In-situ X-ray diffraction study of the electrochemical reaction on lead electrodes in sulphate electrolytes
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ABSTRACT: Fundamentals and practical applications of diffraction for researchers, engineers, and students Materials science relies heavily on diffraction for the analysis of materials. Introduction to Diffraction in Materials Science and Engineering is a survey of the practical aspects of this valuable tool. Though it contains basic discussion of the theory and physics of diffraction, this book emphasizes understanding and the practical application of diffraction in materials science-making it a valuable text and resource for students, professionals, and researchers. Designed as a teaching and self-study text, this resource begins with a treatment of the fundamentals of crystallography and crystal structure and its importance in diffraction before moving on to cover important aspects of diffraction applications. Numerous examples and problems at the end of each chapter, including critical thinking questions, make this an excellent tool for learning and understanding. The book includes treatments of: * Basics of crystallography * Geometrical representation of crystals and reciprocal space * X-rays and neutrons * Structure factors and intensity * Powder diffraction * Qualitative (Powder Diffraction File) and quantitative phase analysis * Use of the International Tables for more complex structures and the Reitveld method * Residual stress * Introductions to texture, small diffracting units, and long-range order Aaron Krawitz provides both a practical introduction to diffraction that suits the needs of students and a resource for professionals already at work in materials science or engineering who want to utilize the power of diffraction in the study of materials.Introduction to Diffraction in Materials Science and Engineering, by Aaron D. Krawitz, pp. 424. ISBN 0-471-24724-3. Wiley-VCH , April 2001. 03/2001; -1.
Materials Chemistry and Physics 114 (2009) 983–989
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Materials Chemistry and Physics
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In situ X-ray diffraction study of the electrochemical reaction on lead
electrodes in sulphate electrolytes
P. Angerera, R. Manna, A. Gavrilovica, G.E. Nauera,b,∗
aECHEM Kompetenzzentrum für angewandte Elektrochemie GmbH, Viktor-Kaplan-Straße 2, A-2700 Wiener Neustadt, Austria
bUniversity of Vienna, Faculty of Chemistry, Währinger Straße 42, A-1090 Wien, Austria
a r t i c l e i n f o
Received 1 July 2008
Received in revised form 16 October 2008
Accepted 2 November 2008
Grazing incidence X-ray diffraction
a b s t r a c t
The anodic oxidation of pure lead in two acidic sulphate electrolytes with identical ionic strength
(pH∼0 and pH∼−0.1) was studied by in situ grazing incidence X-ray diffraction method (GIXD). Crys-
talline products such as lead sulphate (anglesite, PbSO4, orthorhombic), ?- and ?-lead dioxide (?-PbO2,
sition 3PbO·PbSO4·H2O (triclinic) were detected at defined potentials. A method for the semi-quantitative
determination of the thickness of the deposited layer from diffraction data is described. After the in situ
measurement, the washed and dried working electrodes were additionally characterized ex situ by GIXD
measurements at different angles of incidence. The phase litharge (lead oxide, t-PbO, tetragonal) and lead
sulphate were observed at the surface of the lead substrate. The quantitative evaluation of the diffraction
intensity of this measurement series enables the modelling of a qualitative depth profile of the layer gen-
erated during the electrochemical treatment. The anglesite phase is located in the uppermost layer, while
the litharge phase was detected closer to the lead substrate.
© 2008 Elsevier B.V. All rights reserved.
This paper describes an interdisciplinary approach in the in
situ characterization of electrode surfaces combining a fast X-ray
diffraction (XRD) technique with established electrochemical pro-
cedures using a specifically adapted diffractometer device. The in
situ monitoring of the phase formation during the anodic oxida-
tion of lead electrodes in various sulphate containing electrolytes
is described. This system is of eminent importance for the lead-
acid battery and has been a topic of intense research for many
years. Many ex situ XRD investigations of this system have been
conducted in the past by Pavlov et al. [1,2], and several articles con-
cerning this electrochemical system have been recently published
in this journal, e.g. [3–5].
During the last years, efficient and highly sensitive image-plate
detectors were developed for X-ray diffraction applications. These
devices enable the fast and instantaneous recording of the diffrac-
tion pattern over the whole range of diffraction angles up to 140◦
in 2? and therefore the in situ study of comparatively rapid elec-
trochemical processes on electrode surfaces by grazing incidence
∗Corresponding author at: ECHEM Kompetenzzentrum für angewandte Elektro-
chemie GmbH, Viktor-Kaplan-Straße 2, A-2700 Wiener Neustadt, Austria.
Tel.: +43 2622 222 66 13; fax: +43 2622 222 66 50.
E-mail address: email@example.com (G.E. Nauer).
usage of a linear position sensitive detection system (Linear-PSD)
for the fast detection of the diffraction intensity in a restricted 2?
diffraction range. Such an equipment can be used in the investi-
gation of systems, where changes of the electrode surface can be
monitored in a relatively small range of diffraction angles or via
consecutive measurements in the appropriate 2? ranges.
In the textbook of Krawitz  a general description of the
XRD method including the fundamental problems relevant for the
present work such as the role of absorption and influence of the
diffraction geometry on the intensity of the diffracted X-ray beam
is given. The quantitative determination of the phase composition
was carried out by the Rietveld method . A useful paper con-
cerning the refinement strategy using this method was presented
by McCusker and coworkers . In the work of Nauer et al.  the
procedure of semi-quantitative depth profiling of a layered sam-
ple by variation of the incidence angle is described in detail. This
technique was applied for the investigation of electrochemically
prepared multi-layered structures. A deeper analytical treatise of
this topic is presented in the papers of Kötschau and Schock 
and of Colombi and coworkers . An in situ GIXD investigation
of lead electrodes in 5M sulphuric acid was presented by Nauer in
1996 , using a classical ?–? goniometer and an improved elec-
trochemical cell. The author reports the formation of lead sulphate
ing the oxidation. An in situ study of electrochemical processes on
0254-0584/$ – see front matter © 2008 Elsevier B.V. All rights reserved.
P. Angerer et al. / Materials Chemistry and Physics 114 (2009) 983–989
silver electrodes in aqueous solutions of halogenides by means of
GIXD methods was presented by Sathiyanarayanan and coworkers
. The results of similar investigations on copper electrodes in
et al. .
In another publication the oxidation and reduction reactions of
lead electrodes were studied by a complementary in situ method
using external reflection absorption infrared spectroscopy . In
that paper the amount of lead sulphate on the electrode surface
was determined by measuring the intensity of specific vibrational
absorption bands. The group of D. Pavlov presented several papers
concerning the electrochemical processes of lead electrodes in
sulphuric acid (e.g. [16,17]). They propose a mechanism of lead
oxidation in sulphuric acid where initially a layer of lead sul-
phate is produced, then the pH at the electrode rises because of
H+-migration and t-PbO (tetragonal) is formed. This t-PbO is con-
oxidation; ?-PbO2(tetragonal) is subsequently produced by elec-
trochemical reaction from the solution . The phases ?-PbO2,
?-PbO2, and t-PbO were detected ex situ. Furthermore, the varia-
were determined. In particular, the size of the ?-PbO2crystals
varies strongly with the pH of the electrolyte. An increased amount
of ?-PbO2and ?-PbO2in the region close to the lead electrode
surface was reported. Further papers were presented concerning
the technological relevance of the ratio of the various lead dioxide
phases in the active mass, its variation with the H2SO4concentra-
and cycle life performance .
Lead in contact with sulphuric acid exhibits various anodic
tions, i.e., oxidation processes):
Dissolution of metallic lead according to the reaction scheme
→ Pb2++2e−(E0= −0.1263Vvs.normalhydrogenelectrode, NHE)
The precipitation/dissolution process of lead sulphate according
Pb2++SO42−↔ PbSO4↓ (Solubilityproduct : 1.06×10−6)
is not a chemical reaction sensu stricto but is very important for
the kinetic of the lead electrode processes. Since lead sulphate is
only sparingly soluble, the combined reaction can be written as:
Pbmetal+SO42−↔ PbSO4↓ +2e−(E0= −0.356Vvs.NHE)
If the transport of sulphate to the electrode surface is slower than
the dissolution of lead, hydrolysis occurs:
Pb2++2H2O ↔ Pb(OH)2↓ +2H+
In the presence of residual amounts of sulphate the formation of
basic lead sulphates is also possible according to the equations:
4Pb2++4H2O + SO42−→ 3PbO·PbSO4·H2O + 6H+
5Pb2++4H2O + SO42−→ 4PbO·PbSO4+8H+
The anodic oxidation of lead sulphate to lead dioxide occurs at a
more anodic potential:
PbSO4+2H2O → PbO2+SO42−+4H++2e−(E0= 1.685Vvs.NHE)
Establishing a method for the observation of the formation of
ventional chemical methods was one of the topics of the present
study. Furthermore, the possibility of depth profiling of the in situ
generated electrode surfaces combined with improved data eval-
uation techniques should be demonstrated. In addition, the phase
compositions, crystallite sizes and depth profiles were measured
2.1. Electrochemical measurements
The structural parts of the electrochemical cell used for this study are made
from acrylic glass (“Plexiglas”, manufactured by Röhm Degussa-Group, Germany).
Rectangular counter electrodes (2mm×24mm) were inserted both left and right
parallel to the working electrode (11mm×24mm) made of lead (battery grade soft
lead, provided by Banner, Austria) and fixed with epoxy resin. The electrodes were
ground flush with the acrylic glass using grinding SiC-paper of decreasing grain size
down to 4000 mesh, using water as fluid medium. The electrodes were contacted
by copper wires passing through the bottom of the cell. The cell was connected via
two boreholes, tube connectors and tubes to the reference electrode (Hg/Hg2SO4in
5M H2SO4) and the electrolyte reservoir. The cell was subsequently covered with a
polymer film of 4?m thickness (Prolene, Chemplex Industries Inc., USA). Test mea-
surements at low incidence angles in the range of 0.5–2◦showed that this material
has no relevant X-ray reflections at diffraction angles >20◦in 2?. During the electro-
chemical reaction the electrolyte was continuously flowing through the cell under
a hydrostatic pressure of about 1kPa; the flow and the hydrostatic pressure in the
electrochemical cell were adjusted by varying the height of the reservoirs relative
to the cell. For the XRD measurements the reservoir flasks were lowered below
the cell level; the resulting suction effect caused the Prolene foil to cover the lead
electrode smoothly with an electrolyte film less than 150?m in between. This is
necessary because even a small positive hydrostatic pressure raises the Prolene film
from the electrode surface and the resulting thicker electrolyte film attenuates the
X-ray beam considerably.
During the experiments the electrochemical cell was controlled by a potentio-
stat/galvanostat IMP83 (Jaissle Elektronik GmbH, Germany). The anodic oxidation
was performed galvanostatically with a current of 100?A (current density of
0.38?Acm−2); every 15min the system was set to potentiostatic control, the elec-
trolyte pressure was lowered and the in situ XRD measurement was carried out.
When the X-ray beam has been switched off the cell was flooded again and the gal-
vanostatic oxidation was resumed. The electrolytes used for the investigations were
2). The ion concentrations and the pH in these two electrolytes according to  are
given in Table 1. The ionic strength of both electrolytes is 3.17M.
The in situ GIXD experiments were performed using a thin film diffractome-
ter device assembled at ECHEM (Cu K? radiation 40kV, 30mA) equipped with a
curved image-plate position sensitive detector (IP-PSD) with a radius of 140mm,
a resolution of better than 0.1◦FWHM and a 2? range of 140◦(Stoe & Cie GmbH,
Germany). The exposure time was 200s. The angle of incidence ˛ was fixed to 2◦
during the in situ measurement series. For the investigation of the initial phases
of the electrochemical process a flat position sensitive detector (Linear-PSD) of the
same manufacturer with a resolution <0.06◦FWHM and a 2? range of 5–7◦was
attached at the same device (2◦angle of incidence and 50s exposure time).
After the in situ measurements, the electrochemical cell was washed and dried
and subsequently investigated ex situ by scanning electron microscopy (SEM) using
20kV acceleration voltage. An ESEM-FEG (environmental scanning electron micro-
scope with field emission gun, XL30, FEI, Netherlands) device was used for that
purpose. A careful ex situ characterization of the electrode surfaces with respect to
phase composition, crystallite size, depth profile was carried out. In addition the
phase depth profile was qualitatively determined.
Ion concentrations and pH values in the two investigated electrolyte solutions
according to .
P. Angerer et al. / Materials Chemistry and Physics 114 (2009) 983–989
Fig. 1. Schematic drawing of the diffraction geometry of the applied grazing inci-
dence X-ray diffraction method (GIXD); the angle of incidence is indicated by ˛,
2? −˛=ˇ refers to the emergent angle, and d denotes the layer thickness.
etry of the dry cell were both performed on a X’Pert powder diffractometer device
(PANalytical, Netherlands) using Cu K? (40kV and 30mA) radiation. The measure-
ments using Bragg-Brentano diffraction geometry were performed in step-scan
mode from 5 to 80◦in 2? with a step size of 0.05◦and a counting time of 30sstep−1.
For the ex situ GIXD experiments using low incidence angle diffraction geometry
with a specific thin film collimator (0.27◦) the corresponding settings were: diffrac-
tion angle range 10–60◦in 2?, 0.05◦step size and 10sstep−1counting time. In Fig. 1,
a schematic drawing of the corresponding diffraction geometry of the GIXD exper-
iments is displayed. For an estimation of the sensitivity of the method, penetration
curves were calculated for the occurring phases metallic lead, lead dioxide, and lead
sulphate. In Fig. 2, the penetration depth in the phases lead, ?-PbO2, and PbSO4is
plotted as a function of the incidence angle according to the Eq. (1) :
−ln(1 − G)
1/(sin ˛) + 1/(sin(2? − ˛))?
the material up to the specific depth t, ˛ denotes the angle of incidence, 2? −˛=ˇ
the emergent angle, and ? denotes the attenuation coefficient of the corresponding
phase for Cu K? radiation as given in .
A Rietveld refinement of the XRD data was performed using the program TOPAS
V3.0 (Bruker AXS GmbH, Germany) . This program uses the “fundamental
parameter approach” which enables the full convolution based synthesis of line
profiles . The progress of the refinement was controlled by monitoring the fit
where t denotes the penetration depth, G the fraction of the radiation absorbed in
Fig. 2. Penetration depth t in ?m of Cu K? radiation in different phases (defined
as depth up to which 99% of the radiation is absorbed) plotted as a function of the
angle of incidence ˛. The solid lines correspond to a diffraction angle 2? =31.28◦
(corresponding to the 111 plane of lead), the dotted lines to 2? =62.15◦(311 plane
of lead). For these two values of 2? the graphs of the penetration depth in lead
(lowest penetration depth), ?-PbO2, and lead sulphate (highest penetration depth)
parameter Rwp, the Durbin-Watson factor, and the goodness of fit (GOF). In general,
the refinement of the data obtained in Bragg-Brentano geometry showed a better
convergence of the fit than the in situ data obtained by low incidence angle diffrac-
tion. The difference between observed and simulated pattern is caused by a peak
asymmetry which is commonly related to the GIXD diffraction geometry. To min-
imize this problems, starting instrumental parameter settings for the subsequent
Rietveld refinement procedure were used. These parameters were obtained from
measurements of a LaB6reference sample (powder embedded in an epoxy resin
with a polished surface) under identical experimental conditions. In addition, the
layered surface structure (depth profile) of the investigated samples also influences
the results of the Rietveld refinement.
3. Results and discussion
Initial GIXD measurements of the polished lead electrode sur-
face on air show only the diffraction peaks of the lead phase. If
residual moisture is present from the polishing process, lead oxide
(PbO) is formed in significant amounts and has to be carefully
removed by repeating the polishing procedure. Immediately after
flooding the cell with the electrolyte a test measurement was per-
formed and lead sulphate peaks were found as expected. In order
to remove all oxidation products from the surface prior to the in
situ experiments the lead working electrode was polarized with a
potential of −800 to −900mV vs. the Hg/Hg2SO4/5M H2SO4refer-
of 1–2mA) for 10–15min to reduce the lead sulphate on the elec-
trode surface to metallic lead.
In Fig. 3, the results of the in situ GIXD measurements of the
anodic oxidation process of a pure lead electrode in 1M sulphuric
acid are displayed. The first trace from below corresponds to the
polished lead surface. Here only the diffraction pattern of lead can
be detected (ICDD-PDF 03-065-2873). The second trace displays
the situation in currentless state after flooding the cell with the
electrolyte and subsequent potentiostatically reduction of the
PbSO4at −900mV. The following diffractograms are indicated by
the related consumed anodic charge (Cm−2) before starting the
Fig. 3. In situ GIXD measurements in 1M H2SO4 (angle of incidence ˛=2◦). The
observed diffraction peaks of anglesite (PbSO4) are indicated by asterisks, the ?-
PbO2peaks are denoted by “?”, the ?-PbO2peaks are denoted by “?”, the tribasic
and the lead substrate peaks are indicated by the symbol “Pb”. Initially, the dry
the cell has been flooded with the electrolyte (2nd trace from below), polarized at
−900mV (vs. Hg/Hg2SO4/5M H2SO4) to remove primary lead sulphate and then
the specific anodic charge consumed until the start of the measurement (at the
equilibrium potential) is indicated (Cm−2).
P. Angerer et al. / Materials Chemistry and Physics 114 (2009) 983–989
corresponding measurement. For a more distinct display of the
changes, the measured diffraction patterns are plotted in larger
steps of consumed charge. During the oxidation process the inten-
while the intensity of the lead substrate peaks decreases. After a
consumed charge per geometric electrode area of approximately
1000Cm−2the diffraction pattern of the lead dioxide phases
already appears (?-PbO2corresponding to ICDD-PDF 01-075-2414
tribasic lead sulphate hydrate phase 3PbO·PbSO4·H2O (ICDD-PDF
01-088-0551) was observed.
The Rietveld calculations display a maximum total lead diox-
ide content of 18–26% (weight percentage) and a content of lead
sulphate in the range between 74 and 82% at 7000Cm−2. The exact
phases is difficult due to overlapping diffraction peaks. It should be
noted that these contents refer only to the composition of the sam-
ple region penetrated by the radiation. This issue will be discussed
in detail afterwards. The observed values are also strongly influ-
enced by the layered structure of the sample and by the different
absorption coefficients of the phases. These data should be viewed
only as a relative indicator of the reaction turnover. It should also
taken into consideration that an amorphous fraction of lead diox-
ide cannot be detected by XRD methods. In Fig. 4, the resulting
weight fractions of lead, lead sulphate, and crystalline lead oxides
resulting from the Rietveld calculations are displayed for both elec-
parts can be distinguished: (1) a short period with slowly increas-
ing potential of ≈−850mV between t=0 and t=500s. During this
surface and the electrical resistance increases slowly. No lead diox-
ide is formed during this period. (2) Rapid increase of the potential
caused by an considerably increased electrode resistance. The elec-
trode surface is now almost completely covered by lead sulphate.
(3) A slow decrease of the potential at t>2800s. The beginning
of the formation of lead dioxide on the lead surface reduces the
measurements (?=2◦). The observed fractions as determined by Rietveld refine-
lines, the corresponding data obtained using an electrolyte containing 0.687mol
H2SO4and 0.25mol NaHSO4are indicated by dashed lines.
plotted as a function of elapsed time. The vertical bars refer to the triggering time
of the GIXD measurements under potentiostatic conditions. The numbers indicate
the corresponding transferred specific charge on the anode in units of Cm−2at the
refer to measurements not included in the diagram in Fig. 3.
resistance and therefore the corresponding voltage drop on the
electrode–electrolyte interface. In the diagram the periods of the
XRD measurements, which were performed under potentiostatic
conditions, can be easily identified by the plateaus in the potential
curve. The spikes refer to the end of the potentiostatic sections. The
in units of Cm−2by annotated vertical bars allow the correlation
with the diffractograms in Fig. 3 (non-labelled vertical bars refer to
XRD measurements were not included in Fig. 3). The observation
of the initial phase of the electrochemical reaction was performed
using the flat position sensitive detector (Linear-PSD) with its high
sensitivity. In Fig. 6, these data are shown. The early lead sulphate
formation can be seen while the intensity of the diffraction peaks
attributed to the ?-PbO2phase remains very low.
In addition, the crystallographic lattice constants of the
observed phases lead, lead sulphate, lead dioxide (?-PbO2and ?-
PbO2) were determined for each measurement during the in situ
Fig. 6. In situ GIXD measurements with the Linear-PSD detector (high sensitivity)
in 1M H2SO4at an incidence angle ˛=2◦. The observed diffraction peaks of lead
sulphate (PbSO4) are indicated by asterisks, the lead peak is indicated by the symbol
Pb and the position of a possible ?-PbO2peak is denoted by “?”. The consumed
specific charge on the anode for each measurement is indicated in units of Cm−2.
P. Angerer et al. / Materials Chemistry and Physics 114 (2009) 983–989
Fig. 7. Cell volume values of the lead sulphate phase (indicated by boxes) and the
anodic charge per geometric electrode surface unit. The data of the experiment in
electrolyte containing 0.687mol H2SO4and 0.25mol NaHSO4are indicated by open
symbols. The dashed horizontal lines indicate the cell volume for lead sulphate and
lead as given in the ICDD database. The vertical error bars indicate the relative error
(5?) during the in situ measurement series.
series. In Fig. 7, the corresponding values of the crystallographic
cell volume of the lead sulphate phase and of the lead substrate
are displayed as a function of the consumed charge. The vertical
error bars indicate the relative error (5?) as obtained from the
decreases almost linear from an initial value near the theoretical
number VICDD=318.49Å3as given in ICDD database (indicated by a
horizontal dashed line) to a value of 0.981VICDD. On the other hand,
the cell volume values of the lead substrate remain constant within
the experimental error. In the case of electrolyte 2, a reasonable
evaluation of the cell volume was only possible up to a consumed
anodic charge below 1000Cm−2. The corresponding curves of the
variations within the precision of the measurements. The errors
here are generally higher due to the small content of these phases.
This effect possibly originates from restructuring processes in the
lead sulphate during the lead dioxide formation reaction. Another
effect would affect mainly the lead sulphate phase which is resid-
ing in the uppermost sample region (quantitive discussion will be
presented later). It can be estimated that at 2◦angle of incidence a
parameter shift .
For a more extensive analysis of the diffraction data the effect
of X-ray absorption in the deposited layer was taken into account.
The radiation diffracted by the lead substrate phase is weakened
during the passage through the deposited layer. The path length
in the layer is equal to d·(1/sin˛+1/sinˇ), whereby ˛ denotes the
incidence angle of the X-ray beam, while ˇ=2? −˛ refers to the
corresponding excidence angle and d refers to the layer thickness.
Assuming the validity of the Beer-Lambert law we can write
−? · d?
(1/sin ˛) + (1/sin ˇ)??
whereby I(Pb)layerrefers to the diffracted intensity after absorption
in the layer as it is actual observed during the in situ experiment,
pristine cell before the in situ experiment without consideration of
lead diffraction peaks are displayed as a function of the consumed charge density in
Cm−2. Values obtained from the (111) maximum are denoted by closed symbols,
open symbols. Triangles refer to data obtained in 1M H2SO4, circles denote results
obtained in electrolyte 2. The dotted lines refer to theoretical values for ?·d calcu-
lated under the assumption that the consumed charge was completely converted
into a homogeneous and fully dense layer of PbSO4or ?-PbO2, respectively.
the absorption in the layer. The value ? corresponds to the attenu-
ation coefficient of the layer material. This quantity depends on the
composition of the layer, i.e., the ratio between sulphate and oxide
phase. However, if the transmittance is known, Eq. (2) enables only
the determination of the dimensionless number ?·d (attenuation
product) for the layer.
In the diagram presented in Fig. 8, the observed attenuation
product ?·d is displayed as a function of the consumed charge per
area unit. The data were obtained during the in situ experiment
in 1M H2SO4. Two different values for ?·d where calculated from
the integrated area intensity of the two strongest lead diffraction
peaks (111) and (200). In this diagram additional straight lines
were plotted indicating the calculated values for ?·d assuming that
the transferred charge was completely consumed by the formation
of a dense and homogeneous layer of lead sulphate or lead dioxide,
respectively. For lead sulphate a value for the attenuation coeffi-
cient ?=2331cm−1and for lead dioxide (?-PbO2) a corresponding
value of ?=2447cm−1was assumed . The observed effective
values for ?·d are smaller by a factor of 3–5 considering that the
layer consists predominantly of lead sulphate, as it is suggested by
the XRD observations. Therefore we suggest an alternative model:
in a first approach the homogeneous layer with a specific thickness
d is substituted by cubic particles with diameter a and distance b
rial per surface unit in the two cases we get the relation a3=b2·d.
Neglecting shadowing effects between the cubes (as it is the case if
b is clearly larger than a) and assuming a path length a in each cube
only a fraction of a2/b2of the incident radiation will be affected by
absorption effects and Eq. (2) can be substituted by the expanded
= 1 −a2
b2· exp(−? · a)
= 1 −d2/3
b2/3· exp(−? · d · (b2d)
Instead of the theoretical value of ?·d calculated from the cor-
responding transferred charge an “effective attenuation product”
P. Angerer et al. / Materials Chemistry and Physics 114 (2009) 983–989
Fig. 9. Typical micrograph obtained by scanning electron microscopy (SEM) of the
lead anode surface of the washed and dried electrochemical cell after the in situ
measurement series. The idiomorphic anglesite crystals with a size in the range of
1–3?m can be easily identified. The fine-grained fraction is also partially composed
of anglesite. Ultra-fine litharge crystallites have been formed in direct contact with
the lead substrate.
?*·d<?·d which can be defined as
?∗· d = −ln
is observed during the in situ run. The combination of Eqs. (3)
and (4) enables the calculation of values for the crystallite size a
between 5 and 20?m. A linear ascent as a function of the trans-
ferred charge can be observed during the measurement series.
After the processing of the in situ experiments the electro-
chemical cell was washed with deionized water and dried with
compressed air. A SEM micrograph of the washed and dried elec-
trode surface is displayed in Fig. 9. Here the observed size of the
lead sulphate crystals ranges between 2 and 3?m and is some-
what smaller than the calculation suggests. The real crystal size
distribution (a very fine-grained component consisting of lead sul-
phate and possible minor amounts of litharge phase is coexisting
besides the large crystals) and the layered sample structure with
lead oxide phase also present can surely cause such differences. As
noted above, an amorphous fraction of lead dioxide not detectable
by XRD suggests a more oxide rich layer composition. Such a layer
must have a lower ?·d value and would be also closer to the obser-
vations. However, it should be remarked that a simple model of
a homogeneous dense sulphate layer cannot describe the real cir-
Additionally, the dry cell was characterized by Bragg-Brentano
and GIXD measurements (Fig. 10). These measurements with
their comparatively high angular resolution showed predominant
diffraction peaks of lead sulphate (anglesite). Additionally, a minor
pattern of litharge (t-PbO, ICDD-PDF 00-005-0561) with broad
diffraction peaks could be identified; however, no PbO2was found
ex situ. The PbO-phase has most likely been formed during the
washing process, partly by a process according to the reaction
PbO2+Pb → 2PbO
(Planté reaction) and partly by the corrosion of the metallic lead
during exposure of the moist cell to the atmosphere.
In Fig. 11, the calculated weight fractions (by Rietveld refine-
ments) of the phases anglesite (PbSO4and t-PbO) are shown as
a function of the angle of incidence. In the diagram both results
obtained from the experiment using 1M H2SO4and electrolyte 2
Fig. 10. Diffractograms obtained by ex situ GIXD measurements of the dried cell.
The electrode surface was investigated after the in situ experiment displayed in
Fig. 3 (electrolyte: 1M H2SO4). The diffraction peaks of the lead substrate phase are
indicated by the symbol Pb, the peaks of lead sulphate are denoted by asterisks, the
litharge peaks are denoted by the symbol “o”. The angle of incidence is indicated
below the traces.
are given. A lower angle of incidence is strictly correlated with a
smaller penetration depth of the radiation. With increasing inci-
dence angle deeper layer regions are gradually irradiated and a
semi-quantitative depth profile can be constructed.
actual absorption coefficients of the oxide and sulphate layers are
not known due to their porosity. However, the diagram in Fig. 10
shows clearly that the anglesite phase is residing in the uppermost
zone of the corrosion layer while the amount of litharge is increas-
ing with a higher angle of incidence and must therefore be located
directly on the metallic lead surface. This result is in accordance to
the results given in . The general character of the depth profile
is the same at electrodes oxidized in both electrolytes.
The crystallite size was determined using the ex situ diffraction
data obtained at the washed and dried cell in the Bragg-Brentano
diffraction geometry. The FWHM of the diffraction peaks of the in
iments. The observed weight fractions are plotted as a function of the angle of
incidence ˛. The contents of anglesite (PbSO4) are indicated by boxes and values
referring to litharge (PbO) are indicated by triangles. Closed symbols and solid lines
refer to the data obtained in 1M H2SO4,open symbols and dashed lines refer to
measurements performed in electrolyte 2.
P. Angerer et al. / Materials Chemistry and Physics 114 (2009) 983–989
situ measurements series were much larger and the residual of
such a determination would be unacceptable. The obtained crys-
tallite size values of the phases differ substantially. The crystallite
size of the lead sulphate is in the range of 130–350nm while the
corresponding value for the litharge phase is 13–17nm. Further-
more, the calculated crystallite size of lead ranges between 200
and 900nm. This is close to the upper detection limit due to the
confined angular resolution of the instrument. The values for the
substrate should not be compared with the results of the electro-
of the material. The measurements could not display any system-
atic influence of the electrolyte on the crystallite size of the formed
phases. Furthermore, it should be emphasized that the crystallite
size obtained by XRD corresponds strictly to the diffracting coher-
ence length in the material, which is in turn influenced by the real
structure (e.g., stacking faults, dislocations, point defects, mosaic
structure) of the diffracting crystallites. Therefore the XRD results
differ from the data obtained by SEM but they are appropriate to
obtain a good relative determination of the crystallite size depend-
ing on the preparation procedure.
Electrochemical in situ GIXD measurements were undertaken
using an improved experimental arrangement combined with
simultaneous observation of the potential and electric current. The
first step of the electrochemical oxidation of lead in sulphate con-
electrode is sufficiently covered with a sulphate layer, the poten-
tial jumps to values where the formation of lead dioxide starts. The
diffraction pattern of ?-PbO2, and ?-PbO2was observed besides
the prevalent lead sulphate peaks. Additionally, small amounts of
the attenuation of the lead substrate pattern by the layer was used
for an estimation of the crystallite size of the sulphate phase. Ex
situ studies of these oxidation processes are complicated due to the
reaction of the lead dioxide phases with the lead substrate to lead
oxide (t-PbO) during the washing and drying procedure. Obviously,
this process is often not strictly reproducible. However, GIXD mea-
surements at different incidence angles of the washed and dried
zone is situated directly on the lead metal between the substrate
and the lead sulphate layer. No significant differences were found
between the series conducted in the different electrolytes. Further
struction of an electrochemical cell suited for direct measurements
with no need for lowering the hydrostatic electrolyte pressure and
the adaption of the Rietveld refinement algorithm to layered sam-
ples including the analysis of texture and crystallite size.
The authors want to thank Prof. F. Kubel, Vienna for his valu-
able hints concerning the application of the Rietveld method.
The work was supported within the K plus programme by the
Austrian Research Promotion Agency (Österreichische Forschungs-
förderungsgesellschaft, FFG) and the government of Lower Austria.
Appendix A. Supplementary data
Supplementary data associated with this article can be found,
in the online version, at doi:10.1016/j.matchemphys.2008.11.006.
 D. Pavlov, C.N. Poulieff, E. Klaia, N. Iordanov, J. Electrochem. Soc. 116 (1969) 316.
 D. Pavlov, N. Iordanov, J. Electrochem. Soc. 117 (1970) 1103.
 Z. Yan, X. Hu, Mater. Chem. Phys. 77 (2002) 202.
 Y. Cartigny, J.M. Fiorani, A. Maître, M. Vilasi, Mater. Chem. Phys. 103 (2007) 270.
Mater. Chem. Phys. 108 (2008) 337.
 A.D. Krawitz, Introduction to Diffraction in Materials Science and Engineering,
Wiley, New York, 2001.
 H.M. Rietveld, J. Appl. Cryst. 2 (1969) 65.
 L.B. McCusker, R.B. Von Dreele, D.E. Cox, D. Louër, P. Scardi, J. Appl. Cryst. 32
 I.M. Kötschau, H.W. Schock, J. Appl. Cryst. 39 (2006) 683.
 P. Colombi, P. Zanola, E. Bontempi, L.E. Depero, Spectrochim. Acta B 62 (2007)
 G.E. Nauer, Mater. Sci. Forum 228–231 (1996) 387.
 S. Sathiyanarayanan, M. Sahre, W. Kautek, Electrochim. Acta 43 (1998) 2985.
 W. Kautek, S. Mirwald, M. Sahre, G.E. Nauer, Electrochim. Acta 43 (1998) 2979.
 G.L.J. Trettenhahn, G.E. Nauer, A. Neckel, Electrochim. Acta 41 (1996) 1435.
 D. Pavlov, A. Kirchev, M. Stoycheva, B. Monahov, J. Power Sources 137 (2004)
 B. Monahov, D. Pavlov, A. Kirchev, S. Vasilev, J. Power Sources 113 (2003) 281.
 D. Pavlov, J. Electroanal. Chem. 118 (1981) 167.
 D. Pavlov, V. Naidenov, S. Ruevski, J. Power Sources 161 (2006) 658.
 E.B. Robertson, H.B. Dunford, J. Am. Chem. Soc. 86 (1964) 5080.
 S.J. Skrzypek, A. Baczmanski, W. Ratuszek, E. Kusior, J. Appl. Cryst. 34 (2001)
 J.H. Hubbell, W.H. McMaster, N.K. Del Grande, J.H. Mallett, Sec. 2.1: X-ray cross-
der diffraction data, Karlsruhe, 2005.
 R.W. Cheary, A.A. Coelho, J. Appl. Cryst. 25 (1992) 109.
Röntgendiffraktometrie, Freiberger Forschungsheft B 273, Deutscher Verlag
für Grundstoffindustrie, Leipzig, 1992, p. 142.