By Michael Leitner, University of Vienna
The world we live in is essentially solid. Solid matter makes up the ground we stand on, the houses we live in, the circuits in our electronic devices, even the bones that give us shape. Solid is not necessarily synonymous to static, however: it is known that the atoms that make up a solid begin to migrate through the material, given a moderately elevated temperature. Exactly how they do that was the question we set out to solve.
An exemplary manifestation of the migration of atoms through a solid is the very common effect of corrosion. We all know from our school days that rust is just iron oxide. But for this compound to form we need an intermixing of iron and oxygen. This is only possible because the small oxygen atoms can easily jump through the material; more precisely, they diffuse (as the physicists say) from the surface into the sample.
The quantitative treatment of this problem is due to Albert Einstein. In his doctoral thesis he showed us how small (then even immeasurable), random displacements of particles in a liquid lead to a macroscopic motion, visible under the microscope and known as Brownian motion. His theory also holds for the motion of atoms in a solid. So now we know that the spreading-out or diffusion of foreign atoms in a material is due to a totally random movement of the atoms on a very small scale. But what does this movement look like?
In contrast to a liquid, a solid is rigid. This holds also on the atomic scale: an atom cannot roam freely but is constricted by its neighbours and can leave its cage only via discrete jumps. We now can measure the macroscopic spreading, plug it into Einstein's formula, and estimate the microscopic jump frequency. But this does not tell us how the jumping happens. This is where our experiment comes in.
We follow the atomic motion by scattering photons and exploiting the principle of interference. Just think of the pattern resulting from Young's famous double-slit experiment. If we make the source of the pattern more complex by adding more and more slits in irregular positions, the pattern itself will also become more complex until it looks completely random. The positions of the slits are still unambiguously recorded in the pattern, however. This is the situation of our experiment, where each atom in the sample acts as one slit.
It is not necessary for the study of dynamics to keep track of the positions of the atoms, which would be an impossible task anyway because of sheer numbers. What we do instead is we place our sample in a photon beam and record the patterns of the scattered photons over time. The changing positions of the atoms in the material give changing scattering patterns; the nature of these atomic jumps is also encoded. To illustrate this with a simple example, if the atoms jump mostly to the left or to the right but only rarely up or down, then the scattering pattern will also fluctuate much faster in the horizontal direction than in the vertical direction.
To do such an experiment we have quite demanding requirements on the photons that we probe our sample with: first, their wavelength has to be comparable to atomic distances, i.e., we need photons with a wavelength shorter than a thousandth of the wavelength of visible light. Such photons are known as X-rays. Second, in contrast to the X-rays you get at the physician’s, our photons have to be coherent. This means that all the photons have to be essentially equal: they have to travel in the same direction, come from a very small common source, and have the same wavelength. In the case of visible light such sources of radiation are readily available: lasers. In fact, the principle of our measurements has been used with optical light for a few decades now, but the longer wavelengths didn't allow for measuring the dynamics on the atomic scale. No, for that you need coherent X-rays, and there are just three facilities (they are called synchrotrons) that can deliver X-rays with the necessary intensity and quality in the whole world. One of them is the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. By passing the beam through apertures and selecting a certain wavelength by a monochromator, we succeeded for the first time in obtaining a beam that is at the same time sufficiently coherent and intensive. This beam now allows us to measure atomic dynamics.
In our experiment we measured the diffusion in a copper-gold alloy. Contrary to most metallic samples, which are composed of a large number of very small crystals, our sample consisted of a single crystal. Measuring the fluctuations at several position in the scattering pattern relative to the crystal gave us all the information about the jumps of the atoms: as was expected, the atoms jumped to neighbouring positions in the crystal lattice. However, as gold atoms prefer copper atoms as neighbours, they jump more often onto sites that have only copper neighbours, and they also stay longer in these sites. One could even say that they flee from their own kind. The rate at which all of that happens is about one jump per hour at 270 degrees Celsius. We also observed that raising the temperature leads to a doubling of the jump frequency for each step of 10 °C; lowering the temperature slows the diffusion accordingly. The successful realisation of this experiment opens up the future possibility of measuring the diffusion of atoms in many technically important metallic systems that haven't been accessible to previously existing methods. Measurements of this kind will also become part of the field of application of the new X-ray-Free Electron Lasers, the biggest of which is currently being built in Hamburg. With these new sources we will be able to form a complete picture of the restless bustling in materials on the atomic scale.
Michael Leitner
University of Vienna
www.atomiumculture.eu
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