5 Properties of wavefields

Abstract

Abstract This chapter is the first of the next few chapters devoted to plane-wave advanced dynamical theory. The fundamental equations of dynamical diffraction are derived for vector waves and the expression of the dispersion equation is given in the two-beam case and for absorbing crystals, the following discussion being limited to geometrical situations where neither the incidence nor the emergence angle is grazing. The notion of wavefields and the dispersion surface are introduced, and it is shown that the Poynting vector, which gives the direction of propagation of the energy, is normal to it. The boundary conditions at the entrance surface are then introduced. Transmission and reflection geometries are treated separately. For each case, the deviation parameter is introduced geometrically and the coordinates of the tiepoints determined, the Pendellösung distance (extinction distance in the reflection geometry), Darwin width, the anomalous absorption coefficient, index of refraction, the phase and amplitude ratios of the reflected and refracted waves are calculated. Borrmann's standing wave interpretation of the anomalous absorption effect is given. The last section is to the case where Bragg's angle is close to π/2.