Theoretical considerations on phase determination by three-beam interference

Abstract

For tp-scan experiments rotating the crystal through a three-beam case the rocking-curve: profiles have been calculated on the basis of the dynamical theory of X-ray diffraction. Divergence and wavelength spread of the incident beam have been taken into account. It is shown that for centrosymmetric crystal structures the asymmetry of the profiles is related to the sign of the triple product of the structure factorswhich are involved in a three-beam case. If anomalous absorption ('double Borrmann' effect) can be neglected the typical asymmetry is independent of the diffraction geometry (Laue or Bragg case). For Laue geometry and thick crystals Co t > 1) corrections are necessary. For centrosymmetric structures it may be possible to determine the phase sum of a triplet by inspection of the rocking curve without computer calculations. The general features of the rocking curve are discussed and a physical interpretation is given.

Experimental procedures for the determination of invariant phases of centrosymmetric crystals

“…Gradually, as more phases were determined, it became clear that, for r.l.p.s entering the Ewald sphere, positive phases were invariably associated with the 'attenuation followed by enhancement sequence'. These experimental findings are inconsistent with the theoretical predictions of Hummer & Billy (1982). The criteria outlined above were used to assign phases to the triplets listed in Table 1 and displayed in Fig.…”

On the shape of umweg peaks

“…V is the volume of the unit cell, and T , the classical electron radius. In a similar way the electric field amplitude for the set of planes of the multiple diffracted beam is given by the relation for a crystal cut parallel to the (222) plane, the asymmetry parameter, b, is given by the relation (6) sin (OH) sin (0,) -2 sin (0,) cos (OHJ ' b, = and bH-, is given by where 8, is the Bragg angle for the (313) reflection and wHL the angle between the (222) and (313) planes.…”

“…In this work we use the same basic principle of the interference effects [6], carrying out the calculations for the intensities of the primary and the additional diffractions, considering that they are existing separately and independently of each other. The additional diffraction is considered as an "internal double crystal diffractometer" inside the crystal.…”

Polar scanning in multi-beam diffractometry

“…If diffraction vector H and rotation axis pl are normal t o the crystal plane, we arrive a t the well-known Renninger geometry. Nevertheless, the use of such a geometry is hindered since the primary-beam divergence "snioothes" multi-beam profiles of the I,(p) curves [ 2 ] . For example, in order t o obtain phase relationships for Ge crystals, a complex nionochromator-collimator with two inclined crystals had t o be designed.…”