<i>X</i>-ray line profiles analysis of plastically deformed metals

András Borbély; Tamás Ungár

doi:10.1016/j.crhy.2011.12.004

Use of large scale facilities for research in metallurgy

X-ray line profiles analysis of plastically deformed metals
[Profils de raie en rayons X sur des matériaux métalliques déformés plastiquement]

András Borbély ¹ ; Tamás Ungár ²

¹ SMS Materials Centre and CNRS UMR 5146, École des mines de Saint Etienne, 158, cours Fauriel, 42023 Saint Etienne, France
² Department of Materials Physics, Eötvös University Budapest, P.O. Box 32, Budapest H-1518, Hungary

Comptes Rendus. Physique, Volume 13 (2012) no. 3, pp. 293-306.

Résumé
Abstract

Nous présentons la base théorique de lʼanalyse des profils de raie en rayons X, et son application à la caractérisation microstructurale de métaux déformés plastiquement. La microstructure est décrite en termes de taille de domaine cohérent, densité de défauts planaires, densité de dislocations et un paramètre dʼarrangement des dislocations. Nous introduisons deux méthodes dʼanalyse : la méthode des moments, et la méthode étendue dʼajustement par analyse Convolutional Multiple Whole Profile. Nous présentons des exemples dʼutilisation de ces mesures sur la déformation plastique de monocristaux, de monocristaux résidant dans le volume dʼun polycristal, et dans le cas de familles de grains constituant des composantes de texture. Les exemples sélectionnés montrent le potentiel de la technique dʼanalyse du profil de raies obtenues soit par des sources de laboratoire ou par rayonnement synchrotron.

The theoretical basis of X-ray line profile analysis and its application to microstructural characterization of plastically deformed metallic alloys is presented. The microstructure is described in terms of coherent domain size, planar fault density, dislocation density and a dislocation arrangement parameter. Two evaluation methods are introduced: the momentum method and the extended Convolutional Multiple Whole Profile fit procedure. Their use is exemplified on plastically deformed single crystals, single grains residing in the bulk of a polycrystal and family of grains making up texture components. The selected examples show the potential of X-ray line profile analysis applied to diffraction patterns recorded with laboratory or synchrotron sources.

Publié le : 2012-01-28

DOI : 10.1016/j.crhy.2011.12.004

Keywords: Metals and alloys, X-ray diffraction, Line profile analysis, Dislocation density, Planar faults
Mot clés : Métaux et alliages, Diffraction des rayons X, Analyse des profils de raie, Densité de dislocations, Défauts planaires

Affiliations des auteurs :

András Borbély ¹ ; Tamás Ungár ²

¹ SMS Materials Centre and CNRS UMR 5146, École des mines de Saint Etienne, 158, cours Fauriel, 42023 Saint Etienne, France
² Department of Materials Physics, Eötvös University Budapest, P.O. Box 32, Budapest H-1518, Hungary

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     title = {\protect\emph{X}-ray line profiles analysis of plastically deformed metals},
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     pages = {293--306},
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     number = {3},
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     doi = {10.1016/j.crhy.2011.12.004},
     language = {en},
}

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András Borbély; Tamás Ungár. X-ray line profiles analysis of plastically deformed metals. Comptes Rendus. Physique, Volume 13 (2012) no. 3, pp. 293-306. doi : 10.1016/j.crhy.2011.12.004. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2011.12.004/

Bibliographie
Cité par

[1] H.M. Rietveld Acta Cryst., 22 (1967), pp. 151-152

[2] J.I. Langford Accuracy in Powder Diffraction (S. Block; C.R. Hubbard, eds.), NBS Special Publication, vol. 567, National Bureau of Standards, Washington DC, 1980, p. 255

[3] R.A. Young; D.B. Wiles J. Appl. Cryst., 15 (1982), pp. 430-438

[4] M. Ahtee; L. Unonius; M. Nurmela; P. Suortti J. Appl. Cryst., 17 (1984), pp. 352-357

[5] H. Toraya J. Appl. Cryst., 19 (1986), pp. 440-447

[6] J.I. Langford; R. Delhez; Th.H. de Keijser; E.J. Mittemeijer Aust. J. Phys., 41 (1988), pp. 173-187

[7] D. Balzar J. Appl. Cryst., 28 (1995), pp. 244-245

[8] D. Balzar Defect and Microstructure Analysis from Diffraction (R.L. Snyder; H.J. Bunge; J. Fiala, eds.), IUCr Monographs on Crystallography, vol. 10, Oxford University Press, New York, 1999, p. 94

[9] A.R. Stokes; A.J.C. Wilson Proc. Cambridge Philos. Soc., 38 (1942), pp. 313-322

[10] B.E. Warren; B.L. Averbach J. Appl. Phys., 21 (1950), pp. 595-597

[11] E.F. Bertaut Acta Cryst., 3 (1950), pp. 14-18

[12] M.A. Krivoglaz; K.P. Rjaboshapka Fiz. Metallov Metalloved., 15 (1963), pp. 18-31

[13] M.A. Krivoglaz Theory of X-ray and Thermal Neutron Scattering by Real Crystals, Springer-Verlag, Berlin, 1996

[14] M. Wilkens Phys. Stat. Sol. (a), 2 (1970), pp. 359-370

[15] M. Wilkens, in: J.A. Simmons, R. de Wit, R. Bullough (Eds.), Fundamental Aspects of Dislocation Theory, vol. II, Spec. Publ. No. 317, Nat. Bur. Stand. (US), Washington, DC, USA, 1970, p. 1195.

[16] I. Gaál Proc. 5th Riso Int. Symp. Met. Mat. Sci. (N.H. Andersen et al., eds.), Risø Nat. Lab., Roskilde, Denmark, 1984, pp. 245-254

[17] I. Groma; T. Ungár; M. Wilkens J. Appl. Cryst., 21 (1989), pp. 47-53

[18] T. Ungár; I. Groma; M. Wilkens J. Appl. Cryst., 22 (1989), pp. 26-34

[19] I. Groma Phys. Rev. B, 57 (1998), pp. 7535-7542

[20] A. Borbély; I. Groma Appl. Phys. Lett., 79 (2001), pp. 1772-1774

[21] L. Velterop; R. Delhez; Th.H. de Keijser; E.J. Mittemeijera; D. Reefman J. Appl. Cryst., 33 (2000), pp. 296-306

[22] E. Estevez-Rams; A. Penton-Madrigal; R. Lora-Serrano; J. Martinez-Garcia J. Appl. Cryst., 34 (2001), pp. 730-736

[23] P. Scardi; M. Leoni Acta Cryst. A, 58 (2002), pp. 190-200

[24] E. Estevez-Rams; M. Leoni; P. Scardi; B. Aragon-Fernandez; H. Fuess Phil. Mag. A, 83 (2003), pp. 4045-4057

[25] M.M.J. Treacy; J.M. Newsam; M.W. Deem Proc. Roy. Soc. London A, 433 (1991), pp. 499-520

[26] T. Ungár; I. Dragomir; Á. Révész; A. Borbély J. Appl. Cryst., 32 (1999), pp. 992-1002

[27] T. Ungár; J. Gubicza; G. Ribárik; A. Borbély J. Appl. Cryst., 34 (2001), pp. 298-310

[28] L. Balogh; G. Ribárik; T. Ungár J. Appl. Phys., 100 (2006), p. 023512

[29] L. Balogh; G. Tichy; T. Ungár J. Appl. Cryst., 42 (2009), pp. 580-591

[30] G. Ribárik; T. Ungár; J. Gubicza J. Appl. Cryst., 34 (2001), pp. 669-676

[31] T. Ungár; H. Mughrabi; M. Wilkens Acta Metall., 30 (1982), pp. 1861-1867

[32] T. Ungár; H. Mughrabi; D. Rönnpagel; M. Wilkens Acta Metall., 32 (1984), pp. 333-342

[33] E. Schafler; K. Simon; S. Bernstorff; P. Hanák; G. Tichy; T. Ungár; M.J. Zehetbauer Acta Mater., 53 (2005), pp. 315-322

[34] P. Cordier; T. Ungár; L. Zsoldos; G. Tichy Nature, 428 (2004), pp. 837-840

[35] T. Ungár; G. Ribárik; L. Balogh; A.A. Salem; S.L. Semiatin; G. Vaughan Scripta Mater., 63 (2010), pp. 69-72

[36] P. Scardi; M. Leoni Diffraction Analysis of the Microstructure of Materials (E.J. Mittemeijer; P. Scardi, eds.), Springer Ser. Mater. Sci, vol. 68, Springer-Verlag, Berlin, 2004, p. 51

[37] G. Ribárik; J. Gubicza; T. Ungár Mater. Sci. Eng. A, 387–389 (2004), pp. 343-347 http://www.renyi.hu/cmwp (a free software can be found at the homepage:)

[38] P. Scardi; M. Leoni Acta Mater., 53 (2005), pp. 5229-5239

[39] R.W. James The Optical Principles of the Diffraction of X-Rays, G. Bell and Sons, Ltd., London, 1965

[40] P. Scardi; M. Leoni; R.J. Delhez J. Appl. Cryst., 37 (2004), pp. 381-390

[41] J.I. Langford; D. Louër Rep. Progr. Phys., 59 (1996), pp. 131-234

[42] Ch.D. Terwilliger; Y.M. Chiang Acta Metall. Mater., 43 (1995), pp. 319-328

[43] C.E. Krill; R. Birringer Phil. Mag. A, 77 (1998), pp. 621-640

[44] M. Leoni; P. Scardi J. Appl. Cryst., 37 (2004), pp. 629-634

[45] A.J.C. Wilson X-ray Optics, Methuen, London, 1962

[46] A.J.C. Wilson Proc. Phys. Soc., 80 (1962), p. 286

[47] A.J.C. Wilson Proc. Phys. Soc., 81 (1963), p. 41

[48] J.I. Langford; A.J.C. Wilson J. Appl. Cryst., 11 (1978), pp. 102-113

[49] J.I. Langford; D. Louër; P. Scardi J. Appl. Cryst., 33 (2000), pp. 964-974

[50] N.C. Popa; D. Balzar J. Appl. Cryst., 35 (2002), pp. 338-346

[51] B. Clausen; C.N. Tome; D.W. Brown; S.R. Agnew Acta Mater., 56 (2008), pp. 2456-2468

[52] L. Wu; S.R. Agnew; D.W. Brown; G.M. Stoica; B. Clausen; A. Jain; D.E. Fielden; P.K. Liaw Acta Mater., 56 (2008), pp. 3699-3707

[53] W. Massa; S. Wocadlo; S. Lotz; K.Z. Dehnicke Anorg. Allg. Chem., 589 (1990), pp. 79-88

[54] http://metal.elte.hu/~evente/stacking

[55] B.E. Warren X-Ray Diffraction, Dover Publications, New York, 1990

[56] B.E. Warren; B.L. Averbach J. Appl. Phys., 23 (1952), pp. 497-498

[57] V.M. Kaganer; R. Köhler; M. Schmidbauer; R. Opitz; B. Jenichen Phys. Rev. B, 55 (1997), pp. 1793-1810

[58] M. Wilkens; K. Hertz; H. Mughrabi Z. Metallk., 71 (1980), p. 376

[59] F. Székely; I. Groma; J. Lendvai Phys. Rev. B, 62 (2000), pp. 3093-3098

[60] F. Székely; I. Groma; J. Lendvai Mat. Sci. Eng. A, 309 (2001), pp. 352-355

[61] F. Székely; I. Groma; J. Lendvai Scripta Mater., 45 (2001), pp. 55-60

[62] I. Groma; G. Monnet J. Appl. Cryst., 35 (2002), pp. 589-593

[63] H. Mughrabi; T. Ungár; W. Kienle; M. Wilkens Phil. Mag. A, 53 (1986), pp. 793-813

[64] B. Jakobsen; H.F. Poulsen; U. Lienert; W. Pantleon Acta Mater., 55 (2007), pp. 3421-3430

[65] R. Barabash Mat. Sci. Eng. A, 309–310 (2001), pp. 49-54

[66] A. Borbély; C. Maurice; J.H. Driver J. Appl. Cryst., 41 (2008), pp. 747-753

[67] A. Borbély; A. Révész; I. Groma Z. Kristallogr. Suppl., 23 (2006), pp. 87-92

[68] A. Borbély; J. Dragomir; G. Ribarik; T. Ungár J. Appl. Cryst., 36 (2003), pp. 160-162 http://metal.elte.hu/anizc (a free computer program is available at:)

[69] N.C. Popa J. Appl. Cryst., 31 (1998), pp. 176-180

[70] T. Ungár; G. Tichy Phys. Stat. Sol. A, 147 (1999), pp. 425-434

[71] K. Máthis; K. Nyilas; A. Axt; I.D. Cernatescu; T. Ungár; P. Lukáč Acta Mater., 52 (2004), pp. 2889-2894

[72] K. Máthis; F. Chmelík; Z. Trojanová; P. Lukáč; J. Lendvai Mat. Sci. Eng. A, 387–389 (2004), pp. 331-335

[73] T. Ungár J. Powder Diffr., 23 (2008), pp. 125-132

[74] I.P. Jones; W.B. Hutchinson Acta Metall., 29 (1981), pp. 951-968

[75] P.G. Partridge Metallurg. Rev., 118 (1968), pp. 169-193

[76] M.P. Miller; J.S. Park; P.R. Dawson; T.S. Han Acta Mater., 56 (2008), pp. 3927-3939

[77] S. Merkel; C.N. Tomé; H.R. Wenk Phys. Rev. B, 79 (2009), p. 064110

[78] R.A. Lebensohn; C.N. Tome; P. Castaneda Proc. Phil. Mag., 87 (2007), pp. 4287-4322

[79] E.M. Lauridsen; S. Schmidt; R.M. Suter; H.F. Poulsen J. Appl. Cryst., 34 (2001), pp. 744-750

[80] D. Juul Jensen; E.M. Lauridsen; L. Margulies; H.F. Poulsen; S. Schmidt; H.O. Sørensen; G.B.M. Vaughan Mater. Today, 9 (2006), pp. 18-25

[81] X. Fu; H.F. Poulsen; S. Schmidt; S.F. Nielsen; E.M. Lauridsen; D. Juul Jensen Scripta Mater., 49 (2003), pp. 1093-1096

[82] J. Wright ImageD11 http://sourceforge.net/projects/fable/files/ImageD11/

[83] T. Ungár; A. Borbély Appl. Phys. Lett., 69 (1996), pp. 3173-3175

[84] A. Borbély; J.H. Driver; T. Ungár Acta Mater., 48 (2000), pp. 2005-2016

[85] A. Borbély; G. Guiglionda; J.H. Driver Z. Metallk., 93 (2002), pp. 689-693

[86] G. Guiglionda; A. Borbély; J.H. Driver Acta Mater., 52 (2004), pp. 3413-3423

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