Dislocation Structure and Crystallite Size Distribution in Plastically Deformed Metals Determined by Diffraction Peak Profile Analysis

[+] Author and Article Information
T. Ungár, G. Ribárik, J. Gubicza, P. Hanák

Department of General Physics, Eötvös University Budapest, H-1518, P.O.B. 32, Budapest, Hungary

J. Eng. Mater. Technol 124(1), 2-6 (May 21, 2001) (5 pages) doi:10.1115/1.1418364 History: Received February 20, 2001; Revised May 21, 2001
Copyright © 2002 by ASME
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Gil Sevillano,  J., and Aernoudt,  E., 1987, “Low Energy Dislocation Structures in Highly Deformed Materials,” Mater. Sci. Eng., 86, pp. 35–51.
Bay,  B., Hansen,  N., Hughes,  D. A., and Kuhlmann-Wilsdorf,  D., 1992, “Evolution of fcc Deformation Structures in Polyslip,” Acta Metall. Mater., 40, pp. 205–219.
Hughes,  D. A., and Nix,  W. D., 1989, “Strain Hardening and Substructural Evolution in Ni-Co Solid Solutions at Large Strains,” Mater. Sci. Eng., A122, pp. 153–172.
Mughrabi,  H., 1983, “Dislocation Wall and Cell Structures and Long Range Internal Stresses in Deformed Metal Crystals,” Acta Metall., 31, pp. 1367–1379.
Ungár,  T., Mughrabi,  H., Rönnpagel,  D., and Wilkens,  M., 1984, “X-Ray Line Broadening Study of the Dislocation Cell Structure in Deformed [001]-Oriented Copper Single Crystals,” Acta Metall., 32, pp. 333–342.
Gaál, I., 1984, “Effect of Dislocation Distribution on the X-Ray Scattering from Deformed Metals,” Proc. 5th Riso Int. Symp. on Metallurgy and Material Science, N. Hessel Andersen, M. Eldrup, N. Hansen, D. Juul Jensen, T. Leffers, H. Lilholt, O. B. Pedersen and B. N. Singh, eds., Riso National Lab., Roskilde, Denmark, pp. 249–254.
Groma,  I., Ungár,  T., and Wilkens,  M., 1988, “Asymmetric X-Ray Line Broadening of Plastically Deformed Crystals. Part I: Theory,” J. Appl. Crystallogr., 21, pp. 47–53.
Krivoglaz,  M. A., Martynenko,  O. V., and Ryaboshapka,  K. P., 1983, “Influence of correlation in position of dislocations on X-ray diffraction by deformed crystals,” Phys. Met. Metallogr., 55, pp. 1–12.
M. A. Krivoglaz, 1996, Theory of X-ray and Thermal Neutron Scattering by Real Crystals, Plenum Press, N.Y. 1969; and X-ray and Neutron Diffraction in Nonideal Crystals, Springer-Verlag, Berlin Heidelberg, New York.
Wilkens,  M., and Bargouth,  M. O., 1968, “Die Bestimmung der Versetzungsdichte verformter kupfer Einkristalle aus Verbreiterten Roentgenbeugungsprofilen,” Acta Metall., 16, pp. 465–468.
Wilkens,  M., 1970, “The Determination of Density and Distribution of Dislocations in Deformed Single Crystals from Broadened X-Ray Diffraction Profiles,” Phys. Status Solidi A, 2, pp. 359–370.
M. Wilkens, 1970, “Theoretical Aspects of Kinematical X-ray Diffraction Profiles from Crystals Containing Dislocation Distributions,” Fundamental Aspects of Dislocation Theory, J. A. Simmons, R. de Wit, R. Bullough, eds., Vol. II. Nat. Bur. Stand. (US) Spec. Publ. No. 317, Washington, DC, USA, pp. 1195–1221.
Székely,  F., Groma,  I., and Lendvai,  J., 2001, “Statistic Properties of Dislocation Structures Investigated by X-ray Diffraction,” Mater. Sci. Eng., A, 309, pp. 352–355.
Groma,  I., 1998, “X-ray Line Broadening Due to an Inhomogeneous Dislocation Distribution,” Phys. Rev. B, 57, pp. 7535–7542.
Székely,  F., Groma,  I., and Lendvai,  J., 2000, “Characterization of Self-Similar Dislocation Patterns by X-ray Diffraction,” Phys. Rev. B, 62, pp. 3093–3098.
Wilkens, M., 1988, “X-ray diffraction line broadening and crystal plasticity,” Proc. 8th Int. Conf. Strength Met. Alloys (ICSMA 8), Tampere, Finland, P. O. Kettunen, T. K. Lepistö, M. E. Lehtonen, eds., Pergamon Press, pp. 47–152.
Williamson,  G. K., and Hall,  W. H., 1953, “X-Ray Line Broadening from Filed Aluminum and Wolfram,” Acta Metall., 1, pp. 22–31.
Warren,  B. E., and Averbach,  B. L., 1950, “The Effect of Cold Work Distortions on X-ray Pattern,” J. Appl. Phys., 21, pp. 595–610.
Louër,  D., Auffredic,  J. P., Langford,  J. I., Ciosmak,  D., and Niepce,  J. C., 1983, “A Precise Determination of the Shape, Size and Distribution of Size of Crystallites in Zinc Oxide by X-ray Line Broadening Analysis,” J. Appl. Crystallogr., 16, pp. 183–191.
Caglioti,  G., Paoletti,  A., and Ricci,  F. P., 1958, “Choice of Collimators for a Crystal Spectrometer for Neutron Diffraction,” Nucl. Instrum., 3, pp. 223–228.
Schwartz, L. H., and Cohen, J. B., 1977, Diffraction from Materials, Springer-Verlag, Berlin.
Klimanek,  P., and Kuzel,  R., 1988, “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, pp. 59–66.
van Berkum,  J. G. M., Vermuelen,  A. C., Delhez,  R., de Keijser,  T. H., and Mittemeijer,  E. J., 1994, “Applicabilities of the Warren-Averbach Analysis and an Alternative Analysis for Separation of Size and Strain Broadening,” J. Appl. Crystallogr., 27, pp. 345–357.
Ungár,  T., and Borbély,  A., 1996, “The effect of dislocation contrast on X-ray line broadening: a new approach to line profile analysis,” Appl. Phys. Lett., 69, pp. 3173–3175.
Scardi,  P., and Leoni,  M., 1999, “Fourier modelling of the anisotropic line broadening of X-ray diffraction profiles due to line and plane lattice defects,” J. Appl. Crystallogr., 32, pp. 671–682.
Chatterjee,  P., and Sen Gupta,  S. P., 1999, “Microstructural investigation of plastically deformed Pb(1−x)Snx alloys: an X-ray profile-fitting approach,” J. Appl. Crystallogr., 32, pp. 1060–1068.
Cheary,  R. W., Dooryhee,  E., Lynch,  P., Armstrong,  N., and Dligatch,  S., 2000, “X-ray diffraction line broadening from thermally deposited gold films,” J. Appl. Crystallogr., 33, pp. 1271–1283.
Le Bail,  A., and Jouanneaux,  A., 1997, “A Qualitative Account for Anisotropic Broadening in Whole-Powder-Diffraction-Pattern Fitting by Second-Rank Tensors,” J. Appl. Crystallogr., 30, pp. 265–271.
Dinnebier,  R. E., Von Dreele,  R., Stephens,  P. W., Jelonek,  S., and Sieler,  J., 1999, “Structure of sodium para-hydroxybenzoate, NaO2C−C6H4OH by powder diffraction: application of a phenomenological model of anisotropic peak width,” J. Appl. Crystallogr., 32, pp. 761–769.
Stephens,  P. W., 1999, “Phenomenological Model of Anisotropic Peak Broadening in Powder Diffraction,” J. Appl. Crystallogr., 32, pp. 281–288.
Wilkens,  M., 1987, “X-ray Line Broadening and MeanSquare Strains of Straight Dislocations in Elastically Anisotropic Crystals of Cubic Symmetry,” Phys. Status Solidi A, 104, pp. K1–K6.
Ungár,  T., and Tichy,  G., 1999, “The Effect of Dislocation Contrast on X-ray Line Profiles in Untextured Polycrystals,” Phys. Status Solidi A, 171, pp. 425–434.
Ungár,  T., Dragomir,  I., Révész,  A., and Borbély,  A., 1999, “The Contrast Factors of Dislocations in Cubic Crystals: the Dislocation Model of Strain Anisotropy in Practice,” J. Appl. Crystallogr., 32, pp. 992–1002.
Ungár,  T., Gubicza,  J., Ribárik,  G., and Borbély,  A., 2001, “Crystallite Size-Distribution and Dislocation Structure Determined by Diffraction Profile Analysis: Principles and Practical Application to Cubic and Hexagonal Crystals,” J. Appl. Crystallogr., 34, pp. 298–310.
Guinier, A., 1963, X-ray Diffraction, Freeman, San Francisco, CA.
Gubicza,  J., Szépvölgyi,  J., Mohai,  I., Zsoldos,  L., and Ungár,  T., 2000, “Particle size distribution and the dislocation density determined by high resolution X-ray diffraction in nanocrystalline silicon nitride powders,” Mater. Sci. Eng., A, 280, pp. 263–269.
Hinds, W. C. 1982, Aerosol Technology: Properties, Behavior and Measurement of Airbone Particles, Wiley, New York.
Krill,  C. E., and Birringer,  R., 1998, “Estimating Grain-Size Distribution in Nanocrystalline Materials from X-ray Diffraction Profile Analysis,” Philos. Mag. A, 77, pp. 621–640.
Ungár,  T., Ott,  S., Sanders,  P. G., Borbély,  A., and Weertman,  J. R., 1998, “Dislocations, grain size and planar faults in nanostructured copper determined by high resolution x-ray diffraction and a new procedure of peak profile analysis,” Acta Mater., 46, pp. 3693–3699.
Ribárik,  G., Ungár,  T., and Gubicza,  J., 2001, “MWP-fit: a Program for Multiple Whole Profile Fitting Using Theoretical Functions,” J. Appl. Crystallogr., 34, pp. 669–676.
Groma,  I., and Mohammed,  G., 2001, “Analysis of asymmetric broadening of X-ray line profiles caused by randomly distributed polarized dislocation dipoles and dislocation walls,” Acta Mater., submitted for publication.
Goettler,  E., 1973, “Versetzungstruktur und Verfestigung von 100-Kupfereinkristallen I. Versetzungsanordnung und Zellstruktur zugverformter Kristalle,” Philos. Mag., 28, pp. 1057–1076.


Grahic Jump Location
(a) The measured (open circles) and the fitted theoretical (solid line) Fourier coefficients as a function of the Fourier variable L for the specimen deformed by tension to 82 MPa. The differences between the measured and fitted values are also shown in the lower part of the figure. The indices of the reflections are also indicated. (b) The measured intensity profiles (open circles) and the inverse Fourier transform of the fitted Fourier coefficients (solid lines) for the specimen deformed by tension to 82 MPa. The differences between the measured and fitted intensity values are also shown in the lower parts of the linear scale plots.
Grahic Jump Location
Size distribution density-functions for the tensile deformed and the fatigued specimens



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