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X-Ray and Neutron Dynamical Diffraction: Theory and Applications (NATO Science Series: B:): Andre Authier, Stefano Lagomarsino, Brian K. Tanner

Two basic theories may be used to describe the diffraction of radiation by crystalline matter. The first one, the so-called geometrical, or kinematical theory, is approximate and is applicable to small, highly imperfect crystals. It is used for the determination of crystal structures and describes the diffraction of powders and polycrystalline materials. The other one, the so-called dynamical theory, is applicable to perfect or nearly perfect crystals. For that reason, dynamical diffraction of X-rays and neutrons constitutes the theoretical basis of a great variety of applications such as:

* the techniques used for the characterization of nearly perfect high technology materials, semiconductors, piezoelectric, electrooptic, ferroelectric, magnetic crystals,

* the X-ray optical devices used in all modern applications of Synchrotron Radiation (EXAFS, High Resolution X-ray Diffractometry, magnetic and nuclear resonant scattering, topography, etc.), and

* X-ray and neutron interferometry.

A new interest has developed in the applications of the dynamical theory because of the possibilities offered by synchrotron radiation for in situ and real time studies, the production of polarized X-rays, by the recent developments in X-ray magnetic and nuclear scattering, and by the use of X-ray and neutron interferometry in modern metrology. The arrival of the third generation synchrotron radiation sources with their enhanced properties has made the course and the publication of its proceedings very timely.

The first part of these proceedings reviews the basic principles of the dynamical diffraction of X-rays and neutrons by perfect and nearly perfect crystals, with special attention to highly asymmetrical cases, the optical devices used in the synchrotron beamlines, polarization of X-rays and various types of crystal polarizers for X-rays, and statistical theory for highly imperfect crystals.

The second, third and fourth parts of these proceedings describe the principles of the techniques used to characterize the structural imperfections of materials. Several chapters are devoted to X-ray and neutron diffraction topography which enables the direct imaging of crystal defects (dislocations, stacking faults, low angle grain boundaries, microprecipitates or inclusions, magnetic or ferroelectric domains, etc.). The various settings are presented and the new possibilities opened up by the third generation

enough to record a white beam topograph or a diffraction spectrum. A chapter is devoted to the theoretical interpretation of the contrast for the various types of defects. The main applications presented include the characterization of high technology materials, the in situ study of crystal growth and the relation of crystal defects to the growth conditions, in situ study of plastic deformation and phase transitions, and the analysis of the distribution and shape of domains in magnetic materials. It is, for instance, possible to follow the Molecular Beam Epitaxy growth of layers at the atomic scale, the movement of dislocations under an applied stress or the recrystallization of an alloy during a strain-anneal cycle. Another technique for the characterization of defects in imperfect materials and the analysis of strains is the high resolution diffraction of X-rays, which is applied in particular to layered or hetero-stractures such as those used in electronic materials. The theory of reciprocal space mapping is presented in detail and examples of strain-analysis are given in the case of ?-V multilayer compounds and ion-implanted silicon. New developments in the theory of the diffraction of X-rays by imperfect crystals and the improvement in computer power have now made possible the determination of the strain distribution in a component for microelectronics. The third type of application concerns the location of impurity atoms at crystal surfaces or interfaces by means of the fluorescence emitted at X-ray standing waves antinodes. It is possible by means of this technique to analyze the structure of the surface and the thermal vibrations of the atoms. The same technique is also applied to the study of thin films or long period structures.

The fifth part of the proceedings describes a very promising new application of dynamical theory, the use of multiple Bragg scattering for the determination of crystal structures. The phenomenon of multiple beam diffraction is well known; it occurs very often in electron diffraction and is usually avoided in X-ray diffraction. Due to the fact that electromagnetic waves are vector waves while the wave associated with an electron or a neutron beam is scalar, the theory is complicated for X-rays. New developments were presented at the course relative to the analysis of the -beam diffraction of X-rays and it was shown that it is possible to determine the absolute phase of structure factors from diffraction profiles in the neighborhood of three-beam diffraction. This is a very important development and will help in solving crystal structures even for macromolecules such as small proteins.

In the last part, the principles of X-ray and neutron interferometers are described. They produce interference patterns with a fringe spacing, equal to the lattice spacing of the crystal used and therefore, much smaller than the fringe spacing available with optical interferometry. They require extremely perfect crystals and the use of dynamical theory of diffraction for the interpretation of data. X-ray and neutron interferometery permit calibration of extremely small linear or angular displacements to be made at the subnanometer scale. They have been used for the absolute evaluation of the Avogadro number and for the measurement of X-ray dispersion corrections. They have very promising applications in the fields of phase contrast microscopy and metrology in the nanometer regime.

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