The fastest determination of the atomic structure

Parallel measurement of X-ray Bragg reflections via the Kossel lines allows determining 3D atomic structure in femtoseconds.
Published in Chemistry, Materials, and Physics
The fastest determination of the atomic structure

The arrangement of atoms in a solid, the atomic structure, is crucial to the understanding of the properties of the material. The first, and still widely used method to determine crystalline structures is X-ray diffraction. The time required for a diffraction measurement is defined by the amount of structural information to be determined, the amount of material, the experimental technique, and the properties of the probe beam. With the advent of 4th generation X-ray sources, the X-ray free electron lasers (XFEL), the compression of photons in the phase space has reached an unprecedented level. This means, that a single 25fs XFEL pulse, a 1s long synchrotron beam consisting of thousands of pulses, and tens of hours of continuous laboratory source provide about the same order of magnitude usable photons. One would think that the time to take a diffraction measurement proportionally scales down. But this is not the case.

A limiting factor in shortening the measurement time, is the extreme form of radiation damage, the coulomb explosion. In this process, the material becomes plasma due to a high degree of ionization by the probe beam. Somewhat counterintuitively, this problem can be solved by further shortening the pulse length and giving no time for the damage to develop, before the scattering from the sample is recorded. This measure before destruction principle was described decades ago and is the base for most experiments performed with the most intense 10-100 fs long XFEL pulses.

Still, a conventional single crystal diffraction measurement cannot be shortened arbitrarily and performed using a single XFEL pulse. The reason lies in the Bragg reflection condition. To record a Bragg reflection, the incoming beam must have a specified angle with the crystal lattice planes. The reflections are recorded serially, while the crystal is rotated. However, there is no chance to change the orientation of the sample - especially in a controlled manner - in femtoseconds. There are alternative diffraction techniques, that could be a workaround: Powder-, or polycrystalline diffraction requires no sample rotation, as a sample consists of crystals in random orientation, but this technique provides limited information. Laue diffraction simultaneously measures many reflections of a stationary single crystal sample due to the non-monochromatic primary radiation, but such a source is not available with ultrashort pulses.

In our recent publication [1] we presented and demonstrated an experimental technique that measures a large number of Bragg reflections of a single crystal sample in parallel, without the need for sample rotation, hence it can give the complete 3D structure of the crystal using a single 25fs long XFEL pulse. This method relies on the Kossel lines first observed and explained at the dawn of X-ray research. In the process, a secondary source of spherical radiation field reaches the crystal planes from all directions, and only the components satisfying the Bragg condition are reflected and form a conical radiation field leaving the sample. The secondary sources are some atoms of the sample itself, that are excited by the XFEL pulse and emit fluorescent radiation in the ~10keV X-ray energy range. Since the source atoms are part of the crystal structure, their location is in registry with the lattice, and this results in an interference signal across the Bragg reflection, encoding the phase of the given reflection's structure factor.

In our demonstration experiment at the European XFEL facility, we used an XFEL pulse to excite Ga atoms of stationary GaAs and GaP single crystal samples and recorded all the Kossel lines appearing as conic sections on a flat detector surface. The samples were thinned wafers of semiconductor-quality single crystals to obtain high-contrast, good-quality Kossel lines. A 4MPixel integrating detector enabled recording the pattern from a single XFEL pulse.

A Kossel line pattern first of all contains geometrical information. The axis and opening angle of the cone for each Kossel line give a reciprocal lattice vector and ultimately define the crystal lattice. The high enough angular resolution of the recorded pattern also revealed the fine interference signal across each Kossel line enabling us to derive both the amplitude and the phase information of the corresponding structure factor. This information provided an elegant way of avoiding the phase problem, and the electron density within the unit cell was obtained by a Fourier synthesis, using about 100 Fourier components (reflections).

The current results are not without preliminary research. We showed long ago, that amplitudes of structure factors can be obtained from the measurement of pseudo-Kossel lines using a home laboratory experiment and used in conventional structure determination [2]. Later we demonstrated that Kossel lines can be measured in seconds using synchrotron radiation as excitation [3]. Developing the theory and matching it with the data obtained at the European Synchrotron Radiation Facility we proved that the phase of the structure factors can also be determined [4]. After working out the steps of the data evaluation chain [5], we brought this kind of measurement to the European XFEL source and pushed down the measurement time to a single XFEL pulse [1]. We expect that beyond this proof of principle experiment, the technique will develop and find its application in real scientific problems.

Until then, parallel measurement of structure factors via Kossel lines still has future challenges and prospects, for example: - other inside sources of radiation might remove the requirement to have X-ray fluorescent atoms in the sample; - more complicated structures, containing several inequivalent source-atoms in the primitive unit cell requires new data evaluation methods; - in case of imperfect crystals described by the kinematic theory of diffraction, the narrow Kossel lines of mosaic blocks are averaged out and the phase information is lost. These issues require further research in this area.


  1. Gábor Bortel, Miklós Tegze, Marcin Sikorski, Richard Bean, Johan Bielecki, Chan Kim, Jayanath C. P. Koliyadu, Faisal H. M. Koua, Marco Ramilli, Adam Round, Tokushi Sato, Dmitrii Zabelskii and Gyula Faigel:
    3D atomic structure from a single X-ray free electron laser pulse
    Nature Communications 15, 970 (2024).
  2. G. Bortel, M. Tegze, G. Faigel:
    Structure factors from pseudo-Kossel line patterns
    J. Appl. Cryst. 38, 780-786, (2005).
  3. G. Bortel, G. Faigel, M. Tegze and A. Chumakov:
    Measurement of synchrotron-radiation-excited Kossel patterns
    J. Synchrotron Rad. 23, 214-218 (2016).
  4. G. Faigel, G. Bortel & M. Tegze:
    Experimental phase determination of the structure factor from Kossel line profile
    Scientific Reports 6:22904+8 (2016).
  5. Gábor Bortel, Miklós Tegze and Gyula Faigel:
    Constrained geometrical analysis of complete K-line patterns for calibrationless auto-indexing
    J. Appl. Cryst. 54, 123-131, (2021).

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X-Ray Diffraction
Physical Sciences > Materials Science > Materials Characterization Technique > Crystallography and Scattering Methods > Diffraction > X-Ray Diffraction
Free-Electron Lasers
Physical Sciences > Physics and Astronomy > Optics and Photonics > Laser > Free-Electron Lasers
Crystallography and Scattering Methods
Physical Sciences > Chemistry > Physical Chemistry > Crystallography and Scattering Methods

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