, Volume 52, Issue 16, pp 2049–2053 | Cite as

Reflectometry of X-ray Whispering Gallery Waves Propagating along Liquid Meniscuses

  • L. I. GorayEmail author
  • V. E. Asadchikov
  • B. S. Roshchin
  • Yu. O. Volkov
  • A. M. Tikhonov


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).


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • L. I. Goray
    • 1
    • 2
    • 3
    Email author
  • V. E. Asadchikov
    • 4
  • B. S. Roshchin
    • 4
  • Yu. O. Volkov
    • 4
  • A. M. Tikhonov
    • 5
  1. 1.St. Petersburg Academic UniversitySt. PetersburgRussia
  2. 2.ITMO UniversitySt. PetersburgRussia
  3. 3.Institute for Analytical InstrumentationSt. PetersburgRussia
  4. 4.Shubnikov Institute of CrystallographyMoscowRussia
  5. 5.Kapitza Institute for Physical ProblemsMoscowRussia

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