Three-dimensional x-ray diffraction microscopy : mapping polycrystals and their dynamics

158 Pages·2004·2.611 MB·English

by  Henning Friis Poulsen

Henning F. Poulsen
Three-Dimensional
X-Ray Diffraction
Microscopy
Mapping Polycrystals and their Dynamics
With49Figures
123
HenningF.Poulsen
RisøNationalLaboratory
CenterforFundamentalResearch:
MetalStructuresinFourDimensions
4000Roskilde,Denmark
E-mail:[email protected]
LibraryofCongressControlNumber:2004109594
PhysicsandAstronomyClassificationScheme(PACS):
61.10.Nz,07.85.Qe,81.
ISSNprintedition:0081-3869
ISSNelectronicedition:1615-0430
ISBN3-540-22330-4SpringerBerlinHeidelbergNewYork
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To Hanne and Mathilde
Preface
In nature most materials, such as rocks, ice, sand and soil, appear to be ag-
gregates composed of a set of crystalline elements. Similarly, modern society
isbuiltonapplicationsofmetals,ceramicsandother“hardmaterials”,which
also are polycrystalline. So are drugs, bones and trace particles relevant to
environmental matters, as well as many objects of artistic or archaeological
significance.
Remarkably, until recently, no nondestructive method existed for pro-
viding comprehensive three-dimensional information on the structure and
dynamics of polycrystals at the scale of the individual elements (the grains,
subgrains,particlesordomains).X-rayandneutrondiffractionhavebeencon-
finedtotwolimiting cases:powderdiffraction,whichaveragesoverelements,
anddiffractionperformedonsingle crystals.Mostreal-worldmaterialsoccur
asheterogeneousaggregateswithsubstantialinternalstructure,andthusfall
between these two extremes. Local information has been provided by tools
suchasoptical,electron,ionbeamandscanningprobemicroscopy.However,
these methods probe the near-surface regions only. Hence, the characteriza-
tion is only two-dimensional and prohibits studies of bulk dynamics.
Three-dimensional x-ray diffraction (3DXRD) is a novel experimental
methodforstructuralcharacterizationofpolycrystallinematerials.Itisbased
on two principles: the use of highly penetrating hard x-rays from a syn-
chrotron source and a “tomographic” approach to the acquisition of diffrac-
tion data. Uniquely, the method enables a fast and nondestructive charac-
terization of the individual microstructuralelements (grains and sub-grains)
within millimeter-to-centimeter-sized specimens. The position, morphology,
phase and crystallographic orientation can be derived for hundreds of ele-
ments simultaneously,andthe elastic andplastic strainscanalsobe derived.
Furthermore,the dynamicsofthe individualelementscanbe monitoreddur-
ing typical processes such as deformation or annealing. Hence, for the first
time, information on the interaction between elements can be obtained di-
rectly. The provision of such data is vital if we are to extend our knowledge
beyond the current structural models.
The aim of this book is to give a comprehensive account of 3DXRD mi-
croscopy,withafocusbothonmethodologyandonapplications.Themethod-
ology is presented from a geometric/crystallographicpoint of view, but with
VIII Preface
sufficient details of algorithmsand hardwareto enable the reader to plan his
or her own 3DXRD experiments and analyze the resulting data. The main
applications are introduced by a short preamble, intended to motivate the
useof3DXRD.Tounderlinetheprospectsfor3DXRD,anumberofuntested
suggestionsformethodologicalimprovementsandalternativeapplicationsare
included.
The book is written for a general reader who has a background in the
naturalsciencesandabasicunderstandingofx-raydiffraction.Forhistorical
reasons,themajorityoftheapplicationspresentedrelatetomaterialsscience.
However, as the structure of polycrystals is of more general interest it is my
hope that the book may serve to stimulate researchin other fields also,such
as geophysics, geology,chemistry and pharmaceutical science.
Synchrotron instrumentation requires, by its nature, a collaborative ef-
fort. Hence, I welcome this opportunity to thank the group of people who
have contributed towards the development of 3DXRD methodology. These
include JacobBowen,XiaoweiFu, Stephan Garbe,CarstenGundlach,Dorte
Juul Jensen, Erik Knudsen, Axel Larsen, Erik Mejdal Lauridsen, Torben
Lorentzen, Lawrence Margulies, Søren Fæster Nielsen, Wolfgang Pantleon,
Søren Schmidt, John Wert and Grethe Winther at Risø; Erik Offerman and
Jilt Sietsma at the Technical University of Delft; Robert Suter at CMU;
Rene Martins at GKSS; and, last but not least, Ulrich Lienert at the APS.
The development of the method into the 3DXRD microscope at ESRF was
only possible thanks to the dedication and expertise of the in-house staff,
in particular Andy Goetz, ˚Ake Kvick and Gavin Vaughan from beamline
ID11. The Danish National Research Foundation is gratefully acknowledged
for supporting “Center for Fundamental Research: Metal Structures in Four
Dimensions”.
The work presented in this book would not have been possible without
thepioneeringstudiesinhardx-raydiffractionbyJochenSchneider.Further-
more, for numerous very valuable discussions, I thank Roger Doherty, Niels
Hansen,GaborHerman,VeijoHonkima¨ki,TorbenLeffers,WolfgangLudwig,
Adam Morawiec and Jan Teuber.
Finally,I’mgratefultoRogerDoherty,DorteJuulJensenandBrianRalph
for reading and discussing this manuscript.
Roskilde, July 2004 Henning Friis Poulsen
Contents
1 Introduction.............................................. 1
References ................................................. 5
2 Methods for Mesoscale Structural Characterization....... 7
2.1 Electron and Optical Microscopy ........................ 7
2.2 X-Ray Diffraction with Low-Energy X-Rays................ 9
2.3 Conventional Bulk-Sensitive Methods ..................... 11
2.4 Hard X-Rays: Properties ................................ 12
2.5 Hard X-Ray Work Using Synchrotron Sources.............. 14
References ................................................. 17
3 Geometric Principles ..................................... 21
3.1 The Basic 3DXRD Setup ................................ 22
3.2 Diffraction Geometry ................................... 25
3.3 Representation of Crystallographic Orientation............. 27
3.4 Representation of Position–OrientationSpace .............. 31
3.5 Representation of Elastic Strain .......................... 33
References ................................................. 33
4 GRAINDEX and Related Analysis ....................... 35
4.1 GRAINDEX........................................... 35
4.1.1 Alternative Experimental Configurations ............ 38
4.2 Spot Overlap .......................................... 38
4.3 Analysis of Single Grains on the Basis of GRAINDEX ...... 40
4.3.1 Grain Maps ..................................... 40
4.3.2 The Orientation, Elastic Strain and Stoichiometry
of a Single Grain ................................. 42
4.3.3 The Orientation Spread Within One Grain .......... 44
4.4 Conical and Spiral Slits ................................. 44
4.5 Characterizationof Large Volumes........................ 46
4.6 Dynamic Experiments................................... 48
References ................................................. 49
X Contents
5 Orientation Mapping ..................................... 51
5.1 Image Analysis......................................... 53
5.2 GRAINSWEEPER ..................................... 54
5.3 2D-ART............................................... 57
5.3.1 Algebraic Formulation ............................ 57
5.3.2 The ART Algorithm .............................. 59
5.3.3 Results.......................................... 60
5.4 3D-ART............................................... 63
5.5 3D-FBP............................................... 64
5.5.1 Geometry ....................................... 64
5.5.2 The FBP Algorithm .............................. 66
5.5.3 Results.......................................... 67
5.6 The General 6D Case ................................... 68
5.7 Discussion............................................. 70
References ................................................. 71
6 Combining 3DXRD
and Absorption Contrast Tomography .................... 73
6.1 Decoration of Al Grain Boundaries by Ga ................. 75
6.2 Plastic Strain Field ..................................... 77
6.3 Grain Mapping on the Basis of Extinction Contrast......... 79
References ................................................. 81
7 Multigrain Crystallography............................... 83
7.1 Structure Determination from Polycrystalline Data ......... 84
7.2 Structural Phases Appearing in ppm Concentrations ........ 87
References ................................................. 87
8 The 3DXRD Microscope.................................. 89
8.1 Optics ................................................ 90
8.2 Diffractometer ......................................... 92
References ................................................. 94
9 Applications .............................................. 95
9.1 Polycrystalline Deformation.............................. 95
9.1.1 The 3D Toolbox.................................. 96
9.1.2 Grain Rotation Experiments....................... 97
9.1.3 Lattice Strain Experiments ........................ 100
9.1.4 Outlook......................................... 103
9.2 Recrystallization ....................................... 103
9.2.1 Growth Curves of Individual Grains ................ 105
9.2.2 Spatial Distribution of Nucleation Sites ............. 107
9.2.3 Outlook for the Statistical Approach................ 109
9.2.4 First-Principles Studies ........................... 110
9.3 Recovery and Nucleation ................................ 112
Contents XI
9.3.1 Static Recovery .................................. 114
9.3.2 Nucleation and the Emergence of New Orientations... 117
9.3.3 Outlook......................................... 120
9.4 Peak Shape Analysis.................................... 120
9.5 Phase Transformations .................................. 123
9.5.1 Steel............................................ 124
9.5.2 Optimization of High-T Superconducting Tapes ..... 127
c
9.6 Grain Size Distributions................................. 130
9.6.1 Methodological Concerns.......................... 131
References ................................................. 133
10 Alternative Approaches................................... 137
10.1 Differential-Aperture X-Ray Microscopy................... 137
10.2 The Moving-Area-DetectorMethod ....................... 140
10.3 Other Depth-Resolved X-Ray Diffraction Methods.......... 141
10.4 Applying 3DXRD Methods to Other Sources............... 143
References ................................................. 144
11 Concluding Remarks ..................................... 147
References ................................................. 149
Index......................................................... 151
1 Introduction
Hard polycrystalline materials such as metals, alloys and ceramics form the
basis of much of modern industry. The physical, chemical and mechanical
propertiesofthesematerialsaretoalargeextentgovernedbytheirstructure.
Hence,acomprehensivedescriptionofstructuralevolutionduringprocessing
is at the heart of materials science.
Describing the structural dynamics is complicated by the inherent com-
plexity ofthe processes.Typically,the structure is organizedona number of
length scales, ranging from the atomic to the macroscopic. Interactions be-
tween the various elements of the structure occur simultaneously. Generally
speaking, models that bridge all of the relevant length scales do not exist.
Arguably, our understanding is best at the atomic and macroscopic scales,
wheremodelscanbebasedonsimulationsusingmoleculardynamicsandcon-
tinuum mechanics, respectively. At the intermediate scale, the mesoscale, a
descriptionistypicallyphenomenologicalinnature.Furthermore,mostmod-
elsaimatpredictingaverageproperties,andindoingsoneglecteffectscaused
by the pronounced heterogeneities often present.
Asanexample,considertheprocessesinvolvedintheplasticdeformation
of a coarse-grained metal. These are illustrated by electron micrographs in
Fig. 1.1. When an external load is applied individual dislocations (line de-
fects) appear on the atomic scale. To reduce their associated strain fields,
these willtendtoscreeneachotherbyformingdislocationstructures.Simul-
taneously,asacollaborativeeffectofthemovementofmillionsofdislocations,
each of the grains will change its shape. The combined result of these local
morphologicalchangesisthattheshapeofthesampleisalteredinaccordance
with the external force applied.
Despite a wealth of experimental studies, it is an open question to what
extenttheplasticresponseofeachgrainisgovernedbyitsinitialorientation,
by its interaction with neighboring grains or by the emerging dislocation
structures. All existing approaches to modeling neglect at least one of these
aspects. Another typical aspect is that the models include certain material
parameters, in casu hardening laws, which are more or less unknown and
which only can be derived from first principles by modeling on a different
(atomic) length scale.
HenningF.Poulsen(Ed.):Three-DimensionalX-rayDiffractionMicroscopy,
STMP205,1–5(2004)
(cid:1)c Springer-VerlagBerlinHeidelberg2004
2 1 Introduction
a b c
200 (cid:80)m 2 (cid:80)m 5 (cid:80)m
Fig. 1.1. Evolution of typical structures in a metal during deformation, as ob-
served by various electron microscopes. In the undeformed state, the structure is
characterizedbygrainboundaries(a).Aftersomedeformation,tangleddislocations
appear(b).Theseformintodislocationstructuresaftermoredeformation(c).Note
thedifference in scales
Historically, advances in understanding have often been linked to the in-
troductionofnewandmorepowerfulstructuralcharacterizationtools.Hence,
the introduction of optical microscopy by So¨rby [1] is generally seen as the
birthofmodernmetallurgy.Likewise,numerousfieldswererevolutionizedby
the advent of electron microscopy [2].
In a similar way,in the view of the author the present difficulty in estab-
lishing a comprehensive description of mesoscale behavior is at least partly
due to a lack of appropriate experimental tools. As discussed below, charac-
terizationontherelevantscaleisalmostexclusivelyperformedbyapplication
of surface-sensitive probes.Owing to effects such as stress relaxation,migra-
tion of dislocations and atypical diffusion, samples must be sectioned before
investigation to obtain results representative of bulk behavior. This destruc-
tive procedure prohibits studies of the dynamics of the individual elements
of the structure.
Hence, a given process can only be studied postmortem by comparing
a set of specimens produced by interrupting the process at different stages.
While such studies have been – and will continue to be – indispensable in
many areas, it is clear that they provide no direct information of the local
interactionsand,therefore,aboutthegoverningmechanisms.Moregenerally,
it is difficult to characterize the effect of heterogeneities.
It appears that what is required is an experimental technique with the
following properties:
– sufficient penetration power and flux for nondestructive 3D characteriza-
tion of the material within the bulk and on a micrometer scale;
– contrastmechanismsbywhichtheindividualelementsofthestructurecan
be completely characterized with respect to their position, morphology,
phase, crystallographic orientation, and elastic and plastic strain;