Phys. Rev. Lett. Phys. Rev. A Phys. Rev. B Phys. Rev. C Phys. Rev. D Phys. Rev. E Phys. Rev. ST AB Rev. Mod. Phys. Phys. Rev. (Series I) Phys. Rev. Volume: Page/Article:

Phys. Rev. B 38, 2297–2311 (1988)

[Issue 4 – 1 August 1988 ]

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X-ray and neutron scattering from rough surfaces

S. K. Sinha, E. B. Sirota, and S. Garoff

Corporate Research Science Laboratory, Exxon Research and Engineering Company, Clinton Township, Route 22 East, Annandale, New Jersey 08801

H. B. Stanley

University of Maryland, College Park, Maryland 20742

The scattering of x rays and neutrons from rough surfaces is calculated. It is split into specular reflection and diffuse scattering terms. These are calculated in the first Born approximation, and explicit expressions are given for surfaces whose roughness can be described as self-affine over finite length scales. Expressions are also given for scattering from liquid surfaces, where it is shown that ``specular'' reflections only exist by virtue of a finite length cutoff to the mean-square height fluctuations. Expressions are also given for the scattering from randomly oriented surfaces, as studied in a typical small-angle scattering experiment. It is shown how various well-known asymptotic power laws in S(q) are obtained from the above theory. The distorted-wave Born approximation is next used to treat the case where the scattering is large (e.g., near the critical angle for total external reflection), and its limits of validity are discussed. Finally, the theory is compared with experimental results on x-ray scattering from a polished Pyrex glass surface.

©1988 The American Physical Society

URL: http://link.aps.org/abstract/PRB/v38/p2297
DOI: 10.1103/PhysRevB.38.2297
PACS: 78.20.Ci, 78.70.Ck, 61.12.Bt

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