Total internal reflection of x-rays is used to determine the thickness of thin films.

Slight above the critical angle of total reflection fringes show up in the angular dependence of the x-ray reflectivity. They are called Kiessig fringes and are used to determine the film thickness.

These fringes are already known to you via the papers of Parrat(1954) and Henke (1972).

In the following link there is a nice collection of formulars dealing with the optical constants involved with x-ray reflection and refraction:

https://www-ssrl.slac.stanford.edu/conferences/workshops/xrs2016/documents/hgs_sxr2016_sxrd.pdf

There are also investigations with respect to guide x-rays via fiber optics, i.e in this case hollow fibers:

Please have a look for paper tiltles here (see the section OSA recommended articles):

https://www.osapublishing.org/ao/abstract.cfm?uri=ao-28-1-19

The full text of the main paper mentioned there is here:

Article Soft x-ray transmission characteristics of hollowcore soda-g...