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One sees that the main effect is to obtain the same diffraction pattern as in air, but at a distance A times nearer. This effect has been confirmed by experiment [66]. It must be remembered that in the middle of the reflection range A is of the order of 104 or 10 5 ! Expression (IV-5-3) shows also that the diffraction pattern is the same it would be in air, but with a wave-length equal to CH-1. Remembering that at the exact Bragg angle max = 2sin2fl AQ cos(9 X A. Authier 48 one notices also that the expression of w becomes similar to that taken in air if one replaces the wave-length X by the Pendellosung fringe distance A0 multiplied by a numerical factor; this quantity is of the order of the optical wave-lengths and the diffraction patterns are therefore of the same type as those observed in the same con­ ditions (slit width e\ distance d) with visible light!

Phys. Soc. Japan, 20, 1047 (1965). Kato, N. , Phys. Rev. Letters, 19, 22 (1967). Hart, M. , Acta Cryst. A 25, 134 (1969). Borne, U. , Zeit. fur Physik, 188, 154 (1965). Borne, U. , Zeit. fur Physik, 190, 455 (1966). Borne, U. , Zeit. fur Physik, 194, 1 (1966). Penning, P. , Philips Res. repts, 16, 419 (1961). , J. Phys. Soc. Japan, 18, 1785 (1963). , J. Phys. Soc. Japan, 19, 67 (1963). , J. Phys. Soc. Japan, 19, 971 (1964). , Z. Naturforsch. 18a, 1010 (1963). , Advances in X-ray analysis, Plenum Press, 10, 9 (1967).

In the last few years there have appeared various investi­ gations concerning the interesting problem of diffraction of waves scattered with energy loss. We can here mention only the theoretical work of Kainuma (1955) [10], Takagi (1958) [11], Howie (1959) [12], Fujimo to and Kainuma (1963) [13], Heidenreich (1963) [14], Fukuhara (1963) [15], Kainuma (1965) [16], G&nnes (1962, 66) [17] [18]. A discussion of this work is beyond the scope of this article. II. Theory II. 1 Bethe's Theory The dynamical theory of electron diffraction was developed by Bethe [19] in 1928.

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