High-angle Annular Dark-field Scanning Transmission Electron Microscopy Research Articles

Engineered Core-Shell SiC@SiO2 Nanofibers for Enhanced Electromagnetic Wave Absorption Performance.

To enable SiC material to achieve high electromagnetic wave (EMW) absorption performance, solving its impedance mismatch with EMW is necessary. Therefore, a novel approach is proposed for the precise control of impedance matching by adjusting the shell thickness of SiO2 nanolayers on the surface of SiC nanofibers (NFs). High-angle annular dark field-scanning transmission electron microscopy (HAADF-STEM) reveals the atomic scale oxidation process of SiC, providing fresh insights into the oxidation mechanism. By oxidizing to construct a heterogeneous core-shell structure nanofiber (NF) can effectively lock the incident EMW inside the NF through the generated charges gathered at the interface, forming an electronic barrier that prevents the outward propagation of EMWs. The produced SiC@SiO2 NFs-3 exhibits exceptional EMW absorption properties, including an impressive minimum reflection loss (RLmin) of -53.09dB and a broad maximum effective absorption bandwidth (EABmax) of 8.85GHz. These findings not only deepen understanding of the oxidation mechanism of SiC but also offer valuable insights for further enhancing the EMW absorption capabilities of SiC materials, paving the way for their application in advanced EMW technologies.

Efficient selective hydrogenation of phenylacetylene over Pd-based rare earth dual-atomic catalysts

Selective hydrogenation of phenylacetylene to styrene plays a vital role in fine chemical synthesis with palladium (Pd)-based catalysts as the active components and usually suffered from low selectivity due to over-hydrogenation and low stability through polymerization (c.a. green oil generation). In this work, we found that by confining the Pd atom within a Pd-Ln (Ln: rare earth elements, such as Y, Lu, etc. ) diatomic structure [diatomic catalyst (DAC)], the reaction performance of selective hydrogenation of phenylacetylene has been greatly promoted, in which 92% styrene selectivity has been determined at 100% phenylacetylene conversion. This would be attributed to the diatomic structure established, which was achieved by introducing Pd-Ln precursors and confirmed by high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and X-ray adsorption fine structure (XAFS) characterizations and it was demonstrated that slight electron transfer from Ln to the adjacent isolated Pd makes it slightly negatively charged and facilitated the styrene formation. Besides, a Langmuir-Hinshelwood model was established to describe the whole reaction mechanism. After a systematic kinetic investigation, it suggests that the C8H6* + H* elementary step is probably the kinetically relevant for the whole reaction and the surface of the catalyst is mainly covered by C8H6*. The energy relationship of each step along phenylacetylene hydrogenation was quantitatively described by means of parity fitting and gas isothermal adsorption, providing insights into the selective hydrogenation of phenylacetylene over 0.02%Pd-Ln/C (Ln = Y/Lu) catalysts and pave the way of catalytic design at the atomic level.

Influence of NH3 flow rate on the photoelectric properties of high Al content p-AlGaN.

High Al content (60%) p-AlGaN with different NH3 flow rates was grown using metal-organic chemical vapor deposition (MOCVD), and changes in its photoelectric properties were studied using the Hall effect tester (Hall) and cathodoluminescence (CL) spectrometer. The results show that the film resistivity increases from 3.8 Ω·cm to 46.5 Ω·cm with increasing NH3 flow rate. The impurity peak intensity of p-AlGaN grown under high NH3 flow conditions is particularly high, indicating numerous point defects. The results of high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) show a large number of Ga interstitial atoms (Gai) at the interface. As Gai acts as a donor, this may be the main reason for the increase in resistivity. And under high NH3 flow conditions, a lattice distortion and a high density of dislocation occur between p-AlGaN and p-GaN, which can lead to enhanced carrier scattering and decreased mobility. Additional validation via LED growth experiments indicates that the luminescence intensity of samples with low ammonia concentration increased by more than 13000 times.

Quantitative revealing the solute segregation behavior at melt pool boundary in additively manufactured stainless steel using a novel processing method for precise positioning by HAADF-STEM

Laser-powder bed fusion (LPBF) enables the fabrication of complex metallic components by manipulating various laser scan strategies to control microstructure and texture. Multiple thermal cycling and rapid solidification lead to non-equilibrium, non-uniform microstructure, and micro-segregation at the melt pool boundary (MPB), whose accurate location is still invisible by transmission electron microscopy (TEM), and quantitative concentration remains imprecise. In this study, we proposed a novel method to make it clear by controlling the crystallographic texture of 316 L stainless steel through unique LPBF processing parameters to obtain a single-crystal-like microstructure of the cellular structures along the laser scanning direction. The accurate location of the track-track MPB is distinguishable by means of the transverse and longitudinal cellular dislocation structures on both sides. The edge-on state of the track-track MPB makes the quantitative concentration analysis precisely using high-angle annular dark-field scanning TEM with energy-dispersive X-ray spectroscopy, which is in good agreement with the Scheil-Gulliver solidification simulations.

Grain rotation mechanisms in nanocrystalline materials: Multiscale observations in Pt thin films.

Near-rigid-body grain rotation is commonly observed during grain growth, recrystallization, and plastic deformation in nanocrystalline materials. Despite decades of research, the dominant mechanisms underlying grain rotation remain enigmatic. We present direct evidence that grain rotation occurs through the motion of disconnections (line defects with step and dislocation character) along grain boundaries in platinum thin films. State-of-the-art in situ four-dimensional scanning transmission electron microscopy (4D-STEM) observations reveal the statistical correlation between grain rotation and grain growth or shrinkage. This correlation arises from shear-coupled grain boundary migration, which occurs through the motion of disconnections, as demonstrated by in situ high-angle annular dark-field STEM observations and the atomistic simulation-aided analysis. These findings provide quantitative insights into the structural dynamics of nanocrystalline materials.

Boosting catalytic activity of π-π interactions-stabilized PdNPs for water-mediated Suzuki couplings of aryl chlorides

Utilizing unique interactions to enhance the catalytic performance of supported metal catalysts is a crucial strategy in catalyst design, albeit one that presents a significant challenge. This study introduces an original approach involving the use of π-π interactions to stabilize palladium nanoparticles (PdNPs) with a 2Br-substituted imidazolium-based covalent organic framework (COF, IHP-Br-PdNPs) for efficient water-mediated Suzuki reactions involving deactivated aryl chlorides and arylboronic acids at ambient conditions. Through extensive structural characterization employing techniques including Fourier transform infrared spectroscopy (FT-IR), cross-polarization magic angle spinning carbon-13 nuclear magnetic resonance (CP/MAS 13C NMR), scanning electron microscopy (SEM), transmission electron microscopy (TEM), high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM), X-ray diffraction (XRD), thermogravimetric analysis (TGA), N2 adsorption, and X-ray photoelectron spectroscopy (XPS), we demonstrate the immobilization of highly stable and well-dispersed PdNPs was obtained. The designed IHP-Br-PdNPs demonstrate stability for up to 36 months in ambient air and can be efficiently recycled. After 9 catalytic cycles, there was no significant decline in catalytic performance, and the particle size of PdNPs remained constant at approximately 4-8 nm throughout the reactions. The coordination mode between the stabilizer and metal, specifically the π-π interaction between the 2Br-substituted imidazolium moiety and the Pd metal surface, plays a key role in stabilizing various active species and facilitating distinct catalytic pathways. This study provides valuable insights into the development of π-π interactions supported metal catalysts, which enhance stability and catalytic activity in advanced water-mediated synthesis applications.

Evolution of strengthening precipitates in Al-4.0Zn-1.8Mg-1.2Cu (at.%) alloy with high Zn/Mg ratio during artificial aging

Evolution of strengthening precipitates, including their types, sizes, volume fraction, and chemical compositions in Al-4.0Zn-1.8Mg-1.2Cu (at.%) alloy during artificial aging, were investigated using anomalous small-angle X-ray scattering (ASAXS), three-dimensional atom probe techniques (APT), high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and density functional theory (DFT) calculation. Upon aging, Cu-containing clusters merge with adjacent clusters to form larger clusters, which then act as nucleation sites for GPη' zones. As aging proceeds, GPη' zones grow up to η'I metastable phase with seven atomic layers on {111}Al planes, and this process is controlled by diffusion of Mg atoms. Cu atoms have a low diffusion rate and do not participate into the growth of precipitates within the first 60mins of aging. As aging time increases, Cu atoms enter the η'I metastable phase, leading to a significant increase in Cu content and (Zn+Cu)/Mg ratio; η'I metastable phase grow, and after exceeding about 7nm, gradually transform into the η'II metastable phase with ten atomic layers by adding three new atomic layers at one side. GPη' zones, η'I metastable phase and η'II metastable phase have symmetric interface structures. The precipitation sequence during aging to peak state can be summarized as: atomic clusters → GPη' zones → η'I metastable phase → η'II metastable phase.

Amorphous-Crystalline Interface Induced Internal Electric Fields for Electrochromic Smart Window.

Balancing optical modulation and response time is crucial for achieving high coloration efficiency in electrochromic materials. Here, internal electric fields are introduced to titanium dioxide nanosheets by constructing abundant amorphous-crystalline interfaces, ensuring large optical modulation while reducing response time and therefore improving coloration efficiency. Aberration-corrected high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) reveals the presence of numerous amorphous-crystalline phase boundaries in titanium dioxide nanosheets. Kelvin probe force microscopy (KPFM) exhibits an intense surface potential distribution, demonstrating the presence of internal electric fields. Density functional theory (DFT) calculations confirm that the amorphous-crystalline heterointerfaces can generate internal electric fields and reduce diffusion barriers of lithium ions. As a result, the amorphous-crystalline titanium dioxide nanosheets exhibit better coloration efficiency (35.1cm2C-1) than pure amorphous and crystalline titanium dioxide nanosheets.

Oxygen reduction reaction on Ag nanocatalysts prepared by the microemulsion method

The microemulsion (water-in-oil) method is used to prepare novel silver catalysts onto three different carbon supports (multi-walled carbon nanotubes (MWCNT), mesoporous carbon (MC) and Vulcan carbon (C)). It allows to control the Ag particle growth and produces particles that range between 2 and 3 nm. The Ag-based catalysts are characterised by scanning transmission electron microscopy (STEM) with energy-dispersive X-ray spectroscopy (EDS). The electrocatalytic activity towards the oxygen reduction reaction (ORR) in 0.1 M KOH is studied using the rotating disc electrode method. High-angle annular dark-field (HAADF) STEM images reveal the Ag particle size range between 1.8 and 2.4 nm, and the EDS mapping shows uniform Ag distribution on the substrates used. Ag1/MC (two-step synthesis) and Ag2/MC (one-step synthesis) catalysts prepared onto the MC support show the highest mass activity of 30–37 A g−1. The two-step synthesis method is preferred to prepare Ag/MWCNT and Ag/C catalysts. The mass activity of the Ag1/MWCNT catalyst is more than two times higher than that of Ag2/MWCNT. Ag1/MWCNT shows the highest electrochemical stability after the accelerated durability test, with only a 6 mV shift in half-wave potential. The microemulsion method is very promising for the production of highly stable Ag-based catalysts with Ag particles smaller than 3 nm in size.

Highly Selective Conversion of Carbon Dioxide to Methane by Copper Single Atom Electrocatalysts.

Electrocatalytic carbon dioxide reduction into high-value chemicals is one of the important solutions to the greenhouse effect and energy crisis. However, the slow kinetic process of eight electrons requires the development of efficient catalysts to improve the yields. Single atom catalysts (SACs) with high activity and selectivity have become an emerging research frontier in the field of heterogeneous catalysis. Herein, a catalyst comprised of Cu single atoms loaded on carbon substrate (Cu-NC) is developed for highly selective electrocatalytic reduction of CO2 to methane (CH4). The optimal catalyst (Cu-NC-1-4) exhibits a faradaic efficiency (FE) of over 50 % for CH4 within a wide potential window from -1.3 V to -1.8 V (vs. RHE) and the highest FE of CH4 is up to 67.22 % at -1.6 V (vs. RHE). Meanwhile, the product selectivity of CH4 among all the carbon products reaches 93.00 %, and the activity decay can be negligible via the 70-hour-stability-test. The existence of atomic dispersed Cu-N3 sites was verified by high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) and X-ray absorption near edge structure (XANES). Density functional theory (DFT) calculations show that the effective adsorption of the key intermediate *CO on Cu-N3 sites prompts the generation of CH4.

Demonstration of β-(Al x Ga1−x )2O3/β-Ga2O3 superlattice growth by mist chemical vapor deposition

This study demonstrates the successful growth of a β-(Al x Ga1−x )2O3/β-Ga2O3 superlattice structure with six periods using mist CVD. High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) analysis revealed that the superlattice consisted of six periods of β-(Al x Ga1−x )2O3/β-Ga2O3 with an individual layer thickness of 12.9 nm and 9.1 nm, respectively. XRD analysis further confirmed the periodicity of the structure, yielding a period of 22.7 nm, which is in good agreement with the STEM result. Additionally, the Al composition was determined to be x = 0.085 based on XRD peak positions. Both atomic force microscopy and HAADF-STEM observations revealed atomically flat surfaces and sharp interfaces. This achievement highlights the potential of mist CVD for fabricating complex oxide heterostructures, offering a cost-effective and scalable alternative to conventional methods. The findings open new avenues for developing advanced electronic and optoelectronic devices based on wide-bandgap oxides.

Silver nanoparticles modified with MoS2 and β-cyclodextrin as SERS substrate for rapid determination of cysteamine hydrochloride in meat products

An efficient Surface-enhanced Raman scattering (SERS) method for the detection of cysteamine hydrochloride (CSH) was developed by synthesizing a composite substrate comprising silver nanoparticles (AgNPs) functionalized with MoS2 and β-cyclodextrin (β-CD). The enhanced Raman signals of CSH by β-CD/MoS2/AgNPs substrate were the contribution of electromagnetic enhancement (EM) as well as chemical enhancement (CM), and the enhancement factor (EF) can reach up to 3.11 × 106 (peak at 633 cm−1). Various instrumental techniques were used to characterize the substrate, such as X-ray diffraction (XRD), thermogravimetric analysis (TGA), transmission electron microscopy (TEM), high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) and ultraviolet visible (UV–vis). The binding of β-CD/MoS2/AgNPs and CSH was confirmed by UV–vis and Fourier transform infrared (FT-IR). The optimal experimental conditions were determined by single factor experiments as well as response surface model. The influences of different metal ions and analogous drugs on the detection of CSH were investigated. Under optimum conditions, a good linear correlation (R = 0.9997) was established for CSH in the range of 10.00–1000.00 nmol/L, and the limit of detection (LOD) was as low as 0.78 nmol/L (S/N = 3). The contents of CSH in meat samples were detected. The recovery was 96.6–103.1 %, and the relative standard deviation (RSD) of the measurement was 0.7–3.9 % (n = 7).

The beginning of iron corrosion - high-resolution visualization with 3D electron tomography

Understanding the genesis and early-phase reactions of iron corrosion is essential for the early detection, mitigation and prevention of metal degradation. In this work, high-resolution 3D tomography of metallic iron oxidation was acquired using high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). In particular, dendritic capillaries (<0.5 nm) were observed during the initial oxidation of fresh nanoscale zero-valent iron due to the differential oxygen diffusion and iron atoms migration. This observation led to the proposal of a nanoscale “pothole” model for early-phase corrosion, wherein hollowing out of the metal nanoparticle and formation of nanovoids beneath the iron/oxide interface through Kirkendall effect. Coalescence of the nanocapillaries results in the ultimate collapse of metal structure and/or functional failure. Using nanoscale zero-valent iron as a research model, this work provides unprecedented insights into the nano- and atomic-scale mechanisms of iron oxidation, paving the way for advanced detection and prevention strategies for iron corrosion.

TEM Investigation on High Dose Al Implanted 4H-SiC Epitaxial Layer

Within this work, the effect of high dose Al ion implantation on 4H-SiC epitaxial layer is displayed. Through TEM investigation it is demonstrated that the implanted surface is suitable as seed for subsequent epitaxial regrowth generating a crystal free of extended defects. In order to assess the defects within the projected range of the ion implanted area, High Angle Annular Dark Field STEM (HAADF-STEM) analyses were performed demonstrating the atomic arrangement of the lattice in correspondence of the dislocation loop and the deviation of the crystallographic planes of 4H-SiC, driven by stress relaxation, that determine the staircase configuration of the implant pattern. Further emphasis is given to the detailed analysis of the precipitates atomic structure, whose preferential localization is ascertained. Using Energy-Dispersive X-ray spectroscopy (EDS) analysis, the precipitate is finally established as Al crystal with an FCC structure.

Simultaneous 2D Projection and 3D Topographic Imaging of Gas-Dependent Dynamics of Catalytic Nanoparticles.

Catalyst deactivation through pathways such as sintering of nanoparticles and degradation of the support is a critical factor when designing high-performance catalysts. Here, structural changes of supported nanoparticle catalysts are investigated in controlled gas environments (O2, H2O, and H2) at different temperatures by imaging simultaneously the nanoparticle structures in 2D projection and the 3D surface-sensitive topography. Platinum nanoparticles on carbon support as a model system are imaged in an environmental transmission electron microscope (ETEM), with concurrent acquisition of high-angle annular dark field scanning TEM (HAADF-STEM) and secondary electron (SE) images. Particle migration and coalescence occurs and shows gas-dependent kinetics, with nanoparticles moving across and through the support during and after coalescence. The temperature required for motion is lower in O2 than in H2O and H2, explained through the nature of the gas/nanoparticle interactions. In O2 and H2, the carbon support degrades by trench formation along migration pathways, and the particles move continuously, indicating a chemical reaction between gas and support. In H2O gas, motion is more discontinuous and oriented particle attachment occurs, as expected from theoretical predictions. These results suggest that multimodal imaging in ETEM that combines HAADF-STEM and SE data provides comprehensive information regarding catalyst dynamics and degradation mechanisms.

Morphology and crystallography of E-(Al18Cr2Mg3) nano dispersoids in 7475 Al alloy

The morphology and crystallography of E-(Al18Cr2Mg3) nano dispersoids in 7475 Al alloy have been studied by using transmission electron microscopy (TEM), high resolution transmission electron microscopy (HRTEM), high angle annular dark field scanning transmission electron microscopy (HAADF-STEM) and electron tomography (ET). Seven distinct morphologies have been three-dimensionally distinguished at the nanoscale: (i) triangular plates on {111}Al, (ii) hexagonal plates on {111}Al, (iii) rods parallel to <110>Al, (iv) small tetrahedra with {111}Al facets, (v) small octahedra, (vi) spheres and (vii) irregular shapes. Twinning can contribute to the diverse morphologies of E nano dispersoids. The orientation relationships (ORs) between E nano dispersoids and Al matrix have been systematically investigated by selected area electron diffraction (SAED) patterns, HRTEM and matrix calculation. The results from the matrix calculation indicate the absence of clear ORs between E nano dispersoids and Al matrix in 7475 Al alloy.

Capturing low-concentration benzene: Design and mechanism of high-performance Cu1-Ox,Ny-C single-atom adsorbents

Common adsorbents, such as active carbons, zeolites, and metal–organic frameworks (MOFs), struggle to capture low concentrations of benzene. Single-atom adsorbents (SAAs), boasting exceptional atomic utilization efficiency and precisely tailored electronic structures, offer a promising solution. This study first designed Cu1-Ox,Ny-C SAAs and explored their enhanced benzene adsorption through density functional theory (DFT). Particularly, a crucial link between the SA coordination configuration and its affinity for benzene was established. Next, Cu1-Ox,Ny-C was synthesized from the MOF MIL-101(Cr) and extensively characterized using high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and X-ray absorption fine structure (XAFS) spectroscopy, etc. to determine the coordination configuration of Cu single atoms. Finally, a thorough evaluation of the Cu1-Ox,Ny-C’ capacity and stability was conducted. Theoretical analysis revealed that Cu single atoms within the Ox,Ny-C matrix act as the primary adsorption sites for benzene. Notably, O and N atoms work synergistically: oxygen atoms promote adsorption, while nitrogen atoms mainly stabilize single-atom sites. Cu1-Ox,Ny-C was successfully synthesized, and characterization revealed that Cu1-O2,N2(trans)-C and Cu1-O3,N1-C were the dominant coordination configurations. Remarkably, despite a fourfold decrease in specific surface area compared to MIL-101(Cr), Cu1-Ox,Ny-C exhibited a threefold increase in chemisorption capacity for low-concentration benzene. Moreover, it exhibits excellent resistance to H2O and can be effectively reused. This study demonstrates a valuable strategy for designing and creating highly efficient SAAs for capturing low concentrations of benzene.

Unveiling microstructural damage for leakage current degradation in SiC Schottky diode after heavy ions irradiation under 200 V

Single-event burnout and single-event leakage current (SELC) in silicon carbide (SiC) power devices induced by heavy ions severely limit their space application, and the underlying mechanism is still unclear. One fundamental problem is lack of high-resolution characterization of radiation damage in the irradiated SiC power devices, which is a crucial indicator of the related mechanism. In this Letter, high-resolution transmission electron microscopy (TEM) was used to characterize the radiation damage in the 1437.6 MeV 181Ta-irradiated SiC junction barrier Schottky diode under 200 V. The amorphous radiation damage with about 52 nm in diameter and 121 nm in length at the Schottky metal (Ti)–semiconductor (SiC) interface was observed. More importantly, in the damage site the atomic mixing of Ti, Si, and C was identified by electron energy loss spectroscopy and high-angle annular dark-field scanning TEM. It indicates that the melting of the Ti–SiC interface induced by localized Joule's heating is responsible for the amorphization and the possible formation of titanium silicide, titanium carbide, or ternary phases. The mushroom-like hillock in the Ti layer can be attributed to Rayleigh–Taylor instability, as another evidence for ever-happened localized melting near the Schottky interface. These modifications at nanoscale in turn cause localized degradation of the Schottky contact, resulting in permanent increase in leakage current. This experimental study provides very valuable clues for a thorough understanding of the SELC mechanism in SiC diodes.

Elemental distribution and site occupancy in a Co-Ni-Al-Ti-Ta-W superalloy

γ'-precipitate strengthened cobalt-based superalloys show promise for higher temperature-capability over nickel-based superalloys due to higher melting temperatures. This study investigates a multicomponent CoNi-based superalloy with composition of 54Co-30Ni-9Al-1Ta-4Ti-2-W (at.%) in terms of elemental partitioning and site occupancy. Atom probe tomography (APT) reveals preferential partitioning of Ni, Al, Ti, Ta and W to the γ'-precipitate and Co to the γ-matrix. Aberration-corrected high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and energy dispersive spectrometer (EDS) along the [001] zone axis of γ'-precipitate with L12 structure indicate that Co, Ni substitute at A-sites, whereas Al, Ti, Ta, W prefer the B-sites. Density functional theory (DFT) calculations further confirm the results of partitioning behaviors and site preferences. Clarifying elemental partitioning and site occupancy provides valuable insights into alloy design principles for advanced CoNi-based superalloys.

A new insight into largely defocused HAADF-STEM imaging and visualization of strain field

A crystalline bilayer specimen with a semi-coherent interface can generate moiré fringes in the high-angle annular-dark field scanning transmission electron microscopy (HAADF-STEM) imaging. Moreover, when the probe is significantly defocused, this specimen can produce largely defocused probe (LDP)-STEM patterns. Although the electron channeling effect serves as the fundamental principles for HAADF-STEM imaging, its connection to the emergence of LDP-STEM patterns remains unclear. The missing link lies in identifying the location of the imaged region. To address this issue, we examined the strain field in three-dimensional space and its interaction with the convergent electron beam, taking the PbZrO3/SrTiO3 (PZO/STO) heterostructure as an example. We discovered a new intensity relationship for LDP-STEM patterns in the PZO/STO heterostructure, which can be well explained by our theory. We also found that, generated by imaging the strain zone, these patterns revealed information that might be obscured in traditional high resolution STEM images, showing a unique advantage in characterizing the strain field. Furthermore, we provided discussions on visualizing the strain field, including the misfit dislocation network and array. Our research offers a novel perspective on the LDP-STEM imaging and clarifies the approach to characterizing the strain field.