Spherical EBSD

Authors


A. Day. Tel: 00 44 1600 719 951, e-mail: AustinPDay@gmail.com

Summary

Spheres, or more usually spherical surfaces, are important in electron backscatter diffraction. Both electron backscatter patterns (EBSPs) and pole figure texture data are more accurately represented on the spherical surface, S2; and unit quaternions, which are the optimal method for orientation calculations, exist on the surface of the hypersphere, S3.

This paper is split into two distinct parts. The first shows a little of the history of the EBSP technique, including the use of spheres to assemble a spherical Kikuchi map (SKM) and as calibration artefacts. The second part relates new developments in the analysis of EBSPs on the surface of a sphere, a new spherical Hough transform and ideas for fully automatic, ab initio analysis of unknown phases using collections of EBSPs assembled as spherical Kikuchi maps.

EBSP history

Electron backscatter patterns (EBSPs) have a long history, the earliest reported being an indistinct pattern produced by reflecting 50-kV electrons from a cleaved face of calcite (Nishikawa & Kikuchi, 1928). The first EBSPs that are recognizable to modern eyes were taken by Boersch (1937). Both planar and cylindrical film were used to produce high-quality diffraction patterns from a wide range of minerals and metals: halite (NaCl), sylvite (KCl), galena (PbS), calcite (CaCO3), fluorite (CaF2), quartz, mica, diamond, copper and iron. Example patterns are shown in Fig. 1.

Figure 1.

Early EBSPs from fluorite (left) and iron (from Boersch, 1937). The iron EBSP was taken on cylindrical film and covers approximately 140°.

After this, the EBSP technique slowly evolved over the decades, with notable contributions from Alam et al. (1954), Venables at the University of Sussex (Venables & Harland, 1973) and Dingley at Bristol University (Dingley, 1981).

Dingley and co-workers improved on the early work of Venables by introducing a low-light level camera, analysis software and also EM film for direct exposure to the EBSP. The analysis software ran on a BBC micro-computer with a GenLock graphics overlay board. The operator could use a moveable cursor to mark the positions of, for example the 〈112〉, 〈111〉 and/or 〈114〉 zones (Dingley, 1989). From the measured inter-zonal angles, the orientation of the grain was calculated, as shown in Fig. 2.

Figure 2.

EBSPs taken using a SIT camera, approximately 1985. Top row: silicon calibration; bottom row: nickel base superalloy. For the EBSPs on the left, X marks the pattern centre and ‘*’ indicates a user-marked zone. For the solved EBSPs on the right, the Xs mark the positions of the 〈110〉 and 〈112〉 zones to show the goodness of fit.

The fascinating history of this era is recounted in section 1.2 of ‘The Atlas of Backscattering Kikuchi Diffraction’ (Dingley et al., 1995) and in chapter 1 of ‘Electron Backscatter Diffraction in Materials Science’ (Schwartz et al., 2000).

Early silicon intensified target (SIT) cameras were quite sensitive but could not produce images to rival those from EM film; compare Figs 2 and 3.

Figure 3.

EM film EBSP and film carriage; the EM film slid in and out on brass rails powered by a pneumatic piston. This film camera was ordered from David Dingley by Peter Quested and installed at the National Physical Laboratory, ∼1987.

However, EM film had its own problems, the film insertion carriage (see Fig. 3) would frequently jam; it was difficult to keep the EM film planar; and development of the images was a time-consuming process and printing required considerable skill in ‘dodging’ the image to produce a uniform EBSP, as shown in Fig. 3.

Dingley (Biggin & Dingley, 1977) also developed an EBSP calibration technique that used elliptical shadows from three metal spheres to locate the pattern centre (PC) of Kossel patterns and EBSPs. This calibration technique became known as the ‘Pawnbroker's’ or ‘Dingley's balls’ (Day, 1993.)

In the mid-1980s, EBSP was being used not only for orientation measurement but also for phase identification. Figure 4 shows images from an early report written for Peter Quested at the National Physical Laboratory (Dingley, ∼1985). Kikuchi band intersections (marked with arrows) were used to measure the lattice parameters for the Nickel base superalloy matrix (∼3.80 Å) and particles (∼4.45 Å). This was combined with EDX chemical analysis to aid in the identification of titanium carbide particles. Modern, automated phase ID systems use a similar methodology (Randle & Engler, 2000; Schwartz et al., 2000; Randle, 2003).

Figure 4.

EM film & SIT camera EBSPs and EDX spectra from nickel base superalloy matrix (left side) and a particle (right). The lattice parameters were measured to be 3.80 Å and 4.45 Å, which, along with the EDX spectra (lower left of the main EBSPs), identified the superalloy matrix and titanium carbide particle. Note: The EDX spectra have been colourized and labelled.

Spherical Kikuchi maps

Also around this time, several laboratories were investigating electron channelling patterns (ECPs, see Coates, 1967 and Joy, 1974) and selected area channelling patterns (SACPs). Bevis Hutchinson (Stott et al., 1975) and Geoff Lloyd (Lloyd & Ferguson, 1986) took a large number of channelling patterns at different orientations and stuck them on to the surface of a large sphere, approximately 37 cm diameter, as shown in Figs 5 & 6.

Figure 5.

Ferrite SKM, courtesy of Bevis Hutchinson, and a simulation (right). The patterns cover 1/24th of the spherical surface. The fourfold 〈001〉 zone can be seen at the top, and two threefold 〈111〉 zones are at the far left and right, with a twofold 〈110〉 between them. The moveable scale is for measuring angles.

Figure 6.

Quartz (left) and copper SKMs, images courtesy of Geoff Lloyd. The patterns cover 1/6th and 1/24th of the spherical surface, respectively. For the quartz SKM, the [0001] zone is at the top of the sphere with the – a axis at the bottom, directly below it. The copper SKM has 〈001〉 at the top, a 〈111〉 at the bottom and two 〈110〉 zones at the far left and right.

Simulation of diffraction patterns also has a long history – simulations of spherical Kikuchi maps were done by Lytton and Young (Young & Lytton, 1972) as stereographic projections, Fig. 7(a). The author produced an octant projection in the mid-1980s using a BBC micro and plotter, Fig. 7(b), and a series of polyhedral Kikuchi maps in the late 1980s and early 1990s, see Fig. 7(c) and (pages 50–53 of Randle, 1992; Appendix E of Day, 1993). The polyhedra can also be used to represent the symmetry of the diffracting crystal's unit cell and/or the diffraction pattern.

Figure 7.

(a) Stereographically projected spherical Kikuchi map from Young & Lytton; (b) An octant of a left-handed spherical Kikuchi map; (c) A polyhedral Kikuchi map for an fcc structure (image courtesy of Dr Peter Quested, NPL). (a) Reused with permission from C. T. Young and J. L. Lytton, Journal of Applied Physics, 43, 1408 (1972). Copyright 1972, American Institute of Physics.

Modern planar EBSP detectors

All modern electron backscatter diffraction (EBSD) detectors have a planar scintillator, usually either circular or rectangular as shown in Fig. 8. As a result of this, the EBSP is seen as a gnomonic projection (Randle & Engler, 2000) and is highly distorted near the edges and corners, see Fig. 14 for an example. EBSPs also suffer from non-uniform illumination not only partly from the inherent variation in EBSP signal with angle (Reimer et al., 1986; Reimer, 1998) but also from 1/d2 distance effects and lens vignetting.

Figure 8.

A modern EBSD detector with a planar, rectangular scintillator (as designed by the author). Image courtesy of John Bonevich and Mark Vaudin, NIST.

Figure 14.

Example image of an orthogonal grid (left) showing camera distortion (note how the corners of the grid are pulled inwards) and an EBSP (right) with the pattern centre marked as a cross and a 5° spherical grid.

Spherical or cylindrical detection screens, or film as used by Boersch (1937) and Alam et al. (1954), would minimize EBSP distortion and improve illumination uniformity. However, the optics to couple such a non-planar scintillator to a CCD chip would be complex. Such imaging geometries are used in low-energy electron diffraction (LEED) systems (Winkelmann, 2003, 2004) and developments in transmission electron microscope (TEM) electron imaging (Roberts et al., 1982; Spence & Zuo, 1988; Hawkes, 2007) may lead the way to more direct methods for recording EBSPs and, possibly, to non-planar detectors.

EBSP resolution and speed

To conclude this historical section, Fig. 9 (Hutchinson, 2007, personal communication) shows data for the rate of analysis of several micro-diffraction techniques and their spatial resolutions. By fitting the data to best-fit lines, it is evident that the spatial resolution is improving by a factor of 2 every 4 years, and the acquisition speed is doubling every other year.

Figure 9.

Improvements in spatial resolution (solid symbols) and indexing speed (open symbols) as a function of year for several microdiffraction techniques. Graph courtesy of Professor Bevis Hutchinson.

Recent developments

EBSP simulation

Recent developments in EBSP simulation (Spence & Zuo, 1992; Winkelmann, 2003; Winkelmann et al., 2007) have led to high-quality simulated EBSPs with extraordinary levels of accurate detail. There are many advantages to having accurately simulated EBSPs:

  • 1Any phase, orientation and EBSD geometry can be simulated.
  • 2The simulated EBSPs can be used to test existing and new band detection & indexing algorithms.
  • 3The image quality is potentially much higher than for experimental EBSPs; extremely fine structures can be observed that are blurred in real EBSPs, see Figs 10 & 11.
  • 4Excess and deficiency lines (see Fig. 17) are currently not simulated, which makes the patterns easier to analyze. If required, simple empirical models can be used to introduce ‘vertical’ asymmetries in the Kikuchi bands.
Figure 10.

Simulated 15 kV Ferrite EBSP, courtesy of Dr Aimo Winkelmann. At the centre of the pattern is the fourfold [001] zone.

Figure 11.

Details of the 15 kV ferrite EBSP simulation shown in Fig. 10, and an experimental 15 kV EBSP (right) around 〈001〉. Compare the marked fine details.

Figure 17.

PZT EBSP with Kikuchi band profiles averaged along their visible length. Note the asymmetry of the non-vertical bands. EBSP courtesy of Dr Ken Mingard, NPL.

Figure 10 shows a simulated Ferrite EBSP that has been ‘imaged’ on a hemisphere and projected on to a plane. Depending on the number of reflectors included in the simulation, calculations of this quality can take several hours. Figure 11 shows a comparison between part of an experimental EBSP and the simulation in Fig. 10 to show the excellent agreement.

Spherical Kikuchi maps from EBSPs

Hutchinson and Lloyd's manually assembled spherical Kikuchi maps (SKMs) can also be done with EBSPs; however, since the capture angle is larger, fewer EBSPs are required to cover the sphere but more care has to taken with image distortion, for example due to the camera lens. With modern, digital EBSPs, SKM assembly can be done in software rather than hardware (i.e. film). Figure 12 shows how planar EBSPs can be projected on to the surface of a sphere to form a spherical Kikuchi map.

Figure 12.

Inflation of a cube to produce a sphere. If each face of the cube has a gnomonically projected EBSP on its surface, then a spherical Kikuchi map is formed. Other polyhedra, or just a single plane, can be used, depending on the crystal symmetry and user preference, for example hexagonal prism, icosahedron.

A polycrystalline specimen will, generally, generate a large number of EBSPs at different orientations and each grain will produce many very similar EBSPs. EBSP quality can be improved by averaging. The averaging can be done either with EBSPs from the same point on the specimen but taken over a period of time (temporal averaging) or, if the misorientation spread is low, by averaging the EBSPs from a single grain (co-granular spatial averaging.)

Figure 13 shows experimental EBSPs warped on to the surface of a unit sphere (Heckbert, 1989; Wolberg, 1992; Gomes et al., 1999; Akanine-Möller & Haines, 2002; McReynolds & Blythe, 2005). Once EBSPs can be transformed on to the surface of the sphere, then standard image-processing functions can be used (Imiya et al., 2005). For accurate transformation, it is critical that the EBSP projection geometry and EBSD detector distortion parameters are known (a total of approximately 11 independent parameters).

Figure 13.

A single experimental EBSP mapped on to the surface of a sphere (left) and several montaged EBSPs (right) shown with black outlines.

The EBSP projection geometry consists of three main parameters:

  • 1Pattern centre, PC(X, Y). The point on the phosphor closest to the specimen.
  • 2Specimen to phosphor distance.

Most EBSD detectors contain a camera and a lens, and it is mainly the distortions due to the lens and the non-parallelism of the CCD and phosphor that need to be corrected for. The main parameters are

  • 1Radial lens distortion – which can be modelled using an odd termed polynomial expansion: inline image.
  • 2Misalignment between the camera's optic axis and the EBSP phosphor.
  • 3The effective CCD pixel aspect ratio, horizontal & vertical skews and image rotation.

Rotations of the EBSP about the PC are, generally, not important. The assumption is made that the camera's centre of distortion is close to the centre of the image (i.e. the EBSP); this will, generally, not coincide with the EBSP PC. See Hartley & Zissermann (2003) for camera calibration details.

Figure 14(left) shows an example image taken using an EBSD detector where the phosphor has been replaced by an orthogonal test grid; on the right is an EBSP with the PC marked with a cross and a 5° spherical grid superposed on top of it (the spherical grid has been corrected for camera distortion.)

On most EBSD detectors, replacing the phosphor with a grid is impractical in which case ultra-precise fitting of a large number of EBSPs combined with a distortion model (having approximately 11 variables) may be used instead. Alternatively, the phosphor may be illuminated or shadowed by an external grid; but care must be taken to ensure the grid is precisely parallel to the phosphor and that the illumination source accurately mimics the usual EBSD geometry.

To speed up the SKM calculations, crystal symmetry can be applied and only a fraction of the spherical surface need be considered. The symmetry elements of a cube are shown in Fig. 15; mirror planes are shown as thin, hollow disks, diads as ellipses, triads as triangles and tetrads as squares; the cube has had a motif applied to show the symmetry. See de Graef (1998, 2003, 2007) and McKie & McKie (1986) for examples of the other Laue and point groups.

Figure 15.

Symmetry elements of a cube (left) with a Dingley motif on its surface; and (right) the cube motif projected up on to a sphere to show the symmetries.

The symmetry elements show how the SKM repetition operates. The smallest triangles outlined by the mirror planes are analogous to the ‘unit triangles’ used in inverse pole figures and can be used to build up spherical Kikuchi maps, as shown in Fig. 16.

Figure 16.

Spherical Kikuchi maps (bottom row) from repetitions of the EBSP fragments (top row). (Left) Experimental 20 kV ferrite EBSP; (Middle) Winkelmann 15 kV simulation; (Right) 15 kV simple simulation.

Kikuchi band profiles

Profiles of Kikuchi bands have been measured from single EBSPs (Alam et al., 1954; Day & Shafirstein, 1996) and calculated using a dynamical diffraction model (Reimer et al., 1986).

Experimentally, their relative intensities have been estimated and compared (Prior & Wheeler, 1999; Wright, page 61 of Schwartz et al., 2000) to values calculated using a kinematical diffraction model (Peng et al., 2004).

Quantitative measurements from EBSP intensities have historically been difficult to make (Quested et al., 1988; Day & Shafirstein, 1996) and remain so. Indeed, the high level of ‘processing’ that an EBSP undergoes during capture (conversion to light in the phosphor, lens vignetting, camera gain and offset, background correction, contrast stretch, possible reduction to eight bits) begs the question – exactly what is the EBSP intensity relative to?

Even with a high-quality EBSP, there are also problems of reproducibly defining the start and finish for the Kikuchi band sampling, and correcting for the intensity variations & the asymmetric effects of excess and deficiency lines (Reimer, 1998), see Fig. 17 for an example.

One solution is to average many EBSPs on the surface of a sphere, that is create a spherical Kikuchi map similar to that in Figs 5 & 6, and measure the profiles in an unbiased manner over the whole sphere. This has the distinct advantage that the effects of excess and deficiency lines (Reimer, 1998) are averaged out and that the large number of EBSPs, usually produced during EBSD mapping, can be used rather than being discarded.

Figure 18 shows a selection of Ferrite Kikuchi bands and their average profiles. The images were constructed by projecting the SKM Kikuchi bands on to the surface of a cylinder (aligned with the plane normal) and then unrolled until it was flat. Note: Only 180° of the cylinder is shown as the other half is similar.

Figure 18.

Unrolled projections of several bands on to cylindrical surfaces; the planes and their average band profiles are shown on the right. Even fainter Kikuchi bands, for example {114}, can still be identified by their profile. The projections extend ±10° from the Kikuchi band centreline and 180° in length.

Table 1 shows Ferrite Kikuchi band profiles and compares the intensities to those from the kinematical diffraction model; the agreement is, generally, not very good. One of the problems with measuring or calculating the Kikuchi band intensities is that there is always a contribution from other intersecting bands. Deconvoluting this contribution may help to understand and empirically model the ‘true’ profiles.

Table 1.  Ferrite Kikuchi band intensities.
Ferrite bandsKinematical intensity %Max-Min Profile %Average Kikuchi band profiles
inline image

Single-crystal silicon is commonly used as an EBSP calibration specimen. The approximate intensities of the Kikuchi bands can be predicted using a kinematical diffraction model (Peng et al., 2004). This model predicts that some Kikuchi bands will be invisible, particularly those that do not fulfill the Diamond structure rules: h+k+l is odd or h+k+l= 4n[where n is an integer and h, k and l are the integer indices of the plane (hkl)]. For example, the {111}, {333} and {444} Kikuchi bands should be visible; however {222} should not. Figure 19 shows an experimental EBSP with the {111} and higher-order planes labelled along with simulations and band profiles. Table 2 shows Silicon Kikuchi band profiles and compares the intensities to those from a kinematical diffraction model.

Figure 19.

20 kV silicon EBSPs showing the presence of ‘forbidden’{222} planes. (a) Experimental EBSP; (b) EBSP simulated using Winkelmann's ECP program; (c) average Kikuchi band profile along the (111) Kikuchi band; (d) Silicon spherical Kikuchi map; (e, f) Unrolled (111) & (220) Kikuchi bands with 〈112〉 at the centre.

Table 2.  Silicon Kikuchi band intensities.
Silicon bandsKinematical intensity %Max-Min Profile %Average Kikuchi band profiles
inline image

By fitting the Kikuchi band profiles to simple functions, and measuring the profiles as a function of accelerating voltage, models of the Kikuchi band profiles can be derived and used for new or improved indexing algorithms, for example Groth (1986) and Arzoumanian et al. (2005). It is also easier to identify subtle differences between phases that produce similar EBSPs by comparing the SKMs. This work is in progress.

Inversion of a spherical Kikuchi map

Image processing & analysis on spherical images (Imiya et al., 2005) and the spherical Hough transform (Torii & Imiya, 2005) have been developed for use with catadioptric computer vision systems. These provide a robot with a full, hemispherical (2π steradians) view of its surroundings and allow it to navigate through an office landscape by identifying ‘linear’ great-circle features, for example the edges of walls, corridors and doors. By applying a modified algorithm to a spherical Kikuchi map, the Kikuchi bands can be ‘inverted’ to disks centred about the plane normal where the diameter is the Kikuchi band width.

The processing can be done in a similar manner to the 2D Hough transform on flat EBSPs (Hough, 1962; Leavers & Boyce, 1986; Krieger Lassen et al., 1992; Leavers, 1992; Krieger Lassen, 1994). However, to optimize the handling of spherical surface data, methods commonly used in geographic information systems (GIS) have been employed, for example Samet (1990, 2006), Kunszt et al. (2001) and Szalay et al. (2005). This spherical, correlated, randomized Hough transform has been named the ‘SCRUFF’ transform – to avoid confusion with the statistical Hough transforms and to echo the naming of the ‘Muff’ transform (Wallace, 1985).

As can be seen in Fig. 20(b), ‘inversion’ minimizes the overlap of Kikuchi bands and allows high-order bands to be identified more easily, for example the marked white disk surrounded by four dark disks corresponds to the (111), (222), (333), (444), (555) planes, which are all normal to the [11-2] zone.

Figure 20.

(a) Ferrite spherical Kikuchi map and (b) its ‘inversion’ using the SCRUFF transform; the (111) disk has been marked.

The SCRUFF transform can be extended to a 3D transformation by the addition of a third parameter that represents the angle that the sampling ‘line’ or circle is displaced from the parent plane (Maurice & Fortunier, 2007) Figure 21 shows some example transform; certain angles produce a very sharp peak over the relevant plane normal indicating that this is close to the Bragg angle for those planes.

Figure 21.

3D SCRUFF transform for a range of angles.

The SCRUFF transform may also be useful for strain measurement (Wilkinson & Hirsch, 1997, 2006) in polycrystalline materials, particularly if a simple, empirical model for the excess and deficiency lines can be derived. A reference SKM could be measured from an undeformed, polycrystalline specimen and then, under identical conditions, EBSPs from a deformed specimen can be taken and correlated or compared with the reference SKM.

Phase identification by X-ray powder diffraction (Snyder et al., 1999) has a long history, and it relies on each phase producing a unique ‘signature’ spectrum. It has long been a goal of EBSP to have such a simple signature for a phase, and it may be possible to use the SCRUFF transform for this, for example by plotting the average intensity as a function of the Bragg angle as measured from the centre of the relevant disk.

There are still a wide variety of problems to be overcome for fully automatic reconstruction of spherical Kikuchi maps and identification of Kikuchi bands, and the calculations are still relatively slow. However, the method does show promise, particularly for the identification of new phases where no crystallographic data are available or for phases where the kinematical diffraction model is inadequate. It could also be used for ab initio EBSP analysis.

Discussion

Ab initio EBSP analysis using spherical Kikuchi maps

The combination of EBSP with EDX chemical data has been used for phase identification, for example Michael & Goehner (1993), Goehner & Michael (1996), and measurements of HOLZ rings in single EBSPs (Michael & Eades, 2000). But, generally, these methods have been applied to single EBSPs in isolation; by combining many EBSPs together, much more quantitative information can be gleaned and the biasing effects of excess and deficiency lines and certain orientations can be avoided.

Ab-initio EBSP analysis has been applied to TEM diffraction (Le Page, 1992) and is analogous to the primitive unit cell fitting used in X-ray diffraction (Giacovazzo et al., 1992; Snyder et al., 1999). The idea is to start with a set of EBSPs from the unknown phase and use them to construct a spherical Kikuchi map, then to identify symmetries in the SKM. The EBSPs must cover a wide range of orientations and, preferably, not have a strong crystallographic preferred orientation or texture. The procedure could be as follows:

  • 1Search the set for the best-quality EBSPs based on Kikuchi band sharpness, contrast and noise levels.
  • 2Identify symmetry features, for example mirrors and rotational axes, diads, triads, tetrads and hexads (and if working with quasi-crystals, pseudo-pentads), and keep a note of their adjacency.
  • 3Place the highest rotational axis at the north pole of a sphere and arrange the other adjacent symmetry elements in as symmetrical a manner as possible. Note: This is a somewhat arbitrary assignment.
  • 4If symmetry operators are known to exist (the most likely one is an inversion centre due to Friedel's law), then these can also be used to duplicate the EBSP and place copies in the appropriate position.
  • 5Randomly choose another EBSP, giving weight to the better-quality EBSPs and randomly try to match parts of it to the existing EBSPs. If this cannot be done, then choose another EBSP. Note: Care must be taken not to bias the ‘random’ orientation of this candidate EBSP.
  • 6Repeat until all the EBSPs have been processed.
  • 7Search the assembled spherical Kikuchi map for true symmetry elements, for example mirrors and triads that extend over the whole sphere. These will help identify the crystal system, Laue group.
  • 8Locate the Kikuchi bands and transform them to reciprocal space.
  • 9Scan reciprocal space and locate candidate unit cell vectors.
  • 10Identify systematic absences and use these to help to identify the probable point group and possible space group. Subtle sub-structure within low-order zones on the SKM may also be important.

The identification of Laue, point and space group for EBSPs has been tackled manually (Dingley & Baba Kishi, 1986; Baba-Kishi & Dingley, 1989; Dingley et al., 1995; Michael in Schwartz et al., 2000). However, methodologies for analyzing TEM and other diffraction patterns are more widely applied and advanced, for example Steeds & Vincent (1983), Snyder et al. (1999), de Graef (2003), Winkelmann (2003) and Peng et al. (2004).

Note: Quaternions (Morawiec, 2004; Hansen, 2006) are more suitable for the rotation calculations than Euler angles, particularly as they suffer none of the degeneracies near certain angle combinations. In engineering applications, this problem is known as ‘Gimbal lock’ and it almost destroyed the gyroscopes in Apollo 10's lunar module, Snoopy, see page 19 of Hansen (2006). For rotations, quaternions are also faster than orientation matrices, see appendix A.4.3 of Schneider & Eberly (2003), and considerably faster than Euler angles, which are usually converted to orientation matrices.

What limits EBSP sharpness?

It is clear from comparing simulated EBSP with experimental ones, for example Figs 10 & 11, that the simulated EBSPs are much sharper.

For a general EBSD detector, with, say, a CCD sensor of 1280 × 1024 pixels and a 40-mm-wide phosphor, each CCD pixel, when back-projected on to the phosphor, would be approximately 30 μm and captures approximately 0.05° of the EBSP.

The following factors have an effect on EBSP sharpness:

  • 1Specimen preparation. Poor surface preparation produces blurred EBSPs due to the deformed surface layer.
  • 2Energy spread of EBSP electrons. Maybe a few 10 s of eV.
  • 3) Spread in the aluminium coating, approximately 50 nm thick. It also acts as a mirror.
  • 4Spread in the phosphor. For a standard phosphor (particles deposited at approximately 4 mg−2, approximately 7 μm in size and a density of approximately 8 mg cm−3), the phosphor layer is approximately 20 μm thick, which is approximately three particles. Since the aluminium acts as a mirror, this may double the spread to, say, 50 μm.
  • 5Camera optics. Light from the phosphor takes the following path: Particles → glass → lead-glass window → lens → CCD window → CCD (See Fig. 22).
Figure 22.

Schematic showing how an electron coming from the specimen strikes the phosphor producing light that travels to the CCD. Note: Some items have been exaggerated for clarity and the optical paths are far from accurate.

Of these factors, the most important ones are probably (1) specimen preparation and (4) spread in the phosphor. The EBSP pixel resolution could be improved by retracting the detector and imaging a smaller region, for example Wilkinson & Hirsch (1997) or by using a single-crystal scintillator, for example YAG (Michael & Goehner, 1993).

Conclusions

Spheres are important for the EBSP technique and may offer new methods for

  • 1Automatic reconstruction of spherical Kikuchi maps
  • 2New indexing and band detection algorithms, in particular:
    • – Measurement of Kikuchi band profiles
    • – Models for excess and deficiency lines
    • – High-accuracy orientation measurement
  • 3Polycrystalline strain measurement
  • 4Ab initio analysis of unknown phases
  • 5EBSP fingerprinting – for phase identification

Acknowledgements

The assistance of Dr Aimo Winkelmann in producing the Ferrite EBSP simulations and for providing a copy of his sublime ECP simulation program is gratefully acknowledged. As are the many contributions, over the decades, of Dr Peter Quested, National Physical Laboratory, Teddington, and Professor David Dingley, Bristol University.

Ancillary