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Nonlinear Neutron and X-Ray Reflectance for Surface Films

Published online by Cambridge University Press:  22 February 2011

Xiao-Lin Zhou
Xiao-Lin Zhou*
Affiliation:
Massachusetts Institute of Technology, 24-215, 77 Mass Ave., Cambridge, MA 02139, USA.
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Abstract

This paper presents an analysis of the relationship between Parratt's recurrence formula and several existing analytical formulations for the neutron and x-ray reflectance of a surface film. In particular, it was shown that the Born approximation and the weighted-superposition approximation (WSA) for the neutron and x-ray reflectance can both be derived directly from Parratt's recurrence formula. It was also shown that the well-known nonlinear differential equation for the reflectance at an arbitrary point inside a film can be obtained from Parratt's recurrence formula and the WSA was an approximate solution to this equation. Finally, the nonlinearity in the WSA was discussed through a comparison between the Born approximation and the WSA. It was pointed out that the exponential factor in the WSA correctly accounted for both the phase shift effect due to the scattering length density of the film and the amplitude attenuation effect due to evanescence.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 376: Symposium BB – Neutron Scattering in Materials Science , 1994 , 193
Copyright
Copyright © Materials Research Society 1995

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References

REFERENCES

1 Zhou, X.-L. and -H. Chen, S., "Theoretical Foundation of X-ray and Neutron Reflectometry", (to appear in Physics Reports, 1994).Google Scholar
2 Zhou, X.-L., Felcher, G. P. and Chen, S.-H., Physica B 173, 167–179 (1991).Google Scholar
3 Zhou, X.-L., -H. Chen, S. and Felcher, G. P., J. Phys. Chem., 95, 9025–9029(1991).Google Scholar
4 Zhou, X.-L., Chen, S.-H. and Felcher, G. P., in Inverse Problems in Scattering and Imaging. edited by Bertero, M. and Pike, E. R. (Hilger, Bristol, 1991) pp. 109-130.Google Scholar
5 Zhou, X.-L., -H. Chen, S., Chen, S.-H. and Felcher, G. P., Phys. Rev. A., 46, 1839 (1991).Google Scholar
6 Ishimaru, A., Wave Propagation and Scattering in Random Media. (Academic Press, New York, 1978), p. 71.Google Scholar
7 Vineyard, G. H., Phys. Rev. B, 26, 4146 (1982).Google Scholar
8 Sears, V. F., Phys. Rev. B 48 (17), 477–485 (1993).Google Scholar
9 Landau, L. D. and Lifshits, E. M., Quantum Mechanics. 3rd ed. (Pergamon Press, New York, 1977) pp. 164–189.Google Scholar
10 Zhou, X.-L. and He, L., Phys. Rev. E 49 (6), 5345–5353 (1994).Google Scholar
11 Parratt, G., Phys. Rev. 95, 359 (1954).Google Scholar
12 Jacobsson, J., in Progress in Optics, edited by Wolf, E., (North Holland, Amsterdam, 1966).Google Scholar
13 Als-Nielsen, J., Phys, Z.. B: Condensed Matter, 61, 411–414 (1985).Google Scholar
14 Warren, B. E., X-ray Diffraction. (Addison-Wesley, Reading, Mass, 1969).Google Scholar
15 Zhou, X.-L. and Chen, S.-H., Phys. Rev. E 47 (5), 3174 (1993).Google Scholar
16 Zhou, X.-L., Lee, L.-T., Chen, S.-H., and Strey, R., Phys. Rev. A 46 (10), 6479 (1992).Google Scholar
17 Chen, S.-H., Zhou, X.-L. and Carvalho, B. L., Progr. Colloid Polym Sci, 93, 85 (1993).Google Scholar