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Correlation between subgrains and coherently scattering domains

  • T. Ungár (a1), G. Tichy (a2), J. Gubicza (a2) and R. J. Hellmig (a3)

Crystallite size determined by X-ray line profile analysis is often smaller than the grain or subgrain size obtained by transmission electron microscopy, especially when the material has been produced by plastic deformation. It is shown that besides differences in orientation between grains or subgrains, dipolar dislocation walls without differences in orientation also break down coherency of X-rays scattering. This means that the coherently scattering domain size provided by X-ray line profile analysis provides subgrain or cell size bounded by dislocation boundaries or dipolar walls.

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Audebrand N., Raite S., and Louër D. (2003). “The layer crystal structure of [In2(C2O4)3(H2O)3]∙7H2O and microstructure of nanocrystalline In2O3 obtained from thermal decomposition,” Solid State Sci.SSSCFJ 5, 783794.
Bakonyi I., Tóth-Kádár E., Pogány L., Cziráki A., Geröcs I., Varga-Josepovits K., Arnold B., and Wetzig K. (1996). “Preparation and characterization of dc-plated nanocrystalline nickel electrodeposits,” Surf. Coat. Technol.SCTEEJ 78, 124136.
Balzar D., Audebrand N., Daymond M. R., Fitch A., Hewat A., Langford J. I., Le Bail A., Louër D., Masson O., McCowan C. N., Popa N. C., Stephens P. W., and Toby B. H. (2004). “Size-strain line-broadening analysis of the ceria round-robin sample,” J. Appl. Crystallogr.JACGAR10.1107/S0021889804022551 37, 911924.
Bertaut E. F. (1950). “Raies de Debye-Scherrer et repartition des dimensions des domaines de Bragg dans les poudres polycristallines,” Acta Crystallogr.ACCRA910.1107/S0365110X50000045 3, 1418.
Bolmaro R. E., Brokmeier H. G., Signorelli J. W., Fourtz A., and Bertinetti M. A. (2004). “Interaction between phases in Co-deforming two-phase materials: The role of dislocation arrangements,” in Diffraction Analysis of the Microstructure of Materials, edited by Mittemeijer E. J. and Scardi P. (Springer, Berlin), 391 pp.
Boulle A., Legrand C., Guinebretière R., Mercurio J. P., and Dauger A. (2001). “Planar faults in layered bi-containing perovskites studied by X-ray diffraction line profile analysis,” J. Appl. Crystallogr.JACGAR 34, 699703.
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.JACGAR10.1107/S0021889800009936 33, 12711283.
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.JACGAR10.1107/S0021889899005233 32, 761769.
Estevez-Rams E., Leoni M., Scardi P., Aragon-Fernandez B., and Fuess H. (2003). “On the powder diffraction pattern of crystals with stacking faults,” Philos. Mag.PMHABF 83, 40454057.
Gaál I. (1984). Proceedings of the Fifth Riso International Symposium on Metallurgy and Material Science, edited by Andersen N. H. et al. , Riso National Laboratory, Roskilde, Denmark, 249 pp.
Gil Sevillano J. and Aernoudt E. (1987). “Low energy dislocation structures in highly deformed materials,” Mater. Sci. Eng.MSCEAA10.1016/0025-5416(87)90441-1 86, 3551.
Groma I. (1998). “X-ray line broadening due to an inhomogeneous dislocation distribution,” Phys. Rev. BPRBMDO10.1103/PhysRevB.57.7535 57, 75357542.
Groma I., Ungár T., and Wilkens M. (1988). “Asymmetric X-ray line broadening of plastically deformed crystals. 1. Theory,” J. Appl. Crystallogr.JACGAR10.1107/S0021889887009178 21, 4753.
Gubicza J., Chinh N. Q., Horita Z., and Langdon T. G. (2004). “Effect of Mg addition on microstructure and mechanical properties of aluminum,” Mater. Sci. Eng., AMSAPE3 387–389, 5559.
Gubicza J., Ribárik G., Bakonyi I., and Ungár T. (2001). “Crystallite-size distribution and dislocation structure in nanocrystalline HfNi5 determined by X-ray diffraction profile analysis,” J. Nanosci. Nanotechnol.JNNOAR10.1166/jnn.2001.039 1, 343348.
Gubicza J., Szépvölgyi J., Mohai I., Ribárik G., and Ungár T. (2000a). “The effect of heat-treatment on the grain-size of nanodisperse plasmathermal silicon nitride powder,” J. Mater. Sci.JMTSAS10.1023/A:1004800607605 35, 37113717.
Gubicza J., Szépvölgyi J., Mohai I., Zsoldos L., and Ungár T. (2000b). “Particle size distribution and the dislocation density determined by high resolution X-ray diffraction in nanocrystalline silicon nitride powders,” Mater. Sci. Eng. A 280, 263269.
Hellmig R. J., Baik S. C., Bowen J. R., Estrin Y., Juul Jensen D., Kim H. S., and Seo M. H. (2004). “Evolution of mechanical and microstructural properties of ECAP deformed copper,” in Proceedings of the Second International Conference on Nanomaterials by Severe Plastic Deformation: Fundamentals—Processing—Applications, Wien, Austria, 9–13 December 2002, edited by Zehetbauer M. J. and Valiev R. Z. (Wiley VCH, Weinheim), 420 pp.
Hinds W. C. (1982). Aerosol Technology: Properties, Behavior and Measurement of Airbone Particles (Wiley, New York).
Hughes D. A. and Hansen N. (1993). “Microstructural evolution in nickel during rolling from intermediate to large strains,” Metall. Trans. AMTTABN 24, 20212037.
Hughes D. A. and Hansen N. (2000). “Microstructure and strength of nickel at large strains,” Acta Mater.ACMAFD10.1016/S1359-6454(00)00082-3 48, 29853004.
Hughes D. A. and Nix W. D. (1989). “Strain hardening and substructural evolution in Ni–Co solid solutions at large strains,” Mater. Sci. Eng., AMSAPE310.1016/0921-5093(89)90627-8 122, 153172.
Ida T., Shimazaki S., Hibino H., and Toraya H. (2003). “Diffraction peak profiles from spherical crystallites with lognormal size distribution,” J. Appl. Crystallogr.JACGAR 36, 11071115.
Krill C. E. and Birringer R. (1998). “Estimating grain-size distributions in nanocrystalline materials from X-ray diffraction profile analysis,” Philos. Mag. APMAADG10.1080/014186198254281 77, 621640.
Krivoglaz M. A. (1996). X-ray and Neutron Diffraction in Nonideal Crystals (Springer, Berlin).
Kuhlmann-Wilsdorf D. (2002). “The LES theory of solid plasticity,” in Dislocations in Solids, edited by Nabarro F. R. N. and Duesbery M. S. (Elsevier Science, Amsterdam), 211 pp.
Langford J. I., Boultif A., Auffrédic J. P., and Louër D. (1993). “The use of pattern decomposition to study the combined X-ray diffraction effects of crystallite size and stacking faults in ex-oxalate zinc oxide,” J. Appl. Crystallogr.JACGAR10.1107/S0021889892007684 26, 2233.
Langford J. I. and Louër D. (1996). “Powder diffraction,” Rep. Prog. Phys.RPPHAG10.1088/0034-4885/59/2/002 59, 131234.
Langford J. I., Louër D., and Scardi P. (2000). “Effect of a crystallite size distribution on X-ray diffraction line profiles and whole-powder-pattern fitting,” J. Appl. Crystallogr.JACGAR10.1107/S002188980000460X 33, 964974.
Le Bail A. and Louër D. (1978). “Smoothing and validity of crystallite-size distributions from X-ray line-profile analysis,” J. Appl. Crystallogr.JACGAR 11, 5055.
Leoni M. and Scardi P. (2004). “Nanocrystalline domain size distributions from powder diffraction data,” J. Appl. Crystallogr.JACGAR 37, 629634.
Levine L. E. and Thomson R. (1997). “X-ray scattering by dislocations in crystals. General theory and application to screw dislocations,” Acta Crystallogr., Sect. A: Found. Crystallogr.ACACEQ10.1107/S0108767397005989 53, 590602.
Louër D., Auffrédic 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.JACGAR10.1107/S0021889883010237 16, 183191.
Macherauch E. (1980). “State-of-the-art and prospects of the X-ray stress analysis. 1,” Metall 34, 443452.
Marmy P., Yuzhen R., and Victoria M. J. (1991). “The tensile and fatigue properties of type-1.4914 ferritic steel for fusion reactor applications,” J. Nucl. Mater.JNUMAM 179, 697701.
Mughrabi H. (1983). “Dislocation wall and cell structures and long-range internal-stresses in deformed metal crystals,” Acta Metall.AMETAR10.1016/0001-6160(83)90007-X 31, 13671379.
Mughrabi H., Ungár T., Kienle W., and Wilkens M. (1986). “Long-range internal-stresses and asymmetric X-ray line broadening in tensile deformed [001]-oriented copper single crystals,” Philos. Mag. APMAADG 53, 793813.
Noyan I. C. and Cohen J. B. (1987). Residual Stress (Springer, New York).
Révész A., Lendvai J., and Ungár T. (2000). “Melting point depression and microstructure in ball-milled nanocrystalline aluminium powders,” Mater. Sci. ForumMSFOEP 343–3, 326331.
Ribárik G., Ungár T., and Gubicza J. (2001). “MWP-fit: A program for multiple whole profile fitting of diffraction profiles by ab-initio theoretical functions,” J. Appl. Crystallogr.JACGAR10.1107/S0021889801011451 34, 669676.
Sanders P. G., Fougere G. E., Thompson L. J., Eastman J. A., and Weertman J. R. (1997). “Improvements in the synthesis and compaction of nanocrystalline materials,” Nanostruct. Mater.NMAEE710.1016/S0965-9773(97)00167-0 8, 243252.
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.JACGAR10.1107/S002188989900374X 32, 671682.
Scardi P. and Leoni M. (2002). “Whole powder pattern modelling,” Acta Crystallogr., Sect. A: Found. Crystallogr.ACACEQ 58, 190200.
Scardi P., Leoni M., and Delhez R. (2004). “Line broadening analysis using integral breadth methods: A critical review,” J. Appl. Crystallogr.JACGAR10.1107/S0021889804004583 37, 381390.
Stephens P. W. (1999). “Phenomenological model of anisotropic peak broadening in powder diffraction,” J. Appl. Crystallogr.JACGAR10.1107/S0021889898006001 32, 281288.
Terwilliger Ch. D. and Chiang Y. M. (1995). “Size dependent solute segregation and total solubility in ultrafine polycrystals-Ca in TiO2,” Acta Metall. Mater.AMATEB10.1016/0956-7151(94)00231-6 43, 319328.
Tóth-Kádár E., Bakonyi I., Sólyom A., Hering J., Konczos G., and Pavlyák F. (1987). “Preparation and characterization of electrodeposited amorphous Ni–P alloys,” Surf. Coat. Technol.SCTEEJ 31, 3143.
Treacy M. M. J., Newsam J. M., and Deem M. W. (1991). “A general recursion method for calculating diffracted intensities from crystals containing planar faults,” Proc. R. Soc. London, Ser. APRLAAZ 433, 499520.
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.APPLAB10.1063/1.117951 69, 31733175.
Ungár T., Borbély A., Goren-Muginstein G. R., Berger S., and Rosen A. R. (1999). “Particle-size, size distribution and dislocations in nanocrystalline tungsten-carbide,” Nanostruct. Mater.NMAEE710.1016/S0965-9773(99)00023-9 11, 103113.
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.JACGAR10.1107/S0021889801003715 34, 298310.
Ungár T., Martinetto P., Ribárik G., Dooryhee E., Walter P., and Anne M. (2002). “Revealing the powdering methods of black makeup in Ancient Egypt by fitting microstructure based Fourier coefficients to the whole x-ray diffraction profiles of galena,” J. Appl. Phys.JAPIAU10.1063/1.1429792 91, 24552465.
Ungár T. and Tichy G. (1999). “The effect of dislocation contrast on X-ray line profiles in untextured polycrystals,” Phys. Status Solidi APSSABA10.1002/(SICI)1521-396X(199902)171:2<425::AID-PSSA425>3.0.CO;2-W 171, 425434.
Ustinov A. I., Olikhovska L. O., Budarina N. M., and Bernard F. (2004). “Line profile fitting: The case of fcc crystals containing stacking faults,” in Diffraction Analysis of the Microstructure of Materials, edited by Mittemeijer E. J. and Scardi P. (Springer, Berlin), 309 pp.
Valiev R. Z., Kozlov E. V., Ivanov Yu. F., Lian J., Nazarov A. A., and Baudelet B. (1994). “Deformation behavior of ultra-fine grained copper,” Acta Metall. Mater.AMATEB10.1016/0956-7151(94)90326-3 42, 24672476.
van Berkum J. G. M., Vermuelen A. C., Delhez R., de Keijser Th. 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.JACGAR10.1107/S0021889893010568 27, 345357.
Warren B. E. (1990). X-ray Diffraction (Dover, New York).
Wilkens M. (1970). Fundamental Aspects of Dislocation Theory (National Bureau of Standards Special Publication, Washington, DC.) Vol. II, No. 317, 1195 pp.
Wilkens M., Ungár T., and Mughrabi H. (1987). “X-ray rocking curve broadening of tensile deformed [001]-oriented copper single crystals,” Phys. Status Solidi APSSABA 104, 157170.
Zehetbauer M. J., Kohout J., Schafler E., Sachslehner F., and Dubravina A. (2004). “Plastic deformation of nickel under high hydrostatic pressure,” J. Alloys Compd.JALCEU 378, 329334.
Zhilyaev A. P., Gubicza J., Nurislamova G., Révész Á, Suriñach S., Baró M. D., and Ungár T. (2003). “Microstructural Characterization of Ultrafine-Grained Nickel,” Phys. Status Solidi APSSABA10.1002/pssa.200306608 198, 263271.
Zhu Y. T., Huang J. Y., Gubicza J., Ungár T., Wang Y. M., Ma E., and Valiev R. Z. (2003). “Nanostructures in Ti processed by severe plastic deformation,” J. Mater. Res.JMREEE 18, 19081917.
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Powder Diffraction
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