Introduction to Backscatter Kikuchi Diffraction

Pattern Formation
Backscatter Kikuchi patterns (BKP) are produced by incoherent wide-angle scattering of a stationary beam of high-energy electrons from a virtually perfect volume of crystal. A small fraction of these electrons are channeled along low-index lattice planes, leave the crystal and form a Backscatter Kikuchi pattern on a phosphor screen placed close to the specimen. It consists of straight Kikuchi bands whose widths are, according to the channeling conditions, proportional to the Bragg's angles. The center lines of the bands correspond to the (imaginary) section lines of the lattice planes with the screen, the star-like band crossings to zone axes of the crystal lattice, and the angles between the bands to interplanar angles. Therefore, the crystal orientation of the grain under the beam can be determined with high accuracy by simply measuring the widths and the positions of several bands in a pattern. In the SEM, the patterns are recorded with a low-light level CCD camera, digitized, corrected for background and transmitted to a PC for indexing.

Advanced BKD Systems
Texture analysis and characterization of microstructure require a large number of grain orientations to be measured on a selected area on the specimen without the interaction of the operator (Automated Crystal Orientation Measurement/Microscopy = ACOM). In advanced BKD systems, preference is given to digital beam scan, due to higher speed and precision, over a mechanical stage scan. To make allowance for the strong forward scattering of fast electrons and to obtain sufficiently intense patterns, the specimen is steeply inclined to make a shallow angle of typically 20° with the primary beam.
The specimen tilt, however, has an unwanted side effect on systems with digital beam scan in that the diffraction geometry changes from one measured point to the next and that the beam spot runs out of focus when scanning down the specimen one line after the other. Therefore, the specimen-to-screen distance and the pattern center have to be calibrated automatically from point to point, as well as the probe-forming lens has to be focused dynamically. The microscope is under full control of the ACOM program during automated measurement. When automated calibration is implemented in the BKD system, the operator need not bother about keeping a fixed working distance.
The band geometry is extracted on-line in a fast pattern recognition subroutine by applying a Radon transform. The higher the diffracting crystal volume is plastically deformed, the more diffuse the Kikuchi pattern appears to be. Pattern quality, as a measure of local plastic deformation, is hence determined by applying a 1D FFT on the Radon transformed pattern and by weighting the high spatial frequencies of the Radon peaks of the most prominent bands.

Performance
Spatial resolution is better than a tenth of a micron, depending on the spot size of the beam, the accelerating voltage and the density of the material. Resolution does in principle not depend neither on the beam current nor on the actual microscope magnification. The specimen area accessible to ACOM measurement is thus only limited by the lowest microscope magnification provided that the beam is focused dynamically. Since some EBSD systems are equipped with a camera of poor sensitivity, the spot size of the SEM has then to be widened unduly in order to obtain sufficient beam current, and hence spatial resolution gets worse.
Depth of information beneath the surface is in the range of the mean free path of the backscattered electrons (estimated at some 10 nm only). BKD is thus a surface sensitive method. Special care is required in preparing clean specimen surfaces free from artifacts. The accuracy of grain orientation measurement is < 0.5°. A test of spatial resolution and accuracy can be performed by mapping a specimen that contains fine deformation twins. Dynamic system calibration can be checked by scanning across a large single crystal (e.g. silicon) at low SEM magnification and verifying the uniformity of orientation data. Speed of advanced BKD systems exceeds several ten to several hundred thousand measured orientations per hour (see Fast EBSD).

(Typical shortcomings of out-of-date EBSD systems are:

• Neither automated system calibration nor pattern calibration "on-the-fly" is available. =>The pattern center, as one reference direction for calculating the grain orientation, as well as the specimen-to-screen distance (= pattern magnification) is determined experimentally for one working distance, e.g. with a reference crystal or by pulling back the camera (zoom center = pattern center). The operator is well advised to place the sample at the fixed working distance and to avoid digital beam scan at medium or low microscope magnifications. Insufficient calibration may lead to false indexing.
• Dynamic focusing is not provided, or the standard dynamic focusing appliance of the SEM is employed. Due to the steep specimen tilt and the high sensitivity of the quality of BKD on spot size, precise focusing is essential not only at low magnifications, but also for studying fine grain materials.
• Camera sensitivity is insufficient. => The pattern is either integrated, on the expense of speed, on the camera chip or by software to reduce noise, or the beam current has to be increased excessively. In the latter case, spatial resolution is lost since the probe-forming lenses are not operated under optimal conditions. In addition, contamination rate increases with beam current density, in particular when using a FE gun.
• Indexing is performed by only considering the center lines of Kikuchi bands rather than the center lines and the band widths, i.e. the interplanar angles and the Bragg angles => indexing is less reliable.
• Indexing is done with only a few bands since the Hough transform and the band tracing algorithm are inadequate to provide a sufficient number of located bands => propensity to false indexing.
  (N.B.: Typically 7 or more bands should be available for cubic symmetry, and about 10 bands or more are desirable for lower symmetries.)
  

Quantitative Evaluation and Orientation Stereology
The prime objective of ACOM is the acquisition of grain orientation data. They are usually represented by three Euler angles or by the rotation matrix which rotate the coordinate system of the specimen in the coordinate system fixed to the particular crystal lattice. Crystal orientation maps (COM) are constructed by depicting colors in every measured point on the scanning grid that are characteristic for the particular grain orientations or the orientation differences between next neighbors or relative to a reference orientation, or for the phases in a sample. "Images" of the microstructure are thus produced which reveal the detailed grain structure in quantitative orientation and material contrast, respectively.
Stereological or „quantitative metallographic“ evaluation can be performed straightforwards. The misorientations between neighboring raster points are calculated and, assuming specified threshold values, grain boundaries (GB) as well as phase boundaries can be marked out in the COM. However, a grain boundary in a planar sample section forms a closed perimeter line which must not „leak“. A special „path finding“ algorithm along the grain boundary segments is applied to fill missing spots where indexing may have locally failed, and a (binary) grain boundary network of the microstructure is obtained. The lines may be further skeletonized to one pixel in width. The advantages of GB COM over conventional light microscopical images of grain boundary networks are for stereological evaluation:
+ The GB COM is based quantitatively on measured crystallographic orientations rather than on tricky methods of surface (GB) etching and imaging.
+ A high contrast on an even background is obtained over the whole GB COM due to a yes/no discrimination.
+ The data are available in a digital (binary) format on a regular raster grid.
Therefore, standard methods of quantitative metallography can directly be applied. In many labs sophisticated stereological programs are already available. 2D microstructure parameters can be determined such as the area fraction, planar size, average grain size, shape and arrangement of grains, and their statistical distributions. If the phases in the material have sufficiently different lattice constants or – with the aid of simultaneous EDS analysis – differ in their element composition such that the phases can be differentiated in every pixel, quantitative metallography can be extended to a phase discriminating stereology. Under usual stereological assumptions, 2D stereology is often extended to 3D stereology to calculate such parameters as volume fraction, average grain volume, 3D shape and arrangement, contiguity of phases, and their statistical distributions. Approaches are made to reveal the true 3D microstructure on a grain specific scale by combining BKD with in-situ serial sectioning in a FIB&SEM instrument.
Since a grain in the GB COM is represented by the group of pixels with similar grain orientations within the GB loop, its area fraction is simply measured by counting the raster points which are enclosed by the grain boundary perimeter line. This point counting method is superior over the line intercept method because it is not affected by concave sections of the grain boundary line nor by „islands“ formed by a second grain which may shine through the sample surface.  A rapid but less precise alternative for estimating size and shape of grains is the visual comparison of a GB COM with standard grain charts or reticules.
Further material characteristics are deduced from the measured set of individual grain orientations, such as the global and local texture described by pole figures or the orientation distribution function (ODF), the misorientation distribution function (MODF), orientation correlation functions, stereological data like grain size distributions, phase distributions, the statistical distribution of grain boundary character (S grain boundaries), and local material properties based on grain crystallography. (Local) texture analysis and conventional stereology and quantitative metallography are about to merge in a comprehensive new field of materials science named "Orientation Stereology".

Further reading

Schwarzer, R.A.
Automated crystal lattice orientation mapping using a computer-controlled SEM.
Micron 28 (1997) 249-265.

H.J. Bunge and R.A. Schwarzer
Orientation stereology - A new branch in texture research.
Adv. Engin. Materials 3 (2001) 25-39

A.J. Schwartz, M. Kumar and B.L. Adams (eds.)
Electron Backscatter Diffraction in Materials Science.
Kluwer Academic / Plenum Press, 2000