Lattice Strain Measurements Research Articles

Dose and compositional dependence of irradiation-induced property change in FeCr

Ferritic/martensitic steels will be used as structural components in next generation nuclear reactors. Their successful operation relies on an understanding of irradiation-induced defect behaviour in the material. In this study, Fe and FeCr alloys (3–12%Cr) were irradiated with 20 MeV Fe-ions at 313 K to doses ranging between 0.00008 dpa to 6.0 dpa. This dose range covers six orders of magnitude, spanning low, transition, and high dose regimes. Lattice strain and hardness in the irradiated material were characterised with micro-beam Laue X-ray diffraction and nanoindentation, respectively.Irradiation hardening was observed even at very low doses (0.00008 dpa) and showed a monotonic increase with dose up to 6.0 dpa. Lattice strain measurements of samples at 0.0008 dpa allow the calculation of equivalent Frenkel pair densities and corrections to the Norgett-Robinson-Torrens (NRT) model for Fe and FeCr alloys at low dose. NRT efficiency for FeCr is 0.2, which agrees with literature values for high irradiation energy. Lattice strain increases with dose up to 0.8 dpa and then decreases when the damage dose is further increased. The strains measured in this study are lower and peak at a larger dose than predicted by atomistic simulations. This difference can be explained by taking temperature and impurities into account.

Determination of single crystal thermal expansion in Uranium-6wt%Niobium shape memory alloy using in-situ diffraction and modeling of textured polycrystalline samples

In-situ neutron diffraction and ex-situ dilatometry experiments were performed on a chemically banded, quenched uranium-6wt% niobium shape memory alloy to study the impact of deformation-(detwinning-) induced texture on the evolution of thermally induced strains (and associated stresses). Thermal heating and cooling cycles between 5K and 473K were performed in-situ with neutron diffraction, and the lattice strain evolution is reported for the observed monoclinic α″ phase. Comparisons between the measured diffraction strains and macroscopic dilatometry experiments reveal relationships between micro- and macro-level thermal expansion. Softening of the texture during heating suggests that twin boundary motion can accommodate the large internal thermal strains which are approximately 2% greater than that typically observed during the 175K heating interval used to age more randomly oriented polycrystalline material. Assuming weak constraint of neighboring grains in randomly textured polycrystals, the single crystal thermal expansion tensor is extracted from measurements of lattice strains over the range 5K to 473K. Predictions of polycrystalline thermal expansion, based upon this single crystal thermal expansion tensor, are shown to compare favorably with bulk thermal expansion observations of the as quenched microstructure. However, such a lower-bound estimate is insufficient to explain all aspects of the behavior of the textured material, where the matrix is not isotropic. It is hypothesized that relaxation processes which occur within the quenched microstructure during heating are responsible for the distinct thermal expansion behavior observed during the initial heating cycle compared to cooling and subsequent cycling.

Scanning time-resolved measurement of transient lattice strain on quartz oscillators resonating under alternating electric field

Distributions of transient and local lattice strains on resonating AT-cut quartz oscillators were measured in situ by scanning time-resolved X-ray diffraction under an alternating electric field to reveal the effects of the crystal shape and electrode thickness on their piezoelectric vibration. The concentration of the lattice vibration amplitude and energy at the electrode center in a plano-convex type oscillator and enhancement of the lattice strain in a plano–plano type oscillator within the electrode area with increasing electrode thickness have been unambiguously demonstrated by the method without any surface modifications.

Refinements for Bragg coherent X-ray diffraction imaging: electron backscatter diffraction alignment and strain field computation.

Bragg coherent X-ray diffraction imaging (BCDI) allows the 3D measurement of lattice strain along the scattering vector for specific microcrystals. If at least three linearly independent reflections are measured, the 3D variation of the full lattice strain tensor within the microcrystal can be recovered. However, this requires knowledge of the crystal orientation, which is typically attained via estimates based on crystal geometry or synchrotron microbeam Laue diffraction measurements. Presented here is an alternative method to determine the crystal orientation for BCDI measurements using electron backscatter diffraction (EBSD) to align Fe-Ni and Co-Fe alloy microcrystals on three different substrates. The orientation matrix is calculated from EBSD Euler angles and compared with the orientation determined using microbeam Laue diffraction. The average angular mismatch between the orientation matrices is less than ∼6°, which is reasonable for the search for Bragg reflections. The use of an orientation matrix derived from EBSD is demonstrated to align and measure five reflections for a single Fe-Ni microcrystal via multi-reflection BCDI. Using this data set, a refined strain field computation based on the gradient of the complex exponential of the phase is developed. This approach is shown to increase accuracy, especially in the presence of dislocations. The results demonstrate the feasibility of using EBSD to pre-align BCDI samples and the application of more efficient approaches to determine the full lattice strain tensor with greater accuracy.

Film thickness and architecture effects in biaxially strained polymer supported Al/Mo bilayers

Multilayers on polymer substrates are of interest for several technical applications. However, the true understanding of how one layer affects the other during mechanical loading is still unknown. In order to address this lack of knowledge, single and bilayer thin films of Al (250, 125, and 75 nm) and Mo (50 nm) were sputter deposited onto polyimide (PI, 50 µm) and biaxially strained in-situ with X-ray diffraction. The technique allows for the simultaneous measurement of lattice strains of Al and Mo to correlate the observed mechanical behavior of both materials. Using the evaluated film stress and full width at half maximum evolutions, four domains of mechanical behavior are identified. The presence of the domains in either Al or Mo depends on the thickness of the Al films and, more importantly, the bilayer architecture (Al/Mo/PI vs. Mo/Al/PI). Domain boundaries in Al were found to correspond well with domain boundaries in the Mo, such as necking in Al with fracture in Mo or simultaneous fracture in both materials. The maximum stress achieved in the Mo layers during biaxial straining was also found to highly depend on the architecture and depend less on the Al film thickness. Results will demonstrate that the film architecture (layer order) is more important than the film thickness to enhance fracture resistance.

Linescan Lattice Microscopy: A Technique for the Accurate Measurement and Mapping of Lattice Spacing and Strain with Atomic Force Microscopy.

Lateral resolution and accuracy in scanning probe microscopies are limited by the nonideality of piezoelectric scanning elements due to phenomena including nonlinearity, hysteresis, and creep. By taking advantage of the well-established atomic-scale stick-slip phenomenon in contact-mode atomic force microscopy, we have developed a method for simultaneously indexing and measuring the spacing of surface atomic lattices using only Fourier analysis of unidirectional linescan data. The first step of the technique is to calibrate the X-piezo response using the stick-slip behavior itself. This permits lateral calibration to better than 1% error between 2.5 nm and 9 μm, without the use of calibration gratings. Lattice indexing and lattice constant determination are demonstrated in this way on the NaCl(001) crystal surface. After piezo calibration, lattice constant measurement on a natural bulk MoS2(0001) surface is demonstrated with better than 0.2% error. This is used to measure nonuniform thermal mismatch strain for chemical vapor deposition (CVD)-grown monolayer MoS2 as small as 0.5%. A spatial mapping technique for the lattice spacing is developed and demonstrated, with absolute accuracy better than 0.2% and relative accuracy better than 0.1%, within a map of 12.5 × 12.5 nm2 pixels using bulk highly oriented pyrolytic graphite (HOPG) and MoS2 as reference materials.

Influence of Microstructure on Synchrotron X-ray Diffraction Lattice Strain Measurement Uncertainty

Accurate residual lattice strain measurements are highly dependent upon the precision of the diffraction peak location and the underlying microstructure suitability. The suitability of the microstructure is related to the requirement for valid powder diffraction sampling statistics and the associated number of appropriately orientated illuminated. In this work, these two sources of uncertainty are separated, and a method given for both the quantification of errors associated with insufficient grain sampling statistics and minimization of the total lattice strain measurement uncertainty. It is possible to reduce the total lattice strain measurement uncertainty by leveraging diffraction peak measurements made at multiple azimuthal angles. Lattice strain measurement data acquired during eight synchrotron X-ray diffraction experiments, monochromatic and energy dispersive, has been assessed as per this approach, with microstructural suitability being seen to dominate total measurement uncertainty when the number of illuminated grains was <106. More than half of the studied experimental data fell into this category, with a severe underestimation of total strain measurement uncertainty being possible when microstructural suitability is not considered. To achieve a strain measurement uncertainty under 10−4, approximately 3×105 grains must be within the sampled gauge volume, with this value varying with the multiplicity of the family of lattice planes under study. Where additional azimuthally arrayed data are available an in-plane lattice strain tensor can be extracted. This improves overall strain measurement accuracy and an uncertainty under 10−4 can then be achieved with just 4×104 grains.

Operando measurement of lattice strain in internal combustion engine components by neutron diffraction

Engineering neutron diffraction can nondestructively and noninvasively probe stress, strain, temperature, and phase evolutions deep within bulk materials. In this work, we demonstrate operando lattice strain measurement of internal combustion engine components by neutron diffraction. A modified commercial generator engine was mounted in the VULCAN diffractometer at the Spallation Neutron Source, and the lattice strains in both the cylinder block and head were measured under static nonfiring conditions as well as steady state and cyclic transient operation. The dynamic temporal response of the lattice strain change during transient operation was resolved in two locations by asynchronous stroboscopic neutron diffraction. We demonstrated that operando neutron measurements can allow for understanding of how materials behave throughout operational engineering devices. This study opens a pathway for the industrial and academic communities to better understand the complexities of material behavior during the operation of internal combustion engines and other real-scale devices and systems and to leverage techniques developed here for future investigations of numerous new platforms and alloys.

In-situ high energy X-ray diffraction study of microscopic deformation behavior of martensite variant reorientation in NiTi wire

This study investigated the collective evolution of martensite variant structures, the development of crystallographic textures and the load partitioning among the variants during tensile deformation in a commercial polycrystalline NiTi wire by means of in-situ high-energy X-ray diffraction technique. The cold-worked and then crystallized NiTi wire was found to have three fiber textures along the wire axial direction in its thermally formed self-accommodating B19′ martensite, including (1¯20)/(120), (1¯02) and (102). These textural orientations are inheritance of the texture of the B2 phase and are associated with the <011> type II twins and (001) compound twins. Tensile deformation via martensite variant reorientation converted the (102) and (120) fiber textures into (1¯02). The texture evolutions and variant selections are driven by the difference in d-spacing values between the pairing variants in each twin structure in order to achieve maximum elongation deformation in the tensile loading direction. At the meantime, the lattice strains of the favored variants increased whereas those of the unfavored variants decreased (even to negative) abruptly at the occurrence of the Lüders deformation event when at the global stress remained constant over the stress plateau. These changes of the lattice strains are attributed to load transfer and repartitioning among the variants. Based on the lattice strain measurements, the load partitioning among variants is also estimated.

Measurements of lattice strain in cold-rolled CR4 steel sheets using X-ray diffraction

In this study, the effect of orientation and bending has been investigated on CR4 steel for lattice constant, crystallite size and lattice strain. The one mm thick sheet of CR4 steel was bent through air-bending. The samples were prepared by using wire electric discharge machining (WEDM) followed by polishing for X-ray diffraction study. The peaks were analysed using QualX 2.1 software and lattice constant was analysed using Bragg’s law and lattice strain using Williamson-Hall’s method. Result shows, lattice constant is smallest on rolled face and after bending it increases along thickness. Whereas, the lattice strain is compressive in nature for all three orientations. However, for 0°orientation lattice strain (0.5%) is more across the thickness as compared to 90°orientation lattice strain (0.34%). Crystallite size was analysed by Scherrer’s method and Williamson-Hall’s method. Williamson-Hall’s crystallite size is observed to be smaller than Scherrer’s crystallite size. Further, crystallite size is observed to be the smallest on the rolled face. Moreover, after bending force application, enhancement in the lattice strain is observed while the size of the crystallite is reduced noticeably.

Characterising Ion-Irradiated FeCr: Hardness, Thermal Diffusivity and Lattice Strain

Ion-irradiated FeCr alloys are useful for understanding and predicting neutron damage in the structural steels of future nuclear reactors. Previous studies have largely focused on the structure of irradiation-induced defects, probed by transmission electron microscopy (TEM), as well as changes in mechanical properties. Across these studies, a wide range of irradiation conditions has been employed on samples with different processing histories, which complicates the analysis of the relationship between defect structures and material properties. Furthermore, key properties, such as irradiation-induced changes in thermal transport and lattice strain, are little explored.Here we present a systematic study of Fe3Cr, Fe5Cr and Fe10Cr binary alloys implanted with 20 MeV Fe3+ ions to nominal doses of 0.01 dpa and 0.1 dpa at room temperature. Nanoindentation, transient grating spectroscopy (TGS) and X-ray micro-beam Laue diffraction were used to study the changes in hardness, thermal diffusivity and strain in the material as a function of damage and Cr content. Our results suggest that Cr leads to an increased retention of irradiation-induced defects, causing substantial changes in hardness and lattice strain. However, thermal diffusivity varies little with increasing damage and instead degrades significantly with increasing Cr content in the material. We find significant lattice strains even in samples exposed to a nominal displacement damage of 0.01 dpa. The defect density predicted from the lattice strain measurements is significantly higher than that observed in previous TEM studies, suggesting that TEM may not fully capture the irradiation-induced defect population.

Multiscale modeling of cruciform dwell tests with the uncertainty-quantified parametrically homogenized constitutive model

This paper presents a novel multiscale approach for analyzing multi-axial stress-strain evolution in Ti-7Al cruciform specimens under dwell loading, through the use of an uncertainty-quantified, parametrically homogenized constitutive model (UQ-PHCM). The thermodynamically-consistent UQ-PHCM is built from rigorous upscaling of crystal plasticity FE models (CPFEM) using machine learning and uncertainty quantification. They explicitly incorporate microstructural information in the form of representative aggregated microstructural parameters (RAMPs). Uncertainty quantification accounts for uncertainty in model reduction, data sparsity and microstructural descriptors. This paper integrates advanced multiscale, multi-axial experiments with computational modeling at multiple scales to establish the UQ-PHCM as an effective tool for bridging the gap between laboratory specimen-scale experimental observations and micro-scale stresses and strains using CPFEM. The CPFEM is calibrated and validated by experimental data from surface strain measurements using digital image correlation (DIC) and grain-by-grain lattice strain measurements with in-situ far field high energy diffraction microscopy (ff-HEDM). A computational method is developed in CPFEM, to incorporate initial residual stresses consistent with measured lattice strains. The UQ-PHCM is validated with biaxial tensile dwell test results performed on the cruciform specimen with satisfactory prediction of gauge strain evolution in DIC measurements. Uncertainty in the strain field due to microstructural variability is also corroborated by the DIC measurements.

HAADF-STEM block-scanning strategy for local measurement of strain at the nanoscale

Lattice strain measurement of nanoscale semiconductor devices is crucial for the semiconductor industry as strain substantially improves the electrical performance of transistors. High resolution scanning transmission electron microscopy (HR-STEM) imaging is an excellent tool that provides spatial resolution at the atomic scale and strain information by applying Geometric Phase Analysis or image fitting procedures. However, HR-STEM images regularly suffer from scanning distortions and sample drift during image acquisition. In this paper, we propose a new scanning strategy that drastically reduces artefacts due to drift and scanning distortion, along with extending the field of view. It consists of the acquisition of a series of independent small subimages containing an atomic resolution image of the local lattice. All subimages are then analysed individually for strain by fitting a nonlinear model to the lattice images. The method allows flexible tuning of spatial resolution and the field of view within the limits of the dynamic range of the scan engine while maintaining atomic resolution sampling within the subimages. The obtained experimental strain maps are quantitatively benchmarked against the Bessel diffraction technique. We demonstrate that the proposed scanning strategy approaches the performance of the diffraction technique while having the advantage that it does not require specialized diffraction cameras.

Development of cryogenic tensile testing apparatus for lattice strain measurement using synchrotron radiation for REBCO composite conductors

REBa2Cu3O7−δ (REBCO) composite tapes are candidate conductors for future accelerator magnets. Given that REBCO is a brittle oxide film, stress/strain management is important in the mechanical design of a magnet. Therefore, the strain state of a superconducting film should be predicted under various operating conditions. A quantum beam is a useful tool in evaluating the strain state of a superconducting material in a composite conductor. Although various cryogenic tensile testing machines, in combination with neutron beam and synchrotron radiation, have been developed, they are not necessarily optimized for measuring highly textured materials such as REBCO films. This study reports a novel cryogenic tensile testing apparatus that can be used at the beamline of a synchrotron radiation facility. In this system, a superconducting tape is cooled using a Gifford–McMahon (GM) cryocooler through 2.5 m long thermal links made of 5 N high-purity aluminum. This enables a compact cryogenic loading system that can be mounted on the goniometer of a beamline. Lattice strain measurements using synchrotron radiation were conducted at 40 K, 77 K, and 300 K for a commercially available (Y,Gd)BCO coated conductor at BL28B2 in SPring-8. The onset strain of film fracture determined from the lattice strain measurement at 77 K agreed well with the irreversible strain of critical current at the same temperature. The residual and fracture strain of the (Y,Gd)BCO film at 77 K was evaluated as well.

Experimental determination of precision, resolution, accuracy and trueness of time-of-flight neutron diffraction strain measurements

A simple statistical analysis which yields the precision, resolution, accuracy and trueness of diffraction-based lattice strain measurements is discussed. The procedure consists of measuring the thermal expansion induced in each component of an ideal non-reacting two-component crystalline powder sample in situ. One component, with a high coefficient of thermal expansion (CTE), serves as an internal thermometer. The quantities of interest are obtained by determining the smallest statistically significant thermal lattice strain which can be detected through diffraction analysis in the second, low-CTE, component in response to controlled temperature changes. This procedure also provides a robust check of the alignment of the diffraction system and is able to reveal the presence of systematic errors. The application of this technique to a time-of-flight engineering diffractometer/strain scanner is presented.

Lattice strains and diffraction elastic constants of cubic polycrystals

In situ synchrotron X-ray and neutron diffraction experiments provide a powerful approach to measure lattice strains in bulk polycrystalline materials. They are being increasingly used for quantitative characterization of microscale deformation within and between grains and phases. Here we use a self-consistent micromechanics model to obtain a general analytic solution of the grain-level lattice strains and diffraction elastic constants for a broad class of elastically isotropic polycrystals with cubic crystal symmetry. This analytic solution reveals a direct linear relationship between the reciprocal of the elastic diffraction constant and the orientation index parameter along the direction of any diffraction vector, including tensile loading and transverse directions. The straightforward numerical implementation of this solution provides diffraction elastic constants for 26 representative cubic polycrystals. Analytic solutions of this kind can serve to benchmark in situ diffraction measurements of lattice strains and also facilitate high-throughput studies of microscale stresses and diffraction elastic constants in polycrystalline materials.

Diffraction-based determination of single-crystal elastic constants of polycrystalline titanium alloys.

Single-crystal elastic constants have been derived by lattice strain measurements using neutron diffraction on polycrystalline Ti-6Al-4V, Ti-6Al-2Sn-4Zr-6Mo and Ti-3Al-8V-6Cr-4Zr-4Mo alloy samples. A variety of model approximations for the grain-to-grain interactions, namely approaches by Voigt, Reuss, Hill, Kroener, de Wit and Matthies, including texture weightings, have been applied and compared. A load-transfer approach for multiphase alloys was also implemented and the results are compared with single-phase data. For the materials under investigation, the results for multiphase alloys agree well with the results for single-phase materials in the corresponding phases. In this respect, all eight elastic constants in the dual-phase Ti-6Al-2Sn-4Zr-6Mo alloy have been derived for the first time.

Lattice Strain In Aluminium After Plastic Deformation Process at A Cryogenic Temperature

Aluminium is a lightweight metal that is difficult to improve its mechanical properties. High plastic deformation on aluminium makes mechanical properties increase slightly. Aluminium at low temperatures has a lower inter-atomic spacing than at room temperature. Deformation at a cryogenic temperature is expected to increase the mechanical properties higher than at room temperature. The increasing mechanical properties is caused by increasing deformation density.The dislocation density of the aluminium can be predicted by measuring the lattice strain. In this paper, we used X-ray diffraction to measure the lattice strain. The aluminium used in this study was pure industrial aluminium, with a size of 10 x 10 mm and a length of 100 mm respectively. The plastic deformation process was carried out at -75 ° C using the impact test apparatus.The results of lattice strain measurement were verified throughmicrohardness testing. The measurement showed that the plastic deformation process at a cryogenic temperature increased the lattice strain; this complies with microhardness measurementStart your abstract here…

Neutron Diffraction Study of Phase Stresses in Al/SiCp Composite During Tensile Test

The stress partitioning between phases, phase stress relaxation as well as origins of Al/SiCp composite strengthening are studied in the present work. In this aim, the measurements of lattice strains by neutron diffraction were performed in situ during tensile test up to sample fracture. The experimental results were compared with results of elastic–plastic self-consistent model. It was found that thermal origin phase stresses relax at the beginning of plastic deformation of Al/SiCp composite. The evolution of lattice strains in both phases can be correctly simulated by the elastic–plastic self-consistent model only if the relaxation of initial stresses is taken into account. A major role in the strengthening of the studied composite plays a transfer of stresses to the SiCp reinforcement, however the hardness of Al metal matrix is also important.

Helium-implantation-induced lattice strains and defects in tungsten probed by X-ray micro-diffraction

Tungsten is the main candidate material for plasma-facing armour components in future fusion reactors. Bombardment with energetic fusion neutrons causes collision cascade damage and defect formation. Interaction of defects with helium, produced by transmutation and injected from the plasma, modifies defect retention and behaviour. Here we investigate the residual lattice strains caused by different doses of helium-ion-implantation into tungsten and tungsten‑rhenium alloys. Energy and depth-resolved synchrotron X-ray micro-diffraction uniquely permits the measurement of lattice strain with sub-micron 3D spatial resolution and ~10−4 strain sensitivity. Increase of helium dose from 300 appm to 3000 appm increases volumetric strain by only ~2.4 times, indicating that defect retention per injected helium is ~3 times higher at low helium doses. This suggests defect retention is not a simple function of implanted helium dose, but strongly depends on material composition and presence of impurities. Conversely, analysis of W-1 wt% Re alloy samples and of different crystal orientations shows that both the presence of rhenium, and crystal orientation, have a comparatively small effect on defect retention. These insights are key for the design of armour components in future reactors where it will be essential to account for irradiation-induced dimensional change when predicting component lifetime and performance.