Reflectometry of X-ray Whispering Gallery Waves Propagating along Liquid Meniscuses
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X-ray reflectometry of whispering galleries (WGs), which propagate along meniscuses of deionized water or silica hydrosols (Ludox® SM) enriched by Cs+ ions, was analyzed for the first time. The measurements were performed using the diffractometer with a moving tube-detector system. The X-ray beam rotation angle reached a maximum value of 4° on a silica hydrosol sample at CuKα radiation, while for H2O it is only 1°. The intensities of WG modes propagating near the surface of a concave meniscus were found from the rigorous solution of the respective Helmholtz equation and applying the Monte Carlo technique for the random surface. For analysis of intensities of the X-ray scattering we used a hybrid model of the liquid surface with the upper transition layer having sinusoidal ripples in which the concentration of levitating Cs+ ions has a maximum near the surface, derived from the experiment, while the concentration maximum for SiO2 particles with sizes of ~6–15 nm is positioned at the depth of ~15 nm from the hydrosol’s surface. Our numerical results for reflectances are in a good agreement with the experimental data.
This work was partially supported by the Federal Agency of Scientific Organizations (Agreement no. 007-GZ/Ch3363/26), Ministry of Education and Science of the Russian Federation (16.9789.2017/8.9) and Russian Foundation for Basic Research (17-02-00362, 16-29-11697).
- 8.V. E. Asadchikov, V. G. Babak, A. V. Buzmakov, Yu. P. Dorokhin, I. P. Glagolev, Yu. V. Zanevskii, V. N. Zryuev, Yu. S. Krivonosov, V. F. Mamich, L. A. Moseiko, N. I. Moseiko, B. V. Mchedlishvili, S. V. Savel’ev, R. A. Senin, L. P. Smykov, et al., Instrum. Exp. Tech. 48, 364 (2005).CrossRefGoogle Scholar
- 11.L. I. Goray and G. Schmidt, in Gratings: Theory and Numerical Applications, Ed. by E. Popov, 2nd ed. (AMU, Marseilles, 2014), p. 447.Google Scholar
- 12.B. M. Ocko, in Spectroscopic and Diffraction Techniques in Interfacial Electrochemistry, Ed. by C. Gutiérrez and C. Melendres (NATO Series, 1990), p. 343.Google Scholar
- 18.http://www.pcgrate.com/.Google Scholar