Diffraction and Imaging Techniques in Material Science. by S Amelinckx (Eds.)

By S Amelinckx (Eds.)

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Additional resources for Diffraction and Imaging Techniques in Material Science. Electron Microscopy

Sample text

The wave in the crystal will now be of the form exp ( 2 π ί Κ · Γ ) exp ( - 2 π δ ζ ) (44) the exponential decay describing absorption. WHELAN 60 Absorption can be described equally well by allowing the atomic scattering amplitude for electron waves to become complex; + (47) since V'Q will be related t o / ' ( 0 ) by an expression similar to (41). We then find (48) In keeping with the notation of the previous section, we define "absorption distances", ξ'0, ξ' by an expression similar to eq. (2) of sect.

Solution in the Laue case It is useful to introduce a notation due to Takagi for describing deviations from the exact Bragg condition. We introduce a parameter β by the relation w = cot/3 . (23) In fig. WHELAN 52 the Brillouin zone boundary, w = 0 (β=π/2) occurs when A is at the zone boun­ dary, which is the exact Bragg position, w = - ° ° (β=π) occurs when A is far to the left of the zone boundary. It is usual to take s positive if the reciprical lat­ tice point is inside the reflecting sphere and negative in the reverse situation.

WHELAN J$ " θ- Fig. 6. Rocking curve in the Bragg case. The region where the reflected intensity is unity v, given by |w| ^ 1. The rocking curve given by (36) is shown in fig. 6. Over the region \w\ < 1 there is total reflection of the incident wave. The Bragg case was first studied for X-ray diffraction by Darwin [ 1 ] . The case is important in the theory of grazing angle electron diffraction. The exponential solution for the crystal waves shows that evanescent waves are excited in the crystal.

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