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Ballistic-electron-emission microscopy has been used to investigate the effects of strain on Si l-x Ge x alloys. Lifting of the degeneracy of the conduction-band minimum of SiGe due to lattice deformation has been directly measured by application of BEEM spectroscopy to Ag/Si structures.
Ballistic-electron-emission microscopy (BEEM) has been used to investigate the effects of strain on Si(sub 1-x)Ge(sub x) alloys. Lifting of the degeneracy of the conduction-band minimum of Si(sub 1-x)Ge(sub x), due to lattice deformation has been directly measured by application of BEEM spectroscopy to Ag/Si structures. Experimental values for this conduction-band splitting agree well with calculations. In addition, an unexpected heterogeneity in the strain of the Si(sub 1-x)Ge(sub x) layer is introduced by deposition of Au. This effect, not observed with Ag, is attributed to species interdiffusion and has important implications for metal-semiconductor devices based oil pseudomorphic Si(sub 1-x)Ge(sub x)/Si material systems.
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Recent advances in Bragg coherent diffraction imaging (BCDI) experimental techniques permit routine measurement of multiple Bragg peaks from a single crystalline grain. The resulting images contain the full lattice distortion vector field which can be differentiated to provide lattice strain and rotation. With the advent of fourth-generation synchrotron light sources, such multi-peak datasets are produced at high rates, facilitating the need for rapid phase retrieval of the multiple peaks and subsequent image analysis. Here we describe and demonstrate a new implementation of a coupled phase retrieval technique for multi-peak BCDI which simultaneously treats each Bragg peak of the dataset and produces a three-dimensional image of the crystal's morphology and lattice distortion field. In addition, this method uses the redundant information contained in the various Bragg diffraction patterns to detect and suppress spurious signal appearing on the detector in a subset of the measurements. Compared with manual data editing, adaptive coupling produces a more consistent phase profile in reciprocal space and sharper surfaces in direct space, with no significant difference in computational cost. These improvements reduce the need for manual preprocessing and enable robust high-throughput analysis of multi-peak BCDI data, supporting near-real-time strain microscopy at modern synchrotron facilities.
The Nye tensor, which quantifies the density of Burgers vector for a given dislocation line direction, can be effectively used to characterize dislocation content in bulk crystals from atomic-resolution transmission electron microscopy images. The Nye tensor can be calculated from these images, in part because the reference state is simply defined by the lattice of the perfect crystal. The application of the Nye tensor to interfacial line defects, for which the natural reference state is the dichromatic pattern of the two grains in their reference orientation, poses additional challenges. In this work, we present a method that employs the Nye tensor to characterize the edge dislocation content of line defects at grain boundaries from atomic-resolution images. This approach enables us to rapidly characterize all edge dislocation content along a grain boundary. Additionally, the Nye tensor provides information about line defect core structure. Finally, we demonstrate this method on two exemplar defects: a twin boundary disconnection and a facet junction in face-centered cubic Au.
Variation of strain rate sensitivity among different families of slip systems in the hexagonal close-packed (α) phase of titanium (Ti) alloys has the potential to alter microscale load redistribution during both creep and dwell fatigue loading. However, existing literature contains conflicting reports regarding the degree of anisotropy present in the strain rate sensitives between α slip system families across Ti alloys. Here, we quantify the strain rate sensitivity of α slip system families in Ti-6Al-4V using high-energy X-ray diffraction microscopy (HEDM). We present a novel procedure in which we utilize the HEDM-measured grain-scale stress states during stress relaxation to determine the strain rate sensitivities of the basal $\langle a \rangle$ , prismatic $\langle a \rangle$, and first-order pyramidal $\langle c + a \rangle$ slip system families. In addition, we measure the strain rate sensitivity exponent of the macroscopic response and the α phase for comparison. We find rate sensitivities for the different slip system families to range from 0.02 to 0.04, which—while varied—are relatively isotropic in comparison with some values presented in the literature. We also demonstrate the effects of the measured anisotropic rate sensitivities using crystal plasticity finite element simulations.
Grain boundaries (GBs) are frequently implicated as key defect structures facilitating metal hydride formation, yet their specific role remains poorly understood due to their structural complexity. Here, we investigate hydrogen insertion in Pd nanostructures enriched with well-defined Σ3(111) GBs (Pd GB ) synthesized via electrolysis-driven nanoparticle assembly. In situ synchrotron X-ray diffraction reveals that Pd GB exhibits dramatically accelerated hydriding and dehydriding kinetics compared with ligand-free and ligand-capped Pd nanoparticles with similar crystallite sizes. Strain mapping using environmental transmission electron microscopy shows that strain is highly localized at GBs and intensifies upon hydrogen exposure, indicating preferential hydrogen insertion along GB sites. Density functional theory calculations provide mechanistic insight supporting these findings, showing that hydrogen insertion near Σ3(111) GBs is energetically more favorable and that tensile strain lowers insertion barriers. Furthermore, these results provide atomic-level insights into the role of GBs in hydride formation and suggest new design strategies for GB-engineered Pd-based functional materials.
A noncontacting technique using scanning laser acoustic microscopy for making in situ tensile strain measurements of small diameter fibers was implemented for the tensile strain analysis of individual Nicalon SiC fibers (nominal diameter 15 microns). Stress versus strain curves for the fibers were plotted from the experimental data. The mean elastic modulus of the fibers was determined to be 185.3 GPa. Similar measurements were made for Carborundum SiC fibers (nominal diameter 28 microns) and Saphikon sapphire fibers (nominal diameter 140 microns), yielding and elastic modulus of 401 and 466.8 GPa, respectively.
A noncontacting technique using scanning laser acoustic microscopy for making in situ tensile strain measurements of small diameter fibers was implemented for the tensile strain analysis of individual Nicalon SiC fibers (nominal diameter 15 microns). Stress vs strain curves for the fibers were plotted from the experimental data. The mean elastic modulus of the fibers was determined to be 185.3 GPa. Similar measurements were made for Carborundum SiC fibers (nominal diameter 28 microns) and Saphikon sapphire fibers (nominal diameter 140 microns).
Ballistic-electron-emission microscopy (BEEM) useful in determining strains in semiconductors under some conditions. More specifically, BEEM is variant of scanning tunneling microscopy and sensitive to electronic structure of probed material. In present approach, BEEM used to obtain data on those aspects of variations in electronic structures related to variations in strains. Then by use of mathematical modeling of relationships between electronic structures and strains, variations in strains deduced from BEEM data.
Epitaxially strained germanium-on-silicon (Ge-on-Si) heterostructures are central to next-generation photonic and electronic devices, yet their performance remains strongly constrained by defect-limited carrier lifetimes. In this work, we investigate the impact of defects on the carrier lifetime in relaxed Ge-on-Si and strained Ge-on-Si heterostructures. High-resolution X-ray diffraction quantifies the strain-state in Ge and reveals signatures of strain relaxation due to lattice mismatch. Cross-sectional and plan-view transmission electron microscopy analyses enable direct visualization of interfacial defects and quantification of threading dislocation densities (TDDs) within the Ge layer. However, the presence of a dense misfit dislocation network obscures the threading dislocation signatures, preventing reliable TDD determination by plan-view transmission electron microscopy in strained-Ge (..epsilon..-Ge). To assess the defect density in this case, etch-pit density measurements were performed, providing an alternative means of quantifying the TDDs in the ..epsilon..-Ge layer. Carrier lifetime measurements by microwave-reflection photoconductive decay reveal a clear relationship with TDDs ranging from 5 x 103 cm-2 to 2 x 1010 cm-2, confirming Shockley-Read-Hall recombination as the limiting mechanism at lower defect densities, with TDD-dominated recombination at higher defect densities. The Ge-on-Si relaxed heterostructure exhibited lifetimes much lower (~12 ns) than the lattice-matched Ge on gallium arsenide (GaAs) (~158 ns) heterostructure. Introducing controlled tensile strain reduces defect formation, suppresses strain-relaxation pathways, and leads to measurable improvements in minority carrier lifetime from 12 ns to 171 ns. These results establish a direct relation between defect suppression and carrier recombination dynamics in both relaxed Ge-on-Si grown directly on Si and strained Ge-on-Si heterostructures incorporating compound-semiconductor buffer layers, offering a materials-driven pathway for engineering Ge with improved carrier lifetime for photonic applications.
Quantitative studies of material behavior characteristics are essential for predicting the functionality of a material under its operating conditions. A nonintrusive methodology for measuring the in situ strain of small dimeter (to 11 microns) ceramic fibers under uniaxial tensile loading and the local internal strains of ceramics and ceramic composites under flexural loading is introduced. The strain measurements and experimentally observed mechanical behavior are analyzed in terms of the microstructural development and fracture behavior of each test specimen evaluated. Measurement and analysis of Nicalon silicon carbide (SiC) fiber (15 microns diameter) indicate that the mean elastic modulus of the individual fiber is 185.3 GPa. Deviations observed in the experimentally determined elastic modulus values between specimens were attributed to microstructural variations which occur during processing. Corresponding variations in the fracture surface morphology were also observed. The observed local mechanical behavior of a lithium alumino-silicate (LAS) glass ceramic, a LAS/SiC monofilament composite, and a calcium alumino-silicate (CAS)/SiC fully reinforced composite exhibits nonlinearities and apparent hysteresis due to the subcritical mechanical loading. Local hysteresis in the LAS matrices coincided with the occurrence of multiple fracture initiation sites, localized microcracking, and secondary cracking. The observed microcracking phenomenon was attributed to stress relaxation of residual stresses developed during processing, and local interaction of the crack front with the microstructure. The relaxation strain and stress predicted on apparent mechanical hysteresis effects were defined and correlated with the magnitude of the measured fracture stress for each specimen studied. This quantitative correlation indicated a repeatable measure of the stress at which matrix microcracking occurred for stress relief of each material system. Stress relaxation occurred prior to the onset of steady state cracking conditions. The relaxation stress occurred at 18.5 percent of the fracture stress in LAS and 11.0 percent of the yield stress in CAS/SiC. The relaxation stress ratio was dependent upon the dominant fracture mode of the LAS/SiC specimens. Relaxation stress ratios greater than 0.30 were observed for specimens which fractured due to shear at the fiber matrix interface; specimens which fracture due to tensile cracking had relaxation stress ratios less than 0.30. The stress relaxation ratio appeared to be a specific characteristic of the glass ceramic material. The measured stress relaxation for LAS indicated a measure of the inherent residual stresses in the material due to processing and suggested localized toughening mechanisms for brittle material structures.
Geometric frustration—where geometry prevents simultaneous satisfaction of local interactions—generates pseudosymmetry and emergent behaviors across physical and biological systems. At the nanoscale, pseudosymmetric features in crystalline materials manifest as local strain and distortion, but how they depend on particle size and control structural stability remains unclear. Here, we report the first study of a size-dependent crossover in pseudosymmetry in multi-twinned gold nanoparticles (NPs), combining four-dimensional scanning transmission electron microscopy with nanoscale strain mapping grounded in continuum solid mechanics. Analysis of more than 20 decahedral NPs (20–55 nm) reveals pronounced heterogeneity in multiple modes of in-plane strain and displacement field in small NPs as five tetrahedral grains close the geometric gap, without extended defects. With increasing particle size, strain fields homogenize across grains and local phases shift from predominantly low-symmetry body-centered tetragonal motifs at small sizes to face-centered cubic character approaching the bulk limit. We identify a crossover particle size of ~35 nm, well below bulk, correlating with a transition from modified-Wulff shapes to pentagonal bipyramids, consistent with finite element predictions. This quantitative framework for mapping size-dependent strain and pseudosymmetry enables precise design and control of functional crystalline solids and phase transformation for catalysis, photonics, electronics, and energy storage.
To improve prognostics for predicting component life, coupon tests were conducted on Ti-6Al-4V to investigate the development of damage. Various test types were employed (tension, creep, stress relaxation, and fatigue) under a wide range of temperatures and loading rates to engage various amounts of time-dependent and damage behavior. Both stiffness degradation and Poisson’s ratio were monitored to see if they were useful in indicating the initiation and accumulation of damage and subsequently the onset of failure. Stiffness exhibited large decreases with increasing strain when calculated using engineering stress and strain. However, minimal stiffness change was observed when using the true-stress and true- strain values. Detailed microscopy and image analysis were performed to document the actual physical damage that occurred within the various specimens. Two types of damage were observed: shallow surface cracks and internal pores. The severity of damage was greater in the region of localized necking and diminished further away from the neck. The area fraction of pores was higher in the necked region, yet even there it did not exceed more than a few percent and, in most cases, was significantly lower. It was observed that conditions that induced more time-dependent deformation (e.g., slower strain rate testing) resulted in a larger number of pores and larger pore sizes. The pores were always found to occur in the softer β-phase. The severity of observed damage was inconsistent with the large drop in engineering stiffness, but was more aligned with stiffness changes from the true-stress and -strain values. Poisson’s ratio was monitored on every test and showed promise as a damage indicator. It was found to be more sensitive than either the ultimate tensile strength or the inception of tertiary creep. However, calculation of Poisson’s ratio was found to be more involved than expected because of anisotropy and the presence of strain gradients along the specimen at large applied strains. First, the material had a moderate texture and resulted in anisotropy of the strains. Second, the evolution of Poisson’s ratio as a function of axial strain showed strange and unexpected behaviors, which necessitated more extensive analyses of its development. This led to an investigation on the use of small versus large strain approaches and the importance of making consistent measurements; that is, axial and transverse strain measurements over the same volume of material. Additionally, finite element analysis of a tensile sample indicated that non- uniform strain occurred in the sample prior to attaining the maximum strength. This, along with the location at which transverse strain was measured, had a significant influence on the resulting values of Poisson’s ratio. Based on this, lessons learned are offered for future testing.
Samples from the Noerdlingen 1973 drill core contain abundant shock-induced microfractures which exhibit varying amounts of healing and sealing. Many of the microcracks resemble morphologically the open microcracks present in returned lunar samples. Data derived from petrography, scanning electron microscopy, and differential strain analysis indicate that fewer microcracks were formed at greater depths and crack sealing processes are more effective for cracks associated with planar elements. Although the microcracks in the Ries core are now sealed, they are valid analogues of the open shock-induced cracks of lunar rocks and demonstrate that open cracks do form in rocks at depth during a naturally-occurring shock event. The healing of the shock-induced cracks in the Ries core also precludes their use for laboratory measurements of physical properties intended to be used as analogue measurements of lunar samples in situ.
Major obstacles to the use of NiAl-based alloys and composites are low ductility and toughness. These shortcomings result in part from a lack of sufficient slip systems to accommodate plastic deformation of polycrystalline material (von Mises Criterion). It has been reported that minor additions of chromium to polycrystalline NiAl cause the predominant slip system to shift from the usual. If true, then a major step toward increasing ductility in this compound may be realized. The purpose of the present study was to verify this phenomenon, characterize it with respect to chromium level and Ni to Al ratio, and correlate any change in slip system with microstructure and mechanical properties. Compression and tensile specimens were prepared from alloys containing 0 to 5 percent chromium and 45 to 55 percent aluminum. Following about one percent strain, transmission electron microscopy foils were produced and the slip systems determined using the g x b = 0 invisibility criterion. Contrary to previous results, chromium was found to have no effect on the preferred slip system of any of the alloys studied. Possible reasons for the inconsistency of the current results with previous work are considered. Composition-structure-property relationships are discerned for the alloys, and good correlation are demonstrated in terms of conventional strengthening models for metallic systems.
Electronic nematic order arises when correlated electrons spontaneously break the rotational symmetry of a crystal lattice. When electronic nematic order couples bilinearly to symmetry-breaking lattice strain, both appear together at a single ferroelastic phase transition, producing structural twin domains with distinct orientations of the nematic director. While the effects of applied strain on these domains are well established, the intrinsic behavior of spontaneous subdomain strain fields has remained unexplored. Here, we report the discovery of spontaneous mesoscopic strain waves within individual nematic domains of an iron-based superconductor, observed using dark-field x-ray microscopy (DFXM). Using this advanced full-field imaging technique, we visualize subdomain strain modulations emerging concurrently with nematic order. Elastic compatibility relations governing inhomogeneous strains provide a natural mechanism for the strain waves. Our findings reveal a broadly relevant form of strain self-organization and position DFXM as a powerful probe of the local interplay between lattice strain and electronic order.