Electron backscatter diffraction

EBSD is used for impurities and defect studies, plastic deformation, and statistical analysis for average misorientation, grain size, and crystallographic texture.

[4][5] A high-energy electron beam (typically 20 kV) is focused on a small volume and scatters with a spatial resolution of ~20 nm at the specimen surface.

[17][18] 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.

It is typically mounted using a conductive compound (e.g. an epoxy thermoset filled with Cu), which minimises image drift and sample charging under electron beam irradiation.

Typically the sample is 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.

[26] Usual settings for high-quality EBSPs are 15 nA current, 20 kV beam energy, 18 mm working distance, long exposure time, and minimal CCD pixel binning.

[27][28][29][30] The EBSD phosphor screen is set at an 18 mm working distance and a map's step size of less than 0.5 μm for strain and dislocations density analysis.

[37] In contrast, Isabell and David[40] concluded that depth resolution in homogeneous crystals could also extend up to 1 μm due to inelastic scattering (including tangential smearing and channelling effect).

[46][47] Both the EBSD experiment and simulations typically make two assumptions: that the surface is pristine and has a homogeneous depth resolution; however, neither of them is valid for a deformed sample.

[37] If the setup geometry is well described, it is possible to relate the bands present in the diffraction pattern to the underlying crystal and crystallographic orientation of the material within the electron interaction volume.

[57] 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.

[50] 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.

Later developments involved exploiting various geometric relationships between the generation of an EBSP and the chamber geometry (shadow casting and phosphor movement).

Thus, most commercial EBSD systems use the indexing algorithm combined with an iterative movement of crystal orientation and suggested pattern centre location.

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.

[73] Microscope misalignment, image shift, scan distortion that increases with decreasing magnification, roughness and contamination of the specimen surface, boundary indexing failure and detector quality can lead to uncertainties in determining the crystal orientation.

[74] The EBSD signal-to-noise ratio depends on the material and decreases at excessive acquisition speed and beam current, thereby affecting the angular resolution of the measurement.

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).

[1] Cross-correlation-based, high angular resolution electron backscatter diffraction (HR-EBSD) – introduced by Wilkinson et al.[83][84] – is an SEM-based technique to map relative elastic strains and rotations, and estimate the geometrically necessary dislocation (GND) density in crystalline materials.

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.

), and the relationship is simplified; thus, eight out of the nine displacement gradient tensor components can be calculated by measuring the shift at four distinct, widely spaced regions on the EBSP.

) is zero (i.e., traction-free surface[88]), 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.

To address this problem, Ruggles et al.[94] improved the HR-EBSD precision, even at 12° of lattice rotation, using the inverse compositional Gauss–Newton-based (ICGN) method instead of cross-correlation.

For simulated patterns, Vermeij and Hoefnagels[95] 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.

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.

Nevertheless, VFSD images do not include the quantitative information inherent to traditional EBSD maps; they simply offer representations of the microstructure.

[48][137] EBSD, when used together with other in-SEM techniques such as cathodoluminescence (CL),[138] wavelength dispersive X-ray spectroscopy (WDS)[139] and/or EDS can provide a deeper insight into the specimen's properties and enhance phase identification.

[140][141] 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.

The serial sectioning can be performed using a variety of methods, including mechanical polishing,[156] focused ion beam (FIB) milling,[157] or ultramicrotomy.

[158] The choice of sectioning method depends on the size and shape of the sample, on its chemical composition, reactivity and mechanical properties, as well as the desired resolution and accuracy of the 3D map.

An electron backscatter diffraction pattern of monocrystalline silicon, taken at 20 kV with a field-emission electron source. The Kikuchi bands intersect at the centre of the image
An electron backscatter diffraction pattern of monocrystalline silicon , taken at 20 kV with a field-emission electron source
Pictorial diagram showing the major components of a field emission gun scanning electron microscope. The electron gun is at the top. Below the gun is a disk of diffraction cones in which the specimen is embedded at an oblique angle. To the left of the sample is a CCD camera assembly, including lenses and a phosphor screen. The electron beam emerges from the gun, impinging on the side of the sample facing the camera.
EBSD typical hardware configuration inside a field emission gun scanning electron microscope [ 2 ]
Electron backscatter diffraction's pattern degradation due to carbon deposition in a highly magnified location after 3-hour EBSPs acquisition around a deformation twin in the ferrite phase of duplex stainless steel.
Pattern degradation due to carbon deposition in a highly magnified location after 3-hour EBSPs acquisition around a deformation twin in the ferrite phase of duplex stainless steel [ 22 ]
Pictorial diagram showing signals generated when an electron beam interacts with a sample of matter. At the top, the primary electron beam impinges on the sample. Various types of emissions are shown in order of increasing penetration depth of the beam. Near the top are Auger Electrons, followed by Secondary Electrons, then Backscattered Electrons, all emerging in the general direction towards the impinging beam. Next are four types of radiation (shown with wavy arrows): Characteristic X-rays, Continuum X-rays, Cathodo-luminescence, and Fluorescent X-rays. The later two are shown as being emitted from the same depth. Finally, shown having passed through the body of the sample are, in increasing order of angular displacement from the beam axis, Transmitted Electrons, Diffracted Electrons, and Scattered Elections.
Electron-matter interaction volume and various types of signal generated
Formation of Kossel cone which intersect with CCD screen to form EBSP which can be Bravais-Miller indexed
Formation of Kossel cone which intersect with CCD screen to form EBSP which can be Bravais-Miller indexed
A. EBSD map of ferrous martensite with high-angle (>10°) boundaries hilighted. Colour scheme follows the typic IPF for BCC crystal plotted in Z-direction
A map of indexed EBSD orientations for a ferrous martensite with high-angle (>10°) boundaries
Schematic shifting between a reference and deformed crystals in the EBSP pattern projected on the phosphor screen
Schematic shifting between a reference and deformed crystals in the EBSP pattern projected on the phosphor screen [ 22 ]
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, maximum in-plane principal strain, rotation magnitude, correlation peak height, mean angular error and GND density.
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 ( ), maximum in-plane principal strain ( ), rotation magnitude ( ), correlation peak height (PH), mean angular error (MAE) and GND density. [ 1 ]
3D EBSD map for WC-6%Co compiled from 62 slices after sectioning 10×10×3 mm size and 50 nm resolution in x, y and z directions
3D EBSD map for WC -6% Co with 62 slices of 10×10×3 mm size and 50 nm resolution in x, y and z directions [ 153 ]