Nhiễu xạ điện tử tán xạ ngược

Phân tích nhiễu điện tử tia lùi (EBSD) là một kỹ thuật sử dụng máy quét điện tử (SEM) để nghiên cứu cấu trúc tinh thể của các vật liệu. EBSD được thực hiện trên một SEM trang bị bộ cảm biến EBSD bao gồm ít nhất một màn hình phát quang, một ống kính nhỏ gọn và một máy ảnh ccd. Trong cấu hình này, tia phát xạ SEM đập vào mẫu nghiêng. Khi các electron tia ngược trở lại rời khỏi mẫu, chúng tương tác với các mặt phẳng tuần hoàn nguyên tử của tinh thể và phân khuếch theo định luật Bragg ở các góc phân tán khác nhau trước khi đến màn hình phát quang tạo thành các mẫu Kikuchi (EBSPs). Độ phân giải không gian EBSD phụ thuộc vào nhiều yếu tố, bao gồm tính chất của vật liệu được nghiên cứu và chuẩn bị mẫu. Do đó, các EBSP có thể được chỉ số hóa để cung cấp thông tin về cấu trúc hạt của vật liệu, hướng hạt và pha tại tỉ lệ micro. EBSD được áp dụng cho nghiên cứu nhiễu và khuyết tật tinh thể, biến dạng nhựa và phân tích thống kê cho trung bình lệch hướng, kích thước hạt và cấu trúc tinh thể. EBSD cũng có thể được kết hợp với phổ xạ tia X phân tán năng lượng (EDS), quang xạ điện cực (CL) và phổ xạ tia X phân tán bước sóng (WDS) để xác định pha tiên tiến của khám phá vật liệu.

Tổng quát, EBSD là một kỹ thuật đa dụng và mạnh mẽ có thể cung cấp thông tin quý giá về cấu trúc và tính chất của rất nhiều loại vật liệu. Do đó, EBSD được sử dụng rộng rãi trong khoa học và kỹ thuật vật liệu, địa chất và nghiên cứu sinh học. Nó là một công cụ chủ chốt để phát triển các vật liệu mới và hiểu hành vi của chúng trong các điều kiện khác nhau.

The change and degradation in electron backscatter patterns (EBSPs) provide information about lattice distortion in the diffracting volume. Pattern degradation (i.e., diffuse quality) can be used to assess the level of plasticity. The EBSP zone axis position change can measure the residual elastic stress and small lattice rotations. EBSD can also provide information about geometrically necessary dislocations (GND) density. However, the lattice distortion is measured relative to a reference pattern (EBSP₀). The reference pattern choice affects the measurement precision; e.g., a reference pattern deformed in tension will directly reduce the HR-EBSD map tensile strain magnitude while indirectly influencing the other component magnitude and the strain’s spatial distribution. Furthermore, the choice of EBSP₀ slightly affects the GND density distribution and magnitude.

Pattern formation and collection

Setup geometry and pattern formation

Xem thêm thông tin: Electron diffraction và Kikuchi lines (physics)

EBSD typical hardware configuration inside field emission gun scanning electron microscope

For electron backscattering diffraction microscopy, a flat polished crystalline specimen is usually placed inside a scanning electron microscope (SEM) chamber, tilted ~70° from SEM original specimen positioning and 110° to the diffraction camera. Tilting the sample elongates the interaction volume perpendicular to the tilt axis, allowing more electrons to leave the sample due to elastic scattering, providing better contrast. The high-energy electron beam (typically 20 kV) is focused on a small volume and scatters at a spatial resolution of ~20 nm at the specimen surface. The spatial resolution varies with angular width, interaction volume, nature of the material under study, and in transmission Kikuchi diffraction with the specimen thickness; thus, increasing the beam energy increases the interaction volume and decreases the spatial resolution.

The phosphor screen is located within the specimen chamber of the SEM at an angle of approximately 90° to the pole piece. It is coupled to a compact lens which focuses the image from the phosphor screen onto the CCD (or Complementary Metal Oxide Semiconductor, CMOS) camera and excites the phosphor causing it to fluoresce. In this configuration, as these backscattered electrons leave the sample, they interact with the crystal’s periodic atomic lattice planes and diffract according to Bragg's law at a range of scattering angles ($2\theta _{hkl}$). The backscattered electrons form Kikuchi lines – having different intensities – on an electron-sensitive flat film/screen (commonly phosphor), gathered to form a Kikuchi band. These Kikuchi lines are the trace of a hyperbola formed by the intersection of Kossel-cones with the plane of the phosphor screen. The width of a Kikuchi band is related to the scattering angles and, thus, lattice spacing ($d_{hkl}$). These Kikuchi lines and patterns were named after Seishi Kikuchi, who, together with Shoji Nishikawa, was the first to notice this diffraction pattern in 1928 using transmission electron microscopy (TEM) which is similar in geometry to X-ray’s Kossel pattern.

The systematically arranged Kikuchi bands, which have a range of intensity along their width, intersect around the centre of the regions of interest (ROI), describing the probed volume crystallography. These bands and their intersections form what are known as Kikuchi patterns or electron backscatter patterns (EBSPs). To improve contrast, the patterns’ background is corrected by removing anisotropic/inelastic scattering using static background correction or dynamic background correction.

Single crystal 4H SiC (gnomically projected) EBSP collected using (left) conventional, (centre) dynamic, and (right) combined background correction

Formation of Kossel cone which intersect with CCD screen to form EBSP which can be Bravais-Miller indexed

If the system geometry is well described, it is possible to relate the bands present in the diffraction pattern to the underlying crystal and orientation of the material within the electron interaction volume. Each band can be indexed individually by the Miller indices of the diffracting plane which formed it. In most materials, only three bands/planes intersect and are required to describe a unique solution to the crystal orientation (based upon their interplanar angles). Most commercial systems use look-up tables with international crystal databases to index. This crystal orientation relates the orientation of each sampled point to a reference crystal orientation.

While this 'geometric' description related to the kinematic solution (using the Bragg condition) is very powerful and useful for orientation and texture analysis, it only describes the geometry of the crystalline lattice. It ignores many physical processes involved within the diffracting material. To adequately describe finer features within the electron beam scattering pattern (EBSP), one must use a many beam dynamical model (e.g. the variation in band intensities in an experimental pattern does not fit the kinematic solution related to the structure factor).

EBSD detectors

EBSD is conducted using an SEM equipped with an EBSD detector containing at least a phosphor screen, compact lens and low-light CCD camera. Commercially available EBSD systems typically come with one of two different CCD cameras: for fast measurements, the CCD chip has a native resolution of 640×480 pixels; for slower, and more sensitive measurements, the CCD chip resolution can go up to 1600×1200 pixels.

The biggest advantage of the high-resolution detectors is their higher sensitivity, and therefore the information within each diffraction pattern can be analysed in more detail. For texture and orientation measurements, the diffraction patterns are binned to reduce their size and computational times. Modern CCD-based EBSD systems can index patterns at up to 1800 patterns/second. This enables very rapid and rich microstructural maps to be generated.

Sample preparation

Ideally, the sample should be vacuum-stable and mounted using a conductive compound (e.g. Cu and SiO₂ filled epoxy thermoset) because it minimises image drift and the intensity blooming caused by the electron beam charging. Due to EBSPs quality being highly sensitive to the surface preparation, the sample should be ground using SiC papers from 240 down to 4000 grit, and polished using diamond paste (from 9 to 1 µm) then in 50 nm colloidal silica for 2 hours (50rpm speed and 5N force) to produce a flat surface without preparation-induced artefacts and also to maintain consistency – for comparison – between samples. Afterwards, the sample should be cleaned for 20 minutes in an Ultrasonic cleaning bath using ethanol, then rinsed with deionised water, before eventually being dried with a hot air blower. This is followed by ion polishing, for final surface preparation, using 7.5 keV dual beam energy for 15 min, with the gun’s angle of 8°.

Inside the scanning electron microscope (SEM), the size of the measurement area determines local resolution and measurement time. For high-quality EBSPs, it is recommended to use 15 nA current, 20 keV beam energy, 18mm working distance, long exposure times and minimal pattern binning. The EBSD phosphor screen should also be at an 18 mm working distance with at least 800*600 resolution, 180 milli-seconds exposure time per pattern, 2*2 pattern binning, and a map’s step size of less than 0.5µm.

Pattern degradation due to carbon deposition in a highly magnified location after 3hr EBSPs acquisition around a deformation twin in the ferrite phase of duplex stainless steel.

The electron-beam-induced decomposition of gaseous hydrocarbons causes the effect of carbon deposition on the quality of the patterns during slow EBSPs acquisition. Carbon depositions degrade the quality of EBSPs inside the probed area compared to the EBSPs outside the acquisition window. The gradient of pattern degradation increases moving inside the probed zone with an apparent accumulation of deposited carbon. The black spots from the beam instant-induced carbon deposition also highlight the immediate deposition even if agglomeration did not happen.

Depth resolution

Xem thêm thông tin: Electron scattering

Electron-matter interaction volume and various types of signal generated

The depth resolution of EBSD is widely accepted to vary between 10 to 40 nm, decreasing with the material atomic number. Nevertheless, using a differently thick transparent amorphous layer of Chromium coating a mono-Silicon crystal, experimental measurements indicated that the depth resolution could be as shallow as 2 nm. This was determined by Si pattern quality deteriorating by ~50% when using a FEG-SEM with 15 kV beam conditions and 15 mm working distance between the beam and sample and 65 mm between the sample and the detector and without considering the channelling effect. However, using a similar experimental approach, different results were reported, e.g., Isabell and David concluded that depth resolution could extend to 1 µm due to inelastic scattering (including tangential smearing and channelling effect).

Illustrate of the interaction of an electron beam with a sample. Where K, L, and M are the electron shells. N is the sample nucleus. Gamma is a characteristic photon emitted by the ejection of SE (Secondary Electron). BSE is a Back-Scattered Electron. Electrons

These experiments are highly cumbersome due to the need for precise and well-calibrated equipment, with the results open to interpretation. This is because

• There is no agreement about the definition of depth resolution. For example, it can be defined as the depth where ~92% of the signal is generated, or defined by pattern quality, or are as ambiguous as “where useful information is obtained”.
• Reported depth of information values do not mention a definition or do not have a rationale for the definition of depth resolution. Moreover, most of the depth of information measurement experiments do not provide information on the beam size, tilt angle, beam-to-sample and sample-to-detector working distance, and – sometimes – even the beam energy. These are critical parameters for determining (or simulating) the depth resolution of the patterns as the interaction volume, which decreases with the sample atomic number or density, increases with beam energy and size. The beam current is generally not considered to affect the depth resolution in experiments or simulations. However, it affects the beam spot size and pattern signal-to-noise (S/N) ratio, affecting the depth resolution and the details in the pattern.

Using Monte Carlo (MC) simulations is also an alternative approach to quantifying the depth resolution for EBSPs formation, which can be estimated using Bloch wave theory, where backscattered primary electrons - after interacting with the crystal lattice - exit the surface carrying information about the crystallinity of the volume interacting with the electrons. The backscattered electrons (BSE) energy distribution depends on the material’s characteristics and the beam conditions. This BSE wave field is also affected by the thermal diffuse scattering process that causes incoherent and inelastic (energy loss) scattering – after the Bragg diffraction events – which does not, yet, have a complete physical description that can be related to mechanisms that constitute EBSP depth resolution.

Most importantly, conclusions drawn from both experiments and simulations assume the surface is pristine with homogeneous depth resolution, neither of which is valid for a deformed sample.

Orientation and phase mapping

Pattern indexing

Overview of EBSD indexing procedure showing pattern capture through to determination of crystal orientation

Indexing is often the first step in the EBSD process after pattern collection. This allows for the identification of the crystal orientation at the single volume of the sample from where the pattern was collected. With EBSD software, pattern bands are typically detected via a mathematical routine using a modified Hough transform, in which every pixel in Hough space denotes a unique line/band in the EBSP. The Hough transform enables band detection, which is difficult to locate by computer in the original EBSP. Once the band locations have been detected, it is possible to relate these locations to the underlying crystal orientation, as angles between bands represent angles between lattice planes. Thus, an orientation solution can be determined when the position/angles between three bands are known. In highly symmetric materials, more than three bands are typically used to obtain and verify the orientation measurement.

The diffraction pattern is preprocessed to remove noise, correct for detector distortions, and normalise the intensity. Then, the preprocessed diffraction pattern is compared to a library of reference patterns for the material being studied. The reference patterns are generated based on the material's known crystal structure and the crystal lattice's orientation. The orientation of the crystal lattice that would generate the best match to the measured pattern is determined using a variety of algorithms. There are three leading methods of the indexing performed by most commercial EBSD software: triplet voting; minimising the 'fit' between the experimental pattern and a computationally determined orientation, and or/and neighbour pattern averaging and re-indexing, NPAR) to give a unique solution to the single crystal orientation that is related to the other crystal orientations within the field-of-view.

Triplet voting involves identifying multiple 'triplets' associated with different solutions to the crystal orientation; each crystal orientation determined from each triplet receives one vote. Should four bands identify the same crystal orientation, then four (four choose three) votes will be cast for that particular solution. Thus the candidate orientation with the highest number of votes will be the most likely solution to the underlying crystal orientation present. The number of votes for the solution chosen compared to the total number of votes describes the confidence in the underlying solution. Care must be taken in interpreting this 'confidence index' as some pseudo-symmetric orientations may result in low confidence for one candidate solution vs another. Minimising the fit involves starting with all possible orientations for a triplet. More bands are included, which reduces the number of candidate orientations. As the number of bands increases, the number of possible orientations converges ultimately to one solution. The 'fit' between the measured orientation and the captured pattern can be determined.

Overall, indexing diffraction patterns in EBSD involves a complex set of algorithms and calculations, but is essential for determining the crystallographic structure and orientation of materials at a high spatial resolution. The indexing process is continually evolving, with new algorithms and techniques being developed to improve the accuracy and speed of the process.

Afterwards, a confidence index is calculated to determine the quality of the indexing result. The confidence index is based on the match quality between the measured and reference patterns. In addition, it considers factors such as noise level, detector resolution, and sample quality.

Pattern centre

To relate the orientation of a crystal, much like in X-ray diffraction, the geometry of the system must be known. In particular, the pattern centre describes the distance of the interaction volume to the detector and the location of the nearest point between the phosphor and the sample on the phosphor screen. Early work used a single crystal of known orientation being inserted into the SEM chamber, and a particular feature of the EBSP was known to correspond to the pattern centre. Later developments involved exploiting various geometric relationships between the generation of an EBSP and the chamber geometry (shadow casting and phosphor movement).

Unfortunately, each of these methods are cumbersome and can be prone to some systematic errors for a general operator. Typically they can not be easily used in modern SEMs with multiple designated uses. Thus, most commercial EBSD systems use the indexing algorithm combined with an iterative movement of crystal orientation and suggested pattern centre location. Minimising the fit between bands located within experimental patterns and those in look-up tables tends to converge on the pattern centre location to an accuracy of ~0.5–1% of the pattern width.

Recent development of AstroEBSD and PCGlobal, open-source MATLAB codes, increased the precision of determining the pattern centre (PC) and – consequently – elastic strains by using a pattern matching approach which simulates the pattern using EMSoft.

EBSD mapping

EBSD orientation (indexed) map about ferrous lath martensite with high angle (>10°) boundaries.

The indexing results are used to generate a map of the crystallographic orientation at each point on the surface being studied. Thus, scanning the electron beam in a prescribed fashion (typically in a square or hexagonal grid, correcting for the image foreshortening due to the sample tilt) results in many rich microstructural maps. These maps can spatially describe the crystal orientation of the material being interrogated and can be used to examine microtexture and sample morphology. Some maps describe grain orientation, boundary, and diffraction pattern (image) quality. Various statistical tools can measure the average misorientation, grain size, and crystallographic texture. From this dataset, numerous maps, charts and plots can be generated.

The orientation data can be visualised using a variety of techniques, including colour-coding, contour lines, and pole figures.

However, microscope alignments, image shifts, scan distortion that increases with decreasing magnification, ill-prepared contaminated and rough specimen surface, changes in material, boundary indexing failure and detector quality can lead to uncertainties in determining the crystal orientation. Fundamentally, the EBSD pattern’s signal-to-noise ratio is material dependent and decreases with high acquisition speeds and beam currents, which directly affects the angular resolution of the measurements.

Strain measurement

Full-field displacements, elastic strains, and the geometrically necessary dislocations (GND) density provide quantifiable information about the material’s elastic and plastic behaviour at the microscale. Measuring strain at the microscale requires careful consideration of other key details besides the change in length/shape (e.g., local texture, individual grain orientations). These micro-scale features can be measured using different techniques, e.g., hole drilling, monochromatic or polychromatic energy-dispersive X-ray diffraction (XRD) or neutron diffraction (ND). However, the electron backscattering diffraction (EBSD) technique provides an impressive combination of sensitivity, spatial resolution and ease of use compared to other techniques. Strain measurements using EBSD can be performed at a high spatial resolution, allowing researchers to study the local variation in strain within a material. This information can be used to study the deformation and mechanical behaviour of materials, to develop models of material behaviour under different loading conditions, and to optimise the processing and performance of materials. Overall, strain measurement using EBSD is a powerful tool for studying the deformation and mechanical behaviour of materials, and is widely used in materials science and engineering research and development.

Earlier trials

The change and degradation in electron backscatter patterns (EBSPs) provide information about the diffracting volume. Pattern degradation (i.e., diffuse quality) can be used to assess the level of plasticity through the pattern/image quality (IQ), where IQ is calculated from the sum of the peaks detected when using the conventional Hough transform. Wilkinson first used the changes in high-order Kikuchi line positions to determine the elastic strains, albeit with low precision (0.3% to 1%); however, this approach cannot be used for characterising residual elastic strain in metals as the elastic strain at the yield point is usually around 0.2%. Measuring strain by tracking the change in the higher-order Kikuchi lines is practical when the strain is small, as the band position is sensitive to changes in lattice parameters. In the early 1990s, Troost et al. and Wilkinson et al. used pattern degradation and change in the zone axis position to measure the residual elastic strains and small lattice rotations with a 0.02% precision.

High-resolution electron backscatter diffraction (HR-EBSD)

Schematic shifting between a reference and deformed crystals in the EBSP pattern projected in the phosphor screen

Cross-correlation-based, high angular resolution electron backscatter diffraction (HR-EBSD) – introduced by Wilkinson et al. – is a scanning electron microscopy (SEM) -based technique to map relative elastic strains and rotations, and estimate the geometrically necessary dislocation (GND) density in crystalline materials. HR-EBSD method uses image cross-correlation to measure pattern shifts between regions of interest (ROI) in different electron backscatter diffraction patterns (EBSPs) with sub-pixel precision. As a result, the relative lattice distortion between two points in a crystal can be calculated using pattern shifts from at least four non-collinear ROI. In practice, pattern shifts are measured in more than 20 ROI per EBSP to find a best-fit solution to the deformation gradient tensor, representing the relative lattice distortion.

The displacement gradient tensor ($\beta$) (or local lattice distortion) relates the measured geometrical shifts from in the pattern between the collected point (${\widehat {p}}$) and associate (non-coplanar) vector (${\widehat {r}}$), and reference point ($p$) pattern and associate vector ($r$). Thus, the (pattern shift) vector ($q$) can be written as in the equations below, where $x_{i}$ and $u_{i}$ are the direction and displacement in $i$th direction, respectively.

$q=\beta r-(\beta r.{\widehat {r}}){\widehat {r}}$

$\beta ={\begin{pmatrix}{\partial u_{1} \over x_{1}}&{\partial u_{1} \over x_{2}}&{\partial u_{1} \over x_{3}}\\{\partial u_{2} \over x_{1}}&{\partial u_{2} \over x_{2}}&{\partial u_{2} \over x_{3}}\\{\partial u_{3} \over x_{1}}&{\partial u_{3} \over x_{2}}&{\partial u_{3} \over x_{3}}\end{pmatrix}},\qquad r={\begin{pmatrix}{r_{1}}\\{r_{2}}\\{r_{3}}\\\end{pmatrix}}$

The shifts are measured in the phosphor (detector) plane ($\beta _{3}r_{3}=0$), and the relationship is simplified; thus, eight out of the nine displacement gradient tensor components can be calculated by measuring the shift ( and ) at four distinct, widely spaced regions on the EBSP. This shift is then corrected to the sample frame (flipped around Y-axis) because EBSP is recorded on the phosphor screen and is inverted as in a mirror. They are then corrected around the X-axis by 24° (i.e., 20° sample tilt plus ≈4° camera tilt and assuming no angular effect from the beam movement). Using infinitesimal strain theory, the deformation gradient is then split into elastic strain (symmetric part, where $ij=ji$), $e_{ij}$and lattice rotations (asymmetric part, where $ii=jj=0$), $\omega _{ij}$.

$e_{ij}={1 \over {2}}(\beta _{ij}+\beta _{ij}^{r}),\qquad \omega _{ij}={1 \over {2}}(\beta _{ij}-\beta _{ij}^{r})$

These measurements do not provide information about the volumetric/hydrostatic strain tensors. By imposing a boundary condition that the stress normal to the surface ($\sigma _{33}$) is zero (i.e., traction-free surface), and using Hooke’s law with anisotropic elastic stiffness constants, the missing ninth degree of freedom can be estimated in this constrained minimisation problem by using a nonlinear solver.

$\sigma _{33}=C_{33kl}e_{kl}=0$

Where $C$ is the crystal anisotropic stiffness tensor. These two equations are solved to re-calculate the refined elastic deviatoric strain ($\varepsilon _{kl}$), including the missing ninth (spherical) strain tensor. An alternative approach that considers the full $\beta$ can be found in.

$e_{ij}={\begin{pmatrix}{e_{11}}\\{e_{22}}\\{e_{33}}\\{2e_{12}}\\{2e_{13}}\\{2e_{23}}\\\end{pmatrix}},\qquad {\begin{pmatrix}{k_{1}}\\{k_{2}}\\{k_{3}}\\\end{pmatrix}}={\begin{pmatrix}{e_{11}-e_{33}}\\{e_{22}-e_{33}}\\{e_{12}C_{3312}+e_{13}C_{3313}+e_{23}C_{3323}}\\\end{pmatrix}}$

$\varepsilon _{33}={k_{1}C_{1133}+k_{2}C{2233}+k_{3} \over C_{1133}+C_{2233}+C_{3333}},\qquad \therefore \varepsilon _{kl}={\begin{pmatrix}{k_{1}+\varepsilon _{33}}\\{k_{2}+\varepsilon _{33}}\\{\varepsilon _{33}}\\{2e_{12}}\\{2e_{13}}\\{2e_{23}}\\\end{pmatrix}}$

Finally, the stress and strain tensors are linked using the crystal anisotropic stiffness tensor ($C_{klij}$), and by using Einstein summation convention with symmetry of stress tensors ($\sigma _{ij}=\sigma _{ji}$).

$\sigma _{ij}=C_{ijkl}\varepsilon _{kl}$

The quality of the produced data can be assessed by taking the geometric mean of all the ROI’s correlation intensity/peaks. A value lower than 0.25 should indicate problems with the EBSPs' quality. Furthermore, the geometrically necessary dislocation (GND) density can be estimated from the HR-EBSD measured lattice rotations by relating the rotation axis and angle between neighbour map points to the dislocation types and densities in a material using Nye’s tensor.

Precision and development

The HR-EBSD method was shown to achieve a precision of ±10^–4 in components of the displacement gradient tensors (i.e., strain and rotation in radians) by measuring the shifts at a pattern image resolution of ±0.05 pixels. Still, it was limited to small strains and rotations (>1.5°). Britton and Wilkinson raised the rotation limit to ≈11° by using a re-mapping technique that recalculated the strain after transforming the patterns with a rotation matrix ($R$) calculated from the 1^st cross-correlation iteration.

$R={\begin{pmatrix}\cos \omega _{12}&\sin \omega _{12}&0\\-\sin \omega _{12}&\cos \omega _{12}&0\\0&0&1\end{pmatrix}}{\begin{pmatrix}1&0&0\\0&\cos \omega _{23}&\sin \omega _{23}\\0&-\sin \omega _{23}&\cos \omega _{23}\end{pmatrix}}{\begin{pmatrix}\cos \omega _{31}&0&-\sin \omega _{31}\\0&1&0\\\sin \omega _{31}&0&\cos \omega _{31}\end{pmatrix}}$

(a) Secondary electron (SE) image for the indentation on the (001) mono crystal. (b) HR-EBSD stress and rotation components, and geometrical necessary dislocations density ($\rho _{GND}$. EBSP₀ is highlighted with a star in $\sigma _{yz}$

However, further lattice rotation, typically caused by severe plastic deformation, will cause errors in the elastic strain calculations. Ruggles et al. demonstrated an improved HR-EBSD precision, even at 12° of lattice rotation, using the inverse compositional Gauss–Newton-based (ICGN) method instead of cross-correlation. Vermeij and Hoefnagels also established a method that achieves a precision of ±10^–5 in the displacement gradient components using a full-field integrated digital image correlation (IDIC) framework instead of dividing the EBSPs into small ROIs. Patterns in IDIC are distortion-corrected to negate the need for re-mapping up to ≈14°. Below comparison of conventional Hough transform EBSD and HR-EBSD

	Conventional EBSD	HR-EBSD
Absolute Orientation	2°	N/A
Misorientation	0.1° to 0.5°	0.006° (1 x 10–4 rad)
GND @ 1 µm step In lines/m2 (b = 0.3 nm)	> 3 x 1013	> 3 x 1011
Relative Residual Strain	N/A	Deviatoric elastic strain 1 x 10–4
Example Tasks	Texture, Microstructure, etc.	Deformation

However, these measurements do not provide information about the volumetric/hydrostatic strains, because there is no change in the plane or angles of the lattice planes (crystallographic directions) but only changes in the position/width of the Kikuchi bands (and their energetic correspondence).

The reference pattern problem

Nonetheless, in HR-EBSD analysis, the lattice distortion field is still calculated relative to a reference pattern or point (EBSP₀) per grain in the map, and is dependent on the lattice distortion at the point. The lattice distortion field in each grain is measured with respect to this point; therefore, the absolute lattice distortion at the reference point (relative to the unstrained crystal) is excluded from the HR-EBSD elastic strain and rotation maps. This ‘reference pattern problem’ is similar to the ‘d₀ problem’ in X-ray diffraction, and affects the nominal magnitude of HR-EBSD stress fields. However, selecting the reference pattern (EBSP₀) plays a key role, as severely deformed EBSP₀ adds phantom lattice distortions to the map values, thus, decreasing the measurement precision.

Linear correlation coefficients between the local conditions at the EBSP0 point and the averaged conditions at the grain for the ferrite (Fe-α) and austenite (Fe-γ) phase of age-hardened DSS, and Silicon (Si). The analysis considers the average deformation gradient tensor determinant ($A^{0}$), maximum in-plane principal strain ($\epsilon _{MAX}$), rotation magnitude ($\omega _{T}={\sqrt {(}}\omega _{32}^{2}+\omega _{13}^{2}+\omega _{21}^{2})$), correlation peak height (PH), mean angular error (MAE) and GND density.

The local lattice distortion at the EBSP₀ influences the resultant HR-EBSD map, e.g., a reference pattern deformed in tension will directly reduce the HR-EBSD map tensile strain magnitude while indirectly influencing the other component magnitude and the strain’s spatial distribution. Furthermore, the choice of EBSP₀ slightly affects the GND density distribution and magnitude, and choosing a reference pattern with a higher GND density reduces the cross-correlation quality, changes the spatial distribution and induces more errors than choosing a reference pattern with high lattice distortion. Additionally, there is no apparent connection between EBSP₀’s IQ and EBSP₀'s local lattice distortion.

The use of simulated reference patterns for absolute strain measurement is still an active area of research and scrutiny as difficulties arise from a variation of inelastic electron scattering with depth which limits the accuracy of dynamical diffraction simulation models, and imprecise determination of the pattern centre which leads to phantom strain components which cancel out when using experimentally acquired reference patterns. Other methods assumed that absolute strain at EBSP₀ can be determined using crystal plasticity finite-element (CPFE) simulations, which then can be then combined with the HR-EBSD data (e.g., using linear ‘top-up’ method or displacement integration) to calculate the absolute lattice distortions.

In addition, GND density estimation is nominally insensitive to (or negligibly dependent upon) EBSP₀ choice, as only neighbour point-to-point differences in the lattice rotation maps are used for GND density calculation. However, this assumes that the absolute lattice distortion of EBSP₀ only changes the relative lattice rotation map components by a constant value which vanishes during derivative operations, i.e., lattice distortion distribution is insensitive to EBSP₀ choice.

Selecting a reference pattern

Existing criteria for EBSP₀ selection can be one or a mixture of:

• Selecting from points with low GND density or low Kernel average misorientation (KAM) based on the Hough measured local grain misorientations;
• Selecting from points with high image quality (IQ), which may have a low defect density within its electron interaction volume, is therefore assumed to be a low-strained region of a polycrystalline material. However, IQ does not carry a clear physical meaning, and the magnitudes of the measured relative lattice distortion are insensitive to the IQ of EBSP₀;
• EBSP₀ can also be manually selected to be far from potential stress concentrations such as grain boundaries, inclusions, or cracks using subjective criteria;
• Selecting an EBSP₀ after examining the empirical relationship between the cross-correlation parameter and angular error, used in an iterative algorithm to identify the optimal reference pattern that maximises the precision of HR-EBSD.

These criteria assume these parameters can indicate the strain conditions at the reference point, which can produce an accurate measurements of up to 3.2 x 10^-4 elastic strain. However, experimental measurements point to the inaccuracy of HR-EBSD in determining the out-of-plane shear strain components distribution and magnitude.

Applications

The EBSD detector has a Forward scattered electron didoes (FSD) at the bottom. MSD note only the position of the diode as being in the middle. Other detectors have a Backscatter diode (BSD) at the top of the EBSD detector.

EBSD is used in a wide range of applications, including materials science and engineering, geology, and biological research. In materials science and engineering, EBSD is used to study the microstructure of metals, ceramics, and polymers, and to develop models of material behaviour. In geology, EBSD is used to study the crystallographic structure of minerals and rocks. In biological research, EBSD is used to study the microstructure of biological tissues and to investigate the structure of biological materials such as bone and teeth.

Scattered electron imaging

(far-field) Virtual forward-scatter detectors (VFSD) image of 475 °C embrittled Duplex stainless steel with the detector at 38 mm working distance (WD) from the sample

EBSD detectors can have a Forward scattered electron diodes (FSD) at the bottom, middle (MSD) and top of the detector. Forward-scattered electron (FSE) imaging involves collecting electrons scattered at small angles (forward-scattered) from the surface of a sample, which provides information about the surface topography and composition. The FSE signal is also sensitive to the crystallographic orientation of the sample. By analysing the intensity and contrast of the FSE signal, researchers can determine the crystallographic orientation of each pixel in the image.

The FSE signal is typically collected simultaneously with the backscattered electron (BSE) signal in EBSD analysis. The BSE signal is sensitive to the average atomic number of the sample, and is used to generate an image of the surface topography and composition. The FSE signal is superimposed on the BSE image to provide information about the crystallographic orientation.

Image generation has a lot of freedom when using the EBSD detector as an imaging device. An image created using a combination of diodes is called virtual or VFSD. It is possible to acquire images at a rate akin to slow scan imaging in the SEM by excessive binning of the EBSD CCD camera. It is possible to suppress or isolate the contrast of interest by creating composite images from simultaneously captured images, which offers a wide range of combinations for assessing various microstructure characteristics. Nevertheless, VFSD images do not include the quantitative information inherent to traditional EBSD maps; they simply offer representations of the microstructure.

Integrated EBSD/EDS mapping

When simultaneous Energy-dispersive X-ray spectroscopy (EDS)/EBSD collection can be achieved, the capabilities of both techniques can be enhanced. There are applications where sample chemistry or phase cannot be differentiated via EDS alone because of similar composition, and structure cannot be solved with EBSD alone because of ambiguous structure solutions. To accomplish integrated mapping, the analysis area is scanned, and at each point, Hough peaks and EDS region-of-interest counts are stored. Positions of phases are determined in X-ray maps, and each element's measured EDS intensities are given in charts. The chemical intensity ranges are set for each phase to select the grains. All patterns are then re-indexed off-line. The recorded chemistry determines which phase/crystal-structure file is used to index each point. Each pattern is indexed by only one phase, and maps displaying distinguished phases are generated. The interaction volumes for EDS and EBSD are significantly different (on the order of micrometres compared to tens of nanometers), and the shape of these volumes using a highly tilted sample may have implications on algorithms for phase discrimination.

EBSD, when used together with other in-SEM techniques such as cathodoluminescence (CL), wavelength dispersive X-ray spectroscopy (WDS) and/or energy dispersive X-ray spectroscopy (EDS) can provide a deeper insight into the specimen's properties and enhance phase identification. For example, the minerals calcite (limestone) and aragonite (shell) have the same chemical composition – calcium carbonate (CaCO₃) therefore EDS/WDS cannot tell them apart, but they have different microcrystalline structures so EBSD can differentiate between them.

Integrated EBSD/DIC mapping

EBSD and Digital Image Correlation (DIC) can be used together to analyse the microstructure and deformation behaviour of materials. DIC is a method that uses digital image processing techniques to measure deformation and strain fields in materials. By combining EBSD and DIC, researchers can obtain both crystallographic and mechanical information about a material simultaneously. This allows for a more comprehensive understanding of the relationship between microstructure and mechanical behaviour, which is particularly useful in fields such as materials science and engineering.

DIC can identify regions of strain localisation in a material, while EBSD can provide information about the microstructure in these regions. By combining these techniques, researchers can gain insights into the mechanisms responsible for the observed strain localisation. For example, EBSD can be used to determine the grain orientations and boundary misorientations before and after deformation. In contrast, DIC can be used to measure the strain fields in the material during deformation. Or EBSD can be used to identify the activation of different slip systems during deformation, while DIC can be used to measure the associated strain fields. By correlating these data, researchers can better understand the role of different deformation mechanisms in the material's mechanical behaviour.

Overall, the combination of EBSD and DIC provides a powerful tool for investigating materials' microstructure and deformation behaviour. This approach can be applied to a wide range of materials and deformation conditions and has the potential to yield insights into the fundamental mechanisms underlying mechanical behaviour.

3D EBSD

3D EBSD map for WC-6%Co with 62 slices dimensions of 10 mm x 10 mm x 3 mm and 50 nm resolution in x, y and z directions

3D EBSD combines EBSD with serial sectioning methods to create a three-dimensional map of a material's crystallographic structure. The technique involves serially sectioning a sample into thin slices, and then using EBSD to map the crystallographic orientation of each slice. The resulting orientation maps are then combined to generate a 3D map of the crystallographic structure of the material. The serial sectioning can be performed using a variety of methods, including mechanical polishing, focused ion beam (FIB) milling, or ultramicrotomy. The choice of sectioning method depends on the size and shape of the sample, as well as the desired resolution and accuracy of the 3D map.

3D EBSD has several advantages over traditional 2D EBSD. First, it provides a complete picture of a material's crystallographic structure, allowing for a more accurate and detailed analysis of the microstructure. Second, it can be used to study complex microstructures, such as those found in composite materials or multi-phase alloys. Third, it can be used to study the evolution of microstructure over time, such as during deformation or heat treatment.

However, 3D EBSD also has some limitations. It requires extensive data acquisition and processing, proper alignment between slices, and can be time-consuming and computationally intensive. In addition, the quality of the 3D map depends on the quality of the individual EBSD maps, which can be affected by factors such as sample preparation, data acquisition parameters, and analysis methods. Overall, 3D EBSD is a powerful technique for studying the crystallographic structure of materials in three dimensions, and is widely used in materials science and engineering research and development.

Transmission Kikuchi diffraction

Transmission Kikuchi Diffraction (TKD or t-EBSD) is a type of electron backscatter diffraction (EBSD) technique that is used to analyse the crystallographic orientation and microstructure of materials at a high spatial resolution. TKD was first introduced in early 2012. It has since become increasingly popular in materials science research, especially for studying materials at the nanoscale.

In TKD, a thin foil sample is prepared and placed perpendicular to the electron beam of a scanning electron microscope (SEM). The electron beam is then focused on a small spot on the sample, and the crystal lattice of the sample diffracts the transmitted electrons. The diffraction pattern is then collected by a detector and analysed to determine the crystallographic orientation and microstructure of the sample.

One of the key advantages of TKD is its high spatial resolution. TKD can achieve spatial resolutions on the order of a few nanometers, which is much higher than conventional EBSD techniques. This high resolution is achieved by using a small electron beam spot size, typically less than 10 nanometers in diameter, and by collecting the transmitted electrons with a small-angle annular dark-field detector (STEM-ADF) in the scanning transmission electron microscope (STEM). Another advantage of TKD is its high sensitivity to local variations in crystallographic orientation. This is because the transmitted electrons in TKD are diffracted at very small angles, which makes the diffraction pattern highly sensitive to local variations in the crystal lattice.

TKD can also be used to study materials that are difficult to prepare as flat surfaces, such as nanoparticles and thin films. This is because the thin foil sample used in TKD can be prepared using techniques such as focused ion beam milling, which can produce very thin samples with minimal surface damage. However, there are also some limitations to TKD. As mentioned earlier, TKD requires a thin foil sample, which can be difficult and time-consuming to prepare. Additionally, the diffraction patterns obtained from TKD can be more complex to interpret than those obtained from conventional EBSD techniques, due to the complex geometry of the diffracted electrons.

On-axis and off-axis TKD are two transmission Kikuchi diffraction (TKD) variants that differ in the sample's orientation with respect to the electron beam. In on-axis TKD, the sample is oriented so that the incident electron beam is nearly perpendicular to the sample surface. This results in a diffraction pattern that is nearly centred around the transmitted beam direction. On-axis TKD is typically used for analysing samples with low lattice strain and high crystallographic symmetry, such as single crystals or large grains.

• Transmission Kikuchi diffraction setup
• 
  (L) Imaging using diodes in On-axis TKD setup. (R) On-axis TKD setup
• 
  (L) Off-axis TKD with an example EBSP. (R) On-axis TKD with an example EBSP.

In off-axis TKD, the sample is tilted with respect to the incident electron beam, typically at an angle of several degrees. This results in a diffraction pattern that is shifted away from the transmitted beam direction. Off-axis TKD is typically used for analysing samples with high lattice strain and/or low crystallographic symmetry, such as nano-crystalline materials or materials with defects. Off-axis TKD is often preferred for materials science research because it provides more information about the crystallographic orientation and microstructure of the sample, especially in samples with a high density of defects or a high degree of lattice strain. However, on-axis TKD can still be useful for studying samples with high crystallographic symmetry or for verifying the crystallographic orientation of a sample before performing off-axis TKD. The on-axis technique can speed up acquisition by more than 20 times, and a low scattering angle setup also gives rise to higher quality patterns.

It is important to note that, like with any EBSD technique, the resolution is influenced by several other factors, not simply the setup. Among these are beam size, electron accelerating voltage, the material's atomic mass and the specimen's thickness. Out of these variables, sample thickness has the greatest effect on the pattern quality and resolution of the image. The thicker the sample, the more beam broadens, thus reducing lateral spatial resolution.

Further reading

• Schwartz, Adam J.; Kumar, Mukul; Adams, Brent L.; Field, David P. biên tập (2009). Electron Backscatter Diffraction in Materials Science (ấn bản 2). New York, NY: Springer New York, NY (xuất bản 12 tháng 8 năm 2009). doi:10.1007/978-0-387-88136-2. ISBN 978-0-387-88135-5.
• Britton, T. Ben; Jiang, Jun; Guo, Y.; Vilalta-Clemente, A.; Wallis, D.; Hansen, L.N.; Winkelmann, A.; Wilkinson, A.J. (tháng 7 năm 2016). “Tutorial: Crystal orientations and EBSD — Or which way is up?”. Materials Characterization. 117: 113–126. doi:10.1016/j.matchar.2016.04.008. S2CID 138070296.
• Randle, Valerie (tháng 9 năm 2009). “Electron backscatter diffraction: Strategies for reliable data acquisition and processing”. Materials Characterization. 60 (90): 913–922. doi:10.1016/j.matchar.2009.05.011.

External links

Codes

• Hielscher, Schaeben (2008). “MTEX (EBSD analysis)”. MTEX.
• Ruggles, T. J.; Bomarito, G. F.; Qiu, R. L.; Hochhalter, J. D. (1 tháng 12 năm 2018). “OpenXY (HR-EBSD)”. GitHub.Quản lý CS1: nhiều tên: danh sách tác giả (liên kết)
• M. De Graef (tháng 7 năm 2017). “EMsoft (simulate EBSP)”. GitHub.
• Vivian, Tong; Ben, Britton (tháng 7 năm 2017). “TrueEBSD: correcting spatial distortions in electron backscatter diffraction maps”. Ultramicroscopy. 221: 113130. arXiv:1909.00347. doi:10.1016/j.ultramic.2020.113130. PMID 33290982. S2CID 202538027.

Videos

• Britton, Ben (11 tháng 1 năm 2021). Introduction to EBSD: Section 1 - What can EBSD tell you?. YouTube.

• Nowell, Matt (22 tháng 2 năm 2022). Learn How I Prepare Samples for EBSD Analysis. EDX (YouTube).

• Electron Backscatter Diffraction Explained: QUANTAX EBSD. Bruker Nano Analytics (YouTube). 1 tháng 9 năm 2020.