Application of Different Diffraction Peak Profile Analysis Methods to Study the Structure Evolution of Cold-Rolled Hexagonal α-Titanium

  • Ivan V. IvanovEmail author
  • Daria V. Lazurenko
  • Andreas Stark
  • Florian Pyczak
  • Alexander Thömmes
  • Ivan A. Bataev


This paper presents a comparison between the “classical” and the modified Williamson–Hall and Warren–Averabach methods applied to an analysis of the microstructure of \(\alpha\)-titanium. The microstructural parameters of cold-rolled titanium specimens were retrieved from analysis of the X-ray diffraction (XRD) peaks. The high-quality XRD patterns were received at the P07 beamline (The High Energy Materials Science) at the German electron synchrotron. The dependence of the crystallite size, the inhomogeneous microstrains, the average dislocation density, the dislocation cut-off radius and some other parameters on the plastic strain were estimated. The results clearly indicate that, due to the consideration of the dislocation contrast effect, the modified models are a much better fit to the experimental data in comparison with the “classical” models. The results of hardness and corrosion resistance measurements of Ti samples can be explained based on the results obtained from the XRD analysis.


Titanium Severe plastic deformation (SPD) X-ray diffraction Diffraction peak profile analysis Crystallite size Dislocation density 



This work was supported by Ministry of Education and Science of the Russian Federation according to Federal Task 11.7662.2017/BCh.


  1. 1.
    M. Roy, V.K. Balla, A. Bandyopadhyay, S. Bose, MgO-doped tantalum coating on Ti: microstructural study and biocompatibility evaluation. ACS Appl. Mater. Interfaces 4(2), 577 (2012)CrossRefGoogle Scholar
  2. 2.
    S. Prasad, M. Ehrensberger, M.P. Gibson, H. Kim, E.A. Monaco, Biomaterial properties of titanium in dentistry. J. Oral Biosci. 57(4), 192 (2015). CrossRefGoogle Scholar
  3. 3.
    J.J. Gutierrez Moreno, M. Bonisch, N.T. Panagiotopoulos, M. Calin, D.G. Papageorgiou, A. Gebert, J. Eckert, G.A. Evangelakis, C.E. Lekka, Ab-initio and experimental study of phase stability of Ti–Nb alloys. J. Alloys Compd. 696, 481 (2017). CrossRefGoogle Scholar
  4. 4.
    V.V. Stolyarov, Y.T. Zhu, I.V. Alexandrov, T.C. Lowe, R.Z. Valiev, Influence of ECAP routes on the microstructure and properties of pure Ti. Mater. Sci. Eng. A 299(1–2), 59 (2001)CrossRefGoogle Scholar
  5. 5.
    M. Hoseini, P. Bocher, A. Shahryari, F. Azari, J.A. Szpunar, H. Vali, On the importance of crystallographic texture in the biocompatibility of titanium based substrate. J. Biomed. Mater. Res. A 102(10), 3631 (2014). CrossRefGoogle Scholar
  6. 6.
    A. Panigrahi, B. Sulkowski, T. Waitz, K. Ozaltin, W. Chrominski, A. Pukenas, J. Horky, M. Lewandowska, W. Skrotzki, M. Zehetbauer, Mechanical properties, structural and texture evolution of biocompatible Ti–45Nb alloy processed by severe plastic deformation. J. Mech. Behav. Biomed. Mater. 62, 93 (2016)CrossRefGoogle Scholar
  7. 7.
    C. Kittel, P. McEuen, P. McEuen, Introduction to Solid State Physics, vol. 8 (Wiley, New York, 1996)Google Scholar
  8. 8.
    J. Friedel, Dislocations: International Series of Monographs on Solid State Physics, vol. 3 (Elsevier, Amsterdam, 2013)Google Scholar
  9. 9.
    W.D. Callister, D.G. Rethwisch, Fundamentals of Materials Science and Engineering, vol. 471660817 (Wiley, London, 2000)Google Scholar
  10. 10.
    J. Lemaitre, Handbook of Materials Behavior Models, Three-Volume Set: Nonlinear Models and Properties (Elsevier, Amsterdam, 2001)Google Scholar
  11. 11.
    H. Parvin, M. Kazeminezhad, Two-internal variable thermodynamics modelling of severe plastic deformation: dislocation and flow stress evolutions. Mater. Sci. Technol. 31(14), 1788 (2015)CrossRefGoogle Scholar
  12. 12.
    R. Mahmoodian, N.S.M. Annuar, G. Faraji, N.D. Bahar, B.A. Razak, M. Sparham, Severe Plastic Deformation of Commercial Pure Titanium (CP-Ti) for Biomedical Applications: A Brief Review, Jom, pp. 1–8 (2017).
  13. 13.
    R. Valiev, Nanostructuring of metals by severe plastic deformation for advanced properties. Nat. Mater. 3(8), 511 (2004)CrossRefGoogle Scholar
  14. 14.
    R. Valiev, R.S. Musalimov, High-resolution transmission electron microscopy of nanocrystalline materials. Phys. Met. Metallogr. 78(6), 666 (1994)Google Scholar
  15. 15.
    G. Williamson, W. Hall, X-ray line broadening from filed aluminium and wolfram. Acta Metallurgica 1(1), 22 (1953)CrossRefGoogle Scholar
  16. 16.
    B. Warren, B. Averbach, The effect of cold-work distortion on X-ray patterns. J. Appl. Phys. 21(6), 595 (1950)CrossRefGoogle Scholar
  17. 17.
    T. Ungár, A. Borbély, The effect of dislocation contrast on X-ray line broadening: a new approach to line profile analysis. Appl. Phys. Lett. 69(21), 3173 (1996)CrossRefGoogle Scholar
  18. 18.
    T. Ungár, Dislocation model of strain anisotropy. Powder Diffr. 23(2), 125 (2008)CrossRefGoogle Scholar
  19. 19.
    N. Forouzanmehr, M. Nili-Ahmadabadi, M. Bönisch, The analysis of severely deformed pure Fe structure aided by X-ray diffraction profile. Phys. Met. Metallogr. 117(6), 624 (2016). CrossRefGoogle Scholar
  20. 20.
    G. Ashiotis, A. Deschildre, Z. Nawaz, J.P. Wright, D. Karkoulis, F.E. Picca, J. Kieffer, The fast azimuthal integration python library: pyFAI. J. Appl. Crystallogr. 48(2), 510 (2015)CrossRefGoogle Scholar
  21. 21.
    T. Ungár, G. Tichy, The effect of dislocation contrast on X-ray line profiles in untextured polycrystals. Physica Status Solidi (a) 171(2), 425 (1999)CrossRefGoogle Scholar
  22. 22.
    W.H. Hall, X-ray line broadening in metals. Proc. Phys. Soc. Sect. A 62(11), 741 (1949). CrossRefGoogle Scholar
  23. 23.
    M.A. Krivoglaz, Theory of X-Ray and Thermal Neutron Scattering by Real Crystals (Plenum Press, New York, 1969)Google Scholar
  24. 24.
    I. Dragomir, T. Ungár, Contrast factors of dislocations in the hexagonal crystal system. J. Appl. Crystallogr. 35(5), 556 (2002)CrossRefGoogle Scholar
  25. 25.
    P. Klimanek, R. Kužel, X-ray diffraction line broadening due to dislocations in non-cubic materials. I. general considerations and the case of elastic isotropy applied to hexagonal crystals. J. Appl. Crystallogr. 21(1), 59 (1988)CrossRefGoogle Scholar
  26. 26.
    T. Ungár, O. Castelnau, G. Ribárik, M. Drakopoulos, J. Béchade, T. Chauveau, A. Snigirev, I. Snigireva, C. Schroer, B. Bacroix, Grain to grain slip activity in plastically deformed Zr determined by X-ray micro-diffraction line profile analysis. Acta Materialia 55(3), 1117 (2007)CrossRefGoogle Scholar
  27. 27.
    J.I. Langford, A. Wilson, Scherrer after sixty years: a survey and some new results in the determination of crystallite size. J. Appl. Crystallogr. 11(2), 102 (1978)CrossRefGoogle Scholar
  28. 28.
    M. Wilkens, Theoretical aspects of kinematical X-ray diffraction profiles from crystals containing dislocation distributions (Fourier transform of X-ray diffraction line profiles from crystals with dislocations). NBS Fundamental Aspects of Dislocation Theory, vol. 2 (1970)Google Scholar
  29. 29.
    Y.I. Sirotin, M. Shaskolskaya, Basic Crystallophysics (Science, Moscow, 1979)Google Scholar
  30. 30.
    D. Tromans, Elastic anisotropy of HCP metal crystals and polycrystals. Int. J. Res. Rev. Appl. Sci 6(4), 462 (2011)Google Scholar
  31. 31.
    S.H. Nedjad, F.H. Nasab, M.M. Garabagh, S. Damadi, M.N. Ahmadabadi, X-ray diffraction study on the strain anisotropy and dislocation structure of deformed lath martensite. Metall. Mater. Trans. A 42(8), 2493 (2011)CrossRefGoogle Scholar
  32. 32.
    Z. Fan, B. Jóni, L. Xie, G. Ribárik, T. Ungár, Dislocation structure in textured zirconium tensile-deformed along rolling and transverse directions determined by X-ray diffraction line profile analysis. J. Nucl. Mater. 502(March), 301 (2018). CrossRefGoogle Scholar
  33. 33.
    I. Dragomir, D. Li, G. Castello-Branco, H. Garmestani, R. Snyder, G. Ribarik, T. Ungar, Evolution of dislocation density and character in hot rolled titanium determined by X-ray diffraction. Mater. Charact. 55(1), 66 (2005)CrossRefGoogle Scholar
  34. 34.
    J. Gubicza, I.C. Dragomir, G. Ribárik, Y.T. Zhu, R. Valiev, T. Ungár, in Materials Science Forum, vol. 414 (Trans Tech Publ, 2003), pp. 229–234Google Scholar
  35. 35.
    V. Stolyarov, Y. Zhu, T. Lowe, R. Islamgaliev, R. Valiev, A two step spd processing of ultrafine-grained titanium. Nanostruct. Mater. 11(7), 947 (1999)CrossRefGoogle Scholar
  36. 36.
    H. Mecking, U. Kocks, Kinetics of flow and strain-hardening. Acta Metall. 29(11), 1865 (1981)CrossRefGoogle Scholar
  37. 37.
    G.T. Gray III, High-strain-rate deformation: mechanical behavior and deformation substructures induced. Annu. Rev. Mater. Res. 42, 285 (2012)CrossRefGoogle Scholar
  38. 38.
    L. Tushinskii, Structural theory of structural strength of materials, in NGTU, Novosibirsk (2004) (in Russian) Google Scholar

Copyright information

© The Korean Institute of Metals and Materials 2019

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringNovosibirsk State Technical UniversityNovosibirskRussia
  2. 2.Institute of Materials ResearchHelmholz-Zentrum GeesthachtGeesthachtGermany

Personalised recommendations