Volume 37, Issue 5

The double crystal diffractometer in n,-n position realizes plane wave conditions only approximately. Nevertheless topographs taken with such arrangements are usually interpreted on the basis of contrast simulations starting with plane waves. Observations of diffraction patterns obtained with curved samples in an n,-n setting have lead us to study the validity of such a treatment. Simulations made for different types of the starting wave actually show that plane waves are adequate even in that critical case. However for a full coincidence between simulation and experiment it proved necessary to account for the residual angular spread within the collimated beam by averaging several plane wave simulations.

A concept of X-ray topography for polycrystalline materials has been proposed. In this method X-rays scattered from a specimen produce the image. Various techniques for this kind of topo­graphy are described and their characteristic features are pointed out; some of these techniques offer the possibility to make tomographic observations. The new topographic method has been applied to the observation of commercially used alu­minium sheet and of wood (cedar). The discussion is extended to mechanisms of the image forma­tion and the perspective fields of application.

Dynamical theory of the X-ray diffraction on a crystal containing misfit boundary was applied to the interpretation of the contrast observed in X-ray topographs on 90° magnetic domain walls in single crystals of an Fe-Si alloy. The integrated intensities were computed for several cases corresponding to the actual conditions of experiments. Good agreement of theoretical and experi­mental results was obtained.

A spherical wave theory is given for the calculation of the observed fine structure of Laue case rocking curves [1 - 3] of a pair of perfect crystals. It is shown that under the experimental condition of measuring simultaneously the full width of outgoing beams, the simple plane wave theory presented previously [1] yields identical results.

Double X-ray diffractometry has been used to investigate perfect Si crystals of different orientations, on which SiCO 2 layers of different thickness were grown. For the (111) and (110) orientations no appreciable modification of the theoretical diffraction pattern is observed. An important modification, which depends on the SiO 2 thickness, appears however for the (100) orientation. The observed effect does not change when the SiO 2 is removed and can be interpreted as an enhancement of the lattice parameter.

The phenomenon of n-be&m diffraction (n>2) is discussed with particular attention being devoted to the Bragg case of diffraction. The general method of solution is outlined, and some applications to specific situations are discussed. These include experiments in which strong quasi- monochromatic phonon beams are excited in a crystal using the Acousto-Electric effect, phase determination using the concept of „Virtual Bragg Scattering”, and high resolution Bragg reflec­tion topographs. In all cases the agreement between theory and experiment has been found excellent.

A correction term for high precision lattice constant investigations has been derived, which is caused by geometrical and absorption effects. Surprisingly there is no dependence on absorption and extinction in the case of high absorption and/or “infinite” crystal thickness. Only the half width of the rocking curve has to be considered. In the case of low absorption and/or thin crystal, there are terms of higher order which still depend on p.t but can be neglected compared to the main effect. The main reason for the correction is that the observed rocking curve is the result of a “true” rocking curve multiplied by a geometrical function which is not symmetrical with respect to the rocking angle. For high precision measurements (< 10 -5 ) the application of the correction term is recommended.

X-ray mass attenuation coefficients for polycrystalline samples of copper have been measured with a high-precision energy-dispersive method. Estimates of the scattering contributions to the attenuation coefficients are made. The photoelectric coefficients deduced from the experimental results are compared with theoretical calculations using screened hydrogen-like eigenfunctions as well as more rigorous relativistic wavefunctions.

It is shown that the dynamical diffraction process inside a distorted crystal consists of ordinary dynamical progression inside perfect portions of the crystal and scattering at distortions. The scattered waves proceed as in the perfect crystal and can be multiply scattered. The sum of the primary wave induced at the entrance surface and the waves scattered at distorted parts inside the “inverted Borrmann triangle” gives the resultant wave field at the exit surface.

In view of the renewed interest in surface reflection x-ray topography, a unified theory for the Bragg geometry has been laid out to explain the different types of image formation from the scattering point of view. The means by which the photons “infiltrate” a real crystal have been studied. The theory suggests, for example, a mechanism for image contrast inversion in the Bragg geometry, and will also be found to be important in other topics of high current interest, such as x-ray standing wave surface analysis and x-ray inelastic scattering at the Bragg angle.

The integrated reflection power for perfect crystals has been measured with neutrons and X- Rays for different crystals in a wide range of absorption coefficients and values of |μ h /μ 0 | where μ h is the h Fourier term of the absorption coefficient. The influence of Compton effect and tem­perature factor is discussed. The results are compared to Kato’s theoretical values.

For the purpose of extinction correction in crystal analysis, the secondary extinction factor y is discussed in the light of the new approach developed by the present author. The mosaic crystal model is adopted. A comparison is made between the present theory and the conventional theory (CT) through functional analysis of y in general cases and numerical analysis in the special case of parallel slab crystals. The y values of CT are underestimated by about 4% and 30% at y = 0.5 and 0.15, respectively. For y ≿ 0.7, CT is practically correct.

After the development of a very common formalism for neutron three beam cases, a detailed investigation is given for the case (111, 1̄1̄1/220) and a comparisation with the (different) case (111, 1̄11/200) is presented. It is shown that the former case behaves different by concerning dispersion branches and reflection curves; both are asymmetric in respect to a wave incident in the exact Bragg direction and react more sensitive by upon small deviations of the incident wave from this direction. Simple formulae were found for the reflection curves of the intensities for all three beams behind a perfect crystal slab and the Pendellösung period.

Coherent dynamical interaction in a 6-beam Borrmann diffraction experiment leading to an unusual intensity enhancement of X-ray transmission in crystals is investigated by using a synchrotron radiation source. A sharp enhanced intensity spot of two seconds of arc beam- divergence is observe 1 on the direct beam at the exact 6-beam diffraction position. The plane- wave dynamical theory is employed to account for the experimental results. The polarization dependence of the crystal excitation by the incident beam is discussed.

Changes in 70.53° magnetic domain structure on the surface of a perfect (11̄0) nickel crystal have been observed using white synchrotron X-radiation topography. The crystal was influenced by a variable [11̄0] magnetic field. At field strengths ≿ 100 A/m [111̄]-spike domains, thought to be traces of [011], 70.53° (oblique) magnetic domain walls, appeared within [111]-bands (0.4 mm wide) in the topographs. Reversal of the field produced similar spikes at equivalent field values but in different regions of the crystal.

A diffractometer using perfect crystals in symmetric Bragg arrangement, hence being useful for both neutron and X-ray radiation, has been built. The angular resolution of that instrument is better than 1 microradian, which corresponds to a scattering vector resolution of about 10 -6 Å -1 . This spectrometer was equipped with a laser light adjustment system which is sensitive to the relative angular position of the two perfect crystals. The spectrometer was used for the mea­surement of neutron scattering at very low angles of hydrated niobium and vanadium samples. The experimental results show an anomalously low attenuation of the neutrons when the metal-H sample is within the solubility a region. This property is explained by a lattice gas model of atomic H in the α-phase of the system. In the two phase region (α - β) a stronger attenuation of the neutron beam occurs due to the sample now being in an ordered interstitial solution phase.

The transformation properties of the Dirac-equation derived by Sallhofer from electromagnetic principles are investigated.