Abstract
It is well known that light is reflected and transmitted with a change in the direction of propagation at an interface between two media which have different optical properties. The effects known as reflection and refraction are easy to observe in the visible spectrum but more difficult when x-ray radiation is used (see the introduction for a historical presentation). The major reason for this is the fact that the refractive index of matter for x-ray radiation does not differ very much from unity, so that the direction of the refracted beam does not deviate much from the incident one. The reflection of x-rays is however of great interest in surface science, since it allows the structure of the uppermost layers of a material to be probed. In this chapter, we present the general optical formalism used to calculate the reflectivity of smooth or rough surfaces and interfaces which is also valid for x-rays.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Fresnel Mémoires de l’Académie 11, 393 (1823).
A.H. Compton, Phil. Mag, 45, 1121 (1923).
R. Forster, Helv. Phys. Ada., 1, 18 (1927).
H. Kiessig, Ann. Der Physik, 10, 715 (1931).
J.A. Prins, Z. Phys., 47, 479 (1928).
L.G. Parrat, Phys. Rev. 95, 359 (1954).
F. Abélès, Ann. de Physique 5, 596 (1950).
R.W. James, The optical principles of the diffraction of x-rays, G. Bell and Sons, London, (1967).
International tables for x-ray crystallography, The Kynoch Press, Birmingham, 1968. vol. IV.
R. Petit, Ondes Electromagnétiques en radioélectricité et en optique, Ed. Masson (1989).
M. Born and E. Wolf, Principles of Optics, Pergamon, London, 6th Edition (1980).
B. Vidal and P. Vincent, Applied Optics, 23, 1794 (1984).
J. Lekner, Theory of reflection of electromagnetic and particle waves, Martinus Nijhoff Publishers (1987).
T. P. Russel, Mater. Science Rep. 5, 171 (1990).
A. Gibaud, D. McMorrow and P. P. Swadling, J. Phys. Condens. Matter 7, 2645 (1995).
J.W.S. Rayleigh, Proc. Roy. Soc., 86, 207 (1912).
I. W. Hamley and J. S. Pedersen, Appl. Cryst. 27, 29 (1994).
G. Vignaud, Thèse de l’Université du Maine (1997).
J. Als-Nielsen, Z. Phys. B 61, 411 (1985).
I.M. Tidswell, B.M. Ocko, P.S. Pershan, S.R. Wassermann, G.M. Whitesides, J.D. Axe, Phys. Rev. B 41, 1111 (1990).
G. Vignaud, A. Gibaud, G. Grübel, S. Joly, D. Ausserré, J.F. Legrand, Y. Gallot, Physica B 248, 250 (1998).
L. Névot and P. Croce, Revue de Physique appliquée, 15, 761 (1980).
M. Tolan, Rontgenstreuung an strukturierten Oberflächen Experiment &Theorie Ph.D. Thesis, Christian-Albrechts Universität, Kiel, (1993)
Lord Rayleigh, Proc. R. Soc. London A 79, 339 (1907).
S.O. Rice, Com. Pure Appl. Math. 4, 351 (1951).
D.V. Roschchupkin, M. Brunel, F. de Bergevin, A.I. Erko, Nuclear Inst. Meth. B 72, 471 (1992).
S.K. Sinha, E.B. Sirota, S. Garroff and H.B. Stanley, Phys. Rev. B, 38, 2297 (1988).
D.K.G. de Boer, Phys. Rev. B 49, 5817 (1994).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Gibaud, A. (1999). Specular Reflectivity from Smooth and Rough Surfaces. In: X-ray and Neutron Reflectivity: Principles and Applications. Lecture Notes in Physics Monographs, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48696-8_3
Download citation
DOI: https://doi.org/10.1007/3-540-48696-8_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66195-5
Online ISBN: 978-3-540-48696-1
eBook Packages: Springer Book Archive