ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
Two different kinds of interaction between three waves D0, Dh and Dg in a perfect crystal are investigated in the case of Laue scattering using the Takagi-Taupin equations. Polarization effects (coupling between {\hat \sigma} and {\hat \pi} waves) are neglected, and it is assumed that the incoming vacuum wave D0(e) has a small wave-front area whose spatial extension is simulated by a point source on the crystal surface. The solutions of the diffraction equations thus constitute the boundary-value Green functions for the wave fields. In the first case it is assumed that Dg is only indirectly coupled to D0. In the second case energy is allowed to be exchanged between D0 and Dh and between D0 and Dg, but no Dh-Dg interaction is present. In both of these situations the field amplitudes are given by expressions that contain simple products of zeroth- and first-order Bessel functions. It is suggested that the intensity pattern can be observed directly. The transition to an incoming plane wave is outlined, and it is also demonstrated that the hyperbolic intensity fringes generated by two spherical waves can be deduced from the derived expressions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0108767386099543
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