Atomic Diffusion studied with coherent X-rays

Understanding atomic motion in solids is a fundamental issue in synthesis and stability of technically important materials; this is even more critical in nanomaterials. The timescale of atomic motion is usually uncomfortably long for experimental techniques that rely on high energy resolution (e.g. inelastic neutron scattering or Mößbauer spectroscopy), forcing measurements at unduly high temperatures. Moreover, only a small number of selected isotopes are accessible to these methods. There exists, of course, plenty of information about atomic diffusion from tracer measurements. However, drawing conclusions from tracer measurements on the actual microscopic dynamics is a highly indirect procedure, often contradictory, and always based on assumptions. Hence, a non-resonant method not restricted to certain isotopes and capable of detecting slow diffusion is extremely desirable. We have shown in our previous project the answer to these requirements: X-ray photon correlation spectroscopy (XPCS). This method monitors the temporal variations of the coherently scattered intensity as a function of the wavevector, that is, it measures dynamics directly in the Fourier domain. It has been applied since the emergence of high-energy synchrotron sources in the mid-90s for studies of slow dynamics on the nanometer scale, but had never been practiced before on single atoms. We have taken XPCS to its limits in terms of resolution by using it to reveal the slow atomic dynamics in a copper-gold alloy. The project at hand plans to follow up on this success and to establish XPCS as the preferred method for studying atomic dynamics. Specifically, we are planning to study technically important high-temperature structural materials like Ni-Al alloys, semiconductors like Si-Ge, and metallic glasses. These studies will give a direct microscopic picture of the mechanisms leading to atomic transport, which can be very intricate in the case of ordered alloys. They will also yield the temperature dependence of diffusion (i.e. the activation energy) in the low-temperature region. In our project we will profit from the continually increasing brilliance of existing synchrotron sources (cp. imminent upgrade of the ESRF in Grenoble) and from emerging new sources like PETRA III and the European XFEL in Hamburg.

The dynamics of single atoms affect the fabrication, specific properties and the stability of all materials. Understanding the mechanisms governing them is therefore a fundamental issue in materials science. Although numerous characteristics of solids can be reduced to the motion of single atoms, studies of diffusion mechanisms on the atomic scale are extremely challenging. The new method of atomic-scale X-ray photon correlation spectroscopy (aXPCS), which we developed in our previous project, enables detection of very slow motion and can be applied to study diffusion in a wide range of materials because it is not restricted to certain isotopes. This also includes amorphous materials where information about their dynamics is scarce. When coherent beamlines were first implemented at synchrotrons more than two decades ago, the possibility of studying dynamics in amorphous materials was pointed out as justification. This goal could be met in frame of this project and the following milestones were reached:i. We successfully performed diffusion measurements in disordered and in ordered crystalline phases. We could demonstrate that aXPCS is a powerful method for studying diffusion mechanism in well-ordered intermetallic phases. We also showed that in order to make a proper interpretation of dynamics data it is necessary to access information about the short-range order of constituent atoms.ii. We expanded our measurements to the study of diffusion in nonmetallic systems to prove that the applicability of aXPCS is not limited to selected elements or isotopes. The diffusion of germanium in a silicon crystal was measured and the results show that a vacancy diffusion mechanism should be responsible for atomic jumps at temperatures up to 1200 K.iii. We took a pioneering approach in measuring diffusion in amorphous matter, which allowed for revealing the full capacity of aXPCS. Up to now dynamics of amorphous media could mainly be studied in their liquid phase due to the high diffusivities required by classical methods. Two classes of amorphous systems were studied: metallic glass and network glass. We interpret the dynamics in metallic glass as resulting from the nanoscale and being stress-related displacements. In network glass, surprisingly, dynamics happen via jumps into neighboring positions which lie in a well-defined distance correlated with the nanostructure of the glass.In the course of this project we could reach all scheduled goals and established aXPCS as a central method for a quantitative understanding of atomic diffusion. We are confident that our method will benefit from the continuously increasing brilliance of coherent synchrotron sources in the future.