By L. Marton (Ed.)

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**Extra info for Advances in Electronics and Electron Physics, Vol. 39**

**Example text**

Branches 1 and 2 correspond to forward-propagating Bloch waves, while branches 1' and 2' correspond to backward-propagating waves. This is a considerable simplification in the highenergy case, since the neglect of back-scattered waves enables the boundary conditions to be applied at successive plane interfaces consecutively and independently. The boundary conditions are also simplified. For the complete system of 2n waves there must be 2n boundary conditions. These are the usual conditions arising from the continuity of current at an interface, namely and d+/dz must be continuous.

Let the amplitudes of waves incident on the top surface and transmitted through the bottom surface be 4; and 4,, respectively. If the amplitude of the ith Bloch wave is i,bcn,the boundary conditions at the top and bottom surfaces give C cjli)i,b(O= ,#,;, (98a) i 1 Cjli) exp (27~iy(~)t)i,b(~) = 4, . 24. Illustrating the amplitudes ## and da of waves above and below a slab crystal of thickness t. where Cgi(= C:)) is a unitary matrix and the subscript d denotes a diagonal matrix. I, Eq. (99) is the formal solution for the diffracted beam amplitudes for an incident beam of unit amplitude.

108) and (109) give 3 = 2ni(A + (&)&', dz where (&), is a diagonal matrix whose elements are given by Eq. (69). Equation (110) is the generalization to the n-beam case of Eqs. (68a) and (68b). The transformation from to does not affect intensities 1 +g l2 since the elements of Q have unit modulus. The transformation is analogous to the transformation of Eqs. (67a) and (67b). Equation (108) or (110) can be used to calculate the diffracted n-beam intensities near a dislocation line where R(z) and hence p,(z) vary continuously along the column in Fig.