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The Phase of Scattering Profiles & X-Ray/Neutron Reflectivity

Published online by Cambridge University Press:  22 February 2011

P.S. Pershan
P.S. Pershan*
Affiliation:
Division of Applied Sciences and the Physics Department, Harvard University, Cambridge, MA 02138-2901 USA, PACS No. 61.10.-i X-ray determination of structures by diffraction and scattering. 61.12.-q Neutron determination of structures by diffraction and scattering.
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Abstract

The phase problem that troubles x-ray diffraction is also a problem for x-ray and neutron reflectivity; however, there are a range of small angles just beyond the critical angle for which the reflectivity contains information on the phase of the surface scattering amplitude. In principle this phase information can be used to determine the asymmetry of the normal gradient of the scattering amplitude density. We discuss here practical conditions under which this symmetry can, or cannot, be extracted from reflectivity data.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 376: Symposium BB – Neutron Scattering in Materials Science , 1994 , 157
Copyright
Copyright © Materials Research Society 1995

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References

REFERENCES

1 Als-Nielsen, J., “X-ray reflectivity studies of liquid surfaces” in Handbook on Synchrotron Radiation, Vol. 3, edited by Brown, G. and Moncton, D. E., (Elsevier Science Publishers, 1991) p. 473.Google Scholar
2 Pershan, P.S., Faraday Discuss. Chem. Soc. 89, 231 (1990).Google Scholar
3 Pershan, P.S., Physica A 172, 17 (1991).Google Scholar
4 Schlossman, M.L. and Pershan, P.S. Pershan, P.S., “X-ray and Neutron Scattering from Liquid Surfaces” in Light Scattering By Liquid Surfaces and Complementary Techniques, edited by Langevin, D., (Marcel Dekker, New York, 1990) p. 365.Google Scholar
5 Als-Nielsen, J., “Diffraction refraction and absorption of x-rays and neutrons: A comparative exposition” in Neutron and synchrotron radiation for condensed matter studies, Vol. 1, edited by Baruchen, J., Hodeau, J.-L., Lehmann, M., Rengnard, J.-R. and Schlenker, C., (Springer, New York, 1993)Google Scholar
6 Russell, T.P., Mat. Sci. Repts. 5,171 (1990).Google Scholar
7 Cowley, R.A., “X-ray scattering from surfaces and interfaces” in Equilibrium structure and properties of surfaces and interfaces, edited by Gonis, A. and Stocks, G. M., (Plenum, New York, 1992) p. 1.Google Scholar
8 Chen, S.H., Zhou, X.L. and Carvalho, B.O., Prog, in Col. & Poly. Sci. 93, 85 (1993).Google Scholar
9 Hamley, I.W. and Pedersen, J.S., J. Appl. Cryst. 27,29 (1994).Google Scholar
10 Pedersen, J.S. and Hamley, I.W., J. Appl. Cryst. 27, 36 (1994).Google Scholar
11 Singh, N., Tirrell, M. and Bates, F.S., “Applications of Fourier synthesis methods to the analysis of specular reflectivity”, J. Appl. Cryst., 1994.Google Scholar
12 Zhou, X.-L. and Chen, S.-H., Phys. Rev. E 47, 3174 (1993).Google Scholar
13 Pershan, P.S., Phys. Rev. E 50, 2369 (1994).Google Scholar
14 Pershan, P.S. and Als-Nielsen, J., Phys. Rev. Lett. 52 ,759 (1984).Google Scholar
15 Pershan, P.S., Braslau, A., Weiss, A.H. and Als-Nielsen, J., Phys. Rev. A 35, 4800 (1987).Google Scholar
16 Kunz, K., Reiter, J., Götzelmann, A. and Stamm, M., Macromolecules 26,4316 (1993).Google Scholar
17 Berk, N.P. and Majkrzak, C.F., in proceedings of Materials Research Society, Boston, MA, 1994, pp. 762.,Google Scholar
18 Worcester, D.L., Physica B 183,139 (1991).Google Scholar
19 Sivia, D.S., Hamilton, W.A. and Smith, G.S., Physica B 173, 121 (1991).Google Scholar
20 Sivia, D.S., Hamilton, W.A., Smith, G.S., Rieker, T.P. and Pynn, R., J. Appl. Phys. 70, 732 (1991).Google Scholar
21 Vaknin, D., Kjaer, K., Ringsdorf, H., Blankenburg, R., Piepenstock, M., Diederich, A. and Lösche, M., Langmuir 9,1171 (1993).Google Scholar
22 Vaknin, D., Kjaer, K., Als-Nielsen, J. and Lösche, M., Biophys. J. 59, 1325 (1991).Google Scholar
23 Crowley, T.L., Lee, E.M., Simister, E.A. and Thomas, R.K., Physica B 173, 143 (1990) Workshop on Methods of Analysis and Interpretation of Neutron Reflectivity Data, Argonne II. (USA)Google Scholar
24 Sanyal, M.K., Sinha, S.K., Gibaud, A. and Huang, K.G., “Fourier reconstruction of density profiles of thin films using anomalous X-ray reflecitivty”, 1992.Google Scholar
25 Zhang, H., Gallagher, P.D., Satija, S.A., Lindstrom, R.M., Paul, R.L., Russell, T.P., Lambooy, P. and Kramer, E.J., Phys. Rev. Lett. 72,3044 (1994).Google Scholar
26 Satija, S.A., Zhang, H., Gallagher, P.D., Lindstrom, R.M., Paul, R.L., Russell, T.P., Lambooy, P. and Kramer, E.J., “Resonance enhanced neutron standing waves in thin films”, Proceedings of the Materials Society, 1994.Google Scholar
27 Ludwig, K.F. Jr., Warburton, W.K. and Fontaine, A., J.Chem. Phys. 87, 620 (1987).Google Scholar
28 Perahia, D., Weisler, D., Satija, S.K., Fetters, L.J. and Sinha, S.K., Phys. Rev. Lett. 72, 100 (1993).Google Scholar
29 Lurio, L.B., Rabedeau, T.A., Pershan, P.S., Silvera, I.F., Deutsch, M., Kosowsky, S.D. and Ocko, B.M., Phys. Rev. Lett. 68, 2628 (1992).Google Scholar
30 Lurio, L.B., Rabedeau, T.A., Pershan, P.S., Silvera, I.F., Deutsch, M., Kosowsky, S.D. and Ocko, B.M., Phys. Rev. B 48, 9644 (1993).Google Scholar