Conventional and advanced diffraction techniques

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ISEPS Workshop on
Engineering mineralogy of ceramic materials

Certosa di Pontign
ano, 8
-
11 June 2001


1

Conventional and advanced diffraction techniques




Gilberto Artioli


Dipartimento di Scienze della Terra, Università degli Studi di Milano

e

Centro CNR di Studio per la Geodinamica Alpina e Quaternaria

ar
tioli@iummix.terra.unimi.it





INTRODUCTION


The contribution wishes to review: (1) the traditional applications of diffraction in the
characterization of solid state materials and processes; (2) the advantages of using advanced
radiation sources over co
nventional sources; and (3) current trends and experimental developments.


Diffraction from the solid state is a fundamental technique for the crystallographic characterization
of synthetic and natural materials. It is especially valuable as a complement
to electron microscopy
and spectroscopic techniques in the investigation of complex systems. Since the discovery of
Bragg
-
type X
-
ray diffraction from periodic crystal lattices (AD 1912) the technique has proven an
essential tool for


(a)

the
identification

of

crystalline compounds,

(b)

the
quantitative analysis

of polyphasic mixtures,

(c)

the study of the long
-
range
atomic structure

of crystals, and

(d)

the
physical analysis

of crystalline aggregates including defects, preferred orientation and
texture, crystallite siz
e distribution, and lattice microstrain effects.


Diffractometry has long developed standard procedures of analysis for all the cited applications (a
-
d) and during the last decades they became so widely utilized that data are now available for most
known

inorganic compounds and minerals, to the extent that electronic databases (i.e. PDF, ICSD,
CRYSMET, etc.) are now accessible for the automatic identification and rapid retrieval of
crystallographic and structural information of a large number of crystalli
ne substances. The focus of
the modern crystallographic research on inorganic solids is the interpretation of the physical and
chemical properties of materials in terms of their ideal or defective atomic structure, and the transfer
of the acquired crystal
chemical knowledge to the engineering of solid state compounds with novel
technological properties (Chung and Smith, 2000).

Independently of the nature of the radiation used, the vast majority of structural investigations (i.e.
point c above) are commonly

performed using single crystals (Giacovazzo 1992), although it should
be remarked that the field of structure solution and analysis from powder diffraction data has
developed tremendously in the last 15 years (see for example: Langford and Louer, 1996; Ha
rris
and Tremayne, 1996; Newsam et al., 1999; Turner et al., 2000). As structure solution and analysis is
a very specific and well developed field, it will not be treated here in detail. Attention will be rather
ISEPS Workshop on
Engineering mineralogy of ceramic materials

Certosa di Pontign
ano, 8
-
11 June 2001


2

paid to diffraction techniques and applicati
ons involving polycrystalline materials (Bish and Post,
1989; Jenkins and Snyder, 1996), since most of the important traditional and advanced ceramic
materials of interest to the workshop are synthesized and employed as polycrystals.

The principles of appl
ications of laboratory X
-
ray powder diffraction in the characterization of solid
crystalline materials will be briefly reviewd, and then it will be shown how these applications may
be greatly expanded using advanced radiation sources and techniques.



TRAD
ITIONAL APPLICATIONS OF POWDER DIFFRACTION



Qualitative and quantitative phase analysis


Probably the best known and most widely used application of powder diffraction is as an analytical
tool for both qualitative and quantitative analysis of crystalline

materials. As far as identification is
concerned, it should be reminded that the Bragg's
d
hkl

spacings and relative intensities of the
diffraction cones generated by a given polycrystalline material are a function of the chemical nature
of the substance u
nder investigation and of its crystal structure. Powder diffraction became a widely
used technique for the identification of polycrystalline unknowns in the thirties as a result of both
the clear definition of the minimum number of parameters required to p
reliminary identify a
specimen as a member of a more or less restricted group of substances, and also of the compilation
of a file containing the diffraction patterns of a number of known crystalline materials sufficiently
large to give a reasonable probab
ility that an unknown would be found among the standards present

in the file. This original file has since been expanded to such an extent that the release in 2000
includes more than 70,000 experimental powder patterns, besides 42,000 patterns calculated
from
the crystal structure data included in the Inorganic Crystal Structure Database (ICSD). The file is
presently known as the Powder Diffraction File (PDF) and it is continuously updated and managed
by the International Centre for Diffraction Data.

Using

the information contained in the PDF it is generally possible to match the measured
diffraction pattern of an unknown to that of one of the known substances present in the file. This
task can be accomplished using both manual and computer methods with an
obvious current
tendency in favor of the latter. The simultaneous identification of more than one component in a
polyphasic sample is also possible using search
-
match procedures, but clearly with a degree of
difficulty that increases with the complexity of

the measured diffraction pattern. Identification of
minor components in a multiphase mixture may be a very hard task to accomplish and all
independently available chemical and structural informations ought to be exploited.


The quantitative analysis of th
e different crystalline phases present in an unknown mixture is
another important application of powder diffraction that is especially relevant for the
characterization of natural and synthetic materials. The basic principle of the method implies that
ther
e is a proportionality between the measured diffraction intensities and the amount of a given
crystalline phase in the sample, although due to matrix absorption effects the proportionality is not
linear in the general case (Klug and Alexander, 1974). The c
alibration curves are commonly
determined experimentally from the intensities measured from samples of known composition and
in the case of more than two components having different absorption coefficients, the calibration
requires the addition of an inter
nal standard. Alternative methods that try to avoid the lengthy
procedure of determining independent calibration curves for each phase have been proposed, such
ISEPS Workshop on
Engineering mineralogy of ceramic materials

Certosa di Pontign
ano, 8
-
11 June 2001


3

as the flushing agent method, the reference intensity ratio (RIR), and similar variants. Details

can be
found in the exhaustive texbook by Zevin and Kimmel (1995).

A substantial advance in the field was made when it was recognized (Hill and Howard, 1987; Bish
and Howard, 1988) that there is a simple relationship between the Rietveld refined scale fa
ctor of
each phase and its weight fraction in the multiphase mixture (for an introduction to the Rietveld
method please refer to the volume by Young, 1993). The Rietveld
-
type quantitative analysis makes
an efficient use of all information contained in the
diffraction pattern and it is a truly standardless
procedure, as it can be performed on the collected diffraction data, without addition of internal
standard and without the need for external calibration curves. The only requirement is that a reliable
stru
cture model exist for the phases to be quantified. The crystal chemical or preferred orientation
problems that make the RIR analysis difficult may be largely overcome in the Rietveld quantitative
analysis by optimization of the crystal structure of each ph
ase, and by the application of adequate
corrections for the sample texture during the Rietveld refinement. If the quantitative Rietveld
analysis is properly performed on high quality diffraction data, the method can reliably be used to
quantify crystalline

phases well below the 1.0 wt % limit.

In case the multiphase mixture contains an amorphous component together with the crystalline
phases, the Rietveld procedure can still be used, but a known amount of internal standard needs to
be admixed with the sampl
e to properly quantify the amorphous (Gualtieri, 1999).



Physical analysis of the polycrystalline sample


A careful analysis of the profile shape of the diffraction maxima of a polycrystalline material can
give information on the size distribution of t
he crystallites and on the presence of lattice strains.
Strain measurements are particularly important in the evaluation of residual stress present in
engineering components. Peak broadening may also be caused by faulted and defective lattices, and
careful

measurement of the anisotropic character of the broadening along different crystallographic
directions may be fundamental to the interpretation of the defect model.

This is commonly referred to as the physical analysis of the sample and it focuses on the
interpretation of the measured diffraction profile as the convolution of the sample
-
dependent effects
with the instrumental contributions, including the energy distribution of the incident radiation, and
the aberrations due to the experimental geometry and

optical components (Klug and Alexander,
1974; Warren 1969; Snyder et al., 2000).

The crystal size and/or strain information on the sample are extracted through the analytical
description of the peak profile shape and its angular dependence, after the ins
trumental contribution
to the peak broadening has been subtracted. A number of different analytical functions have been
used to describe the profile shape, although they mostly adopt a Gaussian
-
type model for the strain
broadening and a Lorentzian
-
type mod
el for the crystal size broadening. The two contributions are
commonly combined by the use of flexible functions (typically Voigt, pseudo
-
Voigt, or Pearson VII
functions). The physical information is then extracted by analysis of the integral breadth or a
Fourier analysis of the individual line profiles (see for example Delhez et al. in Young, 1993; or
Langford and Louer, 1996).

If the polycrystalline material has texture, that is if its crystallites are not randomly oriented, the
intensity of a diffraction

ring will not be homogeneous. In this case, the measurement and analysis
of the intensity variation along the diffraction rings permits quantitative intepretation of the
crystallite orientation in the sample (see for example Bunge, 1993; or Bunge in Chung

and Smith,
2000). Texture determination with powder methods is much faster than the crystallite by crystallite
measurements performed by single crystal methods. However, we should be aware that
ISEPS Workshop on
Engineering mineralogy of ceramic materials

Certosa di Pontign
ano, 8
-
11 June 2001


4

polycrystalline diffraction techniques only yield pole densit
y distributions (fig. 1) of the crystallite
orientation, that is two dimensional projections of the three dimensional texture function. The full
orientation distribution function (ODF) must be calculated using a number of two dimensional pole
figures. Seve
ral mathematical techniques have been proposed to calculate the ODF, and they have
nowadays been implemented in analytical software packages. Linear and area detectors are of great
help in modern texture measurements by powder diffraction, as they allow fa
ster scanning of the
reciprocal space and make the whole powder spectrum available for each sample orientation.

Texture experiments are important to study the deformation and recrystallization processes in
polycrystalline samples (Kocks et al., 1998) produ
ced during manufacturing processes of ceramics.

It should be reminded that for average absorbing materials, texture analysis performed with X
-
rays
having wavelenghts commonly used in the laboratory (0.7
-
1.5 Å) only allows the probing of the
surface layer o
f massive samples, and the technique can therefore be used to study surface
processes, such as alteration, diffusion, etc. If the texture of the bulk is to be characterized, then
deeply penetrating neutrons or highly energetic synchrotron X
-
rays are to be
used, as described
below. The use of finely collimated penetrating beams allows tomographic techniques to be used
for the non
-
destructive characterization of the materials.








Fig. 1. Reconstruction of pole figures from Debye diffraction rings. (a)

Diagram showing the
experimental setup for texture data collection using a CCD detector. The spectrum on the right (b)
shows the azimuthal intensity variation along a diffraction ring and the pole figure (c) shows the
pole density distribution for the ana
lyzed peak (from Heidelbach et al., 1999).

ISEPS Workshop on
Engineering mineralogy of ceramic materials

Certosa di Pontign
ano, 8
-
11 June 2001


5

DIFFRACTION WITH ADVANCED RADIATION SOURCES


The last twenty years have witnessed the development of dedicated second and third generation
synchrotron radiation sources and spallation neutron sources (Baruchel et

al. 1993). These advanced
sources of hard X
-
rays and pulsed neutrons have triggered profound changes in the design and
practice of the diffraction experiments.


Synchrotron radiation has made available extremely brilliant and collimated X
-
ray beams, whic
h
are tunable in energy, polarized, and time structured (Margaritondo, 1988; Coppens, 1992). At
synchrotron facilities it is possible to (1) design traditional experiments with optimized features. For
example by using smaller volume samples, collecting dat
a much faster, and obtaining results with
higher resolution and superb signal/noise ratio; and (2) perform totally new types of experiments
that can not be done with laboratory X
-
ray sources.

Therefore, to start with simple applications, phase identificati
on on multiphase samples is more
efficiently performed on high
-
resolution powder diagrams, as diffraction peak overlap is
substantially lower. It is not uncommon that impurity phases contained in low amounts remain
undetected in preliminary laboratory anal
ysis, and show up in high quality synchrotron data.
Similarly, quantification of phases that are present in multiphase mixtures in amounts of the order
of 0.1 wt % need good peak discrimination and superior peak/background ratio for proper
assessment (for
example Latella and O’Connor, 1997). Although qualitative and quantitative phase
analysis are rather routinary applications, and thus it is not generally conceivable to undergo the
lenghty procedure of beamtime application at synchrotron sources for these
kind of analysis, there
may be exceptional cases when this is necessary. The case of detection and quantification of toxic
inorganic crystalline species in aerodispersed filters and human lungs is a typical case. As the
source materials are only available
in very modest amounts, the brilliance of the synchrotron beam
is essential to perform reliable analyses and to collect quality data within acceptable experimental
times. Other cases may include the analysis of absorbing samples such as Portland clinkers b
y
penetrating synchrotron radiation (de la Torre et al., 2001). Structural studies using high resolution
synchrotron powder diffraction data possibly represent the single most widespread application of
synchrotron powder diffractometry. The high resolution

attainable at dedicated powder beamlines
(FWHM of the order of 0.01 °2


or less when sample broadening is limited) plays an important role
in each one of the steps involved in structure analysis: indexing of the powder pattern, extraction of
the integrate
d intensities for the structure solution, and proper description of the peak profiles for
the full
-
profile refinement. Indeed in the last decade high resolution synchrotron powder
diffractometry was the key to the structural characterization of important c
lasses of materials only
available as microcrystals such as microporous materials and zeolites, fullerenes and
superconducting fullerides.

Besides high resolution, synchrotron powder diffractometry offers the possibility of energy tuning.
This additional f
lexibility is increasingly employed so to collect diffraction data at different
wavelengths. If the select experimental wavelength is close to the absorption edge of an element
contained in the investigated structure, the enhanced intensity contrast due to

resonant scattering
(Materlik et al., 1994) can be advantageously exploited to extract chemically
-
resolved information
on the specific atom. The effect is largely used in the location of the heavy atom in the structure of
macromolecular crystals, through
the use of multiple data sets (Multiwavelength Anomalous
Dispersion, i.e. MAD technique), although it may well be used in the study of inorganic compounds
to investigate the partitioning of specific atoms on independent crystallographic sites, or to perfor
m
the site
-
resolved analysis of the oxidation state of specific cations. The latter application has been
recently expanded into full analysis of the absorption fine
-
edge collected using the energy
-
ISEPS Workshop on
Engineering mineralogy of ceramic materials

Certosa di Pontign
ano, 8
-
11 June 2001


6

dependence of the intensity of selected diffraction peaks.

The technique is called DAFS (Diffraction
Anomalous Fine Structure) and it attempts to simultaneously extract information derived by X
-
ray
diffraction (i.e. long
-
range, crystallographic site
-
specific) and X
-
ray absorption (i.e. short
-
range,
chemically spe
cific). In addition to DAFS, resonant magnetic Bragg scattering may also be
successfully exploited.

Finally, the microstructural and physical analysis of the sample by powder diffraction also benefits
from the peculiarity of synchrotron radiation. For exam
ple, the very small instrumental contribution
to the diffraction peak broadening makes it possible to expand the range of measurable crystallite
size. Furthermore the fine collimation of the parallel synchrotron beam makes it the ideal source for
surface d
iffraction, grazing incident diffraction, depth profiling in materials surfaces, coatings and
thin films (for example Leoni and Scardi, 2000), and non
-
destructive characterization by
tomography (for example Ellingson et al., 1996; Mucke et al., 1998).


Neu
tron beams offer the great advantage of penetration into thick objects. They are therefore ideally
suited to study residual stresses and crack propagation within undisturbed large ceramic bodies, or
to perform non
-
destructive phase analysis of art and arch
aeological objects (for example
Kockelmann et al., 2001). Of course neutron radiography, 3D space mapping, and tomography are
also widely available techniques at both steady
-
state and pulsed neutron sources.




NEW EXPERIMENTAL DEVELOPMENTS AND CURRENT TRE
NDS


Besides optimization of traditional powder diffraction experiments, there are two broad
experimental areas that greatly benefit of the characteristics of advanced radiation sources: (a) in
situ diffraction in non
-
ambient conditions and time
-
resolved d
iffraction; and (b) simultaneous
studies using the combination of different techniques. Both areas are at present actively developed
thanks to the extreme flexibility of synchrotron and neutron experiments in terms of intensity,
resolution, energy tunabili
ty, and available space for instrumentation.



In situ diffractometry


As diffraction techniques are major tools for the study of crystalline matter, they are extensively
used in the investigation of the solid state under non
-
ambient or extreme conditions
. Phase
trasformations induced by gradients in temperature, pressure, or other physical parameters occur in
virtually all types of materials, especially during the processes induced by thermal treatments during
the manufacturing processes of ceramics. The
understanding of the transformation processes in the
solid state is therefore important in many areas of physics, chemistry, engineering, earth sciences,
and materials science, and it often involves the combined measurement of the material properties
and o
f the crystal structure, if possible at the operating conditions.

The measurement of the crystallographic properties of matter when physico
-
chemical gradients or
fields are applied upon the sample is performed by the so
-
called
in situ

techniques. Both
spec
troscopy and diffraction can in principle be directly performed on conditioned samples, and this
offers a number of advantages over experiments performed on treated (i.e. quenched or stabilized)
samples, insofar (a) the structural changes are directly prob
ed at the selected conditions and no
assumption is made on the preservation of the structural properties upon sample treatment, and (b)
time can be explored as an additional variable during the experiment.

ISEPS Workshop on
Engineering mineralogy of ceramic materials

Certosa di Pontign
ano, 8
-
11 June 2001


7

In general, we may say that the powder diffractio
n data represent an intensity profile as a function
of the scattering vector. In situ studies tend to add one dimension to the experimentally measured
variables. This dimension can be time (
time
-
resolved experiments
), temperature (
temperature
-
resolved equi
librium experiments
), pressure (
pressure
-
resolved equilibrium experiments
), space
(
sample space mapping
,
tomographic diffraction imaging

= TEDDI), or indeed any other sample
variable. The current trend in diffraction experiments is not only to measure equi
librium structural
information (i.e. the diffraction data), but rather to exploit the brightness of the advanced sources to
explore the complete evolution of the structure undergoing transformation processes.


































Fig. 2.
Time
-
resolved evolution of a fast rea
ction studied by in situ synchrotron powder
diffractometry. Each spectrum was collected at ESRF ID11 beamline for about 20 ms, using a CCD
Frelon camera.


ISEPS Workshop on
Engineering mineralogy of ceramic materials

Certosa di Pontign
ano, 8
-
11 June 2001


8

Most in situ experiments require non
-
standard instrumentation. Although several diffraction
instrume
nts available commercially are equipped with furnaces, cryostats, or pressure cells, only
high temperature chambers for X
-
ray powder diffraction (mostly based on heating metal strips) and
cryostats for X
-
ray single crystal diffraction (mostly based on cold

gas streams) have met a
widespread diffusion in the crystallographic laboratories. High temperature powder diffraction is
most commonly used for the study of phase transitions in minerals and materials science, whereas
low temperature single crystal diffr
action is commonly used to reduce thermal vibrations in the
crystal structure analysis of macromolecular or small
-
molecule organic compounds.

In the last few years the request for high quality in situ diffraction studies has rapidly increased in a
number o
f different fields and non
-
standard conditioning devices have therefore been developed to
meet the scientific demand. It is virtually impossible to cover all recent technical development in
the area of non
-
ambient studies, as they critically depend on the
specific application and on the
selected experimental system. For example, at synchrotron and neutron facilities many experimental
beamlines have specific equipment available to external users, and each device is optimized on the
energy range of the incide
nt radiation, the sample volume and shape, and the optics and detector
systems. Each experimenter is advised to plan in advance the details of the experiment with the
beamline scientists, and sometimes he is required to develop and carry its own sample cha
mber to
the experimental station.

Conceptually non
-
ambient studies may be designed and performed in different ways, depending on
how fast the external gradients are imposed on the sample, how fast the sample is reacting, and how
fast the diffraction data a
re collected. The two limiting cases are (a)
non
-
ambient static
measurements
, in which the sample is effectively studied at equilibrium or during a very slow
reaction, the data collection time is longer than the rate of transformation, and only the initial

and
final states are recorded; and (b)
non
-
ambient dynamic measurements

(e.g. time
-
resolved), in which
the data collection is faster than the rate of transformation of the sample, and the development of the

reaction can be studied in detail. Between thes
e limiting conditions, a vast range of experimental
configurations is possible. For example the external variable (i.e. T, P) may be varied continuously
during the experiment, or else a rapid change can be imposed at the start of the experiment, and then
t
he sample reaction is followed in time (isothermal mode).

For static measurements it is generally not a problem to obtain a satisfactory signal/noise ratio,
since the experiment has no time limitations. However for dynamic studies the detection time must
b
e considerably shorter than the time scale of the process, and for fast reactions the data may suffer
of signal recording problems and poor counting statistics. In such cases the use of linear or area
detectors and brilliant incident radiation beams are re
quired. The availability of bright synchrotron
radiation and the recent technical developments in non
-
ambient instrumentation have remarkably
expanded the field of time
-
resolved experiments into the domain of very fast measurements. In
many cases it is now

possible to dynamically investigate the structural changes in the solid state
system as a function of external variables with a time resolution well below the ms range. Major
recent developments of time
-
resolved crystallography have been focused in unders
tanding materials
properties during processing and protein functionality. Femtosecond X
-
ray diffraction is beginning
to emerge, although X
-
ray diffraction with time resolution below the ns range is necessarily
performed only on reversible systems and using

stroboscopic mode, mainly because of the limited
performances of the detectors.

In the case of thick samples energy dispersive diffraction imposes
few constrains on the diffraction geometry and is to be preferred (Barnes et al., 2000).

The area of very fa
st time
-
resolved studies is undoubtedly bound to be dominated in future years by
synchrotron radiation produced by insertion devices, because of the extreme photon fluxes thay can
deliver. Neutron beams at reactors and spallation sources are very weak in c
omparison, although it
is expected that neutrons can still play a role in the area of in situ studies by virtue of their excellent
ISEPS Workshop on
Engineering mineralogy of ceramic materials

Certosa di Pontign
ano, 8
-
11 June 2001


9

penetration depth. High temperature studies are especially favored by the design of neutron
furnaces, and they offer access t
o a wide temperature range (both in the very LT and in the HT
regions) and an excellent temperature stability over large volumes of samples.

Further major advantages offered by synchrotron and neutron experiments are the additional
degrees of flexibility i
n the instrumental setup. In particular, the high brilliance and collimation of
the X
-
ray beam offer an unparalleled freedom in the selection of the experimental components, and
in the possibility of trading intensity, resolution, and explored reciprocal s
pace. It is therefore
possible to insert additional experimental components, as this is often required when performing
simultaneous investigations in order to fully characterize the sample during complex
transformations. Most simultaneous studies are final
ized to obtain time
-
resolved complementary
information on the sample using multiple techniques.

For example by using small angle and wide angle diffraction (SAXS/WAXS experiments; e.g. Bras
and Ryan, 1998) it is possible to extract information at different

scales on crystallizing or
polymerizing systems. By combining diffraction and spectroscopy (for example XRD/IR or
XRD/XAS) it is possible to obtain simultaneous information on long
-
range and short range atomic
arrangements, as in the case of reactions cat
alyzed by specific chemical elements (e.g. Colyer et al.,
1997). Fig. 3 shows the experimental setup for performing simultaneous XRD and dynamic light
scattering (DLS) of crystallizing microporous materials under hydrothermal conditions. Crystal
phase info
rmation is obtained by the powder diffraction data, whereas the DLS signal allows
continuous monitoring of the development of the aluminosilicate gel as precursor to the crystalline
phases.

It is expected that time
-
resolved simultaneous studies will pla
y an increasing role in the
characterization of solid state transformation processes.




Fig. 3. Instrumental setup for simultaneous XRD and DLS experiments at the ESRF GILDA CRG
beamline.

ISEPS Workshop on
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Certosa di Pontign
ano, 8
-
11 June 2001


10


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Engineering mineralogy of ceramic materials

Certosa di Pontign
ano, 8
-
11 June 2001


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