Determination Of Dislocation Density Research Articles

Effect of prestrain on tensile behavior of HS800 steel sheet

With the development of advanced high strength steels like HS800 and HS1000, it is imperative to develop an understanding of their tensile properties. The effect of 0%, 5%, 7.5%, and 10% prestrain on the tensile behaviour of HS800 steel sheet was investigated in the current research. The optical micrograph of as received HS800 steels reveals the presence of ferrite grains with polygonal morphology without the presence of pearlite or cementite. Moreover, in higher pre-straining conditions, both polygonal and acicular ferrite phases are observed to coexist with the second phase (martensite/austenite). Tensile tests were performed on base HS800 steel sheets in three different directions (rolling, transverse, and diagonal), and it was found that the strength and ductility in the transverse direction were greater than the rolling and diagonal direction. Tensile strength had a linear relationship with the prestrain condition, whereas ductility had an inverse relationship. XRD analysis was used for phase identification and determination of dislocation density. A scanning electron microscope (SEM) was used to observe the ductile fracture behaviour in tensile specimens. The strain hardening exponent of HS800 steel was determined by comparing tensile data to Hollomon and Ludwik's mathematical equations. To understand the dislocation structure evolution of as received and various prestraining conditions samples, a transmission electron microscope (TEM) study was performed. The prestraining study of the HS800 steel gives a new horizon to high strength materials that can be utilized to design the current and future automobile industries requirements.

Analysis of the dislocation activity of Mg-Zn-Y alloy using synchrotron radiation under tensile loading.

An understanding of deformation behavior and texture development is crucial for the formability improvement of Mg alloys. X-ray line profile analysis using the convolutional multiple whole profile (CMWP) fitting method allows the experimental determination of dislocation densities separately for different Burgers vectors up to a high deformation degree. A wider use of this technique still requires exploration and testing of various materials. In this regard, the reliability of the CMWP fitting method for Mg-Zn-Y alloys, in terms of the dislocation activity during tensile deformation, was verified in the present study by the combined analysis of electron backscatter diffraction (EBSD) investigation and visco-plastic self-consistent (VPSC) simulation. The predominant activity of non-basal 〈a〉 dislocation slip was revealed by CMWP analysis, and Schmid factor analysis from the EBSD results supported the higher potential of non-basal dislocation slip in comparison with basal 〈a〉 dislocation slip. Moreover, the relative slip activities obtained by the VPSC simulation also show a similar trend to those obtained from the CMWP evaluation.

Effect of thermal shock induced dislocation multiplication on the thermal conductivity of 60 vol% SiCp/Al–7Si composites

Dislocation affects the thermal conductivity and coefficient of the thermal expansion of high-volume fraction SiCp/Al composites. However, it still remains unclear to what extent the dislocation density in the composite would be increased by thermal shock. Herein, the as-cast 60 vol% SiCp/Al–7Si composites produced via the gas-infiltration technique possess a relatively low porosity but significant lattice misfit at the interfaces. The aqueous- and liquid nitrogen-quenching exerted on the as-cast samples can produce fractures at the SiCp/Al interfaces at different extent. The neutron diffraction technique is carried out to investigate the effect of thermal shock treatments on volume-averaged dislocation densities in the composites. Results show that the dislocation configuration of the composites with as-cast and aqueous-quenching states are similar, but different from that of the sample with a liquid nitrogen-quenching state. Compared with the as-cast composite, the aqueous-quenching and liquid nitrogen-quenching treatments cause the significant increase of dislocation density. However, it only results in a relatively slight reduction of the thermal conductivity of the aluminum matrix. This work provides some references for the dislocation density determination in the high-volume fraction metal matrix composites.

Yellow luminescence and carrier distribution due to polarity-dependent incorporation of carbon impurities in bulk GaN by Na flux

We have grown a high growth rate, and low dislocation density (DD) Ga-polar GaN (DD: 4 × 105/cm2) and N-polar GaN (DD: 8 × 105/cm2) bulk single crystal using Na Flux. Variable temperature PL shows that the yellow luminescence (YL) peak energy of Ga-polar GaN (Ga-GaN) and N-polar GaN (N-GaN) are 2.31–2.30 eV and 2.28–2.26 eV, respectively. It can be found that N-GaN has a more vigorous YL intensity and a lower peak energy of YL than Ga-GaN. The variable-temperature and variable-power PL results suggest that the YL origin may be a donor-acceptor pair defect. Dislocations and defects associated with gallium vacancies that could cause YL behavior were ruled out by dislocation density determination and Raman spectroscopy, respectively. The different concentrations of carbon and oxygen in the Ga-GaN and N-GaN that were associated with the adsorption energy were discussed and proved by SIMS. The Raman results show that the carrier concentrations of Ga-polar and N-polar GaN are comparable, which may be because the higher content of carbon impurities in N-polar GaN can act as a deep acceptor to compensate for its higher content of shallow donor impurity oxygen. Therefore, it is suggested that carbon-related energy level transitions are the primary source of YL in both Ga-polar and N-polar GaN, and the compensating effect of carbon impurities leads to similar carrier concentrations in both polar planes.

Influence of prior deformation temperature on strain induced martensite formation and its effect on the tensile strengthening behaviour of type 304 SS studied by XRDLPA

Type 304 stainless steel is a metastable austenitic stainless steel that undergoes strain induced transformation from austenite to α′ martensite during deformation at room temperature. Role of prior deformation, by rolling at room temperature and at 200 °C (a temperature at which the strain induced martensitic transformation does not occur), on the subsequent room temperature tensile deformation behaviour of the austenite phase is investigated. The changes in dislocation density of the parent phase and the volume fraction of the martensite formed due to deformation were estimated by X-ray diffraction line profile analysis of data obtained from Beam Line - 12 of the Indus 2 synchrotron. The contrast caused by dislocations in the austenite phase has been addressed using the modified Williamson-Hall method. The character of dislocations changes from screw to edge above a critical equivalent strain of ~0.14. The influence of martensite formation on the increase in dislocation density in the austenite phase is confirmed from XRDLPA. An alternative approach to determine dislocation density is proposed which is independent of elastic constants of the material and is found to correlate well with the values determined by the Williamson-Smallman approach. The results obtained from XRDLPA are corroborated with EBSD analysis. It is also seen that the composite strength of the steel, which has undergone different levels of deformation, is related to the changes in dislocation density of austenite and volume fraction of martensite based on Taylor's equation enabling correlation of structure-property.

Unraveling dislocation mediated plasticity and strengthening in crack-resistant ZnAlMg coatings

Mg-alloyed zinc coatings suffer from early cracking during deformation due to the combined influences of detrimental constituents (e.g., Zn/MgZn2 binary eutectic), unfavorable crystal orientations and incompatible local plastic deformation. This study addresses the crack resistance and deformation mechanisms of a ZnAlMg coating, in the absence of binary eutectic, by using correlative in-situ scanning electron microscopy tensile tests, electron backscatter diffraction, scanning transmission electron microscopy and micro digital image correlation methods. The plasticity and strengthening mechanisms of the binary eutectic-free ZnAlMg coating are thoroughly unravelled via theoretical and experimental approaches including dislocation slip trace analysis, Taylor factor calculations, quantitative dislocation density determination and slip/strain transfer across the grain boundaries. It has been found that the microstructure of the coating, comprising of primary zinc and ternary eutectic, effectively accommodates the applied strain without cracking till fracture of steel substrate. The absence of binary eutectic and the activation of abundant deformation mechanisms in the coating microstructure, promote local compatible plastic deformation and inhibit early damage. Effective slip transfer is unveiled by activation of pyramidal <c+a> slip in addition to primary dislocation slip systems. The present findings deliver significant insights and solution for improvement in the formability of Mg-alloyed zinc coatings on steel sheets by tailoring the microstructure.

Size-distribution of irradiation-induced dislocation-loops in materials used in the nuclear industry

Neutron or proton irradiation induced dislocation loops in Zr and its alloys are usually characterized by electron microscopy methods. In plastically deformed materials X-ray line profile analysis (XLPA) is now a well-established tool to determine dislocation densities (DDs) with excellent agreement between XLPA and TEM analysis. In irradiated zirconium alloys, however, XLPA determined DDs are often considerably larger than those obtained by TEM. In ion irradiated Cu and W it was shown that X-ray diffraction or MD simulations give significantly larger dislocation loop densities than conventional TEM analysis, which suggests that the smallest loops remain undetected by TEM. Based on these results we developed a new methodology to determine power-law size-distributions of irradiation-induced dislocation loops. We assume that only loops larger than a certain threshold are fully counted in TEM micrographs, whereas XLPA detects all the loops in the entire size range. This new analysis procedure shows that in neutron irradiated Zircaloy-2 in the channel-box materials the total DD is larger than in the cladding materials, even though TEM counting shows the opposite. We also found that there is a correlation between the reciprocal square-root of <a>-loop DDs and the diameter of <a>-loops. Our work shows that irradiation induced loop-formation and irradiation-damage in general can be better determined when we combine TEM investigations with XLPA.

In-plane stress analysis of multiple parallel cracks in an orthotropic FGM medium under time-harmonic loading

This study aimed to investigate the fracture behavior of a cracked orthotropic FGM medium when exposed to an in-plane harmonic load. The mechanical feature of the medium exponentially varied along the y-axis. Using the Fourier transform method, stress was analyzed by assessing Volterra edge dislocation in orthotropic FGM media. The obtained solution was then applied to derive Cauchy singular integral equations to analyze multiple cracks. The mentioned equations were numerically solved to determine dislocation density functions on the crack face which were then used to evaluate dynamic mixed stress intensity factors. The influence of crack interaction, non-homogeneity, and load frequency on the dynamic stress intensity was numerically illustrated through examples.

The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure Determination

The analysis of line broadening in X-ray and neutron diffraction patterns using profile functions constructed on the basis of well-established physical principles and TEM observations of lattice defects has proven to be a powerful tool for characterizing microstructures in crystalline materials. These principles are applied in the convolutional multiple-whole-profile (CMWP) procedure to determine dislocation densities, crystallite size, stacking fault and twin boundary densities, and intergranular strains. The different lattice defect contributions to line broadening are separated by considering the hkl dependence of strain anisotropy, planar defect broadening and peak shifts, and the defect dependent profile shapes. The Levenberg–Marquardt (LM) peak fitting procedure can be used successfully to determine crystal defect types and densities as long as the diffraction patterns are relatively simple. However, in more complicated cases like hexagonal materials or multiple-phase patterns, using the LM procedure alone may cause uncertainties. Here, we extended the CMWP procedure by including a Monte Carlo statistical method where the LM and a Monte Carlo algorithm were combined in an alternating manner. The updated CMWP procedure eliminated uncertainties and provided global optimized parameters of the microstructure in good correlation with electron microscopy methods.

Vacancy Clustering in Dislocation-Free High-Purity Germanium

A germanium crystal of high purity was grown in H2 with a maximum dislocation density of 3000 cm−2, which was estimated by white beam x-ray topography. Due to a dynamical diffraction effect, the topographs revealed the existence of vacancy clusters in the form of voids in dislocation-free parts of the crystal. Etch pit density analysis, the standard technique employed for crystalline wafers to determine dislocation density, failed to reliably represent dislocations in dislocation-free parts of the crystal. On the other hand, we were able to identify a different type of etching pattern for a dislocation-free crystal. Microwave photoconductance decay was utilized to determine the charge carrier lifetime, which was found to be up to 500 μs for regions with dislocations, while being only 100 μs for dislocation-free parts of the crystal.

Determination of dislocation density in GaN/sapphire layers using XRD measurements carried out from the edge of the sample

In this paper, we show a novel measurement approach for determination of the threading dislocations density in GaN/sapphire structures using X-ray diffractometry at edge scans geometry. The presented method is based on measurements carried out both: classically from the surface and from the edge of the sample. Edge scans allow measurements of planes parallel to the growth direction, which permit the unambiguous determination of the number of edge dislocations. This is a new measurement approach that facilitates the characterization of structures. In addition, obtained results have been confirmed by using the wet etching method. In comparation with the obtained results, it can be concluded that both methods give the same results within the experimental uncertainty.

TEM characterization of high burnup fast-reactor MOX fuel

This work examines the radial evolution of a high burnup fast reactor mixed-oxide (MOX) fuel pellet irradiated at the Fast Flux Test Facility (FFTF) using scanning (SEM) and transmission electron microscopy (TEM). At 21.3% fissions per initial metal atoms (FIMA), the sample analyzed in this work is likely among the highest burnup oxide fuel samples ever evaluated using TEM. Initial SEM examination focused on the characterization of the fuel microstructure and solid fission product behavior as a function of radial position. The fuel pellet underwent extensive restructuring as demonstrated by columnar grain formation near the central void. Oxide fission product phases were confined to near the fuel centerline and decomposed from perovskite BaZrO3 to the fluorite ZrO2 type crystal structure. Metallic five metal precipitates (FMPs) were observed at all radial positions and the Pd-rich metallic phase increased in area fraction moving toward the pellet surface. TEM examination focused on the determination of dislocation density ranging from the fuel pellet center to the pellet surface. Dislocation density was highest in the cooler regions of the fuel pellet, with the outer edge experiencing grain refinement and high defect concentrations consistent with the rim structure. The results of the paper highlight the variable dislocation behavior as a function of radial position in high burnup MOX fuels, as well as describe the largely unexplored change in crystal structure of the oxide solid fission product phase.

Dislocation densities in cold worked copper by electron and X-ray diffraction methods

ABSTRACTElectron backscatter diffraction (EBSD) and X-ray diffraction line profile analysis (XLPA) methods are suitable to determine dislocation densities within crystalline structures. A software was developed to obtain dislocation density from misorientations measured between the adjacent points by EBSD. However, this EBSD-based method can estimate only the density of geometrically necessary dislocations (GND), while XLPA method can give the total dislocation (TD) density. In this paper, GND densities are determined and compared them to the TD densities in as-received and severe plastic deformed copper samples. Based on these results, estimations are tested to provide reliable GND densities and to appreciate the applicability of this calculation method. Furthermore, correlations are found between TD densities and yield strengths estimated by hardness tests.

Determination of dislocation density in an Inconel 600 nickel alloy by XLPA and automated EBSD

There are two widely used examination methods to study microstructure of polycrystalline materials, namely the automated electron backscatter diffraction (EBSD) and the X-ray diffraction line profile analysis (XLPA). Both methods are suitable to determine quality and quantity of crystallographic defects or irregularities within crystalline structures. However, the EBSD method can be used to estimate the density of only geometrically necessary dislocations (GND), while the XLPA method can give the total dislocation density. A novel software was developed for the determination of GND density from misorientations measured between the neighbouring pixels in EBSD images. Therefore EBSD method is a local, while XLPA method is a non-local procedure to determine dislocation densities. In fact, the calculated GND density depends on the applied step size of EBSD measurements, namely GND densities increase with decreasing the step size. So this leads to a question of how large applied step size of EBSD measurements gives a good approximation for the real GND density in a given polycrystalline material.

Density of bunched threading dislocations in epitaxial GaN layers as determined using X-ray diffraction

X-ray diffraction is one of the most popular experimental methods employed for determination of dislocation densities, as it can recognize both the strain fields and the local lattice rotations produced by dislocations. The main challenge of the quantitative analysis of the dislocation density is the formulation of a suitable microstructure model, which describes the dislocation arrangement and the effect of the interactions between the strain fields from neighboring dislocations reliably in order to be able to determine the dislocation densities precisely. The aim of this study is to prove the capability of X-ray diffraction and two computational methods, which are frequently used for quantification of the threading dislocation densities from X-ray diffraction measurements, in the special case of partially bunched threading dislocations. The first method is based on the analysis of the dislocation-controlled crystal mosaicity, and the other one on the analysis of diffuse X-ray scattering from threading dislocations. The complementarity of both methods is discussed. Furthermore, it is shown how the complementarity of these methods can be used to improve the results of the quantitative analysis of bunched and thus inhomogeneously distributed threading dislocations and to get a better insight into the dislocation arrangement.

Determination of Dislocation Density in Lath Martensite by Means of Electron Backscatter Diffraction

As a novel procedure for determining dislocation density, a software was improved with which data obtained by Scanning Electron Microscope (SEM) measurements can be collected and the value of superficial dislocation density can be calculated. Applying this method we investigated cold rolled lath martensitic steel samples. Besides dislocation density values, microstructure mapped by Electron Backscatter Diffraction (EBSD) will be discussed.

Determination of dislocation density of a class of n-GaN based on the variable temperature Hall-effect method

An analytical model for electron mobility in a class of wurtzite n-GaN, whose carrier concentration is over 1018 cm-3 (Mott's critical limit), is developed. With the dislocation density and two donor levels serving as the important parameters, the proposed model can accurately predict the electron mobility as a function of temperature. The edge and screw dislocation densities in two samples, which are respectively grown on sapphire (001) by metal organic chemical vapor deposition and hydride vapor phase epitaxy, are determined by using this model which is discussed in detail. It is shown that the data-fitting of H-T characteristic curve is a highly suitable technique for accurately determining the edge and screw dislocation densities in n-GaN films. Quantitative analyses of donor concentration and donor activation energy indicate that the impurity band occurs when the carrier concentration is under 1017 cm-3, much lower than the critical carrier concentration of Mott transition (1018 cm-3). Such a behavior can also be confirmed by the results from solving the Boltzmann transport equation by using the Rode iterative method. Another anomaly is that the dislocation density in Mott transition material perhaps is lower than that of material with carrier concentration under 1018 cm-3. This fact indicates that the cause of Mott transition should not be the shallow donor impurities around dislocation lines, but perhaps the deeper donor impurities or other defects. In the theoretical model calculation, two transition characteristics together with the donor distribution and its energy equilibrium are taken into account. Based both on the Mott transition and the H-like electron state model, the relaxation energies for the shallow-donor defects along the screw and edge dislocation lines are calculated by using an electrical ensemble average method. Besides, an assumption that should be made is that there are 6 shallow-donor defect lines around one dislocation line. The research results show that the Hall mobility should be taken as the live degree of the ionizing energy for the shallow-donor defects along the dislocation line. The experimental results indicate that our calculation function can be best fit by the experimental curve, with the values of dislocation density being between our model and others determined by X-ray diffraction or by chemical etching method, which are all in good agreement with each other. The method reported can be applied to the wurtzite n-GaN films grown by various preparation technologies under any condition, with the peak-mobility temperature about or over 300 K, whose Hall mobility near 0 K perhaps is over 10 cm2/(Vs) and even 100 cm2/(Vs).

Shear-Coupled Grain Growth and Texture Development in a Nanocrystalline Ni-Fe Alloy during Cold Rolling

The evolution of texture, grain size, grain shape, dislocation, and twin density has been determined by synchrotron X-ray diffraction and line profile analysis in a nanocrystalline Ni-Fe alloy after cold rolling along different directions related to the initial fiber and the long axis of grains. The texture evolution has been simulated by the Taylor-type relaxed-constraints viscoplastic polycrystal model. The simulations were based on the activity of partial dislocations in correlation with the experimental results of dislocation density determination. The concept of stress-induced shear coupling is supported and strengthened by both the texture simulations and the experimentally determined evolution of the microstructure parameters. Grain growth and texture evolution are shown to proceed by the shear coupling mechanism supported by dislocation activity as long as the grain size is not smaller than about 20 nm.

Joint Raman spectroscopy and HRXRD investigation of cubic gallium nitride layers grown on 3C-SiC

Cubic gallium nitride (GaN) films are analyzed with highresolution X-ray diffraction (HRXRD) and Raman spectroscopy. Several cubic GaN layers were grown on 3C-SiC (001) substrate by radio-frequency plasma-assisted molecular beam epitaxy. The layer thickness of the cubic GaN was varied between 75 and 505 nm. The HRXRD analysis reveals a reduction of the full-width at half-maximum (FWHM) of omega scans for growing layer thicknesses, which is caused by a partial compensation of defects. The Raman characterization confirms well-formed c-GaN layers. A more detailed examination of the longitudinal optical mode hints at a correlation of the FWHM of the Raman mode with the dislocation density, which shows the possibility to determine dislocation densities by Ramanspectroscopy on a micrometer scale, which is not possible by HRXRD. Furthermore, this Raman analysis shows that normalized Raman spectra present an alternative way to determine layer thicknesses of thin GaN films.

Determination of dislocation density by electron backscatter diffraction and X-ray line profile analysis in ferrous lath martensite

The microstructure and the dislocation density in as-quenched ferrous lath martensite were studied by different methods. The blocks, packets and variants formed due to martensitic transformation were identified and their sizes were determined by electron backscatter diffraction (EBSD). Concomitant transmission electron microscopy (TEM) investigation revealed that the laths contain subgrains with the size between 50 and 100nm. A novel evaluation procedure of EBSD images was elaborated for the determination of the density and the space distribution of geometrically necessary dislocations from the misorientation distribution. The total dislocation density obtained by X-ray diffraction line profile analysis was in good agreement with the value determined by EBSD, indicating that the majority of dislocations formed due to martensitic transformation during quenching are geometrically necessary dislocations.