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5.4 X-ray diffraction methods

Hartmut Stöcker

Abstract: X-ray diffraction is a very common and widespread method, which is

routinely applicable also to battery materials. This chapter gives a brief overview
on the information content of X-ray diffraction patterns and on different principal
measurement setups with special regard to battery characterization.

Keywords: X-ray diffraction, X-ray methods, X-ray set-ups

Diffraction techniques using X-rays or neutrons allow a non-destructive access to

structural properties of arbitrary samples. The most frequently extracted properties,
i. e. the information contained in diffraction data, are schematically summarized in
Figure 5.4.1. They include the composition of multi-component samples as well as
lattice parameters, crystallite sizes and texture of individual phases. In the case of
electrochemical storage materials, this allows tracking of chemical reactions or
intercalation processes due to the operation of the device. It is even possible, using
adapted battery set-ups, to investigate these processes in situ or operando.
Since most battery materials are not stable in air, they need to be measured
within an appropriate package, case or chamber. The protective material should be
thin and have low density to minimize absorption. In addition, if possible, it should
not be crystalline to prevent additional reflections. If all components of a complete
 5.4 X-ray diffraction methods 325

Powder diffraction pattern

Background Reflections

Sample holder,
Sample Positions Intensities Profiles
air

Device function
Compton scattering,
thermal diffuse scattering,
amorphous fractions
Crystal structure: Sample properties
Bravais lattice: Atom positions,
Lattice parameter, occupancies,
centering thermal
(extinctions) displacement Real structure:
parameters Crystallite size,
strain, stacking
faults

Qualitative Quantitative
Phase Analysis Phase Analysis

Figure 5.4.1: Information content of an X-ray powder diffraction pattern. The individual parameters
can be assessed with the so-called profile fitting algorithms, of which the Rietveld method is the
most powerful [1, 2].

battery shall be characterized, the photon or neutron energy needs to be high enough
to penetrate all layers. This is usually more of a concern for X-rays since their typical
penetration depths are only in the order of 1…100 µm.
Phase composition and lattice parameter changes are equally well obtained from
X-ray and neutron diffraction (ND) data. However, when it comes to studying the
intercalation of lithium, neutrons are advantageous. For X-rays, the scattering cross-
section increases with the atomic number, so that lithium is contributing only little to
X-ray reflection intensities, in particular, when heavier elements are simultaneously
present in a compound. Since neutrons interact with the nucleus and not with
electrons, lithium atoms have a stronger influence on the neutron reflection inten-
sities. Hence, neutrons are very well suited for studying lithium content within
battery materials (see the following chapter).
Since X-ray diffraction (XRD) is a very widespread and universal method, its
application to battery materials is obvious. All known variants of XRD may in
principle be applied to battery materials. An overview of common X-ray methods
together with a general set-up for such measurements is given in Figure 5.4.2. From
these methods, X-ray powder diffraction is most often applied, since the largest part
326 5 Characterization methods

X-ray
powder
diffraction

Single-
X-ray
crystal
reflecto-
X-ray
metry
diffraction
X-ray
diffraction
(XRD)

High-
In situ
resolution
X-ray
X-ray
diffraction
diffraction
Gracing-
incidence
X-ray
diffraction
(a)

X-
so ray ay
X-r ctor
urc
e t e
Pri
m ry de
op ary da
tic
s e con ics
S pt
o
(b) Sample environment

X-ray Primary Secondary X-ray

source optics Sample optics detector
(c) environment

Figure 5.4.2: Overview of common X-ray diffraction methods (a) and general set-ups for X-ray
diffraction experiments in reflection (b) and transmission geometry (c).

of materials is polycrystalline, i. e. composed of small crystallites with sizes in the

nanometre or micrometre range. A common XRD set-up is shown in Figure 5.4.3. In
Table 5.4.1, typical applications and the usually applied X-ray optics for the different
methods are given.
Polycrystalline samples may be powders, slurries, ceramics, thin films, etc. and
all of them can be analysed by X-ray powder diffraction to determine lattice para-
meters, phase composition, crystallite sizes and more (cf. Figure 5.4.1). Nevertheless,
 5.4 X-ray diffraction methods 327

(a) (b)

Figure 5.4.3: (a) X-ray diffraction system with X-ray tube and optics (left), in situ sample set-up
(centre) and two different detectors (right). All components are mounted to a two-circle goniometer.
(b) Contacted in situ button cell with Kapton window.

Table 5.4.1: Typical optics and applications for the common X-ray diffraction methods.

Method Primary optics Secondary optics Typical applications

X-ray powder Slit, optionally Goebel Slit, filter or Lattice parameters,

diffraction mirror or monochromator phase composition,
monochromator crystallite sizes
Single-crystal X-ray Monochromator or Typically none, with 2D Solution of unknown
diffraction Goebel mirror and area detector structures
aperture
In situ X-ray diffraction Slit, optionally Goebel Typically none, with 1D Monitoring of phase
mirror or 2D detector composition changes
Gracing-incidence Slit, Goebel mirror, Slit, Soller collimator or Investigation of thin
X-ray diffraction optionally monochromator films or surfaces
monochromator
High-resolution X-ray Slit, Goebel mirror, and Slit and Lattice parameter
diffraction monochromator monochromator changes, epitaxial thin
films
X-ray reflectometry Slit and Goebel mirror Slit Thickness, density, and
roughness of thin films

the selection of a suitable set-up helps to improve the accuracy of the obtained
parameters within reasonable measurement times. The classical Bragg–Brentano
set-up uses a divergent X-ray source (a conventional X-ray tube), a planar sample,
a secondary filter or crystal monochromator and a point detector. Measurement times
can be decreased by the use of one- or two-dimensional detectors with energy
discrimination without sacrificing resolution.
Synchrotron X-ray sources have become popular for in situ experiments because
of the higher beam intensity available as compared to X-ray tubes. This increased
328 5 Characterization methods

“intensity” is, however, mostly an increase in brilliance due to the smaller diver-
gence, beam size and energy bandwidth obtained at synchrotron beam lines. Hence,
for some situations, like the measurement of large enough homogenous samples,
comparable results can be obtained with laboratory sources within reasonable mea-
surement time. When used with one- or two-dimensional detectors covering a range
of diffraction angles, laboratory sources are even suited for in situ experiments.
Since most half cells and complete battery packages need to be protected against
air, the design of battery cells suitable for XRD is one of the keys for performing in situ
experiments [3–5]. The key parameter is the energy of the used X-ray source, since the
penetration depth x0 is proportional to the third power of X-ray energy E according to

AE3
x0 ⁓
%Z 4

with atomic mass A, density % and atomic number Z [6, 7]. The total thickness x of the
material to be investigated should be within few absorption lengths x0 , since the
transmitted intensity decreases according to

– xx
I = I0 e 0

with respect to the primary beam intensity I0 [6]. As the materials and their thick-
nesses are typically fixed for a given battery set-up, only the X-ray energy E can be
increased to reach sufficient penetration depths x0 . Laboratory X-ray sources with Mo
or Ag anode (17.5 keV and 22.2 keV, respectively) are useful, but special synchrotron
beamlines can reach energies of 50 keV or even 100 keV. Typical XRD measurements
are done in reflection geometry (see Figure 5.4.2(b)), but transmission geometry (see
Figure 5.4.2(c)) may be beneficial for in situ experiments, where reflections from the
whole battery (and not only from the top electrode) need to be collected.
Evaluation of phase composition, lattice parameters and crystallite sizes is typically
performed by the Rietveld method, which is fitting a modelled diffraction pattern
against the measured one until good agreement in terms of certain quality parameters
(R factors) and visual inspection is reached [1]. This procedure typically gives much
more reliable results than comparing only peak intensities to determine phase percen-
tages or applying the Scherrer equation to determine crystallite sizes. The major risk
with typical Rietveld software is to overfit the data. This means to refine too many
parameters against data that do not provide sufficient information. Careful selection of
modelling parameters and inspection of the different R factors is, therefore, mandatory.
The other XRD methods (see Figure 5.4.2(a)) include single-crystal diffraction to
solve structures of unknown compounds and several techniques typically applied
to thin films: Gracing-incidence diffraction limits the penetration depth to few nano-
metres by choosing a very small angle of incidence with respect to the sample surface.
High-resolution diffraction is typically applied to study the quality of epitaxial thin films.
 5.4 X-ray diffraction methods 329

X-ray reflectometry yields the density, thickness and roughness of thin films. For details
on the special XRD techniques, a multitude of books are available [6, 8–14].
Since XRD methods are widely used, almost all publications on battery materials
make use of them, so that no collection of selected references will be given here. As an
example, a diffraction pattern array collected during a first charge–discharge (lithia-
tion–delithiation) cycle of a Li–S battery is shown in Figure 5.4.4. According to Ref. [15]
the lithium–sulphur system is a very promising candidate for post-lithium-ion batteries.
One of the major challenges is controlling the phase development, the so-called poly-
sulfide shuttle, which impacts the cycling efficiency of those batteries. Using operando
XRD, the authors were able to monitor and analyse the structural signatures of the Li2Sn
species adsorbed at the surface of a glass fibre separator. The obtained results helped
enhancing the performance of the Li–S cell by using fumed silica as electrolyte additive.
The authors stated that operando XRD can serve well in probing the effectiveness of
these adsorbents and discerning their role in the overall reaction mechanism.

a b
Potential (V) (versus Li+/Li)

2.6

2.4
90
80
70 2.2
60
h)

50
e(
Tim

40 2.0
30
20
10 1.8
0 10 20 30 40 50 60 70 80 90
23 24 25 26 27 28 29
Time (h)
2θ (°) ( λ = Cu Kα)
Highest
Li2S

PS2
PS1

intensity
*

c 90
80
70
60
Time (h)

50
40
30
20
10
0
2.6 2.4 2.2 2.0 1.8 22 23 24 25 26 27 28 29 30 Lowest
Potential (V) (versus Li+/Li) 2θ (°) ( λ = Cu Kα) intensity

Figure 5.4.4: (a) Waterfall representation of XRD patterns and (b) the corresponding galvanostatic
curve, recorded during the first cycle of a Li–S cell at C/50 rate. The coloured patterns in (a), indicating
major changes along cycling of the Li–S cell, correspond to coloured dots in (b), representing different
states of charge. (c) XRD contour plot of the data shown in (a), with the same galvanostatic curve as
shown in (b). The intensity chart is given at the very right of (c). The asterisk refers to a reflection arising
from a cell part. α-S8 and β-S8 are represented by white vertical lines with diamond and oval symbols,
respectively. The positions of the reflections labelled PS1 and PS2, attributed to the PSs–SiO2 inter-
actions, are indicated by vertical black dashed lines. Li2S refers to the solid end-of-lithiation product
lithium sulphide and is symbolized by a dashed-dotted black vertical line. The horizontal dotted black
lines are used as guidelines for following the changes in the reflection intensities as function of the
potential and time. Reprinted from Ref. [15], with permission of the Nature Publishing group.
330 5 Characterization methods

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5.5 Neutron methods for tracking lithium in operating electrodes

and interfaces
Mikhail V. Avdeev, Ivan A. Bobrikov and Viktor I. Petrenko

Abstract: The performance characteristics of modern electrochemical energy storage

devices are largely determined by the processes occurring at charge separation
interfaces, as well as by the evolution of the structure, composition and chemistry
of electrodes and electrolytes. The paper reviews the principal applications of neu-
tron scattering techniques in structural studies of electrode materials and

This article has previously been published in the journal Physical Sciences Reviews. Please cite as:
Avdeev, M. V., Bobrikov, I. A., Petrenko, V. I. Neutron methods for tracking lithium in operating
electrodes and interfaces Physical Sciences Reviews [Online] 10.1515/psr-2017-0157