Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-06-22T01:09:31.416Z Has data issue: false hasContentIssue false
  • English
  • Français

Development of a Numerical Procedure for Determining the Depth Profiles of X-Ray Diffraction Data

Published online by Cambridge University Press:  06 March 2019

Xiaojing Zhu  and
Paul Predecki
Xiaojing Zhu
Affiliation:
Engineering Dept., University of Denver Denver, CO 80208, USA
Paul Predecki
Affiliation:
Engineering Dept., University of Denver Denver, CO 80208, USA
Get access

Abstract

A numerical procedure is described and demonstrated for determining z-profiles from measured τ-profiles of diffraction data such as may be obtained by grazing incidence x-ray diffraction (GIXD). The z-profile was approximated by a piece wise linear function and the problem of solving the integral equation for the z-profile was thus converted to one of solving a set of linear equations. With a sufficient number of the linear pieces, the z-pTofile could be accurately determined. The procedure and its sensitivity to data errors was tested with several arbitrarily chosen known functions. It was found that when errors were introduced into either the τ-profile or the sample thickness D the resulting z-profiles become oscillatory.

Type
Research Article
Information
Advances in X-Ray Analysis , Volume 37: Forty-Second Annual Conference on Applications of X-ray Analysis, August 2-6, 1993 , 1993 , pp. 197 - 203
Copyright
Copyright © International Centre for Diffraction Data 1993

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

Doerner, M.F., and Brennan, S. (1988). J. Appl. Phys., 63, 126–131.Google Scholar
Dolle, H. (1979). J. Appl. Cryst. 12, 489–501.Google Scholar
Eigenamnn, B., Scholtes, B., and Macherauch, E. (1989). Mater. Sci. Eng. A118, 1–17.Google Scholar
Predecki, P.K. (1993). Powder Diffr., 8[2], 122–126.Google Scholar
Predecki, P.K., Zhu, X., and Ballard, B. (1993). Adv. X-ray Anal. 36, 237–245.Google Scholar
Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (1992). “NumericalGoogle Scholar
Recipes in FORTRAN, The Art of Scientific Computing”, 2nd Ed.Google Scholar
Roll, E.D., Pangborn, R.R and Amateau, M. F. (1987). Nondestructive Characterization of Materials II edited by Bussiere, J.F., J-P. Monchalin, C. O. Ruud, and R. E, Green, Jr. (Plenum, New York). 595–603.Google Scholar