Dislocation Contrast Factors Research Articles

Synergistic effects of chemical composition on precipitates, dislocations, and mechanical properties of precipitation-strengthened alloys

The properties of materials are intricately dependent on their chemical composition, and microstructures. Achieving a precise modulation in the composition and microstructure of materials to enhance properties significantly is a huge challenge. In this work, we uncovered the effects of nickel and silicon composition on the precipitates, dislocations, and properties of Cu–Ni–Si alloys. The results show that the volume fraction of precipitates increased from 0.84 % to 4.80 % with the increase of Ni and Si contents. The average diameter of the precipitates increased from 6.20 nm to 20.21 nm, and the dislocation density increased from 2.16 × 1013 m−2 to 4.08 × 1015 m−2 concerning the Ni and Si contents. In addition, the dislocation type changes from half-edge dislocation and half-screw dislocation to screw dislocation. The modified WHWA (Williamson Hall-Warren Averbach) method was proved to be the most accurate way of calculating dislocation density. As anisotropy was present in the alloy, adding a dislocation contrast factor and removing some lower-intensity diffraction peaks could further correct the obtained results and reduce the calculation error. Furthermore, the above analysis and findings were employed to design a Cu-3.21Ni-0.66Si alloy with a high yield strength (814 MPa), high ultimate tensile strength (970 MPa), and comparable electrical conductivity of 42.4 % IACS. This work offers a meaningful way to develop precipitation-strengthening alloys.

Synchrotron diffraction characterization of dislocation density in additively manufactured IN 718 superalloy

In the present study, 3-dimensional (3D) parts of Inconel 718 (IN 718) have been fabricated using laser powder bed fusion (L-PBF) processing. Synchrotron diffraction experiments have been carried out on 0.5 mm thick specimens extracted from the as-built 3D parts at an incident energy level and wavelength of 30.05 keV and 0.41377 Å, respectively. The dislocation density ( ρ ) of additively manufactured IN 718 superalloy (AM IN 718) has been characterized using modified Warren-Averbach methodology. Fourier transformation of the synchrotron diffraction data corresponding to the first six reflections i.e., 111, 200, 220, 311, 222 and 400 and using its Fourier coefficients considering modified Warren-Averbach methodology enabled the evaluation of ρ . The ρ in conventionally processed wrought IN 718 (W IN 718) has also been characterized to compliment the results of AM IN 718. The synchrotron diffraction data was also studied considering classical Williamson-Hall and modified Williamson-Hall methodology to understand the influence of strain anisotropy on the peak broadening. The ρ was found to be very high (1.85 ± 0.24 × 10 15 m −2 ) in AM IN 718 which corroborated well with the dislocation substructure observed using transmission electron microscope (TEM). The average dislocation contrast factor ( C ¯ ), as a part of modified Williamson-Hall methodology, was found to account for the strain anisotropy in both AM and W IN 718. • 3D parts of IN 718 have been fabricated using laser powder bed fusion processing. • Dislocation density was characterized using modified Warren-Averbach methodology. • Dislocation character was identified using modified Williamson-Hall methodology. • Additively manufactured IN 718 contains high dislocation density (1.85 × 10 15 m −2 ). • Additively manufactured IN 718 contains high fraction of edge dislocations.

XRD Line Profile Analysis of Ball Milled ODS Ferritic Steel Powder Consolidated by Hot Isostatic Pressing

In this study, an ODS ferritic steel powder of composition Fe–12Cr–2W–1Zr–0.2Y (in wt %) was mechanically alloyed in a planetary ball mill, until the proper solid solution was established and consolidated by hot isostatic pressing. Basic microstructure features, in terms of the nature, density of the dislocations, lattice parameter and lognormal domain sizes distribution,—were determined by X-ray diffraction profile analysis, using the recent, powerful whole powder pattern modelling approach. XRD analysis revealed that microstructure during ball milling evolved towards the nanocrystalline state made of very fine, narrowly dispersed crystallites with strongly correlated dislocation structure of extensive number density of dislocations reaching almost 1017 m–2. Mean coherent domain size was estimated using both whole powder pattern modelling and modified Williamson–Hall methods, which yielded 9.5 and 7.5 nm, respectively. Powder consolidation induced crystallite growth accompanied with restrained drop in dislocation density. The anisotropic strain broadening of bcc iron diffraction peaks was taken into account by incorporating the dislocation contrast factor, directly related to elastic constants of material and to the dislocation slip system.

Inhomogeneous Strains and Dislocation Evolution in Surface-Treated Ni-Base Superalloys

Surface treatment processes such as shot-peening create near-surface residual stresses in the component, which retard the initiation and growth of fatigue cracks. These processes, however, also induce considerable amount of strain hardening and alter the sub-surface dislocation structure of the material, which can impact its mechanical and electrochemical properties. Although these effects are critical for part performance, they have not so far been studied for surface-treated Ni-base superalloys, which are widely used for load-bearing applications. To address this, we have developed an X-ray diffraction (XRD) framework based on Convolutional Multiple Whole Profile (CMWP) fitting approach that can be used to quantify dislocation densities in shot-peened Inconel 718 components. The method exploits physics-based mechanisms for size and strain broadening to model these effects and uses dislocation contrast factors to account for deformation-induced crystallographic anisotropy in the diffraction profile. Our results suggest that shot-peening leads to one order of magnitude increase in the dislocation density of Inconel 718 alloys, which is supported by direct evidence from transmission electron micrographs. The approach developed in this work can be extended to other types of Ni-base superalloys, enabling a simple non-destructive method to calculate dislocation densities in this commercially important class of materials.

The analysis of severely deformed pure Fe structure aided by X-ray diffraction profile

Pure Fe was severely deformed by a combination of shaped cold rolling and cold drawing. X-ray diffraction profiles analysis was applied in accordance with the Williamson-Hall (WH) and modified Williamson-Hall (MWH) methods to identify crystallite sizes of the deformed specimens. It was found that some differences exist between the results of WH and MWH procedures using the hkl dependent Young’s modulus or considering the average dislocation contrast factor. The latter method is more accurate and enables the determination of the character of dislocations in plastically deformed Fe. It was shown that by increasing deformation strain, the screw dislocations dominated. The enhancement of hardness occurs in the deformed Fe due to grain refinement, dislocation accumulation and deformation-induced vacancies.

Evolution in the dislocation structure of austenitic 16Cr-15Ni-3Mo-1Ti steel depending on the degree of cold plastic deformation

High-resolution neutron diffraction is employed to determine the main structural parameters and microstrain levels of several austenitic 16Cr-15Ni-3Mo-1Ti steel samples subjected to different degrees of cold plastic deformation and estimate the dislocation densities thereof. It is demonstrated that the anisotropic diffraction peak broadening observed in the neutron experiment is caused by variations in the dislocation-contrast factor and can be satisfactorily described with the help of the used model. Comparative analysis of the results obtained by neutron diffraction and transmission electron microscopy is performed.

Evolution of microstructure and hardness in AZ31 alloy processed by high pressure torsion

A commercial MgAlZn alloy (AZ31) was processed by high pressure torsion (HPT) at room temperature, resulting in an extreme microstructure refinement down to the grain size of 150–250nm. The microstructure evolution during HPT was investigated by transmission electron microscopy and X-ray diffraction line profile analysis. The microhardness was measured as a function of the distance from the center of the disk and the number of HPT revolutions. The detailed analysis of dislocation contrast factors in X-ray diffraction line profiles enables to determine the population of the different slip systems as a function of the imposed strain. The influence of microstructure and defect structure evolution on microhardness is discussed in detail.

Microstructural Properties of Chemically Synthesized Cubic ZnS Nanocrystals

In this paper we present microstructural properties of chemically synthesized cubic zinc sulfide (ZnS) nanocrystals, investigated by X-ray diffraction (XRD) line profile analysis applying classical Williamson-Hall (WH) and modified Williamson-Hall (MWH) methods, and transmission electron microscopy (TEM) observations. ZnS nanocrystals are synthesized using 1:1 M ratio of Zn and S precursors with 25, 50, and 75 mM, 2-mercaptoethanol as capping agent. WH analyses show that the average crystallite sizes (lattice strain) are 3.98 nm (2.22 × 10−2), 2.69 nm (1.99 × 10−2), and 2.58 nm (2.65 × 10−2). Dislocation contrast factors of ZnS crystals required for the MWH method are calculated from their elastic stiffness constants for various proportions of screw and edge dislocations. The best fit to MWH equation is found to be for dislocation contrast factors corresponding to 100 % edge dislocations and thereby suggesting edge dislocations are main contributors to strain. MWH analyses show dislocation density of 3.65, 2.69, and 2.47 nm crystallites are 3.19 × 1018 m−2, 2.58 × 1018 m−2, and 4.62 × 1018 m−2 , respectively. The crystallite sizes as estimated from the WH, MWH, and TEM studies are found to be intercorrelated. Presence of edge dislocations, as suggested by the MWH analysis, is confirmed by high resolution TEM (HRTEM) studies.

Evolution of the Burgers-vector population of Cu–Nb multilayers with 7 at% He-implantation determined by X-ray diffraction

Extreme environmental conditions have received considerable attention in the last decade in relation to extending lifetime of materials or developing novel capabilities to achieve a higher endurance. Extreme mechanical properties or the extremely high resistance to irradiation are in the limelight. In the present paper, the He implantation-induced lattice-defect structure of Cu/Nb multilayers with different nominal layer widths is investigated based on the evolution of the prevailing Burgers-vector population, the corresponding dislocation density and a varying coherency length. The virgin and the implanted state can be characterized by using individual dislocation contrast factors in the two different phases. After He implantation, the prevailing microstructure displays a majority of out-of-plane, screw-type dislocations in the developed lattice-defect structure.

X-ray peak profile analysis of dislocation type, density and crystallite size distribution in cold deformed Pb-Ca-Sn alloys

The density, nature of the dislocations and distribution of the domain sizes in cold-deformed Pb-Ca-Sn solid solution were determined by X-ray diffraction profile analysis. The dislocation densities are of the order of 1010 cm−2. The strain broadening of diffraction profiles was accounted for by dislocation contrast factor. The coherent domain size was determined by the recently developed PM2K software package. Assuming that the domain size distribution is log-normal, the distribution function (median μ and variance σ) was calculated from the size parameters determined from X-ray diffraction profile analysis.

Processing of Ultrafine Grained Cu-30%Zn Alloy through Severe Plastic Deformation Using Accumulative Roll Bonding

In the present research, the microstructural features of ultrafine grained Cu-30 Zn alloy via ARB at room temperature were investigated by X-ray diffraction peak profile analysis. The character of dislocations was determined by analyzing the dislocation contrast factors. The average contrast factors for the different reflections obtained by determination of the type of dislocations and Burgers vectors in crystals. Also, using the modified Williamson–Hall and Warren–Averbach procedure size parameters, the effective outer cut-off radius and density of dislocations were determined. Assuming that the grain size distribution is log-normal, the median and the variance of the size distribution of sub grains were obtained. It was found that the crystallite size is reduced substantially, while the dislocation density increases up to 2 cycles of ARB. After 2nd cycle, dislocation density decreases. This is attributed to the occurrence of dynamic restoration process which takes place during next ARB cycles.

Strain analysis on freestanding germanium nanocrystals

We report on a detailed study of strain in freestanding Ge nanocrystals (NCs) by using x-ray diffraction (XRD) line profile analysis supported by high resolution transmission microscopy (HRTEM) imaging. Freestanding Ge NCs down to ∼7 nm size are synthesized by using the ball milling technique and investigated regarding the nature of strain. Detailed analysis of size and lattice strain in the NCs reveals that strain is anisotropic in the NCs. NC size and strain anisotropy factor are calculated by taking into consideration a dislocation contrast factor. The analysis further suggests that screw type dislocations are the main contributors to the strain anisotropy and the dislocation density and corresponding strain vary with crystallite size, with a maximum of both quantities for NCs produced after 20 h of milling. Direct evidence for strain caused by dislocations in individual NCs is provided from HRTEM imaging. Relaxation of strain is studied by differential scanning calorimetry, which shows a low temperature heat release at ∼310 °C, clearly indicating a kind of structural relaxation of the strained NCs. The methodology presented here is applicable for embedded as well as freestanding NCs of other materials. Implications of strain on the optical properties of Ge NCs are discussed.

Strain Anisotropy in Freestanding Germanium Nanoparticles Synthesized by Ball Milling

Although embedded Ge nanocrystals (NCs) have been grown by variety of techniques and its properties have been studied extensively, intrinsic properties of isolated Ge NCs have not been studied properly due to lack of proper synthesis technique. Here we report on the synthesis of freestanding Ge nanoparticles (NPs) down to approximately 7 nm using ball milling technique and study its structural evolution as a function of milling time. Morphology and microstructure of the freestanding Ge NPs are studied using atomic force microscopy, transmission electron microscopy and X-ray diffraction (XRD) analysis. A systematic study of the XRD line profile using Williamson-Hall method reveals presence of anisotropic strain in the milled NPs. Strain anisotropy factor is calculated using a modified Williamson-Hall method by taking into consideration a dislocation contrast factor, assuming that dislocations are main contributors to the strain in these NPs. Our calculations suggest that screw type dislocations are main contributors to the strain anisotropy in the Ge NPs. We find that for milling time up to 40 hrs, NPs size monotonically goes down to approximately 7.3 nm and then almost saturates, while the dislocation density first increases from 1.64 x 10(16) m(-2) to 11.62 x 10(17) m(-2) for milling time up to 20 hrs and then decreases drastically during further milling. We have monitored a low temperature heat release at approximately 310 degrees C from the milled NPs using differential scanning calorimetry, clearly indicating a kind of structural relaxation of the strained NPs.

A general approach for determining the diffraction contrast factor of straight-line dislocations

Dislocations alter perfect crystalline order and produce anisotropic broadening of the X-ray diffraction profiles, which is described by the dislocation contrast factor. Owing to the lack of suitable mathematical tools to deal with dislocations in crystals of any symmetry, contrast factors are so far only known for a few slip systems in high-symmetry phases and little detail is given in the literature on the calculation procedure. In the present paper a general approach is presented for the calculation of contrast factors for any dislocation configuration and any lattice symmetry. The new procedure is illustrated with practical examples of hexagonal metals and some low-symmetry mineral phases.

Slip-System-Related Dislocation Study from In-Situ Neutron Measurements

A combined experimental/computational approach is employed to study slip-system-related dislocation-substructure formation during uniaxial tension of a single-phase, face-centered-cubic (fcc), nickel-based alloy. In-situ neutron-diffraction measurements were conducted to monitor the peak-intensity, peak-position, and peak-broadening evolution during a displacement-controlled, monotonic-tension experiment at room temperature. The measured lattice-strain evolution and the macrostress/macrostrain curves were used to obtain the material parameters required for simulating the texture development by a visco-plastic self-consistent (VPSC) model. The simulated texture compared favorably with experimentally-determined texture results over a range of 0 to 30 pct engineering strain. The grain-orientation-dependent input into the Debye-intensity ring was considered. Grains favorably oriented relative to the two detector banks in the geometry of the neutron experiment were indicated. For the favorably oriented grains, the simulated slip-system activity was used to calculate the slip-system-dependent, dislocation-contrast factor. The combination of the calculated contrast factor with the experimentally-measured peak broadening allows the assessment of the parameters of the dislocation arrangement within the specifically oriented grains, which has a quantitative agreement with the transmission-electron-microscopy results.

Dislocation densities in soft and hard oriented grains of compression deformed textured NiAl polycrystals

Abstract NiAl polycrystals with different textures have been compressed at room temperature with and without confining pressure to strains of 6 and 30 %, respectively. Grain orientation dependent dislocation densities have been determined by X-ray line profile analysis using the multiple whole profile procedure. The dislocation density as well as the stored energy in hard grains, <100> oriented with respect to the compression axis, generally is about half of that in soft grains, which are randomly oriented. Taking into account appropriate individual dislocation contrast factors it has been found that in hard grains slip mainly takes place by <111> screw dislocations while in soft grains there is about a 50 % contribution of mixed type <100> dislocations. The results are discussed with respect to the inhomogeneity of deformation of plastically anisotropic materials and its effect on recrystallization.

Análisis de perfiles de difracción de una aleación Cu –2 % en peso Cr –6 % en peso Mo, aleada mecánicamente

By X-ray diffraction line profile analysis it is possible to obtain valid information of structure and properties of materials. This method is a powerful tool for nanomaterials microstructure characterization. In the present work mechanical alloying of ternary system Cu -2 wt. % Cr -6 wt. % Mo was made between 0.25 and 4 h of milling. By means of modified Warren-Averbach and Williamson-Hall methods the crystallite size, dislocation density, microstrain and average distance between dislocations were estimated. The crystallite size values were corrected by stacking fault presence. It was demonstrated that powders have a high anisotropic strain, which was corrected using the average dislocation contrast factors for fcc structures. Also the influence of milling time and percentage of solute on stacking fault probability and stacking fault energy was determined.

Dislocation model of strain anisotropy

Dislocation model of strain anisotropy is presented. The dislocation theorem of strain broadening is suggested which means that strain broadening can only be caused by dislocation-type lattice defects. Based on this theorem strain anisotropy is modeled and accounted for by assuming that strain broadening is caused by dislocations or dislocation-type lattice defects. The effect of strain anisotropy is summarized in hkl dependent dislocation contrast factors, which can be either averaged over the permutations of hkl indices or are different for each different reflection. The dislocation model of strain anisotropy provides a powerful tool to analyze slip activity, Burgers vector populations, and plasticity on the basis of line profile analysis.

Analytical expression for the dislocation contrast factor of the ⟨001⟩{100} cubic slip-system: Application toCu2O

An analytical solution was obtained for the average contrast factor C{sub hkl} of dislocations with (100) slip-system in anisotropic cubic crystals. The expression provides the dislocation contrast factor as an explicit function of the Miller indices (hkl), the elastic anisotropy factor A{sub z}, and the Poisson ratio {nu}, thus avoiding lengthy numerical calculations or approximate parametrizations. The expression was incorporated in the whole powder pattern modelling algorithm and used to study dislocations in ball milled nanocrystalline Cu{sub 2}O.

Dislocation effects in powder diffraction

Owing to the lack of proper models, mainly for the strain broadening component due to dislocations, full exploitation of whole powder pattern modelling for the microstructural analysis of materials has been limited so far to high-symmetry lattices. An extension of the dislocation-induced broadening model, valid for any lattice symmetry, is proposed here. Dislocation effects are modelled through the description of the dislocation contrast factor in terms of a crystallographic invariant whose terms can be either calculated when the material constants and slip systems are known (allowing a dislocation density to be refined) or refined on the experimental data for an effective estimation of dislocation effects.