Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-06-16T20:47:31.216Z Has data issue: false hasContentIssue false
  • English
  • Français

Determination of depth profiles from X-ray diffraction data

Published online by Cambridge University Press:  10 January 2013

Paul Predecki
Paul Predecki
Affiliation:
Engineering Department, University of Denver, Denver, Colorado 80208USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A direct method is described for determining depth profiles (z-profiles) of diffraction data from experimentally determined τ-profiles, where z is the depth beneath the sample surface and τ is the 1/e penetration depth of the X-ray beam. With certain assumptions, the relation between these two profile functions can be expressed in the form of a Laplace transform. The criteria for fitting experimental τ-data to functions which can be utilized by the method are described. The method was applied to two τ-data sets taken from the literature: (1) of residual strain in an A1 thin film and (2) of residual stress in a surface ground A12O3/5vol% TiC composite. For each data set, it was found that the z-profiles obtained were of two types: oscillatory and nonoscillatory. The nonoscillatory profiles appeared to be qualitatively consistent for a given data set. The oscillatory profiles were considered to be not physically realistic. For the data sets considered, the nonoscillatory z-profiles were found to lie consistently above the corresponding τ-profiles, and to approach the τ-profiles at large z, as expected from the relation between the two.

Type
Research Article
Information
Powder Diffraction , Volume 8 , Issue 2 , June 1993 , pp. 122 - 126
Copyright
Copyright © Cambridge University Press 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

Cohen, J. B., Dolle, H., and James, M. R. (1980). “Accuracy in powder diffraction,” NBS Special Publication No. 567 (U.S. Govt. Printing Office, Washington, D.C.), pp. 453–477.Google Scholar
Doerner, M. F., and Brennan, S. (1988). J. Appl. Phys., 63, 126–131.CrossRefGoogle Scholar
Dolle, H. (1979). J. Appl. Cryst. 12, 489–501.CrossRefGoogle Scholar
Eigenmann, B., Scholtes, B., and Macherauch, E. (1989). Mater. Sci. Eng. A118, 1–17.CrossRefGoogle Scholar
Erdelyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F. G. (1954). The Bateman Manuscript Project, Tables of Integral Transforms, Vol. I (McGraw Hill, New York).Google Scholar
Fillit, R. Y., and Perry, A. J. (1988). Surface and Coatings Technology 36, 647–659.CrossRefGoogle Scholar
Hall, E. O. (1951). Proc. Phys. Soc. B64, 747.Google Scholar
Hauk, V. M. (1984). Adv. X-ray Anal. 27, 101–120.Google Scholar
Houska, C. R. (1980). “Treatise on Materials Science and Technology” in Experimental Methods, Part A, edited by Herman, H. (Academic, New York), Vol. 19A, pp. 63–105.CrossRefGoogle Scholar
Hwang, Bing, and Houska, C. R. (1988). J. Appl. Phys. 63 5351–5356.Google Scholar
Noyan, I. C. (1984). Metall Trans. A 14A, 249–258.Google Scholar
Noyan, I. C., and Cohen, J. B. (1984). Adv. X-ray Anal. 27, 129–148.Google Scholar
Noyan, I. C., and Cohen, J. B. (1987). Residual Stress, Measurement by Diffraction and Interpretation (Springer Verlag, New York), p. 144.Google Scholar
Petch, N. J. (1953). JISI 173, 25.Google Scholar
Predecki, P. K., Zhu, X., and Ballard, B. (1993). Adv. X-ray Anal. 36.Google Scholar
Roll, E. D., Pangborn, R. N., and Amateau, M. F. (1987). Nondestructive Characterization of Materials II edited by Bussiere, J. F., Monchalin, J-P., Ruud, C. O., and Green, R. E. Jr., (Plenum, New York) pp. 595–603.CrossRefGoogle Scholar
Sasaki, T., Kuramoto, M., and Yoshioka, Y. (1984). Adv. X-ray Anal. 27, 121–128.Google Scholar
Shiraiwa, T., and Sakamoto, Y. (1972). Sumitomo Search 7, 109–135.Google Scholar
Shute, C. J., and Cohen, J. B. (1991). J. Appl. Phys. 70, 2104–2110.Google Scholar
Somers, M. A. J., and Mittemeijer, E. J. (1990). Metal. Trans. 21A, 189–204.Google Scholar
Warren, B. E., X-Ray Diffraction (Addison-Wesley, Reading, MA, 1969), p. 49.Google Scholar