Home X-ray elastic constants determined by the combination of sin2 ψ and substrate-curvature methods
Article
Licensed
Unlicensed Requires Authentication

X-ray elastic constants determined by the combination of sin2 ψ and substrate-curvature methods

  • Ernst Eiper , Klaus J. Martinschitz , Jürgen W. Gerlach , Jürgen M. Lackner , Ivo Zizak , Nora Darowski and Jozef Keckes EMAIL logo
Published/Copyright: February 16, 2022
Become an author with De Gruyter Brill
Author Information
International Journal of Materials Research
From the journal International Journal of Materials Research Volume 96 Issue 9

Abstract

A new methodology is presented that allows the quantification of experimental X-ray elastic constants of polycrystalline thin films without use of special diffractometer attachments. The approach is based on the combination of sin2 ψ and curvature methods. The elastic strains in the polycrystalline films are characterized by the measurement of lattice spacings at different sample tilt angles, while the macroscopic stress in the film is calculated from the substrate curvature applying the Stoney formula. The radius of the curvature is determined from a sequence of rocking curves measured at different sample positions. The method is demonstrated on Al thin films deposited on Si(100) substrates. The X-ray diffraction measurements were performed at the synchrotron source BESSY in Berlin.

Keywords: X-ray diffraction; Synchrotron; Stress; Thin film; Aluminium
Dr. Jozef Keckes Erich Schmid Institute for Material Science Jahnstraße 12, A-8700 Leoben, Austria Tel.: +43 3842 804 301 Fax: +43 3842 804 116

Dedicated to Professor Dr. Dr. h. c. Hein Peter Stüwe on the occasion of his 75th birthday

References

[1] J.H. Lau: Thermal stress and strain in microelectronic packaging, ITP, New York (1993).10.1007/978-1-4684-7767-2Search in Google Scholar

[2] I.C. Noyan, J.B. Cohen: Residual stress: Measurement by diffraction and interpretation, Springer-Verlag, Berlin (1987).10.1007/978-1-4613-9570-6Search in Google Scholar

[3] P. van Houtte, L. de Buyser: Acta Mater. 41 (1993) 323.10.1016/0956-7151(93)90063-XSearch in Google Scholar

[4] H. Dölle: J. Appl. Cryst. 12 (1979) 489.10.1107/S0021889879013169Search in Google Scholar

[5] R.H. Marion, J.B. Cohen: Adv. X-ray Anal. 20 (1977) 355.10.1154/S0376030800011964Search in Google Scholar

[6] J. Keckes, M. Hafok, E. Eiper, R. Resel, C. Eisenmenger –Sittner: Powder Diff. 19 (2004) 367.10.1154/1.1815340Search in Google Scholar

[7] A. Segmüller, I.C. Noyan, V.S. Speriosu: Prog. Cryst. Growth Charact. Mater. 18 (1989) 21.10.1016/0146-3535(89)90024-5Search in Google Scholar

[8] J. Keckes: J. Appl. Cryst. 38 (2005) 311.10.1107/S0021889805001044Search in Google Scholar

[9] I.C. Noyan, C.E. Murray, J.S. Chey, C.C. Goldsmith: Appl. Phys. Lett. 85 (2004) 724.10.1063/1.1776331Search in Google Scholar

[10] G.G. Stoney: Proc. Roy. Soc. A 82 (1909) 172.10.1098/rspa.1909.0021Search in Google Scholar

[11] G. Dehm, B.J. Inkson, T. Wagner: Acta Mater. 50 (2002) 5021.10.1016/S1359-6454(02)00347-6Search in Google Scholar

[12] H. Wern, N. Koch, T. Maas: Mater. Sci. Forum 404 (2002) 127.10.4028/www.scientific.net/MSF.404-407.127Search in Google Scholar

[13] B.E. Warren: X-ray diffraction, Dover Publications, INC., New York (1990).Search in Google Scholar

[14] S.J. Rant, C.C. Goldsmith, I.C. Noyan: Adv. X-ray Anal. 37 (1994) 157.10.1154/S0376030800015640Search in Google Scholar

[15] I.C. Noyan, C.C. Goldsmith: Adv. X-ray Anal. 33 (1990) 137.10.1154/S0376030800019522Search in Google Scholar
Received: 2005-04-08
Accepted: 2005-05-12
Published Online: 2022-02-16

© 2005 Carl Hanser Verlag, München

Articles in the same Issue

  1. Frontmatter
  2. Kösterpreis
  3. Award/Preisverleihung
  4. Editorial
  5. Editorial
  6. Articles Basic
  7. Effect of interface strength on electromigration-induced inlaid copper interconnect degradation: Experiment and simulation
  8. Application of factor analysis in electron spectrometry (AES, XPS) for materials science
  9. Focussing and defocussing effects at radio frequency glow discharge optical emission spectroscopy analyses of thin films with partly nonconductive components
  10. Semi-flexible star-shaped molecules: conformational analysis of nano-segregated mesogens forming columnar liquid-crystal phases
  11. Articles Applied
  12. Structure, properties and applications of diamond-like carbon coatings prepared by reactive magnetron sputtering
  13. Local texture and back-end defect in hot extruded AZ91 magnesium alloy
  14. A comparison of thermal stability in nanocrystalline Ni- and Co-based materials
  15. Microstructure and phase formation of Heusler thin film compounds
  16. Correlation between the average composition of coherent superlattice and the GMR properties of electrodeposited Co–Cu/Cu multilayers
  17. Articles Basic
  18. Towards a description of complex pearlite structures
  19. Modeling of axial strain in free-end torsion of textured copper
  20. Vacancies in plastically deformed copper
  21. An analytic and generalized formulation of the sin2 ψ-method
  22. Nanoindentation applied on a tungsten–copper composite before and after high-pressure torsion
  23. Articles Applied
  24. The local deformation behaviour of MMCs – an experimental study
  25. X-ray elastic constants determined by the combination of sin2 ψ and substrate-curvature methods
  26. Combining complementary techniques to study precipitates in steels
  27. Precipitation hardening in Mg–Zn–Sn alloys with minor additions of Ca and Si
  28. Notifications/Mitteilungen
  29. Personal
https://doi.org/10.1515/ijmr-2005-0184
Keywords for this article
X-ray diffraction; Synchrotron; Stress; Thin film; Aluminium

Articles in the same Issue

  1. Frontmatter
  2. Kösterpreis
  3. Award/Preisverleihung
  4. Editorial
  5. Editorial
  6. Articles Basic
  7. Effect of interface strength on electromigration-induced inlaid copper interconnect degradation: Experiment and simulation
  8. Application of factor analysis in electron spectrometry (AES, XPS) for materials science
  9. Focussing and defocussing effects at radio frequency glow discharge optical emission spectroscopy analyses of thin films with partly nonconductive components
  10. Semi-flexible star-shaped molecules: conformational analysis of nano-segregated mesogens forming columnar liquid-crystal phases
  11. Articles Applied
  12. Structure, properties and applications of diamond-like carbon coatings prepared by reactive magnetron sputtering
  13. Local texture and back-end defect in hot extruded AZ91 magnesium alloy
  14. A comparison of thermal stability in nanocrystalline Ni- and Co-based materials
  15. Microstructure and phase formation of Heusler thin film compounds
  16. Correlation between the average composition of coherent superlattice and the GMR properties of electrodeposited Co–Cu/Cu multilayers
  17. Articles Basic
  18. Towards a description of complex pearlite structures
  19. Modeling of axial strain in free-end torsion of textured copper
  20. Vacancies in plastically deformed copper
  21. An analytic and generalized formulation of the sin2 ψ-method
  22. Nanoindentation applied on a tungsten–copper composite before and after high-pressure torsion
  23. Articles Applied
  24. The local deformation behaviour of MMCs – an experimental study
  25. X-ray elastic constants determined by the combination of sin2 ψ and substrate-curvature methods
  26. Combining complementary techniques to study precipitates in steels
  27. Precipitation hardening in Mg–Zn–Sn alloys with minor additions of Ca and Si
  28. Notifications/Mitteilungen
  29. Personal
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 22.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ijmr-2005-0184/html
Scroll to top button