Weighted Burgers Vector analysis of orientation fields from high-angular resolution electron backscatter diffraction.

The Weighted Burgers Vector (WBV) method can extract information about dislocation types and densities present in distorted crystalline materials from electron backscatter diffraction (EBSD) maps, using no assumptions about which slip systems might be present. Furthermore, high-angular resolution EBSD (HR-EBSD) uses a cross-correlation procedure to increase the angular precision of EBSD measurements by an order of magnitude compared to conventional EBSD. However, the WBV technique has not previously been applied to HR-EBSD data and therefore it remains unclear as to which low-angle substructures can be reliably characterised by WBV analysis of conventional EBSD data and which require additional HR-EBSD processing. To establish some practical examples that can be used to guide future data-acquisition strategies, we compare the output of the WBV method when applied to conventional EBSD data and HR-EBSD data collected from the most common minerals in Earth's lower crust (plagioclase feldspar) and upper mantle (olivine). The results demonstrate that HR-EBSD and WBV processing are complementary techniques. The increase in angular precision achieved with HR-EBSD processing allows low-angle (on the order of 0.1°) structures, which are obscured by noise in conventional EBSD data, to be analyzed quantitatively using the WBV method. Combining the WBV and HR-EBSD methods increases the precision of calculated WBV directions, which is essential when using information about active slip systems to infer likely deformation mechanisms from naturally deformed microstructures. This increase in precision is particularly important for low-symmetry crystals, such as plagioclase, that have a wide range of available slip systems that vary in relative activity with changing pressure, temperature and differential stress. Because WBV directions are calculated using no assumptions about which slip systems may be present, combining this technique with HR-EBSD to refine the precision of lattice orientation gradients is ideal for investigating complex natural materials with unknown deformation histories.

Character and Distribution of Geometrically Necessary Dislocations in Polycrystalline Tantalum.

Geometrically necessary dislocations (GNDs) play a key role in accommodating strain incompatibility between neighboring grains in polycrystalline materials. One critical step toward accurately capturing GNDs in deformation models involves studying the microstructural features that promote GND accumulation and the resulting character of GND fields. This study utilizes high-resolution electron backscatter diffraction to map GND populations in a large polycrystalline sample of pure tantalum, under simple tension. A total of 1,989 grains, 3,518 grain boundaries (GBs), and 3,207 triple junctions (TJs) were examined in a subsurface region of the sample. Correlations between GND density and GB character, and to some extent, TJ character, are investigated. Statistical geometrical relationships between these entities are quantified, and also visualized, using a novel application of two-point statistics. The nature of GNDs across the sample is also visualized and assessed using a recently developed method of mapping the local net Burgers vectors. The different approaches to characterizing GND distribution are compared in terms of how they quantify the size of near boundary gradient zones.

The Thermo-Mechanical Response of GeTe under Compression.

Thermoelectric generators (TEGs) are devices capable of transforming heat energy into electricity and vice versa. Although TEGs are known and have been in use for around five decades, they are implemented in only a limited range of applications, mainly extraterrestrial applications. This is due to their low technical readiness level (TRL) for widespread use, which is only at levels of 3-5 approaching laboratory prototypes. One of the most setbacks in reaching higher TRL is the lack of understanding of the mechanical and thermo-mechanical properties of TE materials. Out of ~105,000 entries about TE materials only ~100 entries deal with mechanical properties, while only 3 deal with thermo-mechanical properties. GeTe-based alloys with varying other elements, forming efficient p-type thermoelectric materials in the 200 ÷ 500 °C temperature range, have been intensively researched since the 1960s and have been successfully applied in practical TEGs. Yet, their temperature-dependent mechanical properties were never reported, preventing the fulfillment of their potential in a wide variety of practical applications. The combined effects of temperature and mechanical compression of GeTe were explored in the current research by implementing novel quantitative crystallographic methods to statistically describe dislocation activity and modification of the micro-texture as inflecting by the testing conditions. It is suggested, through utilizing these methods, that the combined effect of compression and temperature leads to the dissolving of twin boundaries, which increases dislocation mobility and results in a brittle-to-ductile transition at ~0.45 of the homologous temperature.

Study on Microstructural Evolution of DP Steel Considering the Interface Layer Based on Multi Mechanism Strain Gradient Theory.

A multi-mechanism constitutive model is proposed in this paper to better describe the effect of the local hardening behavior of the interface layer on the mechanical heterogeneity of dual-phase (DP) steel. The constitutive equations considering the geometrically necessary dislocations (GNDs) and back stress at grain level and sample level were established. Based on the finite element simulation results, the influences of local hardening and microstructure characteristics on the strain-stress evolution, statistical storage dislocations, GNDs, and back stress of DP steel were studied and discussed. Due to the local hardening effect, the ferrite phase was treated as an inhomogeneous matrix reinforced by some small islands of martensite in the simulation. The simulation results show that the thickness of the interface layer has a significant effect on the macroscopic hardening property of DP steel, while the number of interface layers has little effect. Meanwhile, the GNDs and back stress at the grain level also have little effect on the strengthening of DP steel. The contribution of GNDs at the sample level to the flow stress is about 47%.

Isotonic regression for metallic microstructure data: estimation and testing under order restrictions.

Investigating the main determinants of the mechanical performance of metals is not a simple task. Already known physically inspired qualitative relations between 2D microstructure characteristics and 3D mechanical properties can act as the starting point of the investigation. Isotonic regression allows to take into account ordering relations and leads to more efficient and accurate results when the underlying assumptions actually hold. The main goal in this paper is to test order relations in a model inspired by a materials science application. The statistical estimation procedure is described considering three different scenarios according to the knowledge of the variances: known variance ratio, completely unknown variances, and variances under order restrictions. New likelihood ratio tests are developed in the last two cases. Both parametric and non-parametric bootstrap approaches are developed for finding the distribution of the test statistics under the null hypothesis. Finally an application on the relation between geometrically necessary dislocations and number of observed microstructure precipitations is shown.

Insights into tribofilm formation on Ti-6V-4Al in a bioactive environment: Correlation between surface modification and micro-mechanical properties.

Ti-6Al-4V has been used as a surgical implant material for a long time because of its combination of strength, corrosion resistance and biocompatibility. However, there remains much that is not understood about how the surface reacts with the environment under tribocorrosion conditions. In particular, the conditions under which tribofilms form and their role on friction and wear are not clear. To evaluate the complicated nature of the dynamic surface microstructural changes on the wear track, high resolution transmission electron microscopy (TEM), scanning transmission electron microscope (STEM) and electron energy loss spectroscopy (EELS) have been used to characterise the structure and chemical composition of the tribofilm. Detailed analysis of the formation and structure of the tribofilm and the metal surface deformation behaviour were studied as a function of applied potential and the role of proteins in the lubricant. For the first time, graphitic and onion-like carbon structures from wear debris were found in the testing solution. The presence of carbon nanostructures in the tribocorrosion process and the formation of the tribofilm leads to an improved tribocorrosion behaviour of the system, in particular a reduction in wear and friction. A detailed, quantitative, analysis of surface deformation was undertaken, in particular, the geometrically necessary dislocation (GND) density was quantified using precession electron diffraction (PET). A clear correlation between applied potential, tribofilm formation and the surface strain was established. STATEMENT OF SIGNIFICANCE: The formation of tribofilm and microstructure modification of the Ti-6Al-4V surface during tribocorrosion in a physiological environment is not fully understood. In particular, the correlation between microstructural changes and electrochemical conditions is not clear. This study presents a detailed investigation of the structure and chemical composition of tribofilms at the nanoscale during tribocorrosion tests in simulated body fluid and gives a detailed and quantitative description of the evolved surface structure. A clear correlation between applied potential, tribofilm formation and the surface strain was established. Moreover, particular attention is paid to the wear debris particles captured from the lubricating solution, including nanocarbon onion structures. The implications for tribocorrosion of the alloy in its performance as an implant are discussed.

Microscopic origins of the crystallographically preferred growth in evaporation-induced colloidal crystals.

Unlike crystalline atomic and ionic solids, texture development due to crystallographically preferred growth in colloidal crystals is less studied. Here we investigate the underlying mechanisms of the texture evolution in an evaporation-induced colloidal assembly process through experiments, modeling, and theoretical analysis. In this widely used approach to obtain large-area colloidal crystals, the colloidal particles are driven to the meniscus via the evaporation of a solvent or matrix precursor solution where they close-pack to form a face-centered cubic colloidal assembly. Via two-dimensional large-area crystallographic mapping, we show that the initial crystal orientation is dominated by the interaction of particles with the meniscus, resulting in the expected coalignment of the close-packed direction with the local meniscus geometry. By combining with crystal structure analysis at a single-particle level, we further reveal that, at the later stage of self-assembly, however, the colloidal crystal undergoes a gradual rotation facilitated by geometrically necessary dislocations (GNDs) and achieves a large-area uniform crystallographic orientation with the close-packed direction perpendicular to the meniscus and parallel to the growth direction. Classical slip analysis, finite element-based mechanical simulation, computational colloidal assembly modeling, and continuum theory unequivocally show that these GNDs result from the tensile stress field along the meniscus direction due to the constrained shrinkage of the colloidal crystal during drying. The generation of GNDs with specific slip systems within individual grains leads to crystallographic rotation to accommodate the mechanical stress. The mechanistic understanding reported here can be utilized to control crystallographic features of colloidal assemblies, and may provide further insights into crystallographically preferred growth in synthetic, biological, and geological crystals.

Charging Reactions Promoted by Geometrically Necessary Dislocations in Battery Materials Revealed by In Situ Single-Particle Synchrotron Measurements.

Crystallographic defects exist in many redox active energy materials, e.g., battery and catalyst materials, which significantly alter their chemical properties for energy storage and conversion. However, there is lack of quantitative understanding of the interrelationship between crystallographic defects and redox reactions. Herein, crystallographic defects, such as geometrically necessary dislocations, are reported to influence the redox reactions in battery particles through single-particle, multimodal, and in situ synchrotron measurements. Through Laue X-ray microdiffraction, many crystallographic defects are spatially identified and statistically quantified from a large quantity of diffraction patterns in many layered oxide particles, including geometrically necessary dislocations, tilt boundaries, and mixed defects. The in situ and ex situ measurements, combining microdiffraction and X-ray spectroscopy imaging, reveal that LiCoO2 particles with a higher concentration of geometrically necessary dislocations provide deeper charging reactions, indicating that dislocations may facilitate redox reactions in layered oxides during initial charging. The present study illustrates that a precise control of crystallographic defects and their distribution can potentially promote and homogenize redox reactions in battery materials.

Novel remapping approach for HR-EBSD based on demons registration.

In this study, the possibility of utilizing a computer vision algorithm, i.e., demons registration, to accurately remap electron backscatter diffraction patterns for high resolution electron backscatter diffraction (HR-EBSD) applications is presented. First, the angular resolution of demons registration is demonstrated to be lower than the conventional cross-correlation based method, particularly at misorientation angles >0.157 rad. In addition, GPU acceleration has been applied to significantly boost the speed of iterative registration between a pair of patterns with 0.175 rad misorientation to under 1 s. Second, demons registration is implemented as a first-pass remapping, followed by a second pass cross-correlation method, which results in angular resolution of ~0.5 × 10-4 rad, a phantom stress value of ~35 MPa and phantom strain of ~2 × 10-4, on dynamically simulated patterns, without the need of implementing robust fitting or iterative remapping. Lastly, the new remapping method is applied to a large experimental dataset collected from an as-built additively-manufactured Inconel 625 cube, which shows significant residual stresses built-up near the large columnar grain region and regularly arranged GND structures.

Ni-base superalloy single crystal (SX) mosaicity characterized by the Rotation Vector Base Line Electron Back Scatter Diffraction (RVB-EBSD) method.

In the present work we present the Rotation Vector Base Line Electron Back Scatter Diffraction (RVB-EBSD) method, a new correlative orientation imaging method for scanning electron microscopy (OIM/SEM). The RVB-EBSD method was developed to study crystal mosaicity in as-cast Ni-base superalloy single crystals (SX). The technique allows to quantify small crystallographic deviation angles between individual dendrites and to interpret associated accommodation processes in terms of geometrically necessary dislocations (GNDs). The RVB-EBSD method was inspired by previous seminal approaches which use cross correlation EBSD procedures. It applies Gaussian band pass filtering to improve the quality of more than 500 000 experimental patterns. A rotation vector approximation and a correction procedure, which relies on a base line function, are used. The method moreover features a novel way of intuitive color coding which allows to easily appreciate essential features of crystal mosaicity. The present work describes the key elements of the method and shows examples which demonstrate its potential.

Study of Geometrically Necessary Dislocations of a Partially Recrystallized Aluminum Alloy Using 2D EBSD.

During recrystallization, the growth of fresh grains initiated within a deformed microstructure causes dramatic changes in the dislocation structure and density of a heavily deformed matrix. In this paper, the microstructure of a cold rolled and partially recrystallized Al-Mg alloy (AA5052) was studied via electron backscattered diffraction (EBSD) analysis. The structure and density of the geometrically necessary dislocations (GNDs) were predicted using a combination of continuum mechanics and dislocation theory. Accordingly, the Nye dislocation tensor, which determines the GND structure, was estimated by calculation of the lattice curvature. To do so, five components of the Nye dislocation tensor were directly calculated from the local orientation of surface points of the specimen, which was determined by two-dimensional EBSD. The remaining components of GNDs were determined by minimizing a normalized Hamiltonian equation based on dislocation energy. The results show the elimination of low angle boundaries, lattice curvature, and GNDs in recrystallized regions and the formation of low angle boundaries with orientation discontinuities in deformed grains, which may be due to static recovery.

Using transmission Kikuchi diffraction in a scanning electron microscope to quantify geometrically necessary dislocation density at the nanoscale.

It is challenging to quantify the geometrically necessary dislocation (GND) density at the nanoscale using conventional electron backscatter diffraction due to its limited spatial resolution. To overcome this problem, in this study, the transmission Kikuchi diffraction (TKD) technique is used to measure lattice orientation and to calculate the corresponding nanoscale GND density. Using the TKD method, a variation of GND density from 6 × 1014 to 1016 m-2 has been measured in a welded super duplex stainless steel sample. The distribution of dislocation density is shown to be in good agreement with transmission electron microscope (TEM) result. Compared with dislocation measurements obtained by TEM, the TKD-GND method is revealed to be a relatively accurate, fast and accessible method.

Mechanically Driven Grain Boundary Formation in Nickel Nanowires.

Metallic nanomaterials are widely used in micro/nanodevices. However, the mechanically driven microstructure evolution in these nanomaterials is not clearly understood, particularly when large stress and strain gradients are present. Here, we report the in situ bending experiment of Ni nanowires containing nanoscale twin lamellae using high-resolution transmission electron microscopy. We found that the large, localized bending deformation of Ni nanowires initially resulted in the formation of a low-angle tilt grain boundary (GB), consisting of randomly distributed dislocations in a diffuse GB layer. Further bending intensified the local plastic deformation and thus led to the severe distortion and collapse of local lattice domains in the GB region, thereby transforming a low-angle GB to a high-angle GB. Atomistic simulations, coupled with in situ atomic-scale imaging, unravelled the roles of bending-induced strain gradients and associated geometrically necessary dislocations in GB formation. These results offer a valuable understanding of the mechanically driven microstructure changes in metallic nanomaterials through GB formation. The work also has implications for refining the grains in bulk nanocrystalline materials.

The Role of Geometrically Necessary Dislocations in Cantilever Beam Bending Experiments of Single Crystals.

The mechanical behavior of single crystalline, micro-sized copper is investigated in the context of cantilever beam bending experiments. Particular focus is on the role of geometrically necessary dislocations (GNDs) during bending-dominated load conditions and their impact on the characteristic bending size effect. Three different sample sizes are considered in this work with main variation in thickness. A gradient extended crystal plasticity model is presented and applied in a three-dimensional finite-element (FE) framework considering slip system-based edge and screw components of the dislocation density vector. The underlying mathematical model contains non-standard evolution equations for GNDs, crystal-specific interaction relations, and higher-order boundary conditions. Moreover, two element formulations are examined and compared with respect to size-independent as well as size-dependent bending behavior. The first formulation is based on a linear interpolation of the displacement and the GND density field together with a full integration scheme whereas the second is based on a mixed interpolation scheme. While the GND density fields are treated equivalently, the displacement field is interpolated quadratically in combination with a reduced integration scheme. Computational results indicate that GND storage in small cantilever beams strongly influences the evolution of statistically stored dislocations (SSDs) and, hence, the distribution of the total dislocation density. As a particular example, the mechanical bending behavior in the case of a physically motivated limitation of GND storage is studied. The resulting impact on the mechanical bending response as well as on the predicted size effect is analyzed. Obtained results are discussed and related to experimental findings from the literature.

Deformation compatibility in a single crystalline Ni superalloy.

Deformation in materials is often complex and requires rigorous understanding to predict engineering component lifetime. Experimental understanding of deformation requires utilization of advanced characterization techniques, such as high spatial resolution digital image correlation (HR-DIC) and high angular resolution electron backscatter diffraction (HR-EBSD), combined with clear interpretation of their results to understand how a material has deformed. In this study, we use HR-DIC and HR-EBSD to explore the mechanical behaviour of a single-crystal nickel alloy and to highlight opportunities to understand the complete deformations state in materials. Coupling of HR-DIC and HR-EBSD enables us to precisely focus on the extent which we can access the deformation gradient, F , in its entirety and uncouple contributions from elastic deformation gradients, slip and rigid body rotations. Our results show a clear demonstration of the capabilities of these techniques, found within our experimental toolbox, to underpin fundamental mechanistic studies of deformation in polycrystalline materials and the role of microstructure.

Size-dependent energy in crystal plasticity and continuum dislocation models.

In the light of recent progress in coarsening the discrete dislocation mechanics, we consider two questions relevant for the development of a mesoscale, size-dependent plasticity: (i) can the phenomenological expression for size-dependent energy, as quadratic form of Nye's dislocation density tensor, be justified from the point of view of dislocation mechanics and under what conditions? (ii) how can physical or phenomenological expressions for size-dependent energy be computed from dislocation mechanics in the general case of elastically anisotropic crystal? The analysis based on material and slip system symmetries implies the negative answer to the first question. However, the coarsening method developed in response to the second question, and based on the physical interpretation of the size-dependent energy as the coarsening error in dislocation interaction energy, introduces additional symmetries. The result is that the equivalence between the phenomenological and the physical expressions is possible, but only if the multiplicity of characteristic lengths associated with different slip systems, is sacrificed. Finally, we discuss the consequences of the assumption that a single length scale governs the plasticity of a crystal, and note that the plastic dissipation at interfaces has a strong dependence on the length scale embedded in the energy expression.