Kikuchi lines

The Whole-Pattern symmetry is the symmetry which takes into account all the features present on a high S5mimetry zone axis diffraction pattern (i.e. the disks, the lines inside the disk and the Kikuchi lines). As mentioned above, in order to identify a 3D S5mimetry, the pattern should, at least, display the First-Order Laue Zone. In the example given on figure 2a, this FOLZ is weak, but clearly visible and the Whole Pattern displays a 3D-4mm S5munetry. 

Electron backscatter diffraction (EBSD) — The focused electron beam of Scanning Electron Microscopes (SEM) can be used to detect the crystallographic orientation of the top layers of a sample. The backscattered electrons (information depth 40-70 nm at 25 kV accelerating potential, lateral resolution around 200 nm) provide characteristic diffraction patterns (Kikuchi lines) on a phosphor screen. The patterns are recorded by a CCD-camera and interpreted by software. The position of the unit cell of the sample is determined by the corresponding Euler angles. In scanning mode, the software produces a surface orientation mapping that consists of... 

A grating pattern from a single crystal containing misorientations of 5°. (d) As for Fig. 4(b), but given a very light etch. Kikuchi lines are visible indicating that material of high perfection has been exposed. 

Figure 3 Examples of (a) selected area electron diffraction, (b) zone-axis CBED pattern, and (c) off-zone axis CBED pattern showing Kikuchi lines in the diffraction pattern...

When the electrons impinge on the crystalline sample, they interact with individual lattice planes. When these interactions satisfy the Bragg condition, they exhibit backscattering diffraction and (due to the tilted sample) are directed toward a phosphor screen where the fluorescent pattern is detected by a CCD camera. The resulting pattern consists of a large number of intersecting bands, known as Kikuchi lines, which represent the unique crystallographic properties of the crystal... 

Figure 3.14. Kikuchi lines in an electron diffraction pattern of quartz. g2 = 2420 is close to the exact Bragg angle. Compare with Figure 3.16(e, f).

In practical electron microscopy, it is often important to be able to determine accurately the deviation A0 from the exact Bragg angle 0. We now consider in some detail how we can use Kikuchi lines for doing this. 

Figure 3.15. (a) Diagram showing the origin of Kikuchi lines. 

The corresponding SAD pattern of spots and Kikuchi lines is shown in Figure 3.16(b). The spacing between adjacent spots of the systematic row is X, and the Kikuchi lines Dj and Ex pass through the diffraction spots O and g, respectively. The second-order Kikuchi lines and Ei pass midway between —g and O and between g and Ig, respectively, and hence are a distance lx apart. 

This tilting causes the Kikuchi lines to move to the right E is displaced from the spot g by a distance AX] and Ei is displaced from the spot 2g by a distance Ax2. This is shown in Figure 3.16(d), and it is clear that... 

A rotation of 20 would cause the Kikuchi lines to move through a distance X. Thus, AX] and A0j are related by the equation... 

Figure 3.16. Ewald sphere diagrams and the corresponding diffraction patterns showing the positions of the Kikuchi lines relative to the main Bragg beam, (a, b) jg = 0 (c, d) Sg < 0 and (e, f) = 0.

It is instructive to estimate the smallest tilt angle A0 which can be measured from displacements of Kikuchi lines. If we assume that a displacement of Ax = O.lx can just be measured, then from Eq. (3.59), A0 = (0.1)20, which is equal to about 0.05 degree with d = 0.5 nm and X = 0.004 nm. Thus, the accuracy with which an orientation can be determined from a diffraction pattern is greatly increased if Kikuchi lines are present. 

The volume of specimen contributing to a CBED pattern is much smaller than that contributing to an SAD pattern. Thus, there is less likelihood that the effects of strain, specimen bending, or crystal defects will influence the nature of a CBED pattern. Consequently, Kikuchi lines are usually more often observed and are usually clearer in CBED patterns than in SAD patterns. 

The nature and origin of Kikuchi lines that arise from planes of the ZOLZ were discussed in Section 3.9. Kikuchi lines can also arise from HOLZ planes and are observed outside the diffraction disks of a CBED pattern. However, within the disks there are the so-called HOLZ lines, which are continuous with the HOLZ Kikuchi lines. 

Kikuchi lines are pairs of parallel lines consisting of one bright and one dark line in the diffraction mode as shown in Figure 3.35. Kikuchi lines are named after the Japanese scientist, Kikuchi, who discovered them in 1928. Kikuchi lines appear when the selected area for diffraction is moved to a thicker section in the specimen where the diffraction spots become weaker, or even disappear. 

Kikuchi lines result from inelastic scattering of electrons in specimens. Generally, an electron scatters elastically when it interacts with an atomic nucleus. The mass of a nucleus is much larger than that of an electron. Thus, their interaction is similar to a ball hitting wall where the ball bounces without energy loss. However, when the electron interacts with an electron in an atomic shell, energy will transfer between the two electrons during collision, which is referred... 

Figure 3.37 Kikuchi line formation by inelastic scattering of electrons at point P in a single crystal. The lower diagram illustrates the intensity of light on the view screen, which is affected by the inelastic...

This exercise was divided into three parts (1) reading an article about kikuchi lines, (2) painting a picture of kikuchi lines, and (3) attending a lecture/seminar. Thus, the assignment consisted of depicting the kikuchi lines, a specific phenomenon within transmission electron microscopy (TEM). 

Kikuchi lines appear after multiple electron diffraction in TEM and are very useful to the operator in finding the orientation of a specimen. In order to understand Kikuchi lines it is necessary to understand diffraction and reciprocal space. 

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