# Study of the grazing-incidence X-ray scattering of strongly disturbed fractal surfaces

## Abstract

The applicability of different approaches to the description of hard X-ray scattering from rough surfaces is generally limited by a maximum surface roughness height of no more than 1 nm. Meanwhile, this value is several times larger for the surfaces of different materials subjected to treatment, especially in the initial treatment stages. To control the roughness parameters in all stages of surface treatment, a new approach has been developed, which is based on a series expansion of wavefield over the plane eigenstate-function waves describing the small-angle scattering of incident X-rays in terms of plane q-waves propagating through the interface between two media with a random function of relief heights. To determine the amplitudes of reflected and transmitted plane q-waves, a system of two linked integral equations was derived. The solutions to these equations correspond (in zero order) to the well-known Fresnel expressions for a smooth plane interface. Based on these solutions, a statistical fractal model of an isotropic rough interface is built in terms of root-mean-square roughness σ, two-point correlation length l, and fractal surface index h. The model is used to interpret X-ray scattering data for polished surfaces of single-crystal cadmium telluride samples.

- Authors:

- Russian Academy of Sciences, Shubnikov Institute of Crystallography, Federal Research Centre “Crystallography and Photonics” (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22645189

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Crystallography Reports; Journal Volume: 62; Journal Issue: 2; Other Information: Copyright (c) 2017 Pleiades Publishing, Inc.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; CADMIUM TELLURIDES; HARD X RADIATION; INTEGRAL EQUATIONS; MONOCRYSTALS; ROUGHNESS; SERIES EXPANSION; SMALL ANGLE SCATTERING; SURFACE TREATMENTS; X-RAY DIFFRACTION

### Citation Formats

```
Roshchin, B. S., E-mail: ross@crys.ras.ru, Chukhovsky, F. N., Pavlyuk, M. D., Opolchentsev, A. M., and Asadchikov, V. E.
```*Study of the grazing-incidence X-ray scattering of strongly disturbed fractal surfaces*. United States: N. p., 2017.
Web. doi:10.1134/S1063774517010205.

```
Roshchin, B. S., E-mail: ross@crys.ras.ru, Chukhovsky, F. N., Pavlyuk, M. D., Opolchentsev, A. M., & Asadchikov, V. E.
```*Study of the grazing-incidence X-ray scattering of strongly disturbed fractal surfaces*. United States. doi:10.1134/S1063774517010205.

```
Roshchin, B. S., E-mail: ross@crys.ras.ru, Chukhovsky, F. N., Pavlyuk, M. D., Opolchentsev, A. M., and Asadchikov, V. E. Wed .
"Study of the grazing-incidence X-ray scattering of strongly disturbed fractal surfaces". United States.
doi:10.1134/S1063774517010205.
```

```
@article{osti_22645189,
```

title = {Study of the grazing-incidence X-ray scattering of strongly disturbed fractal surfaces},

author = {Roshchin, B. S., E-mail: ross@crys.ras.ru and Chukhovsky, F. N. and Pavlyuk, M. D. and Opolchentsev, A. M. and Asadchikov, V. E.},

abstractNote = {The applicability of different approaches to the description of hard X-ray scattering from rough surfaces is generally limited by a maximum surface roughness height of no more than 1 nm. Meanwhile, this value is several times larger for the surfaces of different materials subjected to treatment, especially in the initial treatment stages. To control the roughness parameters in all stages of surface treatment, a new approach has been developed, which is based on a series expansion of wavefield over the plane eigenstate-function waves describing the small-angle scattering of incident X-rays in terms of plane q-waves propagating through the interface between two media with a random function of relief heights. To determine the amplitudes of reflected and transmitted plane q-waves, a system of two linked integral equations was derived. The solutions to these equations correspond (in zero order) to the well-known Fresnel expressions for a smooth plane interface. Based on these solutions, a statistical fractal model of an isotropic rough interface is built in terms of root-mean-square roughness σ, two-point correlation length l, and fractal surface index h. The model is used to interpret X-ray scattering data for polished surfaces of single-crystal cadmium telluride samples.},

doi = {10.1134/S1063774517010205},

journal = {Crystallography Reports},

number = 2,

volume = 62,

place = {United States},

year = {Wed Mar 15 00:00:00 EDT 2017},

month = {Wed Mar 15 00:00:00 EDT 2017}

}