By L. Marton (Ed.)
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Extra resources for Advances in Electronics and Electron Physics, Vol. 39
Courtesy of the Royal Society. the reflecting position (w = 0, B = 42). From Eqs. (47), (48) and (50)-(52) we find that the Bloch functions B(') and B(') can be written as B") = - i@ exp (2ni I kill + fg 1 z) sin ngx, 8'') = @ exp (2ni I k;') + Q Iz) cos ngx, (130) (131) where x is the coordinate normal to the reflecting planes in Fig. 26 and z is the coordinate parallel to these planes. The current flow corresponding to Eqs. (130) and (131) is in the direction of kt)+ ig, parallel to the reflecting planes, and is modulated sinusoidally in the x direction as shown in Fig.
Thus from Eqs. (133a) and (133b)we find that the amplitude absorption coefficients for the two Bloch waves for branches 1 and 2 of the dispersion surface (Fig. 19) are given by (137a) (137b) Providing is positive, which is the case when peaks in the imaginary potential coincide with atomic centers of symmetry, we see that the Bloch wave on branch 1 of the dispersion surface is absorbed less than that on branch 2. An extreme effect occurs when = <,; for then the absorption of wave 1 becomes zero at w = 0.
J. WHELAN It is easily shown from Eqs. (42), (43), (W), and (101) that for unit incident beam amplitude (4' = [ LO]) the amplitudes 4o and c$8 transmitted through a slab crystal of thickness t are given by Eqs. (61a) and (61b). The wavemechanical treatment therefore gives results identical with the wave-optical treatment. e. Imperfect crystal. The simplest case to consider is that of a stacking fault which is the planar interface between two slabs of crystal as in Fig. 25, which have a relative displacement R which is not a lattice vector.
Advances in Electronics and Electron Physics, Vol. 39 by L. Marton (Ed.)