Diffraction Analysis of the Microstructure of Materials

557 Pages·2004·12.98 MB·English

by  J. I. Langford (auth.), Professor Dr. Ir. Eric J. Mittemeijer, Professor Dr. Paolo Scardi (eds.)

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E.J. Mittemeijer P. Scardi (Eds.)
Diffraction Analysis
of the Microstructure
of Materials
With 240 Figures and 39 Tables
" Springer
Professor Dr. Ir. Eric J. Mittemeijer Professor Dr. Paolo Scardi
Max Planck Institute for Metals Research Universita di Trento, Facolta di Ingegneria
Heisenbergstrasse 3 Dipartimento di Ingegneria
70569 Stuttgart, Germany dei Materiali e Tecnologie Industriali
E-mail: [email protected] Via Mesiano 77> 38050 Mesiano, Italy
E-mail: [email protected]
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University ofVirginia Universität Oldenburg, Fachbereich Physik
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Charlottesville, VA 2290,3-2442, USA 26129 Oldenburg, Germany
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Microelectronics Science Laboratory Institut für Festkörper-
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Columbia University Helmholtzstrasse 20
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Diffraction analysis ofthe microstructure ofmaterials 1 E.). Mittemeijer, P. Scardi (eds.).
p. cm. - (Springer series in materials science, ISSN 0933-033X; v. 68)
Includes bibliographical references and index.
1. Crystal optics. 2. Microstructure. 3. Diffraction. I. Mittemeijer, E.). II. Scardi, P. (Paolo) III. Series.
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Preface
The Microstructure
Materials are substances that have now, or are expected to find in a not too
distant future, practical use. Here we will confine ourselves to solid materials.
The microstructure of materials then is a notion that comprises all aspects
of the atomic arrangement in the material that should be known in order
to understand its properties. Mostly we are concerned with crystalline mate
rials. The conception microstructure then narrows to the description of the
so-called crystalline imperjection; the idealized crystal structure, character
ized by the filling of the unit cell, is considered to be known and thus its
determination is not considered in this book.
MicrostruCture encompasses the compositional inhomogeneity, the amount
and distribution of the phases in the material, the grain size and shape and
the distribution functions of the grain-size parameters, the grain(crystal)
orientation distribution function (texture), the grain boundaries/interfaces
and the surface of the material, the concentrations and distributions of crys
tal defects as vacancies, dislocations, stacking and twin faults, and, not least,
lattice distortions due to strains/stresses, etc.
As may be anticipated from the above listing, the microstructure to a
very large extent determines the properties of a material. The central issue
of materials science may be described as: to develop models that provide the
relation between the microstructure and the properties. To this end charac
terization of the microstructure of a material is aprerequisite.
Diffraction Analysis of the Microstructure
Diffraction analysis is perhaps the most powerful technique for investigating
the microstructure by exploiting, especially, its sensitivity for the atomic
arrangement and also the element specificity of the scattering power of an
atom.
Each intensity maximum (called line profile or peak) in the diffraction
pattern represents an average over the diffracting material; in the case of
conventional X-ray diffractometry the diffracting volume is usually of the or
der 1 mm3. This indicates the strength and, at the same time, the limitation
VI Preface
of diffraction analysis: average values for structure parameters (microstruc
ture parameters) are obtained (e.g. the dislocation density, the internal stress)
which have a close bearing on the properties on mesoscopical and macroscop
ical scale, but the atomic configuration around an individual, isolated defect
cannot be revealed in this way.
In this preface we do not intend to review and comment on the whole field
of microstructural analysis by diffraction methods. However, with a view to
the scope of this book, we wish to make the following remarks in order to set
the (historieal) record straight.
Already shortly after the discovery of diffraction of X-rays bycrystals
(1912), it was realized by Scherrer, at the time in döttingen (1918), that the
breadth of arefleetion can be fruitfully used as a measure of the average finite
size of the diffracting crystals. Also, as taught to undergraduates, by differ
entiating Bragg's law it seems obvious that information on lattice-parameter
fluctuations is exhibited by diffraction-line broadening. Probably the first,
seminal work in this area was performed by Dehlinger and Kochendörfer in
Stuttgart (1927 and 1939). It is striking to observe that this work has been
ignored largely in well known books reviewing the history of (X-ray) diffrac
tion analysis (e.g. see "Early Papers on Diffraction of X-rays by Crystals" by
Bijvoet, Burgers and Hägg (Vol. 1, 1969 and Vol. 2, 1972) and "Fifty Years
of X-ray Diffraction" by Ewald (1962)); the name of Scherrer is recalled in
these works, but in particular for his contribution in the development of the
Debije-Scherrer technique (1916). This negligence may be understood from
the underestimation, in particular by (classical) crystallographers in the first
decades of the existence of the (X-ray) diffraction method, of the importance
for mankind of knowledge on the real, imperfect structure and the crucial im
portance of diffraction methods to acquire such data. (Even Scherrer himself,
in a personal reminiscence in the above mentioned book by Ewald, referred
to his now famous formula only in passing).
In particular since, say, 1940, the full analysis of the width and shape of a
diffraction line has become a topic of, until and beyond today, increasing im
portance. On the one hand, one observes the development of more and more
advanced methods to extract microstructural parameters from the broad pa
rameters of a number of diffraction lines using more or less realistic, general
assumptions on the material imperfectionjline shape: line-profile analysis. On
the other hand, arecent, powerful approach of huge future potential appears
to be line-profile synthesis, where the microstructural parameters are deter
mined by fitting line profiles, calculated on the basis of a structure model
specific to the material investigated (i.e. no line-shape assumptions are em
ployed), to measured ones. Further, the emergence of the Rietveld method,
where the whole diffraction pattern is used in a refinement of the filling of
the unit cell (i.e. refinement of the idealized crystal structure), has made one
aware that such an approach also allows the determination of microstructure
parameters in a fitting procedure incorporating the Jull diffraction pattern.
Preface VII
The analysis of residual, internal (macro)stress is based on the measure
ment of the orientation dependence, with respect to the specimen frame of
reference, of the lattice spacing in the (polycrystalline) material investigated.
The analysis 01 (macro)stress has usually not been covered in textbooks on
(X-ray) diffraction (there are a few exceptions where a marginal description is
given). Reasons for this ignorance can be (i) that during decades the develop
ment of this method took place predominantly in Germany and corresponding
publications were written in German and (ii), probably more important, that
there was a strong, not rarely exclusively, engineering interest in this method
and its results. Considering the earlier mentioned historical overviews on the
development of the (X-ray) diffraction method, it will now be no surprise that
only in a personal reminiscence by Glocker, in the earlier mentioned book
by Ewald, the now so important diffraction method to determine stress is
mentioned. Glocker, working in Stuttgart, as the above mentioned Dehlinger
and Kochendörfer, can be considered as one of the pioneers of this method
(see also his own textbook (in German, published in 1927». The availability
nowadays of two textbooks on this method in English and the participation
of materials scientists worldwide, in further development of the method and
its applications (see the proceedings of the (European and worldwide) con
ferences on "residual stress" (ECRS and ICRS», as for example evidenced
by the investigation of grain interaction and stresses in thin films, makes
clear that stress analysis is an inseparable part of the field of microstructural
diffraction analysis.
The Book
This book has been devised to offer an overview of currently "hot" topics
in the field of the diffraction analysis of the microstructure of materials.
We, as editors of this book, selected authors of prospective contributions on
the basis of presentations at the International Conference on the "Analysis of
microstructure and residual stress by diffraction methods" ("Size-Strain Irr" ,
December 2-5, 2001, Trento, Italy), of which we together were the chairmen.
This book should not at all be considered as the proceedings of the con
ference mentioned:
- Firstly, only a fraction (corresponding to about 30%) of the presentations
at the conference could be said to be represented in this book.
Secondly, the prospective authors were asked, after the conference, to
write a contribution for the book of monograph character. Thus, although
the book requires a basic knowledge of materials science, or solid state
physics or chemistry, it allows to get an impression of the current state of
knowledge in the field. Moreover, the detail in the presentation of methods
and techniques suffices for the readers of the book to apply them.
- Thirdly, all submitted manuscripts were subjected to a refereeing pro ce
dure involving at least two referees. A majority of the manuscripts were
VIII Preface
revised on the basis of the comments of these referees. Thereafter the ref
erees were asked for a second consideration of the now revised manuscript.
Thus, the book is neither a conference proceedings nor just a compilation
of high quality research papers as could have been published in a first dass,
international journal. Instead, the book is a collection of twenty high quality
contributions, which together provide an overview 01 the frontline research
on the "Dijjraction Analysis 01 the Microstructure 01 Materials", where the
detailedness of the information offered should allow application of the pre
sented methods by Ph.D. students and professionals working in the field. To
be complete is impossible. For example, we have no contribution dealing with
only texture (preferred orientation) analysis. Yet, we hope to have achieved,
by our choices and quality check and improvement, an important, timely
book of monograph character.
Part I of the book is of special character. It deals with the history of line
profile analysis. In view of the deficiencies of the existing historical books
(see above), such an overview is much needed to provide some background
for those of the following chapters, which outline the current state of research
in the field of line-broadening analysis.
Part II comprises six contributions, whose common denominator is the
analysis of the whole diffraction pattern. This part of the book exposes the
current debate on pattern fitting versus pattern modelling, the former ap
proach is based on assumed (analytical) functions for peak-profile shape and
the latter approach departs from suitable models (of the instrument and/or
the sampIe microstructure), without imposing apriori a profile-shape func
tion.
The first chapter provides a powerful approach, in principle, to the mod
elling of the instrumental peak profile on the basis of an analytical description
of the spectral profile (wavelength distribution in the diffracted, recorded ra
diation) and of the various optical components in the beam path. The follow
ing chapter presents the fundamentals of Whole Powder Pattern Modelling,
with applications to nanocrystalline materials and to highly defective metals.
Full pattern simulation, based on physical models of line broadening due to
line and planar defects, is the subject of the third chapter to study ceramic
as well as metallic nanocrystalline materials. In some way as an alternative
to the previous two contributions, Chap.4 concerns the analysis of resid
ual stress and crystallite size within the framework of a traditional Rietveld
refinement.
The last two chapters in this part address the still controversial issue of
the determination of an amorphous fraction in phase mixtures: the first one
points out the success and the weakness of present-day techniques based on
pattern fitting by the Rietveld method, induding a discussion of the in the
literature intensively discussed treatment of absorption effects, whereas the
second one illustrates recent innovations based on the modelling of crystalline
as well as amorphous phases.
Preface IX
The next part deals with a classieal but still very important and develop
ing topic of powder diffraction analysis: the determination of crystallite size
and shape. Although diffraction analysis in principle allows determination of
the size and shape of coherently scattering domains, the current trend in
volves adoption of appropriate assumptions, such as grain shape, to derive
a grain size distribution from the measured data. Such an approach is espe
cially appropriate for finely dispersed polycrystalline materials, which are the
focal point of interest for the two chapters in this part. In the first chapter
a recently introduced Bayesian/maximum entropy method is presented and
the method is illustrated for the case of a nanocrystalline ceramic powder,
whereas the second chapter concerns the use of small-angle diffuse scatter
ing for the analysis of polydisperse sampies of compact sub-microcrystalline
metallic materials.
Line and planar defects are the subject of Part IV. The first contribution
affords a detailed description of how to calculate the dislocation contrast fac
tor for cubic materials, with ex;amples of materials with face-centred, body
centred and primitive lattices. The next two contributions concern line broad
ening due to inhomogeneous dislocation distributions. The first one presents
a generalization of Wilson's variance method for the case of dislocated single
crystalline and polycrystalline materials, whereas the second one is based on
the Krivoglaz/Wilkens' formulation and deals with the case of textured thin
films. The fourth and final chapter in this part deals with the modelling of
the diffraction pattern of faulted materials, discussing in detail the case of
fcc materials exhibiting intrinsic, extrinsic and twin faulting.
The subject of Part V is grain interaction, in the case of elastie and plastic
deformation. The first of the two contributions deals with the effect of grain
interaction on the determination of residual stress, especially in thin films,
showing how grain inter action leads to macroscopically elastically anisotropie
behaviour, even in the absence of texture. In particular the consequences of
surface anisotropy are indicated: an old problem that never has been dealt
with conclusively; the approach presented may open a new route to settle
the argument definitively. The second chapter concerns the role of grain in
teraction and dislocation structures in plastic deformation of polycrystalline
materials, as described by the evolution of texture.
The following part, Part VI concerns the role of surfaces and interfaces
in polycrystalline materials. The first contribution in this Part describes the
effects of grain-surface relaxation, observed in nanocrystalline powders, on
the diffraction-line broadening, within the Whole Powder Pattern Modelling
approach (see Part 11). The second chapter provides adetermination of the
grain-boundary stress from measured values for the grain size and the strain
free lattice spacing of a nanocrystalline material.
The last part, Part VII presents three contributions on thin film analysis.
The first chapter provides a detailed overview of the existing techniques for
measuring residual stress gradients in thin films by diffraction methods, also
considering possible text ure effects. The following two contributions concern