Measurement of crystallographic preferred orientation using Electron backscatter

Electron backscattered diffraction (EBSD); sometimes also referred to as backscatter Kikuchi diffraction (BKD) is a technological add-on to a scanning electron microscope. It provides an SEM with a microstructural-crystallographic analysis capability. Primarily, EBSD is used to study texture or preferred orientation of any crystalline or polycrystalline material. This is achieved by indexing and identifying the crystal systems. Apart from structure and orientation information, EBSPs (Electron back scatter patterns; See figure No. 2-12 for an example of such a pattern in mineral olivine) contain additional information on crystal lattice perfection, local strain, deformation, and grain boundaries.

Traditionally these types of studies have been carried out using x-ray diffraction (XRD), neutron diffraction and/or electron diffraction in a TEM.

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Figure 2-12: Formation of backscattered Kikuchi patterns by EBSD in the SEM. (a) Origin of Kikuchi lines from the EBSD (i.e., tilted specimen) perspective. (b) EBSD pattern from olivine (accelerating voltage 20 kV).

EBSD system consists of a phosphor screen, compact lens and low light CCD camera attached to a Scanning Electron Microscope (SEM) (Fig. 2-13). A polished sample specimen is placed into the normal position in the specimen chamber, and is tilted to ~70° from the normal position. Doing so boosts the contrast of EBSPs.

EBSPs are generated if a stationary beam interacts with the surface of a crystal [Alam et al., 1954],[Venables and Harland, 1973]. The electrons while interacting with an atom undergo inelastic scattering. It results in a fraction of the electrons losing a small part of their energy. This process creates a divergent source of electrons close to the surface of the sample. Some of these electrons are incident on atomic planes at angles which satisfy the Bragg equation. For each given plane, these electrons emanate in diffraction cones from both the front and back surface of the plane. When these cones intersect the phosphor screen, the Kikuchi lines are formed. The Kikuchi lines appear as almost straight lines because the cones are very shallow as the Bragg angle is of the order of 1°. Small Bragg angle results from the fact that incident electrons have very high energy and hence very small wavelength (λ ≈ 8 pm for a 25 KeV electron beam). Hence, Kikuchi bands are effectively the trace of the plane from which they are formed and the EBSD pattern is therefore a gnomonic projection of the crystal structure.

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Figure 2-13: Schematic setup of an EBSD system showing its principal components

Thus, the whole Kikuchi pattern consists of pairs of parallel lines where each pair, or

“band,” has a distinct width and corresponds to a distinct crystallographic plane. The intersection of bands corresponds to a zone axis (pole), and major zone axes are recognized by intersection of several bands. The Kikuchi pattern therefore essentially embodies all the angular relationships in a crystal—both the - and inter-planar angles—

and hence implicitly contains the crystal symmetry. Figure 2-12 shows an EBSD Kikuchi pattern from mineral San-Carlos olivine. The orientation of the pattern and hence of the volume from which it has arisen is evaluated by “indexing,” that is, identifying the poles and bands in the pattern, and calculating the relationship between these and some chosen reference axes.

From Kikuchi bands to pole figure

Automated identification of a crystal orientation involves identifying the kikuchi lines in the gray scale image containing EBSPs. First step towards this process involves the pre-processing stage of edge detection. This is a non-trivial task because contrast normal to the kikuchi lines rarely change abruptly. The pattern of Kikuchi lines on the phosphor screen is electronically digitized and processed to recognize the individual Kikuchi lines. These data are used to identify the phase, to index the pattern, and to determine the orientation of the

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crystal from which the pattern was generated. Individual mineral grains can be selected for identification and determination of crystal orientation, or data may be acquired on a grid over a selected area of the surface of the sample to determine the identity, orientations, and spatial relations between a large numbers of grains.

These data can be used to make statistical studies of the micro-fabric of the sample, to reveal systematic textural relations between individual grains or phases, and even to determine relative abundances of phases in a poly-phase sample.

Principles of Orientation Determination

From the information about the crystallographic indices with (where is the number of identified bands or poles) and the angles between each band or pole and the beam normal, the orientation of the sample normal in terms of its crystallographic indices can be expressed as

The root term in the equation given above normalizes the indices of the bands or axes, which are typically given as integers, for example or to unity. Hence the resulting vector is directly normalized to unity. It is seen that three equations are necessary to determine the vector , which means that three bands or poles have to be indexed.

Automation of Pattern Indexing and Orientation

To relate the characteristic features of an EBSD pattern – typically zone axes or bands—

from the 2-D computer screen to the 3-D sample coordinate system (denoted by the superscript s in equation below), the 2-D screen coordinates are transformed into 3-D vectors by

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Figure 2-14: Diagram illustrating the evaluation of an EBSD pattern. Sample coordinate has been represented by superscript “s” where as screen coordinate has been represented by superscript

“screen”. Specimen-to-screen distance is . (X*i,Y*i) are coordinates of the center of the pattern and (XPC,YPC ) are the coordinates of the center of the screen.

With an appropriate calibration of the hardware setup, the coordinates of the pattern centre and the specimen-to-screen distance are known (Figure 2-14). The rotation matrix contains all necessary geometrical corrections, most notably the tilting angle α of the sample (usually as well as additional angles between sample and phosphor screen, which may occur in the various EBSD setups.

After indexing the pattern, the orientation of the sampled crystal volume with respect to the external specimen coordinate system can be determined (e.g. [Schwarzer and Weiland, 1988]; [Dingley et al., 1987]. The crystallographic orientation is usually given in terms of its orientation matrix g that transforms the specimen coordinate system into the coordinate system of the crystal (indexed by the superscript c in the following equations):

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Thus, for each vector (zone axis or band normal), its vector in the sample frame and, after the indexing, its crystallographic direction

are known. It follows from definition of (with :

Finally, a pattern can be recalculated from the orientation matrix and overlaid on the original pattern. If the solution is judged by the operator to be correct, the orientation matrix g is stored in a computer file for further evaluation and representation of the data.

Sample preparation for EBSD measurement

At the end of a deformation experiment the entire recovered sample assembly is cut either normal to the shear plane or parallel to it. The sample is then mounted in epoxy resin and the surface of the assembly and sample is polished to microprobe quality polished section using standard mechanical polishing methods with a finish of approximately 0.5 µm.

The electrons that generate EBSD patterns are diffracted from a depth of 10-50nm from the surface of the crystallites, and any residual surface deformation introduced during the mechanical polishing must be minimized to obtain high quality EBSD pattern. Typically standard metallography does not require such a fine surface. It should be noted that while these traditional methods can produce EBSD patterns that can be analyzed; the goal of EBSD sample preparation is to produce a flat deformation free surface that maximizes the pattern quality from the entire surface.

The next polishing stage uses a colloidal silica suspension in a mildly acidic medium.

This chemical polishing removes the top surface of the sample that is mechanically damaged during standard polishing with grits. Thereafter the sample is carbon coated up to a thickness of 4-6 nm to minimize charge accumulation during the analysis.

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2.3.2 Study of dislocation structure using Transmission electron microscope (TEM)