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Dislocation-density evolution and pileups in bicrystalline systems
Here, a dislocation-density crystalline plasticity (DCP) framework based on total and partial dislocation densities interactions was used to investigate the behavior of Cu/Pb bicrystals with a focus on GB effects. The modeling predictions were validated with bicrystal compression micropillar experiments. A key new aspect of the modeling approach is to account for partial dislocation-densities. A GB formulation that is directly linked to GB energies was used to monitor GB transmission and blockages, such that pileups can be monitored and predicted at the GB interfaces for misorientations. The predictions indicate that pileups can form due to fully and partially blocked slip-rates and perfect and partial dislocation-densities. As the nominal strain increases from five to fifteen percent, dislocation-densities and pileups significantly increase by almost an order of magnitude. The proposed validated approach provides a microstructural scale predictive framework that accounts for a myriad of defects related to the interactions of partial and perfect dislocation densities that interact at highly misoriented GBs; it is these interactions that are critical to the formation and evolution of dislocation-density pileups that can lead to physically limiting stress accumulations in bicrystals.
Analytic model of dislocation density evolution in fcc polycrystals accounting for dislocation generation, storage, and dynamic recovery mechanisms
Here, an analytic model of the evolution of dislocation density in fcc polycrystals is described. The evolution equations approximately account for most known dislocation storage, dynamic recovery, and dislocation generation mechanisms in fcc polycrystals. Specifically, the model incorporates network (forest) and grain boundary storage, mobile-network and mobile–mobile annihilation, screw–screw annihilation via athermal and thermal single cross-slip, generation by double cross-slip (Koehler mechanism, including dipole formation), Frank-Read sources, grain boundary nucleation, and mobile–immobile dislocation nucleation due to shock loading. Single cross-slip is assumed to proceed through the Friedel–Escaig (FE) mechanism; the corresponding activation energy is calculated using a modified FE model. The activation energy for double cross-slip is calculated for the first time by extending the FE model. The exact evolution equations are integro-differential equations, and as such are difficult to implement in a code; hence, the evolution equations are simplified by making several approximations. Preliminary results on copper are presented, including comparisons to experimental data.
Relationship of dislocation density of silicon to solar cell current loss at low temperature
Large decreases in short circuit current of silicon solar cells have been reported to occur as temperature is decreased below -60 C. Experimental results are presented which relate high dislocation density of the silicon bulk material of cells to the large current loss effect. Solar cells were made by the same processes from a variety of silicon materials, namely low-dislocation-density, high-dislocation-density float-zone, and Czochralski silicon. All cells were etched in a manner which revealed the dislocation density of the cell bulk silicon. It was found that every cell made from any of the various low-dislocation starting materials obtained from three suppliers still had a low-dislocation bulk after cell processing, and that all such cells belonged to category good. Cells made from float-zone materials showed high dislocation densities in their bulk and either fell into category poor, or had intermediate losses of short-circuit current at low temperature.
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.
Effect of varying threading dislocation densities on the optical properties of InGaN/GaN quantum wells with intentionally created V-shaped pits
The effect of varying threading dislocation densities on the internal quantum efficiencies (IQEs) of InGaN quantum wells (QWs), with and without intentionally created “V-pits,” is reported here. InGaN QW samples grown on GaN-on-sapphire templates with threading dislocation densities of <1 × 108 and <1 × 109 cm−2 are compared, with and without GaN/InGaN superlattice (SL) layers incorporated to intentionally open up the threading dislocation cores and form large-size “V-pits.” The formation of “V-pits” is confirmed by cross-sectional transmission electron microscopy to initiate from threading dislocations in the SL layers. The densities of the pits are confirmed by plan-view SEM to agree with the substrate threading dislocation densities. The experimental room temperature IQEs of the “V-pit” QW samples are enhanced to 15% ± 1% compared to 6% ± 2% for conventional QW samples. Both conventional and “V-pit” samples show insensitivity to the magnitude of the dislocation densities with respect to IQE performance, while the “V-pit” samples show shifts in the peak emission wavelengths compared to the conventional samples, attributed to strain modulation. This study provides additional understanding of the causes of the observed insensitivity of the IQEs to different threading dislocation densities.
Fermi energy control of vacancy coalescence and dislocation density in melt-grown GaAs
A striking effect of the Fermi energy on the dislocation density in melt-grown GaAs has been discovered. Thus, a shift of the Fermi energy from 0.1 eV above to 0.2 eV below its intrinsic value (at high temperature, i.e., near 1100 K) increases the dislocation density by as much as five orders of magnitude. The Fermi energy shift was brought about by n-type and p-type doping at a level of about 10 to the 17th per cu cm (under conditions of optimum partial pressure of As, i.e., under optimum melt stoichiometry). This effect must be associated with the fact that the Fermi energy controls the charge state of vacancies (i.e., the occupancy of the associated electronic states) which in turn must control their tendency to coalesce and thus the dislocation density. It appears most likely that gallium vacancies are the critical species.
Rules for the crystallite size and dislocation density evolution in phases during α-ω transformation in Zr under high-pressure and severe plastic flow
The first in-situ X-ray diffraction (XRD) study of the evolution of the crystallite size and dislocation density in phases during plastic strain-induced phase transformation (PT) is performed utilizing α-ω PT in strongly pre-deformed commercially pure Zr as an important example. Rough diamond anvils (rough-DA) are introduced to intensify all occurring processes during heterogeneous compression of Zr in a diamond anvil cell (DAC). The main rule is found that during α-ω PT the crystallite size and dislocation density in ω-Zr depend solely on the volume fraction of ω-Zr and are independent of pressure, plastic strain tensor, its path, and initial nanostructure. Crystallite size in ω-Zr increases from 10 to 60 nm during the PT, while dislocation density reduces from 1.83×10 15 /m 2 to 0.6×10 15 /m 2 . Rough-DA produce a steady nanostructure in α-Zr before PT with smaller crystallite size and larger dislocation density than smooth-DA, leading to a reduction of the minimum pressure for α-ω PT to a record value 0.67 GPa, 9 times smaller than under hydrostatic loading and 5.1 times lower than the phase equilibrium pressure. In addition to strain, the kinetics of strain-induced PT unexpectedly depends on time. Also, strain-controlled part of kinetics is zero order, in contrast to the first-order kinetics with smooth-DA. The obtained results open a new window for understanding the mutual effects of nanostructure evolution and PT during severe plastic flow in various technological and natural processes. In conclusion, they may bring up economic strategies of producing nanocomposites and single-phase nanostructured materials with optimal properties.
Relationship of dislocation density of silicon to solar cell current loss at low temperature.
Large decreases in short circuit current of silicon solar cells have been reported to occur as temperature is decreased below -60 C. Experimental results are presented which relate high dislocation density of the silicon bulk material of cells to the large current loss effect. These results reveal a direct relationship between low bulk dislocation density and low current loss at low temperature. Oxygen content does not appear to play a significant role in the low temperature-large current loss effect, since some Czochralski cells did not suffer from this effect whereas some float-zone cells did. Other float-zone silicon cells had only medium current losses at low temperature despite their high bulk dislocation density. It appears that use of low-dislocation-density silicon can eliminate the current loss problem in low temperature cell operation.
Edge Stabilized Ribbon (ESR); Stress, Dislocation Density and Electronic Performance
The edge stabilized ribbon (ESR) silicon ribbon was grown in widths of 1, 2.2 and 4.0 inches at speeds ranging from .6 to 7 in/min, which result in ribbon thicknesses of 5 to 400 microns. One of the primary problems remaining in ESR growth is that of thermally induced mechanical stresses. This problem is manifested as ribbon with a high degree of residual stress or as ribbon with buckled ribbon. Thermal stresses result in a high dislocation density in the grown material, resulting in compromised electronic performance. Improvements in ribbon flatness were accomplished by modification of the ribbon cooling profile. Ribbon flatness and other experimental observations of ESR ribbon are discussed. Laser scanner measurements show a good correlation between diffusion length and dislocation density which indicates that the high dislocation densities are the primary cause of the poor current performance of ESR materials. Dislocation densities were reduced and improved electronic performance resulted. Laser scanner data on new and old material are presented.
Challenges of relaxed n -type GaP on Si and strategies to enable low threading dislocation density
We directly show that doping type strongly affects the threading dislocation density (TDD) of relaxed GaP on Si, with n-type GaP having a TDD of ~3.1 × 10 7 cm -2 , nearly 30× higher than both p-type and unintentionally doped GaP at ~1.1 × 10 6 cm -2 . Such a high TDD is undesirable since n-GaP on Si serves as the starting point for the growth of epitaxial III-V/Si multi-junction solar cells. After highlighting additional challenges for highly n-doped GaP on Si including increased surface roughness, anisotropic strain relaxation, and inhomogeneous TDD distributions from blocking of the dislocation glide, we go on to show that the TDD of n-GaP on Si rises by 10× as the doping concentration increases from ~5 × 10 16 to ~2 × 10 18 cm -3 . Next, we investigate the effects of additional dopant choices on the TDD, determining that electronic effects dominate over solute effects on the dislocation velocity at these concentrations. Finally, we demonstrate the respective roles of compressively strained superlattices, low-temperature initiation, and lowered n-type doping concentration on reducing the TDD for n-GaP on Si. By combining all three, we attain relaxed n-GaP on Si with a TDD of 1.54(±0.20) × 10 6 cm -2 , approaching parity with p-GaP on Si. Such high-quality n-GaP on Si will play an important role in boosting the efficiency of epitaxial III-V/Si multi-junction solar cells.
The relationship between dislocation density and flow stress in materials deforming by a Peierls-Nabarro mechanism.
Thermally activated deformation relating flow stress to square root of dislocation density
Influence of the Dislocation Density on the Performance of Heteroepitaxial Indium Phosphide Solar Cells
Calculations are made to study the dependence of heteroepitaxial InP solar-cell efficiency on dislocation density. Effects of surface recombination velocity and cell emitter thickness are considered. Calculated results are compared with the available experimental results on representative InP solar cells. It is shown that heteroepitaxial InP cells with over 20 percent AM0 efficiency could be fabricated if dislocations are reduced to less than 100,000/sq cm.
Subgrain geometrically necessary dislocation density mapping in spalled Ta in three dimensions
Here, in this work, the intragranular distributions of the densities of geometrically necessary dislocations (GNDs) generated in a polycrystalline tantalum (Ta) sample loaded in shock compression to spall are investigated. The sample studied is a highly resolved three-dimensional (3D) map of the orientations, grain boundary morphology, and voids across a 0.276mm 3 (with sample dimensions of 688.5µm x 669µm x 600µm) region of the microstructure about the spall plane obtained by TriBeam tomography. We present a formulation for calculating the crystallographic screw and edge character GND densities at a material point within body centered cubic (BCC) crystals when provided any number of potential slip systems or modes. Combining the 3D characterization, GND formulation, and a sample containing ≈ 6000 grains, we sought statistically relevant correlations between GND density per grain with grain size, grain orientation, void formation, and proximity from the spall plane. We show that GND density per grain increases with decreasing distance from the spall plane. Most grains had heterogeneously distributed GND densities but were free of any detectable voids, at least within the ≈ 1.5µm resolution of the characterization technique. It is found that the GND density for most grains is insensitive to grain size and grain orientation. Only the fraction of grains with the highest GND densities tended to have a [001] parallel to shock-direction orientation. Intragranular 3D maps of GNDs reveals that grains that contain voids have high GND density concentrations in the intragranular region immediately surrounding the void. The local intragranular GND mapping also showed voids that are connected to grain boundaries preferred to grow into the grain with the larger size, regardless of orientation.
Effect of loading path on grain misorientation and geometrically necessary dislocation density in polycrystalline aluminum under reciprocating shear
Solid phase processing (SPP) is a promising alloy fabrication technique to produce fine and homogeneous grain structures for high-performance alloys. However, there is very limited modeling capability to understand and predict the grain refinement during SPP. In this work, the crystal plasticity theory was used to study elastic-plastic deformation in polycrystalline aluminums under large shear deformation. Two approaches, kernel averaged misorientation (KAM) and grain reference orientation deviation (GROD), were used to assess the grain misorientations. The geometrically necessary dislocation (GND) density was computed with the plastic strain rate. The deformation simulations were carried out under two loading conditions to investigate the effect of loading paths on the evolutions of grain misorientation and GND density. The results show that the regions with high misorientation and GND density first appear near grain boundaries. These regions then extend toward interior grains. The loading path affects dislocation system activation and dislocation recovery, hence dislocation evolution and misorientation. In conclusion, both two- and three-dimensional simulations showed that the spatial and temporal evolutions of GROD, KAM, and GND density in are closely correlated, which indicates they all can be used as criteria of grain refinement or recrystallization.
Quantification of grain boundary effects on the geometrically necessary dislocation density evolution and strain hardening of polycrystalline Mg 4Al using in situ tensile testing in scanning electron microscope and HR-EBSD
In situ tensile testing in a scanning electron microscope (SEM) in conjunction with high-resolution electron backscatter diffraction (HR-EBSD) under load was used to characterize the evolution of geometrically necessary dislocation (GND) densities at individual grain boundaries as a function of applied strain in a polycrystalline Mg—4Al alloy. The increase in GND density was investigated at plastic strains of 0 %, 0.6 %, 2.2 %, 3.3 % from the area including 76 grains and correlated with (i) geometric compatibility between slip systems across grain boundaries, and (ii) plastic incompatibility. We develop expressions for the grain boundary GND density evolution as a function of plastic strain and plastic incompatibility, from which uniaxial tensile stress-strain response of polycrystalline Mg—4Al are computed and compared with experimental measurement. The findings in this study contribute to understanding the mechanisms governing the strain hardening response of single-phase polycrystalline alloys and more reliable prediction of mechanical behaviors in diverse microstructures.
Investigation of grain size and geometrically necessary dislocation density dependence of flow stress in Mg-4Al by using nanoindentation
Models for grain size dependence of flow stress typically ignore contributions from geometrically necessary dislocations (GNDs) in the grain boundary regions. Ashby had proposed the following equation for flow stress (τ) as a function of grain size (d) and effective plastic strain ($\bar{ε}$): $τ = τ_{0} + C'G\sqrt{^{b\bar{ε}}_{d}}$ using an unknown empirical coefficient, C’, In this study, the coefficient, C’, and equation for the grain size dependence of flow stress were investigated in Mg-4Al using nanoindentation. C’ ranges from 1.4 to 7.11 that is related to the hardness difference (∆H0) between the adjacent grains as $C' + 0.62\sqrt{ΔH_{0}}$. Ashby equation was used to predict uniaxial stress-strain curves in grain sizes of 55 µm, 187 µm, and 333 µm. The results showed lower flow stress and lower hardening rate compared to experimentally measured tensile stress-strain response. The discrepancy seems to be a result of hardening effect of SSDs. Here, we propose a modified Ashby equation that takes into account the hardening effect of SSDs and GNDs separately, resulting in a better agreement between calculated and experimentally measured values. This analysis demonstrates estimation of uniaxial stress-strain response using nanoindentation measurements that captures effects of grain size, and strain hardening from SSDs and GNDs. The combination of the revised equation and nanoindentation method will enable rapid exploration of stress-strain response of a diverse range of single-phase polycrystalline alloys.