By L. Marton (Ed.)

ISBN-10: 0120145391

ISBN-13: 9780120145393

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This curve was first obtained by Darwin (13) for the Bragg case in X-ray diffraction. The physical reason for the difference between the solutions in the Bragg and Laue cases is easily seen from the dispersion surface of Fig. 19. 20. Rocking curve in the Bragg case of diffraction. The ordinate is the intensity of the reflected wave. ELECTRON DIFFRACTION THEORY A N D ELECTRON MICROSCOPY 31 symmetrical Laue case the normal to the crystal surface through the end A of the wave vector K is parallel to the zone boundary, and real intersections with the two branches of the dispersion surface occur.

B. Hirsch et al. (29). Courtesy of the Royal Society. crystal amplitude. , as Q varies in Fig. 14) the amplitude PP" oscillates with a depth periodicity Az = s- '. The amplitude-phase diagram approach is also useful for evaluating the column integral of Eq. (30) when a is a continuous function of z as for a dislocation. The situation is as shown in Fig. 15. A screw dislocation line A B parallel to the surface causes the column CD in the perfect crystal to deform to the shape EF. For a screw dislocation R = (b/2n)tan-' (33) (z/x), where b is the Burgers vector of the dislocation and a = 2xg * R = n tan-' (z/x); (34) n = g b is an integer for a perfect dislocation where b is a lattice vector.

Theoretical treatments of phonon scattering have been given by Yoshioka and Kainuma (48),Whelan (43), and Hall and Hirsch (49). “ 2. Inelastic Scattering by Crystals a. The complex lattice potential. Yoshioka (50)first showed in a formal quantum-mechanical treatment that the effect of inelastic-scattering processes on the elastic scattering by crystals could be represented by the addition of a small imaginary part V(r) to the crystal lattice potential V(r), which gives rise to absorption of the elastic wave in the same way as a complex refractive index gives rise to absorption of an electromagnetic wave.

### Advances in Electronics and Electron Physics, Vol. 39 by L. Marton (Ed.)

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