Lattice Strain Distribution Research Articles

Investigating mechanical degradation due to fire exposure of aluminum alloy 5083 using crystal plasticity finite element method

Fire exposure causes significant mechanical property degradation of metallic materials. This paper investigates the influence of fire exposure on mechanical response of AA5083 through in situ neutron diffraction tensile tests and crystal plasticity finite element simulations. The Mechanical Threshold Stress (MTS) model is utilized, with a focus on the lattice strain response under tensile loading before and after exposure. A rigorous material parameter calibration procedure is proposed for this MTS model directly based on yield stress, plastic flow, hardening and rate dependency as a function of temperature, requiring only the macroscopic stress–strain curve. Material parameters of virgin material and fire-exposed material with full recrystallization are calibrated separately using this procedure. To initiate the investigation of mechanical degradation caused by fire exposure, a fire-exposed specimen with partial recrystallization is simulated by assigning material parameters and texture of recrystallized grains to selected grains in the virgin material according to the recrystallization fraction. Experimentally measured stress–strain curves and lattice strain evolution are employed to validate the simulations. For the first time, the local mechanical response of AA5083 is compared between in situ testing and finite element simulations, and the discrepancies of lattice strain evolution between virgin and fire-exposed material are discussed. Finally, the influence of fire-exposure on stress and lattice strain distribution is investigated to provide insight into mechanical property degradation.

Determining the strengths of HCP slip systems using harmonic analyses of lattice strain distributions

A robust methodology is presented to extract slip system strengths from lattice strain distributions for polycrystalline samples obtained from high-energy x-ray diffraction (HEXD) experiments with in situ loading. The methodology consists of matching the evolution of coefficients of a harmonic expansion of the distributions from simulation to the coefficients derived from measurements. Simulation results are generated via finite element simulations of virtual polycrystals that are subjected to the loading history applied in the HEXD experiments. Advantages of the methodology include: (1) its ability to utilize extensive data sets generated by HEXD experiments; (2) its ability to capture trends in distributions that may be noisy (both measured and simulated); and (3) its sensitivity to the ratios of the family strengths. The approach is used to evaluate the slip system strengths of Ti-6Al-4V using samples having relatively equiaxed grains. These strength estimates are compared to values in the literature.

Estimation of Lattice Strain in 4H-SiC Commercial Wafer by Synchrotron Monochromatic X-ray Topographic Contour Mapping

The presence of lattice imperfections in n-doped 4H-SiC substrate crystals grown by physical vapor transport (PVT) leads to a non-uniform distribution of lattice strain. Residual stress raised from the lattice strain has a significant impact on the performance of related power devices. It is thus important to estimate the level and the variation of lattice strain in these crystals. In this study, a method is developed based on synchrotron monochromatic X-ray topography (SMBXT) to measure local strain field in 4H-SiC commercial wafers. This method is applied to a 75mm wafer and the strain map of the entire wafer is obtained. Results show that the level of lattice strain is much more significant than that of lattice tilt in 4H-SiC crystals.

Lattice Strain Pole Figures Analysis in Titanium during Uniaxial Deformation

A theoretical and experimental study was carry out to investigate deformation mechanisms in a textured titanium alloy. In situ neutron diffraction measurements were performed to analyze different {hk.l} family planes ({10.0}, {10.1}, {11.0} and {00.2}) and determine the corresponding internal strain pole figures. This method was applied to a pure titanium (a-Ti) submitted to a uniaxial tensile load up to 2 %. The experimental data was then used to validate the EPSC model in order to predict the distribution of lattice strains determined by neutron diffraction for various diffraction vector directions. This comparison reveals that the model results were in good agreement with the experimental data and the simulations reproduced the lattice strain development observed on the strain pole figures determined by neutron diffraction.

Crystalline microstructure of boehmites studied by multi-peak analysis of powder X-ray diffraction patterns

Nanocrystalline boehmite (gamma-aluminium-oxyhydroxide) is a material of industrial importance, the functionality of which follows from its crystalline microstructure. A procedure for preparing boehmite nanoparticles, comprising the formation of a precipitate by the alkalization of an aqueous solution of aluminium nitrate and subsequent hydrothermal aging, was previously elaborated. The application of an additive (maltitol or tartaric acid) to control the sizes and shapes of crystallites in the produced polycrystalline powder of boehmite was developed. The aim of this work is a study of the effect of the hydrothermal treatment time on nanocrystalline characteristics of boehmite, both in absence and in presence of the additive. The obtained materials were investigated by using X-ray diffraction (XRD) as principal technique and additionally by scanning and transmission electron microscopy. The multi-peak analysis of powder XRD patterns was applied to determine the prevalent crystallite shape, volume-weighted crystallite size distribution, and second-order crystalline lattice strain distribution being principal quantitative characteristics of the crystalline microstructure. Based on these characteristics, three types of the microstructure correlated with the production procedures were observed and discussed in detail. The nanoparticles of boehmites were found to be monocrystalline grains with characteristic habits and sizes of order of ten nanometers weakly dependent on the hydrothermal treatment time.

Investigation of frequency effect on electrical fatigue and crack tip domain-switching behaviors in Pb(Mg1/3Nb2/3)0.65Ti0.35O3 ceramics via synchrotron X-ray diffraction

The effect of frequency on the electrical fatigue, crack growth and domain switching in Pb(Mg1/3Nb2/3)0.65Ti0.35O3 ceramics has been investigated. The changes in microstructure, ferroelectric properties and domain-switching behavior of samples fatigued at 1, 10, 50 and 100Hz were determined. In this experiment, we found that the thickness of the damaged layer under the electrodes and the crack length decrease with increasing frequency. The remnant polarization decreases while the coercive field increases with an increasing number of loading cycles. A domain orientation map around the crack tip was revealed using scanning high-energy X-ray diffraction from a synchrotron source. This showed the effect of fatigue frequency on the lattice strain distribution and ferroelectric domain texture around the crack tip.

Interfaces in Heterogeneous Catalysts: Advancing Mechanistic Understanding through Atomic-Scale Measurements.

Developing novel catalysts with high efficiency and selectivity is critical for enabling future clean energy conversion technologies. Interfaces in catalyst systems have long been considered the most critical factor in controlling catalytic reaction mechanisms. Interfaces include not only the catalyst surface but also interfaces within catalyst particles and those formed by constructing heterogeneous catalysts. The atomic and electronic structures of catalytic surfaces govern the kinetics of binding and release of reactant molecules from surface atoms. Interfaces within catalysts are introduced to enhance the intrinsic activity and stability of the catalyst by tuning the surface atomic and chemical structures. Examples include interfaces between the core and shell, twin or domain boundaries, or phase boundaries within single catalyst particles. In supported catalyst nanoparticles (NPs), the interface between the metallic NP and support serves as a critical tuning factor for enhancing catalytic activity. Surface electronic structure can be indirectly tuned and catalytically active sites can be increased through the use of supporting oxides. Tuning interfaces in catalyst systems has been identified as an important strategy in the design of novel catalysts. However, the governing principle of how interfaces contribute to catalyst behavior, especially in terms of interactions with intermediates and their stability during electrochemical operation, are largely unknown. This is mainly due to the evolving nature of such interfaces. Small changes in the structural and chemical configuration of these interfaces may result in altering the catalytic performance. These interfacial arrangements evolve continuously during synthesis, processing, use, and even static operation. A technique that can probe the local atomic and electronic interfacial structures with high precision while monitoring the dynamic interfacial behavior in situ is essential for elucidating the role of interfaces and providing deeper insight for fine-tuning and optimizing catalyst properties. Scanning transmission electron microscopy (STEM) has long been a primary characterization technique used for studying nanomaterials because of its exceptional imaging resolution and simultaneous chemical analysis. Over the past decade, advances in STEM, that is, the commercialization of both aberration correctors and monochromators, have significantly improved the spatial and energy resolution. Imaging atomic structures with subangstrom resolution and identifying chemical species with single-atom sensitivity are now routine for STEM. These advancements have greatly benefitted catalytic research. For example, the roles of lattice strain and surface elemental distribution and their effect on catalytic stability and reactivity have been well documented in bimetallic catalysts. In addition, three-dimensional atomic structures revealed by STEM tomography have been integrated in theoretical modeling for predictive catalyst NP design. Recent developments in stable electronic and mechanical devices have opened opportunities to monitor the evolution of catalysts in operando under synthesis and reaction conditions; high-speed direct electron detectors have achieved sub-millisecond time resolutions and allow for rapid structural and chemical changes to be captured. Investigations of catalysts using these latest microscopy techniques have provided new insights into atomic-level catalytic mechanisms. Further integration of new microscopy methods is expected to provide multidimensional descriptions of interfaces under relevant synthesis and reaction conditions. In this Account, we discuss recent insights on understanding catalyst activity, selectivity, and stability using advanced STEM techniques, with an emphasis on how critical interfaces dictate the performance of precious metal-based heterogeneous catalysts. The role of extended interfacial structures, including those between core and shell, between separate phases and twinned grains, between the catalyst surface and gas, and between metal and support are discussed. We also provide an outlook on how emerging electron microscopy techniques, such as vibrational spectroscopy and electron ptychography, will impact future catalysis research.

Strain localization and dynamic recrystallization in the ice–air aggregate: a numerical study

Abstract. We performed numerical simulations on the microdynamics of ice with air inclusions as a second phase. Our aim was to investigate the rheological effects of air inclusions and explain the onset of dynamic recrystallization in the permeable firn. The simulations employ a full-field theory crystal plasticity code coupled to codes simulating dynamic recrystallization processes and predict time-resolved microstructure evolution in terms of lattice orientations, strain distribution, grain sizes and grain-boundary network. Results show heterogeneous deformation throughout the simulations and indicate the importance of strain localization controlled by air inclusions. This strain localization gives rise to locally increased energies that drive dynamic recrystallization and induce heterogeneous microstructures that are coherent with natural firn microstructures from EPICA Dronning Maud Land ice coring site in Antarctica. We conclude that although overall strains and stresses in firn are low, strain localization associated with locally increased strain energies can explain the occurrence of dynamic recrystallization.

Hydride formation in core–shell alloyed metal nanoparticles

The model and analysis presented are focused on hydride formation in nanoparticles with a Pd shell and a core formed by another metal. The arrangement of metal atoms is assumed to be coherent (no dislocations). The lattice strain distribution, elastic energy, and chemical potential of hydrogen atoms are scrutinized. The slope of the chemical potential (as a function of hydrogen uptake) is demonstrated to decrease with increasing the core volume, and accordingly the critical temperature for hydride formation and the corresponding hysteresis loops are predicted to decrease as well.

Assessment of X-ray diffraction and crystal plasticity lattice strain evolutions under biaxial loading

A methodology to simulate X-ray diffraction lattice strains using crystal plasticity, replicating in-situ synchrotron experimental measurements during the deformation of a low-carbon steel, has been developed. Uniquely, the model calculated lattice strains for full Debye–Scherrer diffraction rings, providing the in-plane lattice strain distributions determined from crystal plasticity. Thus, a direct method of comparison between experimental and crystal plasticity results becomes possible. The model considered two forms of hardening whilst subjecting the material to two dissimilar proportional strain-paths; uniaxial and balanced biaxial deformation. Both deformation paths showed influence on resulting lattice strain distributions which were also found to depend upon texture. Biaxial straining led to a stronger dependence on the material's hardening behaviour and this was attributed to the higher rate of work hardening seen under biaxial compared to uniaxial straining. However, biaxial deformation showed quite isotropic lattice strains distribution, irrespective of initial texture or hardening. Quantitatively, good agreement between the computed and experimentally determined lattice strain distributions was obtained for each strain path. This success demonstrates the possibility of calibrating crystal plasticity model parameters using such methodologies, or simply to provide insight into the governing mechanisms in polycrystal deformation.

Determining Individual Phase Flow Properties in a Quench and Partitioning Steel with In Situ High-Energy X-Ray Diffraction and Multiphase Elasto-Plastic Self-Consistent Method

The micromechanical properties of the constituent phases were characterized for advanced high-strength steels (AHSS) produced by a quenching and partitioning (Q&P) process with in situ tensile loading under synchrotron-based, high-energy X-ray diffraction. The constituent phases present are retained austenite and three martensites (tempered, untampered, and freshly formed martensites). For the material investigated, the 200 and 220 lattice strains of the retained austenite phase were calculated by examining the changes of the X-ray diffraction peak positions during deformation. The 200 and 211 lattice strains of the various martensitic phases with similar crystal structures were determined by separating their overlapped diffraction peaks. Apart from tempered and untempered martensite, the diffraction peaks of freshly formed martensite as a result of austenite-to-martensite transformation can also be separated due to a high initial austenite volume fraction. The phase stresses are first estimated with an empirical relationship through the X-ray diffraction elastic constants. A multiphase elasto-plastic self-consistent model is next used for more accurate determination of the constitutive behaviors of the various phases by comparing the predicted lattice strain distributions and global stress–strain curves with the measured ones. The determined constitutive laws will be used for microstructure-based modeling for sheet formability of the Q&P AHSS steel.

In-situ high temperature stress analysis of Ti(C,N) coatings on functionally graded cemented carbides by energy dispersive synchrotron X-ray diffraction

We report on in-situ high temperature X-ray thermal stress analysis of chemically graded Ti(C,N) coatings deposited on functionally graded cemented carbide substrates by chemical vapor deposition. The in-situ analyses were performed by energy dispersive X-ray diffraction using synchrotron radiation. The samples were subjected to one individual thermal cycle from room temperature to 800°C and cooled down to room temperature again. The stresses were determined using the sin2ψ method in the Ψ geometry combined with scattering vector measurements in order to unravel the compositional influences on the lattice strain distributions. It was found that the Ti(C,N) thin film presents a cycling residual stress behavior (tensile–compressive–tensile) connected to the temperature cycle. If top-blasting is applied on the thin film layer after the coating process, compressive stresses are generated. These compressive stresses induced by top-blasting are partially released after the high temperature thermal cycle. The functionalization of the cemented carbide substrate influences the level of stresses developed in the coating. The stress behavior as a function of temperature is discussed with the support of finite element modeling by introducing a bi-linear plasticity model to calculate strain relationships which is in agreement with the synchrotron measurements.

Microstructure and lattice strain of Mn-, Zn-, and Cd-doped InSb studied by X-ray diffraction

We have studied the microstructure of quenched samples of polycrystalline undoped InSb and materials doped and codoped with Mn, Zn, and Cd. Using X-ray diffraction profile analysis and the Williamson–Hall method, we evaluated the average lattice strain and the lattice strain in various crystallographic directions in the samples. The results demonstrate that the lattice strain in polished sections and powders depends on both the nature of the cation (its size) and doping level. The more complex lattice strain distribution in polished sections suggests that the dislocations generated there play an important role.

Analysis of Critical Dimensions for Nanowire Core-Multishell Heterostructures.

Critical dimensions for nanowire core-multishell heterostructures are analyzed by using finite-element method based on the energy equilibrium criteria. Results show that the nanowire core-shell heterostructure can sufficiently reduce the strain in the shell and increase the critical shell thickness. The critical dimensions for the nanowire core-multishell heterostructure are determined by the stress fields generated at two heterointerfaces. For thin barrier, the critical dimensions decrease as the core radius increases, while when the barrier is thick enough, the critical dimensions show an increase with the increase of core radius conversely. This can be attributed to a competition between the lattice mismatch and strain distribution, which dominate the critical dimensions alternatively. Two critical quantum well thicknesses are obtained in the nanowire core-multishell heterostructure. Below the dislocation-free critical thickness, the structure will be coherent regardless of the barrier thickness. While above the dislocation-unavoidable thickness, dislocations are always energetically favored. In the dislocation-controllable region between the two critical thicknesses, coherent structure can be obtained via controlling the well and barrier thicknesses. The results are in good agreement with the experimental data and may serve as guidance for the design of coherent nanowire core-multishell quantum well structures and devices.

Lattice strain across Na-K interdiffusion fronts in alkali feldspar: an electron back-scatter diffraction study.

Cation exchange experiments between gem quality sanidine (X_mathrm{Or} = 0.85) and KCl melt produced chemical alteration of alkali feldspar starting at the grain surface and propagating inwards by highly anisotropic Na–K interdiffusion on the alkali sublattice. Diffusion fronts developing in b-direction are very sharp, while diffusion fronts within the a–c-plane are comparatively broad. Due to the composition dependence of the lattice parameters of alkali feldspar, the diffusion induced compositional heterogeneity induces coherency stress and elastic strain. Electron back-scatter diffraction combined with the cross-correlation technique was employed to determine the lattice strain distribution across the Na–K interdiffusion fronts in partially exchanged single crystals of alkali feldspar. The strain changes gradually across the broad fronts within the a–c-plane, with a successive extension primarily in a-direction conferring to the composition strain in unstressed alkali feldspar. In contrast, lattice strain characterised by pronounced extension in b-direction is localised at the sharp diffusion fronts parallel to b, followed by a slight expansion in a-direction in the orthoclase-rich rim. This strain pattern does not confer with the composition induced lattice strain in a stress-free alkali feldspar. It may rather be explained by the mechanical coupling of the exchanged surface layer and the mechanically strong substratum. The lattice distortion localised at the sharp diffusion front may have an influence on the diffusion process and appears to produce a self-sharpening feedback, leading to a local reduction of component mobilities.

Pressure induced magneto-structural phase transitions in layered RMn2X2 compounds (invited)

We have studied a range of pseudo-ternaries derived from the parent compound PrMn2Ge2, substituting for each constituent element with a smaller one to contract the lattice. This enables us to observe the magneto-elastic transitions that occur as the Mn-Mn nearest neighbour distance is reduced and to assess the role of Pr on the magnetism. Here, we report on the PrMn2Ge2−xSix, Pr1−xYxMn2Ge2, and PrMn2−xFexGe2 systems. The pressure produced by chemical substitution in these pseudo-ternaries is inherently non-uniform, with local pressure variations dependent on the local atomic distribution. We find that concentrated chemical substitution on the R or X site (e.g., in Pr0.5Y0.5Mn2Ge2 and PrMn2Ge0.8Si1.2) can produce a separation into two distinct magnetic phases, canted ferromagnetic and canted antiferromagnetic, with a commensurate phase gap in the crystalline lattice. This phase gap is a consequence of the combination of phase separation and spontaneous magnetostriction, which is positive on transition to the canted ferromagnetic phase and negative on transition to the canted antiferromagnetic phase. Our results show that co-existence of canted ferromagnetic and antiferromagnetic phases depends on chemical pressure from the rare earth and metalloid sites, on local lattice strain distributions and on applied magnetic field. We demonstrate that the effects of chemical pressure bear close resemblance to those of mechanical pressure on the parent compound.

Nano-scale characterization of GaAsP/GaAs strained superlattice structure by nano-beam electron diffraction

Distribution of lattice strain in a GaAsP/GaAs superlattice with a periodicity of 10 nm thickness, deposited on a 100 nm GaAs basal layer has been measured by nano-beam electron diffraction. The superlattice on the (001) plane of the basal GaAs layer shows a constant lattice strain from the bottom to the top layers, whereas the superlattice on the basal GaAs surface sloped by 16° from the (001) plane shows a variation of the lattice strain and crystal orientation. The difference of the strain distributions was discussed from the viewpoint of average strain. This tilt was explained by an atomistic model.

Lattice strain distributions due to elastic distortions and GND development in polycrystals

Techniques for the determination of lattice spacing distributions resulting from elastic distortion and from the development of a Burger׳s discontinuity (or equivalently, geometrically necessary dislocation density), are presented within a computational crystal plasticity framework, and a number of validatory analyses discussed.The contributions from both elastic distortions and Burger׳s circuit discontinuity to lattice spacing distributions and corresponding peak widths are evaluated and assessed for an fcc single crystal bearing elastic distortion and a plastic strain gradient. The single crystal analyses show that the elastic distortions lead to peak broadening and that at the initiation of plastic slip in the presence of a plastic strain gradient, the Burger׳s discontinuity (or equivalently GND density) also contributes to the peak broadening and may dominate as the strains become larger. After slip initiation, the contribution from elastic distortion remains largely unchanged. Analyses of random and textured polycrystals under uniaxial (100) straining to 5% show that the Burger׳s discontinuity contribution to peak broadening tends to dominate earlier over that from elastic distortion relative to the single crystal behaviour, because of the higher level of heterogeneity present. The randomly textured polycrystal showed more {100} peak broadening than that for the textured sample as a result of the relatively higher heterogeneity in the former.

Analysis of Spiral Lattice Girder Shape in preparation for HSR Speed Increase

A spiral lattice girder-reinforced Bi-block sleeper which has enhanced durability against increasingly growing impact force and vibration by wheel load and improved structural performance while train runs at 350km/h high speed is hereby proposed. The section of a spiral lattice girder has stable and superior structural performance thanks to its confinement effect. To compare and analyze the structural performance of spiral lattice girder-reinforced bi-block sleeper, strain and stress distribution were evaluated after applying same load condition as existing triangular lattice girder-reinforced biblock sleeper, and to compare the structural performance of triangular lattice girder and spiral lattice girder, structural analysis of lattice girder was performed separately. As a result, a spiral lattice girder proved to have had superior structural characteristics to bi-block sleeper, and furthermore as a result of evaluating the fastener interface and constructibility with shape-improved lattice girder, no interference with existing railroad structure was found and in terms of cost efficiency, a spiral lattice girder appeared to be superior to existing lattice girder.

Lattice strain distribution resolved by X-ray Bragg-surface diffraction in an Si matrix distorted by embedded FeSi2nanoparticles

Out-of-plane and primarily in-plane lattice strain distributions, along the two perpendicular crystallographic directions on the subsurface of a silicon layer with embedded FeSi2nanoparticles, were analyzed and resolved as a function of the synchrotron X-ray beam energy by using ω:φ mappings of the ({\overline 1}11) and (111) Bragg-surface diffraction peaks. The nanoparticles, synthesized by ion-beam-induced epitaxial crystallization of Fe+-implanted Si(001), were observed to have different orientations and morphologies (sphere- and plate-like nanoparticles) within the implanted/recrystallized region. The results show that the shape of the synthesized material singularly affects the surrounding Si lattice. The lattice strain distribution elucidated by the nonconventional X-ray Bragg-surface diffraction technique clearly exhibits an anisotropic effect, predominantly caused by plate-shaped nanoparticles. This type of refined detection reflects a key application of the method, which could be used to allow discrimination of strains in distorted semiconductor substrate layers.