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Behavior of X-ray peak widths in the Wilkens model of a restrictedly random distribution of dislocations

  • András Borbély EMAIL logo , Gilles Guiglionda and Julian H. Driver
Published/Copyright: January 3, 2022
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International Journal of Materials Research
From the journal International Journal of Materials Research Volume 93 Issue 7

Abstract

The behavior of the width of X-ray Bragg peaks recorded from dislocated crystals has been investigated both numerically and experimentally. Numerical simulations based on the Wilkens model of a restrictedly random dislocation distribution have shown that the width of the X-ray peaks increases linearly in the modified Williamson-Hall (mWH) plot. The slope of the line is proportional to the square root of the average dislocation density. The method has been used to evaluate the dislocation densities in two texture components of a hot-deformed Al-2.5 wt.% Mg alloy, where peak broadening has additional sources.

Abstract

Die Verbreiterung der Bragg-Reflexe von Kristallen mit Versetzungen wurde numerisch und experimentell untersucht. Numerische Berechnungen nach dem Wilkens-Modell der begrenzt regellosen Verteilung von Versetzungen haben gezeigt, dass die Profilbreiten in der modifizierten Williamson-Hall Darstellung linear zunehmen, wobei die Steigung proportional zur Wurzel der mittleren Versetzungsdichte ist. Die Methode wurde angewandt, um die Versetzungsdichten in zwei Texturkomponenten einer warmverformten Al-2.5 Gew.% Mg Legierung zu bestimmen, wobei die Profilverbreiterung zusätzliche Ursachen hat.

Keywords: Plastic deformation; Dislocation density; X-ray Bragg peaks; Strain anisotropy

Dedicated to Professor Dr. Haël Mughrabi on the occasion of his 65th birthday

The authors thank to J. Wright from ESRF for his help during the measurements. A. B. acknowledges the financial support of the Region Rhône-Alpes and the Hungarian Research Found OTKA (T34999).

Dr. A. Borbély Eötvös Loránd University, Institute for General Physics P.O. Box 32, H-1518, Budapest, Hungary Tel.: +36 1 372 2805 Fax: +36 1 372 2811

References

1 Wilson, A.J.C.: Nuovo Cimento 1 (1955) 277.10.1007/BF02900634Search in Google Scholar

2 Krivoglaz, M.A.; Ryaboshapka, K.P.: Fiz. Met. Metalloved. 15 (1963) 18.Search in Google Scholar

3 Wilkens, M., in: J.A. Simmons, R. de It, R. Bullough (eds.), Fundamental Aspects of Dislocation Theory, Vol. II, National Bureau of Standards (US) Spec. Publ. No. 317, Washington, DC (1970) 1195.Search in Google Scholar

4 Groma, I.; Ungár, T.; Wilkens, M.: J. Appl. Cryst. 21 (1988) 47.10.1107/S0021889887009178Search in Google Scholar

5 Groma, I.: Phys. Rev. B 57 (1998) 7535.10.1103/PhysRevB.57.7535Search in Google Scholar

6 Székely, F.; Groma, I.; Lendvai, J.: Phys. Rev. B 62 (2000) 3093.10.1103/PhysRevB.62.3093Search in Google Scholar

7 Borbély, A.; Groma, I.: Appl. Phys. Lett. 79 (2001) 1772.10.1063/1.1404134Search in Google Scholar

8 Ungár, T.; Borbély, A.: Appl. Phys. Lett. 69 (1996) 3173.10.1063/1.117951Search in Google Scholar

9 Klimanek, P.; Kuzel, R. Jr.: J. Appl. Crystallogr. 21 (1988) 363.10.1107/S002188988800336XSearch in Google Scholar

10 Borbély, A.; Dragomir, J.; Ribarik, G.; Ungár, T.: submitted to J. Appl. Crystallogr. The computer program can be found at the homepage: http:\\metal.elte.hu\anizc.Search in Google Scholar

11 Williamson, G.K.; Hall, W.H.: Acta Metall. 1 (1953) 22.10.1016/0001-6160(53)90006-6Search in Google Scholar

12 Wilkens, M.: phys. stat. sol. (a) 2 (1970) 359.10.1002/pssa.19700020224Search in Google Scholar

13 Ungár, T.; Gubicza, J.; Ribárik, G.; Borbély A.: J. Appl. Cryst. 34 (2001) 298.10.1107/S0021889801003715Search in Google Scholar

14 Borbély, A.; Driver, J.H.; Ungár, T.: Acta Mater. 48 (2000) 2005.10.1016/S1359-6454(99)00457-7Search in Google Scholar

15 Popa, N.C.: J. Appl. Cryst. 31 (1998) 176.10.1107/S0021889897009795Search in Google Scholar

16 Ungár, T.; Tichy, G.: Phys. Stat. Sol. (a) 171 (1999) 425.10.1002/(SICI)1521-396X(199902)171:2<425::AID-PSSA425>3.0.CO;2-WSearch in Google Scholar

17 Delaire, F.; Raphanel, J.L.; Rey, C.: Acta Mater. 48 (2000) 1075.10.1016/S1359-6454(99)00408-5Search in Google Scholar

18 Maurice, C.; Driver, J.H.: Acta Mater. 45 (1997) 4627.10.1016/S1359-6454(97)00115-8Search in Google Scholar

19 Maurice, C.; Driver, J.H.: Acta Mater. 45 (1997) 4639.10.1016/S1359-6454(97)00117-1Search in Google Scholar

20 Borbély, A.; Driver, J.H., in: G. Gottstein, D.A. Molodov (eds.), Recrystallization and Grain Growth, Proc. First Joint Int. Conf., Springer-Verlag, Berlin (2001) 635.Search in Google Scholar
Received: 2002-02-20
Published Online: 2022-01-03

© 2002 Carl Hanser Verlag, München

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https://doi.org/10.3139/ijmr-2002-0116
Keywords for this article
Plastic deformation; Dislocation density; X-ray Bragg peaks; Strain anisotropy

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Editorial
  4. Articles/Aufsätze
  5. A model for the work hardening of WC–Co “hard metals”
  6. On the dispersion strengthening mechanisms in ODS materials
  7. Effect of hydrogen on the mechanical properties of the β titanium alloy Timetal® 21S
  8. Cyclic deformation behaviour of (α + β) titanium alloys under complex mechanical and physiological loading conditions
  9. Assessment of the influence of interdendritic shrinkage cavities on the thermo-mechanical fatigue behaviour of the nickel-base superalloy MAR-M247LC
  10. Effects of static strain aging on residual stress stability and alternating bending strength of shot peened AISI 4140
  11. On the possibilities to enhance the fatigue properties of ultrafine-grained metals
  12. New method of determining stress relaxation behavior in creep machines by controlled unloading
  13. Creep of binary Ni-rich NiTi shape memory alloys and the influence of pre-creep on martensitic transformations
  14. Interaction of high-cycle fatigue with high-temperature creep in superalloy single crystals
  15. A unified description of creep in pure and dispersion-strengthened copper
  16. A new interpretation of flow-stress measurements of high-purity NiAl below room temperature
  17. A mesoscopic plasticity model accounting for spatial fluctuations of plastic strains, internal stresses and dislocation densities
  18. Behavior of X-ray peak widths in the Wilkens model of a restrictedly random distribution of dislocations
  19. Dislocation structure and crystallite size distribution in hexagonal nanomaterials from X-ray peak profile analysis
  20. Werden gewichtsoptimiert konstruierte Bauteile durch die Verwendung von Leichtmetallen wirklich leichter?*)
  21. Strain-induced martensite formation in metastable austenitic steels with varying carbon content
  22. Isothermal bainitic transformation in low alloy steels: factors limiting prediction of the resulting material’s properties
  23. Fatigue damage evolution in a particulate-reinforced metal matrix composite determined by acoustic emission and compliance method
  24. Microstructure and modification mechanisms of Si phase in as-thixoformed alloy A356
  25. Influence of size effect on microstructural changes in cyclically deformed polycrystalline nickel
  26. Self-diffusion of 71Ge and 31Si in Si –Ge alloys
  27. On localised corrosive attack, stress corrosion cracking and corrosion fatigue effects in a hardmetal cutting-tool material
  28. The internal stress during growth of SiC single crystals
  29. Notifications/Mitteilungen
  30. Personal/Personelles
  31. Books/Bücher
  32. DGM Conferences/Training
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