Diffusion studies with coherent X-ray

Diffusion in crystalline solids is of utmost importance in daily life, e.g., rusting of metals, doping of semi- conductors, nitrogen hardening of steels, etc. Macroscopically, diffusion can be mathematically described (Fick`s laws) and investigated (tracer diffusion experiments) with standard methods. However, the underlying processes on an atomic level, i.e., atomic jump vectors and frequencies, are not easily accessible. Up to now only quasielastic methods, particularly quasielastic neutron scattering, quasielastic Mössbauer spectroscopy (QMS), nuclear resonant scattering (NRS) of synchrotron radiation, and (most recently) the neutron-spin echo technique, were capable of resolving the elementary atomic jump process. But all these techniques lack from two big disadvantages. First, only certain isotopes are "visible" for each technique, e.g., the Mössbauer isotope 57Fe in case of QMS and NRS. Second, due to a limited energy resolution of all techniques only very fast diffusion is detectable by the above- mentioned methods. Hence, a non-resonant method - not restricted to certain isotopes -, which can detect slow diffusion, is extremely desirable. X-ray photon correlation spectroscopy (XPCS) is the most promising candidate to fill this gap. It is based on the fact that a highly modulated diffraction pattern - a so-called speckle pattern - is generated if coherent radiation is scattered at a disordered sample. This speckle pattern is in direct relation to all positions of the individual scattering centres in the coherently illuminated sample volume. Thus, the speckle pattern is modified if the spatial configuration of these scattering centres changes. This means that the speckle intensity fluctuates in time if dynamics, e.g., diffusion, takes place in the sample. Analysing the fluctuating speckle intensity yields information about the underlying dynamics. This principle was exploited for the last three decades by photon correlation spectroscopy (PCS) utilising coherent laser light, which limits the application field to the study of dynamics in optically transparent systems on length scales corresponding to the wavelength of visible light. Only since a few years coherent X-rays with sufficient intensity are available for performing XPCS measurements enabling investigation of optically opaque materials. Up to now XPCS was mainly used for investigations of slow dynamics in soft-condensed matter. Our aim is to establish the method of XPCS for diffusion investigations in (crystalline) hard-condensed matter.

Diffusion in crystalline solids is of utmost importance in daily life, e.g., rusting of metals, doping of semi- conductors, nitrogen hardening of steels, etc. Macroscopically, diffusion can be mathematically described (Fick`s laws) and investigated (tracer diffusion experiments) with standard methods. However, the underlying processes on an atomic level, i.e., atomic jump vectors and frequencies, are not easily accessible. Up to now only quasielastic methods, particularly quasielastic neutron scattering, quasielastic Mössbauer spectroscopy (QMS), nuclear resonant scattering (NRS) of synchrotron radiation, and (most recently) the neutron-spin echo technique, were capable of resolving the elementary atomic jump process. But all these techniques lack from two big disadvantages. First, only certain isotopes are "visible" for each technique, e.g., the Mössbauer isotope 57Fe in case of QMS and NRS. Second, due to a limited energy resolution of all techniques only very fast diffusion is detectable by the above- mentioned methods. Hence, a non-resonant method - not restricted to certain isotopes -, which can detect slow diffusion, is extremely desirable. X-ray photon correlation spectroscopy (XPCS) is the most promising candidate to fill this gap. It is based on the fact that a highly modulated diffraction pattern - a so-called speckle pattern - is generated if coherent radiation is scattered at a disordered sample. This speckle pattern is in direct relation to all positions of the individual scattering centres in the coherently illuminated sample volume. Thus, the speckle pattern is modified if the spatial configuration of these scattering centres changes. This means that the speckle intensity fluctuates in time if dynamics, e.g., diffusion, takes place in the sample. Analysing the fluctuating speckle intensity yields information about the underlying dynamics. This principle was exploited for the last three decades by photon correlation spectroscopy (PCS) utilising coherent laser light, which limits the application field to the study of dynamics in optically transparent systems on length scales corresponding to the wavelength of visible light. Only since a few years coherent X-rays with sufficient intensity are available for performing XPCS measurements enabling investigation of optically opaque materials. Up to now XPCS was mainly used for investigations of slow dynamics in soft-condensed matter. Our aim is to establish the method of XPCS for diffusion investigations in (crystalline) hard-condensed matter.