It is a well known fact that crystals reflect X-rays when the incident X-ray beam makes a certain angle to a given set of atomic planes. In other words, this happens when the Bragg diffraction condition, which relates the incident angle, radiation wavelength and the interatomic spacing of the planes is satisfied. A not so trivial question to answer is what fraction of incident radiation is reflected for any given Bragg reflection and why.
The answer is available (from many text books on x-ray diffraction), but commonly only for two extreme cases. In one of them the crystals are rather small and the atoms are disordered. In this case the chances for rescattering of Bragg-reflected X-ray beams within the crystal are rather small. This regime is often referred to as kinematical X-ray diffraction. In the other case the crystal is fairly large and the crystal lattice is perfect such that multiple rescattering occurs, which can be taken into account. This regime is referred to as dynamical X-ray diffraction. In reality, many crystals are neither perfect nor ideally imperfect, which makes it difficult to quantitatively predict X-ray reflectivity. This situation leads to many theories and approximations of no universal character.
A team of CHESS scientists cracked the problem for one of technologically important types of materials, chemically vapor-deposited (CVD) diamond crystals. This lab-grown type of diamond is a typical example of a crystal which is neither perfect nor ideally imperfect. By certain modifications of a well-known mosaic crystal model and careful experimentation it was shown that absolute X-ray reflectivity of CVD diamonds can be quantified and related to microstructural parameters, which describe imperfections of the crystal lattice [1,2].
These results also play an important role in the ongoing CHESS upgrade. Diamond monochromators will be installed for a number of new CHESS beamlines. The theory and conducted experiments have shown that integrated reflectivity and thus the flux delivered by CVD diamond monochromators (radiation energy filters for X-rays generated by the upgraded source) can exceed those of nearly perfect (and about 10X more expensive) synthetic diamond crystals grown in equilibrium conditions of high-pressures and high-temperatures by at least an order of magnitude.
References:
S. Stoupin, J.P.C. Ruff, T. Krawczyk, and K.D. Finkelstein, “X-ray reflectivity of chemically vapor deposited diamond single crystals in the Laue geometry”, Acta Cryst. A74, 567-577 (2018). https://doi.org/10.1107/S2053273318009439
S. Stoupin, T. Krawczyk, J.P.C. Ruff, K.D. Finkelstein, H.H. Lee, and R. Huang, “Performance of CVD Diamond Single Crystals as Side-bounce Monochromators in the Laue Geometry at High Photon Energies”, AIP Conf. Proc. (in press) (2018). https://arxiv.org/abs/1806.02226
Acknowledgement:
We thank A. Macrander for timely allocation of beamtime for experiments conducted at the Advanced Photon Source.
K. Lang is acknowledged for technical support.
Funding:
This work is based upon research conducted at the Cornell High Energy Synchrotron Source (CHESS) which is supported by the National Science Foundation under award DMR-1332208. Use of the Advanced Photon Source was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. Work done in part at the Cornell NanoScale Facility, an NNCI member supported by NSF Grant ECCS-1542081. C. Alpha of CNF is acknowledged for the help and effort of capillary coating.
