolution occurring in polycrystalline materials with a variation in the intra-granular dislocation density. The model accounts for two mechanisms that lead to the grain boundary migration: the driving force due to capillarity and that due to the stored energy arising from a spatially varying dislocation density. In addition to the order parameters that distinguish regions occupied by different grains, we introduce dislocation density fields that describe spatial variation of the dislocation density. We assume that the dislocation density decays as a function of the distance the grain boundary has migrated. To demonstrate and parameterize the model, we simulate microstructure evolution in two dimensions, for which the initial microstructure is based on real-time experimental data. Additionally, we applied the model to study the effect of a cyclic heat treatment (CHT) on the microstructure evolution. Specifically, we simulated stored-energy-driven grain growth during three thermal cycles, as well as grain growth without stored energy that serves as a baseline for comparison. We showed that the microstructure evolution proceeded much faster when the stored energy was considered. A non-self-similar evolution was observed in this case, while a nearly self-similar evolution was found when the microstructure evolution is driven solely by capillarity. These results suggest a possible mechanism for the initiation of abnormal grain growth during CHT. Finally, we demonstrate an integrated experimental-computational workflow that utilizes the experimental measurements to inform the PF model and its parameterization, which provides a foundation for the development of future simulation tools capable of quantitative prediction of microstructure evolution during non-isothermal heat treatment.

Materials Science↗

DOE OSTI2020

Nucleation of Dislocations in 3.9 nm Nanocrystals at High Pressure

As circuitry approaches single nanometer length scales, it has become important to predict the stability of single nanometer-sized metals. The behavior of metals at larger scales can be predicted based on the behavior of dislocations, but it is unclear if dislocations can form and be sustained at single nanometer dimensions. Here, we report the formation of dislocations within individual 3.9 nm Au nanocrystals under nonhydrostatic pressure in a diamond anvil cell. We used a combination of x-ray diffraction, optical absorbance spectroscopy, and molecular dynamics simulation to characterize the defects that are formed, which were found to be surface-nucleated partial dislocations. These results indicate that dislocations are still active at single nanometer length scales and can lead to permanent plasticity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

On the velocity dependence of the dislocation drag coefficient from phonon wind

The phonon wind mechanism, that is, the anharmonic interaction and scattering of phonons by a moving dislocation, imparts a drag force B (v,T,ρ) v on the dislocation. The drag coefficient B has been previously computed and experimentally determined only for dislocation velocities v much less than transverse sound speed, c T . In this paper we derive an expression for the velocity dependence of B up to c T in terms of the third-order elastic constants of the crystal. We compute the velocity dependence of the phonon wind contribution to B in the range 1%–90% c T for Al, Cu, Fe, and Nb in the isotropic Debye approximation, and to better accuracy than in earlier studies. It is proved that the drag coefficient for screw dislocations scattering transverse phonons is finite as v → c T , whereas B is divergent for edge dislocations scattering transverse phonons in the same limit. We compare our results to experimental results wherever possible and identify ways to validate and further improve the theory with more realistic phonon dispersion relations, MD simulations, and more accurate measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Demonstrate new plasticity models for doped UO 2 that capture dislocation mechanisms

In light water reactors, fuel vendors are investigating the use of dopants to modify the properties of UO 2 pellets, with the goal of improving pellet-cladding mechanical interactions during operation. Dopants are expected to ‘soften’ the pellets; that is, the doped pellets have higher plastic deformation than conventional UO 2 . This leads to a reduction in the severity of mechanical pellet-cladding interactions, helping to reduce the hoop strain on the cladding. By minimizing the strain exerted by the pellet on the cladding, it is anticipated that cladding performance under accident conditions can be enhanced (i.e., lowering the risk of burst during a LOCA). Dopants such as chromium (Cr) promote grain growth during pellet fabrication, leading to larger grains; therefore, understanding the link between chemistry, microstructure and mechanical deformation (enhanced creep rates) behavior of UO 2 is critical to helping operators further substantiate the benefits of doping UO 2 . Historically, the nuclear energy industry has relied on empirical models to make assessments of performance. Compared to empirical models, mechanistic physics-based models provide benefits, such as, fewer data points for validation and better extrapolation where experimental data is scarce or non-existent. In this report, Bayesian inference techniques have been applied to a previously developed lower length-scale-informed diffusional creep model. The objective is to i) infer lower-length-scale parameter distributions from available experiment and then ii) determine the uncertainties in the measurable quantity (in this case creep rates) after propagating the inferred lower length scale parameter uncertainties. The approach requires many evaluations of the model, which becomes computationally insurmountable; therefore, a neural-network model is trained to data obtained by sampling the full model over the most important parameters. This neural-network is then used in the Bayesian inference approach to determine probability distributions in the parameter values that represent the uncertainty in the model given what is known from the experiments (posterior). A significant reduction compared to conservative initial (prior) uncertainties is achieved through inference against the experimental data, demonstrating the efficacy of this approach. Furthermore, by accounting for uncertainties in the experimental conditions and sample non-stoichiometry, it is possible to resolve apparent discrepancies in experimental measurements within a self-consistent grain boundary (Coble) creep model that is sensitive to chemistry. This work has been written up and submitted to Nuclear Technology for a special issue on accelerated fuel qualification (AFQ). This uncertainty quantification (UQ) work not only improves the diffusional model, while accounting for uncertainty, but also establishes a framework which can readily be applied to the mechanistic models of dislocation deformation developed in this study. The most likely values from the Bayesian analysis are incorporated into our UO 2 diffusional creep model and a lower length scale-informed irradiation UO 2 creep mechanistic model to generate a dataset. This dataset has been provided to our INL collaborators for training an artificial neural network surrogate model, which will be implemented in the BISON fuel performance code to assess how the results differ from those currently obtained using a fully empirical model and that of using the nominal (uncalibrated) atomic scale parameters in our mechanistic model. Plastic deformation (creep and glide) in UO 2 is a complex phenomenon, governed by multiple underlying processes such as local defect concentrations, applied stresses, and microstructural characteristics. Consequently, there is a need for a meso-scale model with polycrystalline resolution capable of extrapolating to large grain sizes applicable to doped UO 2 , where data is limited and the model can help bridge the knowledge gap. By integrating atomistic data into the polycrystal LApx code, it becomes possible to predict dislocation climb and glide plasticity that simple analytical models cannot accurately represent. The application of atomic-scale data within LApx demonstrated the importance of climb and glide mechanisms in reproducing high-stress UO 2 behavior. Behaviors such as this are crucial to capture and implement in BISON, as parts of the fuel pellet can reach temperatures where glide can occur before pellet cracking. This model which captures dislocation based mechanisms for UO 2 is then used to stand up the doped model accounting for larger grain sizes. It was found that larger grain sizes can lead to enhanced deformation rates in the glide regime, and therefore can help with the pellet cladding mechanical interaction. Therefore if the fuel pellet reaches conditions (stress/temperature) where glide is active, the enhanced creep rates for larger grains in the glide regime (doped UO 2 ) can help with pellet cladding mechanical interactions. Plastic deformation in UO 2 involves multiple mechanisms, including diffusional creep, dislocation climb, and glide. This milestone contains two parts: (1) UQ of a pre-existing lower length scale informed mechanistic diffusional creep model, and (2) development of a new LApx based model for dislocation-mediated creep mechanisms in UO 2 , with application to large-grain doped UO 2 .

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2019

Impact of Compositional Fluctuation on Dislocations in Metamorphic III-V Solar Cells Revealed by Cathodoluminescense Spectrum Imaging

Compositionally graded buffers (CGBs) are essential components of high-efficiency III-V inverted metamorphic solar cells. High-quality CGBs with low defect densities are a requirement for high device efficiencies. In this work we use cathodoluminescence spectrum imaging to investigate the effect of growth conditions on the material properties of AlyGa1-x-yInxAs CGBs with xIn = > 0.30. We find that significant compositional fluctuation exists in these materials, and that it correlates with the distribution of threading dislocations in the CGBs. Threading dislocations collect in regions with large compositional fluctuation, implying that concurrent strain fluctuations in these regions restrict dislocation motion. Thus, the compositional fluctuation leads to elevated threading dislocation densities that degrade CGB quality. We investigate the effectiveness of specific growth conditions at suppressing compositional fluctuation and limiting threading dislocation density, and find that CGBs grown at high temperatures with high Al-content exhibit the lowest defect densities. We also demonstrate that use of a high V/III ratio also suppresses compositional fluctuation and defect density. These materials insights lead directly to the development of metamorphic Ga1-xInxAs solar cells grown on AlyGa1-x-yInxAs CGBs with improved device efficiency.

14 SOLAR ENERGY↗

DOE OSTI2024

Distorted dislocation cores and asymmetric glide resistances in titanium

The determination of Critical Resolved Shear Stress (CRSS) in titanium for basal, prismatic, and pyramidal slip-planes without empirical constants is presented by combining Density Functional Theory (DFT) and anisotropic elasticity. A new mechanism leading to tension-compression (T-C) asymmetry in the CRSS levels has been revealed for the first time. The conditions for this asymmetry are established, involving a complex interplay between the dislocation core-structure and core-advance behavior. The three conditions for T-C asymmetry that need to be simultaneously satisfied can be summarized as: (1) a medium stacking fault width, d, (3 < d/b F < 10, where b F is the magnitude of the Burgers vector of the full dislocation), (2) an asymmetric core-structure of the extended dislocation (ξ 1 ≠ ξ 2 , where ξ 1 and ξ 2 are the core-widths of the first and second partials, respectively), and (3) intermittent motion of the partials (Δd/b F ≠ 0, where Δd is the magnitude of fluctuation in stacking fault width during intermittent motion). Pyramidal-slip in titanium satisfies all three conditions, resulting in significant T-C asymmetry. The CRSS theory considers a Wigner-Seitz (W-S) cell based domain area assigned to each lattice site for the calculations of core-energies accurately capturing the slip-plane lattice. The W-S based approach is essential due to the lower symmetry of the HCP crystal circumventing potential errors associated with the one-dimensional atomic-row approximation. Dislocation core structures are obtained for all the slip-systems in titanium showing significant distortion of the disregistry profile governing the core-advance behavior. The CRSS values predicted from the theory show agreement with the experimental CRSS levels reported in the literature.

Dislocation core↗

DOE OSTI2019

A FFT-based numerical implementation of mesoscale field dislocation mechanics: Application to two-phase laminates

In this study, we present an enhanced crystal plasticity elasto-viscoplastic fast Fourier transform (EVPFFT) formulation coupled with a phenomenological Mesoscale Field Dislocation Mechanics (MFDM) theory here named MFDM-EVPFFT formulation. In contrast with classic CP-EVPFFT, the model is able to tackle plastic flow and hardening due to polar dislocation density distributions or geometrically necessary dislocations (GNDs) in addition to statistically stored dislocations (SSDs). The model also considers GND mobility through a GND density evolution law numerically solved with a recently developed filtered spectral approach, which is here coupled with stress equilibrium. The discrete Fourier transform method combined with finite differences is applied to solve both lattice incompatibility and Lippmann-Schwinger equations in an augmented Lagrangian numerical scheme. Numerical results are presented for two-phase laminate composites with plastic channels and elastic second phase. It is shown that both GND densities and slip constraint at phase boundaries influence the overall and local hardening behavior. In contrast with the CP-EVPFFT formulation, a channel size effect is predicted on the shear flow stress with the present MFDM-EVPFFT formulation. The size effect originates from the progressive formation of continuous screw GND pile-ups from phase boundaries to the channel center. The effect of GND mean free path on local and global responses is also examined for the two-phase composite.

36 MATERIALS SCIENCE↗

DOE OSTI2011

Direct Experimental Measurement of the Speed-Stress Relation for Dislocations in a Plasma Crystal

The speed-stress relation for gliding edge dislocations was experimentally measured for the first time. The experimental system used, a two-dimensional plasma crystal, allowed observation of individual dislocations at the ''atomistic'' level and in real time. At low applied stress dislocations moved subsonically, at higher stress their speed abruptly increased to 1.9 times the speed of shear waves, then slowly grew with stress. There is evidence that immediately after nucleation dislocations can move faster than pressure waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗