Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-23T06:55:05.539Z Has data issue: false hasContentIssue false
  • English
  • Français

Analyzing Specular Reflectivities with Parametric B-Splines

Published online by Cambridge University Press:  22 February 2011

N. F. Berk  and
C. F. Majkrzak
N. F. Berk
Affiliation:
Materials Science and Engineering Laborarory, National Institute of Standards and Technology, Gaithersburg, MD 20899-0001
C. F. Majkrzak
Affiliation:
Materials Science and Engineering Laborarory, National Institute of Standards and Technology, Gaithersburg, MD 20899-0001
Get access

Abstract

A method of using parametric B-spline curves to interpret neutron and x-ray specular reflectivity spectra is described. The introduction of parametric curves for scattering length density profiles greatly expands the function space accessible to low-dimensional representations but also requires means to restrict the space to physically acceptable functions. A practical fitting procedure is outlined, and two examples are shown.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 376: Symposium BB – Neutron Scattering in Materials Science , 1994 , 187
Copyright
Copyright © Materials Research Society 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1 Bartels, R. H., Beatty, J. C., and Barsky, B. A., An Introduction to Splines for use in Computer Graphics and Geometric Modeling (Morgan Kaufmann, Los Altos, 1987).Google Scholar
2 Berk, N. F. and Majkrzak, C. F., to be published. A version of this work first was presented at New Horizons: A Workshop on the State of the Art in Neutron Reflectivity, National Institute of Standards and Technology, Gaithersburg, MD, December 9-10, 1993.Google Scholar
3 Sivia, D. S., Hamilton, W. A., and Smith, G. S., Physica B 173, 121 (1991); and references therein.Google Scholar
4 Pedersen, J. S., J. Appl. Cryst. 25 129 (1992).Google Scholar
5 Singh, N., Tirrel, M., and Bates, F. S., J. Appl. Cryst. 26, 650 (1993).Google Scholar
6 -L. Zhou, X. and -H. Chen, S., Phys. Rev. E 47, 3174 (1993).Google Scholar
7 de Haan, V.-O., and Drijkoningen, G. G., Physica B 198, 24 (1994).Google Scholar
8 Kunz, K., Reiter, J., Götzelmann, A., and Stamm, M., Macromolecules 26, 4316 (1993).Google Scholar
9 Pedersen, J. S. and Hamley, I. W., J. Appl. Cryst., 27, 36 (1994); and references therein.Google Scholar
10 Jacoby, S. L. S., Kowalik, J. S., and Pizzo, J. T., Iterative Methods for Nonlinear Optimization Problems, (Prentice-Hall, Englewood Cliffs, 1972).Google Scholar
11 Yamada, S., Ebisawa, T., Achiwa, N., Akiyoshi, T., and Okamoto, S., Annu. Rep. Res. Reactor Inst. Kyoto Univ 11, 8 (1978).Google Scholar
12 Satija, S. K. and Russell, T. P., private communication.Google Scholar
13 Koenig, B.. Krueger, S., Orts, W. J., Berk, N. F., Majkrzak, C. F., and K., Gawrish, to be published.Google Scholar
14 Krueger, S. and Orts, W. J., private communication.Google Scholar
15 Koenig, B., private communication.Google Scholar
16 Ankner, J. F. and Majkrzak, C. F., Neutron Optical Devices and Applications Proceedings of the SPIE 1738. 260 (1992).Google Scholar