A low-wave-vector expansion for reflectivity

B. L. Carvalho; S. H. Chen

doi:10.1103/PhysRevE.47.743

Access by Xinjiang University

A low-wave-vector expansion for reflectivity

B. L. Carvalho

S. H. Chen

Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

PDF

Phys. Rev. E 47, 743 – Published 1 January, 1993

DOI: https://doi.org/10.1103/PhysRevE.47.743

Abstract

We expand an accurate, closed-form equation for the reflectivity in a power series around $q_{2}$ =0, where $q_{2}$ is the z component of the wave-vector transfer in a film of constant composition. We examine, in particular, the case where $q_{2}$ =0 at the critical edge. Such an example might be realized through a neutron-reflectivity experiment on a microemulsion that exhibits surface layering. We find the coefficients of this low-wave-vector expansion to be the moments of the scattering-length density profile. We demonstrate how the first moment of the profile can be obtained from an accurate reflectivity measurement.

References (12)

R. A. L. Jones, L. J. Norton, E. J. Kramer, R. J. Composto, R. S. Stein, T. P. Russell, A. Mansour, A. Karim, G. P. Felcher, M. H. Rafailovich, J. Sokolov, X. Zhao and S. A. Schwarz, Europhys. Lett. 12, 41 (1990).
I. M. Tidswell, B. M. Ocko, P. S. Pershan, S. R. Wasserman, G. M. Whitesides and J. D. Axe, Phys. Rev. B 41, 1111 (1990).
G. Swislow, D. Schwartz, B. M. Ocko, P. S. Pershan and J. D. Litster, Phys. Rev. A 43, 6815 (1991).
T. P. Russell, Mater. Sci. Rep. 5, 171 (1990).
T. L. Crowley, E. M. Lee, E. A. Simister and R. K. Thomas, Physica B 173, 143 (1991).
E. J. Kramer, Physica B 173, 189 (1991).
L. G. Parratt, Phys. Rev. 95, 359 (1954).
J. Als-Nielsen, Z. Phys. B 61, 411 (1985).
P. S. Pershan, A. Braslau, A. H. Weiss and J. Als-Nielsen, Phys. Rev. A 35, 4800 (1987).
M. K. Sanyal, S. K. Sinha, A. Gibaud, K. G. Huang, B. L. Carvalho, M. Rafailovich, J. Sokolov, X. Zhao, and W. Zhao (unpublished).
B. Pluis, J. M. Gay, J. W. M. Frenken, S. Gierlotka, J. E. Macdonald, A. A. Williams, N. Piggins and J. Als-Nielsen, Surf. Sci. 222, L845 (1989).
X. L. Zhou, L. T. Lee, S. H. Chen and R. Strey, Phys. Rev. A 46, 6479 (1992).

[c1] R. A. L. Jones, L. J. Norton, E. J. Kramer, R. J. Composto, R. S. Stein, T. P. Russell, A. Mansour, A. Karim, G. P. Felcher, M. H. Rafailovich, J. Sokolov, X. Zhao and S. A. Schwarz, Europhys. Lett. 12, 41 (1990).

[c2] I. M. Tidswell, B. M. Ocko, P. S. Pershan, S. R. Wasserman, G. M. Whitesides and J. D. Axe, Phys. Rev. B 41, 1111 (1990).

[c3] G. Swislow, D. Schwartz, B. M. Ocko, P. S. Pershan and J. D. Litster, Phys. Rev. A 43, 6815 (1991).

[c4] T. P. Russell, Mater. Sci. Rep. 5, 171 (1990).

[c5] T. L. Crowley, E. M. Lee, E. A. Simister and R. K. Thomas, Physica B 173, 143 (1991).

[c6] E. J. Kramer, Physica B 173, 189 (1991).

[c7] L. G. Parratt, Phys. Rev. 95, 359 (1954).

[c8] J. Als-Nielsen, Z. Phys. B 61, 411 (1985).

[c9] P. S. Pershan, A. Braslau, A. H. Weiss and J. Als-Nielsen, Phys. Rev. A 35, 4800 (1987).

[c10] M. K. Sanyal, S. K. Sinha, A. Gibaud, K. G. Huang, B. L. Carvalho, M. Rafailovich, J. Sokolov, X. Zhao, and W. Zhao (unpublished).

[c11] B. Pluis, J. M. Gay, J. W. M. Frenken, S. Gierlotka, J. E. Macdonald, A. A. Williams, N. Piggins and J. Als-Nielsen, Surf. Sci. 222, L845 (1989).

[c12] X. L. Zhou, L. T. Lee, S. H. Chen and R. Strey, Phys. Rev. A 46, 6479 (1992).

Physical Review E

Export citation

Export citation

A low-wave-vector expansion for reflectivity

Abstract

References (12)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation