PSI - Issue 40

A. Barannikov et al. / Procedia Structural Integrity 40 (2022) 40–45 A. Barannikov at al. / Structural Integrity Procedia 00 (2022) 000 – 000

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During the experiment, we recorded 30 stereo images corresponding to the angles ±Δ θ while the maximum angle Δ θ was 0.25 o (Fig. 3a). Fig. 3b depicts the contour map obtained by the summation of the images. The Bragg reflection displacement across the sample shows that the Si membrane has two regions with concave and convex surfaces. The concave region is loc ated at the FZP center and has a diameter of 220 μm equal to the distance between two inflection points A and B placed close to the 115 th zone of the FZP. Outside this region is a convex area that goes beyond the FZP structure. The horizontal deformation profiles of the FZP were reconstructed at different positions. In this case, the tangenti al angle of the deformation profile Δ θ ū in Eq. 1 is equal to Δ θ due to the sample was rotating through angles Δ θ only in the horizontal direction. For instance, the reconstructed profiles taken at the center of the FZP, 60 μm and 120 μm below this, are shown in Fig. 3c. The maximum deformation amplitude z is observed in the center of the FZP and is about 0.5 µm. The curvature radius at the apex of the central deformation profile is equal to 2.3 cm and gradually increases with a change in the position of the profile reconstruction (see the blue, red, and green lines in Fig. 3). 4. Conclusion In this paper, the results of experimental studying the deformations of the circular silicon X-ray FZP by diffraction imaging technique were presented. The experiment was performed at the ID06 ESRF beamline using 12.4 keV radiation energy. The set of images of the 220 reflection was recorded during the FZP rotation in the angular range of ±0.25 o . As a result, the deformed shape of the FZP was found. The maximum deformation amplitude of the FZP surface was observed in the center of the FZP and was about 0.5 µm. The calculated curvature radius at the center of the FZP was 2.3 cm. The deformation of the FZP may be related to the intrinsic stresses in its diffraction structure resulting from the manufacturing process The X-ray diffraction imaging technique is well suited for studying deformation fields in a single crystal due to its high sensitivity to the angular orientation of the crystal structure in a monochromatic beam. It should be noted that in addition to the conventional binary X-ray FZP, the presented approach can also be used in studying the Multilayer Laue Lenses (see Bajt et al. (2018)) or zone plates with multilevel (see Di Fabrizio et al. (1999)) or kinoform profile (see Gorelick et al. (2019)). Acknowledgements The research was conducted with the financial support of the Ministry of Science and Higher Education of the Russian Federation, Contract № 075 -15-2021-966 from 30.09.2021. References Snigirev, A., Kohn, V., Snigireva, I. and Lengeler, B., ‘A compound refractive lens for focusing high -energy X- rays’, Nature 384(6604), 49 (1996). Snigirev, A. and Snigireva, I., ‘High energy X -ray micro- optics’, Comptes Rendus Phys. 9(5 – 6), 507 – 516 (2008). Zverev, D., Barannikov, A., Snigireva, I. and Snigirev, A., ‘X - ray refractive parabolic axicon lens’ , Opt. Express 25(23), 28469 (2017). Snigirev, A., Snigireva, I., Kohn, V., Yunkin, V., Kuznetsov, S., Grigoriev, M. B., Roth, T., Vaughan, G. and Detlefs, C., ‘X -ray nanointerferometer based on Si refractive bilenses’, Phys. Rev. Lett. 103(6), 064801 (200 9). Snigirev, A., Snigireva, I., Lyubomirskiy, M., Kohn, V., Yunkin, V. and Kuznetsov, S., ‘X -ray multilens interferometer based on Si refractive lenses’, Opt. Express 22(21), 25842 (2014). Snigirev, A., Zverev, D., Snigireva, I., Sorokovikov, M., Kuznetso v, S. and Yunkin, V., ‘Coherent X -ray beam expander based on a multilens interferometer’, Opt. Express, Vol. 29, Issue 22, pp. 35038 -35053 29(22), 35038 – 35053 (2021). Narikovich, A., Polikarpov, M., Barannikov, A., Klimova, N., Lushnikov, A., Lyatun, I., Bourenkov, G., Zverev, D., Panormov, I., Sinitsyn, A., Snigireva, I. and Snigirev, A., ‘CRL -based ultra-compact transfocator for X- ray focusing and microscopy’, J. Synchrotron Radiat. 26, 1208 – 1212 (2019). Zverev, D., Snigireva, I. and Snigirev, A., ‘Beam -shaping elements based on x- ray refractive optics: theory, modeling, and experiment’, Adv. Comput. Methods X-Ray Opt. V 11493, K. Sawhney and O. Chubar, Eds., 18 (2020). Zverev, D., Snigireva, I., Kohn, V., Kuznetsov, S., Yunkin, V. and Snigirev, A., ‘X -ray phase-sensitive imaging using a bilens interferometer based on refractive optics’, Opt. Express 28(15), 21856 (2020).