Microstructural characterization of polycrystalline materials by synchrotron X-rays

Abstract

Third generation synchrotron X-rays provide an unprecedented opportunity for microstructural characterization of many engineering materials as well as natural materials. This article demonstrates the usage of three techniques for the study of structural materials: differential-aperture X-ray microscopy (DAXM), three-dimensional X-ray diffraction (3DXRD), and simultaneous wide angle/small angle X-ray scattering (WAXS/SAXS). DAXM is able to measure the 3D grain structure in polycrystalline materials with high spatial and angular resolution. In a deformed material, streaked diffraction peaks can be used to analyze local dislocation content in individual grains. Compared to DAXM, 3DXRD is able to map grains in bulk materials more quickly at the expense of spatial resolution. It is very useful for studying evolving microstructures when the materials are under deformation. WAXS/SAXS is suitable for studying materials with inhomogeneous structure, such as precipitate strengthened alloys. Structural information revealed by WAXS and SAXS can be combined for a deeper insight into material behavior. Future development and applications of these three techniques will also be discussed.

Keywords

differential-aperture X-ray microscopy (DAXM) / three-dimensional X-ray diffraction (3DXRD) / wide angle/small angle X-ray scattering (WAXS/SAXS)

References

[1] Hall E O. The deformation and ageing of mild steel: III Discussion of results. Proceedings of the Physical Society Section B , 1951, 64(9): 747–753
[2] Hertzberg R W. Deformation and Fracture Mechanics of Engineering Materials (4th Edition) . New York: Wiley, 1996
[3] Hull D, Bacon D J. Introduction to Dislocations . Oxford, UK: Elsevier, 2001
[4] Kocks U F, Tome C N, Wenk H R. Texture and Anisotropy . Cambridge, UK: Cambridge University Press, 1998
[5] Williams D B, Carter C B. Transmission Electron Microscopy . New York: Plenum Press, 1996
[6] Goldstein J I, Newbury D E, Echlin P, . Scanning Electron Microscopy and X-Ray Microanalysis (3rd Edition) . New York: Springer, 2003
[7] Venables J A, Binjaya R. Accurate micro-crystallography using electron backscattering patterns. Philosophical Magazine , 1977, 35(5): 1317–1332
[8] Dingley D J, Randle V. Microtexture determination by electron back-scatter diffraction. Journal of Materials Science , 1992, 27(17): 4545–4566
[9] Adams B L, Wright S I, Kunze K. Orientation imaging: The emergence of a new microscopy. Metallurgical Transactions A , 1993, 24(4): 819 -831
[10] Schwarz A J, Kumar M, Field D P, . Electron Backscatter Diffraction in Materials Science . New York: Springer, 2000
[11] Bridier F, Villechaise P, Mendez J. Analysis of the different slip systems activated by tension in a α/β titanium alloy in relation with local crystallographic orientation. Acta Materialia , 2005, 53(3): 555–567
[12] Bingert J F, Mason T A, Kaschner G C, . Deformation twinning in polycrystalline Zr: Insights from electron backscattered diffraction characterization. Metallurgical and Materials Transactions A , 2002, 33(3): 955-963
[13] Bieler T R, Eisenlohr P, Roters F, . The role of heterogeneous deformation on damage nucleation at grain boundaries in single phase metals. International Journal of Plasticity , 2009, 25(9): 1655–1683
[14] Kral M V, Spanos G. Three-dimensional analysis of proeutectoid cementite precipitates. Acta Materialia , 1999, 47(2): 711–724
[15] Zaefferer S, Wright S I, Raabe D. Three-dimensional orientation microscopy in a focused ion beam-scanning electron microscope: a new dimension of microstructure characterization. Metallurgical and Materials Transactions A , 2008, 39(2): 374-389
[16] Uchic M D, Groeber M A, Rollett A D. Automated serial sectioning methods for rapid collection of 3-D microstructure data. JOM , 2011, 63(3): 25–29
[17] Willmott P. An Introduction to Synchrotron Radiation: Techniques and Applications . New York: Wiley, 2011
[18] Bilderback D H, Elleaume P, Weckert E. Review of third and next generation synchrotron light sources. Journal of Physics B: Atomic and Molecular Physics , 2005, 38(9): S773–S797
[19] Larson B C, Yang W, Ice G E, . Three-dimensional X-ray structural microscopy with submicrometre resolution. Nature , 2002, 415(6874): 887–890
[20] Ice G E, Barabash R I. White beam microdiffraction and dislocations gradients. Dislocations in Solids , Vol. 13, Chapter 79, 2007, 499-601
[21] Liu W, Ice G E, Larson B C, . The three-dimensional X-ray crystal microscope: A new tool for materials characterization. Metallurgical and Materials Transactions A , 2004, 35(7): 1963 -1967
[22] Liu W, Ice G E, Larson B C, . Nondestructive three-dimensional characterization of grain boundaries by X-ray crystal microscopy. Ultramicroscopy , 2005, 103(3): 199–204
[23] Wang L, Barabash R I, Yang Y, . Experimental characterization and crystal plasticity modeling of heterogeneous deformation in polycrystalline α-Ti. Metallurgical and Materials Transactions A , 2011, 42(3): 626 -635
[24] Larson B C, El-Azab A, Yang W, . Experimental characterization of the mesoscale dislocation density tensor. Philosophical Magazine , 2007, 87(8-9): 1327–1347
[25] Barabash R I, Ice G E, Larson B C, . White microbeam diffraction from distorted crystals. Applied Physics Letters , 2001, 79(6): 749–751
[26] Barabash R I, Ice G E, Walker F J. Quantitative microdiffraction from deformed crystals with unpaired dislocations and dislocation walls. Journal of Applied Physics , 2003, 93(3): 1457–1464
[27] Barabash R I, Ice G E, Liu W, . Polychromatic microdiffraction characterization of defect gradients in severely deformed materials. Micron , 2009, 40(1): 28–36
[28] Maass R, Van Petegem S, Van Swygenhoven H, . Time-resolved Laue diffraction of deforming micropillars. Physical Review Letters , 2007, 99(14): 145505 (4 pages)
[29] Maa? R, Van Petegem S, Ma D, . Smaller is stronger: The effect of strain hardening. Acta Materialia , 2009, 57(20): 5996–6005
[30] Kirchlechner C, Imrich P J, Grosinger W, . Expected and unexpected plastic behavior at the micron scale: An in situ μLaue tensile study. Acta Materialia , 2012, 60(3): 1252–1258
[31] Villechaise P, Sabatier L, Girard J C. On slip band features and crack initiation in fatigued 316L austenitic stainless steel: Part 1: Analysis by electron back-scattered diffraction and atomic force microscopy. Materials Science and Engineering A , 2002, 323(1-2): 377–385
[32] Zaefferer S. A study of active deformation systems in titanium alloys: dependence on alloy composition and correlation with deformation texture. Materials Science and Engineering A , 2003, 344(1-2): 20–30
[33] Li H, Boehlert C J, Bieler T R, . Analysis of slip activity and heterogeneous deformation in tension and tension-creep of Ti-5Al-2.5Sn (wt.%) using in-situ SEM experiments. Philosophical Magazine , 2012, 92(23): 2923–2946
[34] Nye J F. Some geometrical relations in dislocated crystals. Acta Metallurgica , 1953, 1(2): 153–162
[35] Arsenlis A, Parks D M. Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density. Acta Materialia , 1999, 47(5): 1597–1611
[36] Giannuzzi L A, Stevie F A. A review of focused ion beam milling techniques for TEM specimen preparation. Micron , 1999, 30(3): 197–204
[37] Mayer J, Giannuzzi L A, Kamino T, . TEM sample preparation and FIB-induced damage. MRS Bulletin , 2007, 32(5): 400–407
[38] Kalidindi S R, Bronkhorst C A, Anand L. Crystallographic texture evolution in bulk deformation processing of fcc metals. Journal of the Mechanics and Physics of Solids , 1992, 40(3): 537–569
[39] Raabe D, Sachtleber M, Zhao Z, . Micromechanical and macromechanical effects in grain scale polycrystal plasticity experimentation and simulation. Acta Materialia , 2001, 49(17): 3433–3441
[40] Musienko A, Tatschl A, Schmidegg K, . Three-dimensional finite element simulation of a polycrystalline copper specimen. Acta Materialia , 2007, 55(12): 4121–4136
[41] Roters F, Eisenlohr P, Hantcherli L, . Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications. Acta Materialia , 2010, 58(4): 1152–1211
[42] Poulsen H F, Garbe S, Lorentzen T, . Applications of high-energy synchrotron radiation for structural studies of polycrystalline materials. Journal of Synchrotron Radiation , 1997, 4(3): 147–154
[43] Lauridsen E M, Schmidt S, Suter R M, . Tracking: a method for structural characterization of grains in powders or polycrystals. Journal of Applied Crystallography , 2001, 34(6): 744–750
[44] Poulsen H F, Nielsen S F, Lauridsen E M, . Three-dimensional maps of grain boundaries and the stress state of individual grains in polycrystals and powders. Journal of Applied Crystallography , 2001, 34(6): 751–756
[45] Margulies L, Winther G, Poulsen H F. In situ measurement of grain rotation during deformation of polycrystals. Science , 2001, 291(5512): 2392–2394
[46] Poulsen H F. Three-Dimensional X-ray Diffraction Microscopy . Berlin: Springer, 2004
[47] Lienert U, Li S F, Hefferan C M, . High-energy diffraction microscopy at the advanced photon source. JOM , 2011, 63(7): 70–77
[48] Poulsen H F. An introduction to three-dimensional X-ray diffraction microscopy. Journal of Applied Crystallography , 2012, 45(6): 1084–1097
[49] Suter R M, Hennessy D, Xiao C, . Forward modeling method for microstructure reconstruction using X-ray diffraction microscopy: Single-crystal verification. Review of Scientific Instruments , 2006, 77(12): 123905 (12 pages)
[50] Schmidt S, Olsen U L, Poulsen H F, . Direct observation of 3-D grain growth in Al-0.1% Mn. Scripta Materialia , 2008, 59(5): 491–494
[51] Li S F, Lind J, Hefferan C M, . Three-dimensional plastic response in polycrystalline copper via near-field high-energy X-ray diffraction microscopy. Journal of Applied Crystallography , 2012, 45(6): 1098–1108
[52] Margulies L, Lorentzen T, Poulsen H F, . Strain tensor development in a single grain in the bulk of a polycrystal under loading. Acta Materialia , 2002, 50(7): 1771–1779
[53] Martins R V, Margulies L, Schmidt S, . Simultaneous measurement of the strain tensor of 10 individual grains embedded in an Al tensile sample. Materials Science and Engineering A , 2004, 387-389: 84–88
[54] Aydiner C C, Bernier J V, Clausen B, . Evolution of stress in individual grains and twins in a magnesium alloy aggregate. Physical Review B , 2009, 80(2): 024113 (6 pages)
[55] Bernier J V, Barton N R, Lienert U, . Far-field high-energy diffraction microscopy: a tool for intergranular orientation and strain analysis. Journal of Strain Analysis for Engineering Design , 2011, 46(7): 527–547
[56] Beaudoin A J, Obstalecki M, Storer R, . Validation of a crystal plasticity model using high energy diffraction microscopy. Modelling and Simulation in Materials Science and Engineering , 2012, 20(2): 024006 (14 pages)
[57] Nye J F. Physical Properties of Crystals: Their Representation by Tensors and Matrices . New York: Oxford University Press, 1985
[58] Oddershede J, Schmidt S, Poulsen H F, . Grain-resolved elastic strains in deformed copper measured by three-dimensional X-ray diffraction. Materials Characterization , 2011, 62(7): 651–660
[59] Oddershede J, Schmidt S, Poulsen H F, . Determining grain resolved stresses in polycrystalline materials using three-dimensional X-ray diffraction. Journal of Applied Crystallography , 2010, 43(3): 539–549
[60] Oddershede J, Camin B, Schmidt S, . Measuring the stress field around an evolving crack in tensile deformed Mg AZ31 using three-dimensional X-ray diffraction. Acta Materialia , 2012, 60(8): 3570–3580
[61] Christian J W, Mahajan S. Deformation Twinning. Progress in Materials Science , 1995, 39(1-2): 1–157
[62] Tome C N, Maudlin P J, Lebensohn R A, . Mechanical response of zirconium- I. Derivation of a polycrystal constitutive law and finite element analysis. Acta Materialia , 2001, 49(15): 3085–3096
[63] Meyers M A, Vohringer O, Lubarda V A, . The onset of twinning in metals: A constitutive description. Acta Materialia , 2001, 49(19): 4025–4039
[64] Beyerlein I J, Tome C N. A probabilistic twin nucleation model for HCP polycrystalline metals. Proceedings of the Royal Society of London Series A , 2010, 466(2121): 2517–2544
[65] Ma A, Roters F, Raabe D, . A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations. Acta Materialia , 2006, 54(8): 2169–2179
[66] Capolungo L, Marshall P E, McCabe R J, . Nucleation and growth of twins in Zr: A statistical study. Acta Materialia , 2009, 57(20): 6047–6056
[67] Beyerlein I J, Capolungo L, Marshall P E, . Statistical analyses of deformation twinning in magnesium. Philosophical Magazine , 2010, 90(16): 2161–2190
[68] Wang L, Yang Y, Eisenlohr P, . Twin nucleation by slip transfer across grain boundaries in commercial purity titanium. Metallurgical and Materials Transactions A , 2010, 41(2): 421 -430
[69] Wang L, Eisenlohr P, Yang Y, . Nucleation of paired twins at grain boundaries in titanium. Scripta Materialia , 2010, 63(8): 827–830
[70] Young M L, Almer J D, Daymond M R, . Load partitioning between ferrite and cementite during elasto-plastic deformation of an ultrahigh-carbon steel. Acta Materialia , 2007, 55(6): 1999–2011
[71] Cheng S, Wang Y D, Choo H, . An assessment of the contributing factors to the superior properties of a nanostructured steel using in situ high-energy X-ray diffraction. Acta Materialia , 2010, 58(7): 2419–2429
[72] Colas K B, Motta A T, Almer J D, . In situ study of hydride precipitation kinetics and re-orientation in Zircaloy using synchrotron radiation. Acta Materialia , 2010, 58(20): 6575–6583
[73] Weisser M A, Evans A D, Van Petegem S, . In situ room temperature tensile deformation of a 1% CrMoV bainitic steel using synchrotron and neutron diffraction. Acta Materialia , 2011, 59(11): 4448–4457
[74] Guinier A, Fournet G. Small-Angle Scattering of X-rays . New York: Wiley, 1955
[75] Pan X, Wu X, Mo K, . Lattice strain and damage evolution of 9-12%Cr ferritic/martensitic steel during in situ tensile test by X-ray diffraction and small angle scattering. Journal of Nuclear Materials , 2010, 407(1): 10–15
[76] Wang L, Li M, Almer J D. In situ characterization of Grade 92 steel during tensile deformation using concurrent high energy X-ray diffraction and small angle X-ray scattering. Journal of Nuclear Materials (submitted)
[77] Ice G E, Budai J D, Pang J W L. The race to X-ray microbeam and nanobeam science. Science , 2011, 334(6060): 1234–1239
[78] Was G S. Fundamentals of Radiation Materials Science . Berlin: Springer, 2007