Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-06-08T13:12:24.583Z Has data issue: false hasContentIssue false

The analysis of homogeneously and inhomogeneously anisotropic microstructures by X-ray diffraction

Published online by Cambridge University Press:  01 March 2012

Udo Welzel*
Affiliation:
Max Planck Institute for Metals Research, Heisenbergstrasse 3, D-70569 Stuttgart, Germany
Eric J. Mittemeijer
Affiliation:
Max Planck Institute for Metals Research, Heisenbergstrasse 3, D-70569 Stuttgart, Germany
*
a)Electronic mail: u.welzel@mf.mpg.de

Abstract

The microstructure of materials is generally, macroscopically, anisotropic and/or inhomogeneous. Traditional diffraction analyses do not take into account this anisotropy and/or inhomogeneity of microstructural features. Thus obtained results can be incomplete, ambiguous, or even erroneous. In this work instrumental requirements (application of parallel beam diffractometers with X-ray lenses or X-ray mirrors and parallel-plate collimators in the laboratory and at synchrotron beam lines) and methodological approaches for the diffraction analysis of anisotropic and inhomogeneous microstructures have been discussed and have been illustrated on the basis of two experimental examples: analysis of the anisotropic nature of the structural imperfection of a sputterdeposited Ti3Al layer and analysis of the anisotropic and inhomogeneous elastic grain interaction in a sputter-deposited Ni layer.

Type
Invited Articles
Copyright
Copyright © Cambridge University Press 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akiniwa, Y., Tanaka, K., Suzuki, K., Yanase, E., Nishio, K., Kusumi, Y., Okado, H., and Arai, K. (2003). “Evaluation of Residual Stress Distribution in Shot-Peened Steel by Synchrotron Radiation,” J. Mater. Sci. Jpn. 52, 764769 (in Japanese).Google Scholar
Anderko, K., Sagel, K., and Zwicker, U. (1957). “Hexagonale Ordnungsphasen in den Systemen Titan-Aluminium und Titan-Indium,” Z. Metallkd.ZEMTAE 48, 5758.Google Scholar
Andersson, Y., Mittemeijer, E. J., and Welzel, U. (Eds.) (2004). European Powder Diffraction, Proceedings of EPDIC8, Mater. Sci. ForumMSFOEP 443–444.CrossRefGoogle Scholar
Behnken, H. and Hauk, V. (2000). “Determination of Steep Stress Gradients by X-ray Diffraction—Results of a Joint Investigation,” Mater. Sci. Eng., AMSAPE3 300, 4151.CrossRefGoogle Scholar
Bein, S., Le Calvez, C., and Lebrun, J.-L. (1998). “Determination of Stress Gradients by X-ray Diffraction: Comparison of Different Methods and Applications,” Z. Metallkd.ZEMTAE 89, 289296.Google Scholar
Bolle, B., Tidu, A., Jolly, L., Valot, Ch., Laruelle, C., and Heizmann, J. J. (2002). “Controlled Depth Penetration X-ray Diffraction Measurement,” Mater. Sci. ForumMSFOEP 408–412, 233238.CrossRefGoogle Scholar
Bonarski, J. T., Bunge, H. J., Wcislak, L., and Pawlik, K. (1998). “Investigation of Inhomogeneous Surface Textures with Constant Information Depth. 1. Fundamentals,” Textures Microstruct.TEMIDK 31, 2141.CrossRefGoogle Scholar
Bonarski, J. T., Wcislak, L., and Bunge, H. J. (1994). “Investigation of Inhomogeneous Textures of Coatings and Near-Surface Layers,” Mater. Sci. ForumMSFOEP 157–162, 111118.CrossRefGoogle Scholar
Braun, J. and Ellner, M. (2000). “On the Partial Atomic Volume of Aluminium in the Titanium-rich Phases of the Binary System Ti–Al,” Z. Metallkd.ZEMTAE 91, 389392.Google Scholar
Christodoulou, L. (1990). “Titanium Aluminides,” in Encyclopedia of Materials Science and Engineering, edited by Cahn, R. (Pergamon, Oxford), Suppl. Vol. 2, pp. 13461354.Google Scholar
Clark, D., Jepson, K. S., and Lewis, G. I. (1962–63). “A Study of the Titanium-Aluminum System up to 40 At.-% Aluminum,” J. Inst. Met.JIMEAP 91, 197203.Google Scholar
Delhez, R., de Keijser, Th. H., and Mittemeijer, E. J. (1982). “Determination of Crystallite Size and Lattice Distortions through X-ray Diffraction Line Profile Analysis,” Fresenius' Z. Anal. Chem.ZACFAU10.1007/BF00482725 312, 116.CrossRefGoogle Scholar
Fitch, A. N., Catlow, C. R. A., and Atkinson, A. (1991). “Measurement of Stress in Nickel-Oxide Layers by Diffraction of Synchrotron Radiation,” J. Mater. Sci.JMICAR 26, 23002304.CrossRefGoogle Scholar
Genzel, Ch. (1997). “X-ray Stress Gradient Analysis in Thin Layers—Problems and Attempts at Their Solution,” Phys. Status Solidi APSSABA 159, 283296.3.0.CO;2-O>CrossRefGoogle Scholar
Hanabusa, T., Tominaga, K., and Fujiwara, H. (1992). “Residual Stresses in Al and AlN Thin Films Deposited by Sputtering,” in Residual Stresses III, Science and Technology edited by Fujiwara, H., Abe, T., and Tanaka, K. (Elsevier Applied Science, London), Vol. 1, pp. 728734.Google Scholar
Jenkins, R. and Snyder, R. L. (1996). Introduction to X-ray Powder Diffractometry (Wiley, New York), Chap. 7.CrossRefGoogle Scholar
Koch, N., Welzel, U., Wern, H., and Mittemeijer, E. J. (2004). “Mechanical Elastic Constants and Diffraction Stress Factors of Macroscopically Elastically Anisotropic Polycrystals; the Effect of Grain-Shape (Morphologic) Texture,” Philos. Mag.PMHABF 84, 35473570.CrossRefGoogle Scholar
Kumar, A., Welzel, U., and Mittemeijer, E. J. (2005a). “Analysis of Gradients of Mechanical Stresses Employing X-ray Diffraction Measurements at Fixed Penetration Depth” (submitted).Google Scholar
Kumar, A., Welzel, U., and Mittemeijer, E. J. (2005b). “Direction-Dependent Grain Interaction in Nickel and Copper Thin Films, Analysed by X-ray Diffraction,” Acta Mater. ACMAFD (in press).Google Scholar
Kumar, A., Welzel, U., and Mittemeijer, E. J. (2005c). “Diffraction Stress Analysis of Strongly Fibre-Textured Gold Layers,” Z. Kristallogr. ZEKRDZ Supplement (in press).Google Scholar
Kumar, A., Welzel, U., and Mittemeijer, E. J. (2005d). “Analysis of Gradients of Elastic Grain-Interaction Constraints Employing X-ray Diffraction Measurements at Fixed Penetration Depth” (submitted).Google Scholar
Kumpfert, J. (2001). “Intermetallic Alloys Based on Orthorhombic Titanium Aluminide,” Adv. Eng. Mater.AENMFY 3, 851864.3.0.CO;2-G>CrossRefGoogle Scholar
Kuzel, R. Jr., Cerny, R., Valvoda, V., Blomberg, M., and Merisalo, M. (1994a). “Complex XRD Microstructural Studies of Hard Coatings Applied to PVD-Deposited TiN Films. I. Problems and Methods,” Thin Solid FilmsTHSFAP 247, 6478.CrossRefGoogle Scholar
Kuzel, R. Jr., Cerny, R., Valvoda, V., Bolmberg, M., Merisalo, M., and Kadlec, S. (1995). “Complex XRD Microstructural Studies of Hard Coatings Applied to PVD-Deposited TiN Films. II. Transition from Porous to Compact Films and Microstructural Inhomogeneity of the Layers,” Thin Solid FilmsTHSFAP 268, 7282.CrossRefGoogle Scholar
Kuzel, R. Jr., Valvoda, V., Chladek, M., Musil, J., and Matous, J. (1994b). “XRD Microstructural Study of Zn Films Deposited by Unbalanced Magnetron Sputtering,” Thin Solid FilmsTHSFAP 263, 150158.CrossRefGoogle Scholar
Langford, J. I. (1978). “A Rapid Method for Analysing the Breadths of Diffraction and Spectral Lines Using the Voigt Function,” J. Appl. Crystallogr.JACGAR10.1107/S0021889878012601 11, 1014.CrossRefGoogle Scholar
Langford, J. I., Delhez, R., de Keijser, T. H., and Mittemeijer, E. J. (1988). “Profile Analysis for Microcrystalline Properties by the Fourier and Other Methods,” Aust. J. Phys.AUJPAS 41, 173187.CrossRefGoogle Scholar
Langford, J. I. and Louër, D. (1996). “Powder Diffraction,” Rep. Prog. Phys.RPPHAG10.1088/0034-4885/59/2/002 59, 131234.CrossRefGoogle Scholar
Leoni, M., Welzel, U., and Scardi, P. (2004). “Polycapillary Optics for Materials Science Studies: Instrumental Effects and Their Correction,” J. Res. Natl. Inst. Stand. Technol.JRITEF 109, 2748.CrossRefGoogle ScholarPubMed
Meier, G. H. (1996). “Research on Oxidation and Embrittlement of Intermetallic Compounds in the U.S.,” Mater. Corros.MTCREQ 47, 595618.CrossRefGoogle Scholar
Meyers, M. A. and Chawla, K. K. (1984). Mechanical Metallurgy, Principles and applications (Prentice-Hall, Englewood Cliffs., NJ), p. 57.Google Scholar
Mittemeijer, E. J. (2002). “The Role of Powder Diffraction in Materials Science,” Z. Kristallogr.ZEKRDZ 217, 390391.CrossRefGoogle Scholar
Mittemeijer, E. J. and Scardi, P. (Eds.) (2004). Diffraction Analysis of the Microstructure of Materials (Springer, Berlin).CrossRefGoogle Scholar
Okolo, B., Lamparter, P., Welzel, U., and Mittemeijer, E. J. (2004). “Stress, Texture, and Microstructure in Niobium Thin Films Sputter Deposited onto Amorphous Substrates,” J. Appl. Phys.JAPIAU10.1063/1.1631733 95, 466476.CrossRefGoogle Scholar
Parrish, W. (1995). “Powder and Related Techniques: X-ray Techniques,” in International Tables for Crystallography Vol. C, Mathematical, Physical and Chemical Tables edited by Wilson, A. J. C. and Prince, E. (IUCr/Kluwer, Dordrecht), pp. 4253.Google Scholar
Perlovich, Yu and Isaenkova, M. (2004a). “Distributions of Domain Size, Lattice Distortion and Dislocation Density in Tubes of Zr-based Alloys Studied by a Method Combining X-ray Line Profile Analysis with Texture Measurements,” Mater. Sci. ForumMSFOEP 443–444, 255258.CrossRefGoogle Scholar
Perlovich, Yu and Isaenkova, M. (2004b). “New Principles of the Substructure Development in Metal Materials under Plastic Deformation, Revealed by Advanced X-ray Methods,” Mater. Sci. ForumMSFOEP 443–444, 259262.CrossRefGoogle Scholar
Roberts, R. B. (1981). “Thermal Expansion Reference Data: Silicon 300-850 K,” J. Phys. DJPAPBE10.1088/0022-3727/14/10/003 14, L163–L166.CrossRefGoogle Scholar
Scardi, P., Setti, S., and Leoni, M. (2000). “Multicapillary Optics for Materials Science Studies,” Mater. Sci. ForumMSFOEP 321–324, 162167.CrossRefGoogle Scholar
Scherrer, P. (1918). “Bestimmung der Größe und der inneren Struktur von Kolloidteilchen mittels Röntgenstrahlen,” Göttinger Nachrichten 2, 98100.Google Scholar
Somers, M. A. J. and Mittemeijer, E. J. (1990). “Development and Relaxation of Stress in Surface Layers—Composition and Residual Stress Profiles in γ -Fe4N1−x Layers on α-Fe Substrates,” Metall. Trans. AMTTABN 21, 189204.CrossRefGoogle Scholar
Sonneveld, E. J., Delhez, R., de Keijser, Th. H., and Mittemeijer, E. J. (1991). “Quality of Unravelling of Experimental Diffraction Patterns with Artificially Varied Overlap,” Mater. Sci. ForumMSFOEP 79–82, 8590.CrossRefGoogle Scholar
Tamura, N., MacDowell, A. A., Spolenak, R., Valek, B. C., Bravman, J. C., Brown, W. L., Celestre, R. S., Padmore, H. A., Batterman, B. W., and Patel, J. R. (2003). “Scanning X-ray Microdiffraction with Submicrometer White Beam for Strain/Stress and Orientation Mapping in Thin Films,” J. Synchrotron Radiat.JSYRES10.1107/S0909049502021362 10, 137143.CrossRefGoogle ScholarPubMed
Tanaka, K. and Akiniwa, Y. (2004). “Diffraction Measurements of Residual Macrostress and Microstress Using X-rays, Synchrotron and Neutrons,” JSME Int. J., Ser. AJJMMEQ 47, 252263.CrossRefGoogle Scholar
Tanaka, K., Akiniwa, Y., Suzuki, K., Yanase, E., Nishio, K., Kusumi, Y., and Arai, K. (2002). “High-Energy X-ray Synchrotron Radiation Analysis of Residual-Stress Distribution of Shot-Peened Steel,” Mater. Sci. ForumMSFOEP 404–407, 341348.CrossRefGoogle Scholar
Tanaka, K. and Koiwa, M. (1996). “Single-Crystal Elastic Constants of Intermetallic Compounds,” IntermetallicsIERME510.1016/0966-9795(96)00014-3 4, S29–S39.CrossRefGoogle Scholar
Tanaka, K., Okamoto, K., Inui, H., Minonishi, Y., Yamaguchi, M., and Koiwa, M. (1996). “Elastic Constants and their Temperature Dependence for the Intermetallic Compound Ti3Al,” Philos. Mag. APMAADG 73, 14751488.CrossRefGoogle Scholar
van Acker, K., de Buyser, L., Celis, J. P., and van Houtte, P. (1994). “Characterization of Thin Nickel Electrocoatings by the Low-Incident-Beam-Angle Diffraction Method,” J. Appl. Crystallogr.JACGAR10.1107/S002188989300651X 27, 5666.CrossRefGoogle Scholar
Vermeulen, A. C. V., Delhez, R., de Keijser, Th. H., and Mittemeijer, E. J. (1995). “Changes in the Densities of Dislocations on Distinct Slip Systems During Stress Relaxation in Thin Aluminum Layers: The Interpretation of X-ray Diffraction Line Broadening and Line Shift,” J. Appl. Phys.JAPIAU10.1063/1.359312 77, 50265049.CrossRefGoogle Scholar
Vook, R. W. and Witt, F. (1965). “Thermally Induced Strains in Evaporated Films,” J. Appl. Phys.JAPIAU10.1063/1.1714442 36, 21692171.CrossRefGoogle Scholar
Welzel, U. and Leoni, M. (2002). “Use of Polycapillary X-ray Lenses in the X-ray Diffraction Measurement of Texture,” J. Appl. Crystallogr.JACGAR10.1107/S0021889802000481 35, 196206.CrossRefGoogle Scholar
Welzel, U., Leoni, M., and Mittemeijer, E. J. (2003). “The Determination of Stresses in Thin Films; Modelling Elastic Grain Interaction,” Philos. Mag.PMHABF 83, 603630.CrossRefGoogle Scholar
Welzel, U., Leoni, M., and Mittemeijer, E. J. (2004). “Diffraction Elastic Constants and Stress Factors; Grain Interaction and Stress in Macroscopically Elastically Anisotropic Solids; the Case of Thin Films,” in Diffraction Analysis of the Microstructure of Materials, edited by Mittemeijer, E. J. and Scardi, P. (Springer, Berlin), pp. 363390.CrossRefGoogle Scholar
Welzel, U., Ligot, J., Lamparter, P., Vermeulen, A. C., and Mittemeijer, E. J. (2005). “Stress Analysis of Polycrystalline Thin Films and Surface Regions by X-ray Diffraction,” J. Appl. Crystallogr.JACGAR 38, 129.CrossRefGoogle Scholar
Welzel, U. and Mittemeijer, E. J. (2003). “Diffraction Stress Analysis of Macroscopically Elastically Anisotropic Specimens: On the Concepts of Diffraction Elastic Constants and Stress Factors,” J. Appl. Phys.JAPIAU10.1063/1.1569662 93, 90019011.CrossRefGoogle Scholar
Windischmann, H. (1992). “Intrinsic Stress in Sputter-Deposited Thin Films,” Crit. Rev. Solid State Mater. Sci.CCRSDA 17, 547596.CrossRefGoogle Scholar
Xiao, Q. F., Kennedy, R. J., Ryan, T. W., and York, B. R. (1998). “Multifiber Polycapillary Collimator for X-ray Powder Diffraction,” Mater. Sci. ForumMSFOEP 278–281, 236241.CrossRefGoogle Scholar
Zhao, Y. H., Welzel, U., van Lier, J., and Mittemeijer, E. J. (2005). “X-ray Diffraction Analysis of the Anisotropic Nature of the Structural Imperfections in a Sputter-Deposited TiO2∕Ti3Al Bilayer,” Thin Solid FilmsTHSFAP (submitted).Google Scholar