Motivation and introduction

Diffusion is an important and fundamental phenomenon controlling the properties of metals, alloys, semiconductors, ceramics, glasses, and polymers at higher temperatures. It plays an important role in the kinetics of micro structural changes in a material. It is a driving force for nucleation of new phases, recrystallisation and phase transformations with a wide use in current technology, e.g. surface hardening, changing of deformation behaviour by nucleation, diffusion doping or sintering. This thesis focuses on surface diffusion which is a pre-condition for self-assembling nanostructures, determines the growth mode of layers, growth of steps or islands. The surface structure is defined by the dynamics on the surface at certain temperature. The growth mode of thin films and the change of the island shape defined by the diffusion barriers along the island edges are nice examples.
Surface diffusion can be studied in a macroscopic range using the Radioactive Tracer Technique (RTT) [1], Auger Electron Scattering (AES) [2]. These methods give access to the "effective" diffusion. The spatial resolution is in the order of microns. The Field Ion Microscope (FIM) [3] reaches atomic resolution but is limited to a sample size of typically 5 $nm$. Microscopic visualisation techniques as Scanning Tunnelling Microscopy (STM) estimate the jump vectors and jump frequencies using a statistical treatment of the collected pictures being aware of scanning artefacts [4]. Using these methods it is not possible to see the fundamental atomic jump events at the technically relevant temperatures, e.g. vacancy-atom exchange [5], due to the low time-resolution (typically 20 images/s). Moreover, STM, FIM and tracer are not depth-sensitive methods, i.e. they can effectively ``see'' only the uppermost atoms contributing to the diffusion. Atoms a few monolayers below the surface can not be resolved.
To study the fundamental jump diffusion mechanisms, i.e. to gain information about the jump vectors and residence times on different crystal lattice sites, scattering methods like Quasielastic Mössbauer spectroscopy (QMS) [6], Quasielastic Neutron Scattering (QNS) [7], Nuclear Resonant Scattering (NRS) [8,9] or Quasielastic Helium scattering [10,11] have to be used.
The aim of the work done by the author of this thesis is the application of the surface-sensitive NRS method for diffusion and dynamics (phonon density of states). The NRS method uses a combination of the brilliant intensity of third generation synchrotron sources and the excellent characteristics of QMS. The principle idea of an NRS experiment is to measure a time response of a sample enriched with Mössbauer isotopes. The synchrotron radiation is used to excite the resonant nuclei in the sample into a high energy state. The high energy state decays back to the ground state with a characteristic lifetime (141 $ns$ for the 14.4 $keV$ $^{57}$Fe) and the nuclei re-emit a ``delayed radiation''. The re-emitted intensity is collected as a function of time after excitation and orientation of the sample and yields information about hyperfine interaction and dynamics. The resonant effect with synchrotron radiation was observed for the first time 1985 by Gerdau et.al. [12]. In 1996 we demonstrated that this technique is capable to measure bulk diffusion coefficients [13]. Based on the theory of Smirnov and Kohn [8] the results of QMS measurements on Fe$_{3}$Si have been verified. A series of measurements in different geometries like transmission [14,15] or Bragg reflection [16] followed. NRS became one of the standard methods for dynamics studies. The mentioned experiments provide information about the bulk diffusion. Introducing the depth selectivity of the grazing incidence geometry into an NRS experiment would push the limit of the application of nuclear resonant experiments to the field of dynamics in thin films and multilayers. As a consequence the theories for dynamics studies successfully applied in bulk materials have to be modified. The aim of this work is to present briefly the known approach for electronic X-ray scattering from thin films and multilayers and merge it with the nuclear resonant scattering theory using the fundamental material parameter, i.e the refractive index. The energy dependence of the refractive index provides the link to the quasielastic scattering and relaxation theory, used up to now successfully to study jump diffusion and dynamics in bulk materials.