of 16
Probing the reaction pathway in
(La
0.8
Sr
0.2
)
0.95
MnO
3+
d
using libraries of thin
fi
lm
microelectrodes
Robert E. Usiskin,
a
Shingo Maruyama,
b
Chris J. Kucharczyk,
a
Ichiro Takeuchi
b
and Sossina M. Haile
ac
Libraries of (La
0.8
Sr
0.2
)
0.95
MnO
3+
d
(LSM) thin
fi
lm microelectrodes with systematically varied thickness or
growth temperature were prepared by pulsed laser deposition, and a novel robotic instrument was used
to characterize these libraries in automated fashion by impedance spectroscopy. The measured
impedance spectra are found to be described well by an electrochemical model based on a generalized
transmission model for a mixed conducting oxide, and all trends are consistent with a reaction pathway
involving oxygen reduction over the LSM surface followed by di
ff
usion through the
fi
lm and into the
electrolyte substrate. The surface activity is found to be correlated with the number of exposed grain
boundary sites, which decreases with either increasing
fi
lm thickness (at constant growth temperature)
or increasing
fi
lm growth temperature (at constant thickness). These
fi
ndings suggest that exposed grain
boundaries in LSM
fi
lms are more active than exposed grains towards the rate-limiting surface process,
and that oxygen ion di
ff
usion through polycrystalline LSM
fi
lms is faster than many prior studies have
concluded.
1. Introduction
In recent years, numerous studies have used patterned thin
lm
electrodes in combination with electrochemical impedance
spectroscopy to yield rich insights into the behavior of mixed
ionic and electronic conductors (MIECs).
1
The present study
builds on the success of the patterned thin
lm electrode
approach by adding two methodological novelties that increase
throughput and reliability. First, libraries of thin
lm catalyst
microelectrodes with systematically varied
lm thickness or
growth temperature are fabricated and characterized on a single
solid electrolyte substrate. Beyond increasing throughput, this
parallel fabrication approach ideally allows trends in parame-
ters of interest to be reliably observed by minimizing unin-
tended di
ff
erences that can result when samples are prepared in
serial fashion. Second, a novel robotic instrument is imple-
mented that can perform automated acquisition and analysis of
impedance spectra with higher throughput than manual
measurements.
Here these methodological enhancements are used to eval-
uate (La
1

x
Sr
x
)
1

y
MnO
3+
d
(LSM), a material employed in the
cathode of the vast majority of state-of-the-art, pre-commercial
solid oxide fuel cells. Because of the technological signi
cance
of LSM,
2,3
the literature describing its electrochemical proper-
ties is extensive and includes several thin
lm studies, in both
patterned and unpatterned form. Surprisingly, however, a
consensus regarding the oxygen reduction pathway over this
material has not emerged.
Most previous investigations of thin
lm LSM indicate that
at 700
800

C
a temperature range of particular relevance to
commercial systems
a three phase boundary (3PB) pathway,
wherein oxygen incorporation into the electrolyte occurs at the
boundary of the LSM, electrolyte, and gas phases, can be out-
competed by a two phase boundary (2PB), through-
lm
pathway, wherein oxygen ions are incorporated at the LSM
surface, di
ff
use through the LSM
lm, and then cross into the
yttria-stabilized zirconia (YSZ) electrolyte.
4
7
This conclusion is
commonly drawn from two observations: (1) the d.c. electrode
conductance scales with the LSM/YSZ interfacial area (essen-
tially identical to the LSM/gas interfacial area), rather than the
LSM/YSZ perimeter,
4
10
and (2) the electrode conductance
decreases monotonically with increasing LSM
lm thick-
ness.
7
9,11
Perhaps the most compelling results in support of a
through-
lm pathway are those of Fleig and coauthors. In a
series of three papers in which photolithographically fabricated
microelectrodes of LSM on YSZ(100) were evaluated in a
through-plane geometry, these authors found that the electrode
a
Applied Physics & Materials Science, California Institute of Technology, Pasadena,
CA, USA
b
Materials Science and Engineering, University of Maryland, College Park, MD, USA
c
Chemical Engineering, California Institute of Technology, Pasadena, CA, USA
Electronic supplementary information (ESI) available. See DOI:
10.1039/c5ta02428e
Current address: Materials Science and Engineering, Northwestern University,
Evanston, IL, USA; sossina.haile@northwestern.edu
Cite this:
J.Mater.Chem.A
,2015,
3
,
19330
Received 3rd April 2015
Accepted 2nd August 2015
DOI: 10.1039/c5ta02428e
www.rsc.org/MaterialsA
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conductance scales with area,
4
6
and that introduction of an
alumina blocking layer at the LSM/YSZ interface caused the
conductance to fall dramatically, suggesting that the entirety of
the LSM/YSZ interface is involved in the reaction pathway.
5
In
the most recent of these papers, the impedance data (from
lms
with no blocking layer) were analyzed using a rigorous model
for the behavior of a mixed conductor, and two resistance terms
were extracted: a surface reaction resistance and a through-
lm
di
ff
usion resistance.
6
Whereas the latter approximately scaled
with thickness, as expected, a surprising increase with thick-
ness was also noted for the former, suggesting that the surface
is changing in some way as thickness increases. Fleig and
coauthors also found evidence that the most resistive step
changes from surface incorporation under slightly reducing
conditions to through-
lm di
ff
usion under more oxidizing
conditions, with the oxygen partial pressure at the transition
being implied to be dependent on
lm thickness. Such behavior
is, in principle, consistent with the reports from other labora-
tories suggesting that,
under air
, an increase in electrode
resistance with increasing thickness
7,12
is due to reaction
via
the
2PB pathway with di
ff
usion being rate-limiting. It is also
consistent with the observation in electrical conductivity relax-
ation measurements carried out on LSM thin
lms
under rela-
tively reducing conditions
that a surface reaction step is rate-
limiting.
13
However, some investigations give rise to a di
ff
erent inter-
pretation. Radhakrishnan
et al.
14
observed that the LSM elec-
trode conductance increases with increasing LSM/YSZ
perimeter length at constant LSM/YSZ surface area. Accord-
ingly, those authors concluded that the oxygen electro-reduc-
tion reaction is three phase boundary mediated even at
geometric length scales (perimeter-to-area ratio and
lm
thickness) comparable to those evaluated in other works. Other
studies, including those of la O'
et al.
,
9,10
Koep
et al.
8
and a very
recent report from Fleig,
15
suggest a more subtle interpretation
of the data, with multiple pathways (involving both surface and
bulk di
ff
usion through LSM microelectrodes) occurring simul-
taneously, but with varying levels of dominance depending on
temperature and microelectrode geometry. Such a divergence of
interpretations with respect to the most widely deployed SOFC
cathode material provides some of the motivation for the
present study.
A striking aspect of the studies performed to date is that
conclusions based on geometric trends are o
en drawn from
datasets with a rather limited range of geometric characteris-
tics. For example, in the case of thickness studies, which o
en
involve the serial growth of multiple
lms, typically 2 to 3 values
are examined, although in one case 12 thicknesses were
reported.
8
A second challenge arises with respect to interpre-
tation of the impedance response, which o
en takes the form of
multiple depressed and highly overlapping arcs when plotted in
the complex plane. The recorded spectra have been largely
treated in an
ad hoc
manner, where the Fleig study
6
stands out
as a sole counter-example. These considerations suggest that
mechanistic conclusions regarding the oxygen electro-reduc-
tion pathway on dense LSM may be premature, and they drive
the present evaluation of LSM in a rigorous manner. Ultimately,
knowledge of the reaction pathway and the associated rate-
limiting step(s) will enable rational chemical and microstruc-
tural design to optimize devices that use this material.
2. Overview of the automated
impedance microprobe technique
The con
guration of the automated impedance microprobe is
shown schematically in Fig. 1 and to scale in Fig. S1.
Compared
to previously reported instruments for studying microelec-
trodes,
4,10
the most signi
cant new feature here is the scanning
capability: the position of the alumina arm holding the metal
probe tip is controlled by three stepper motors. Thus, the metal
probe tip can be made to contact a microelectrode simply by
entering the appropriate coordinates in the control so
ware.
The temperature and gas environment are also controlled in
so
ware. Moreover, the dimensional tolerances associated with
the patterning process are small enough that the relative
spacing of the microelectrodes on the substrate surface can be
accurately predicted, and three points are su
ffi
cient to de
ne
the plane of that surface. Consequently, once the user manually
locates the coordinates of three reference microelectrodes in a
library, the coordinates of all the other microelectrodes can be
readily computed. Hundreds of microelectrodes can then be
probed in any desired sequence over a range of environmental
conditions, all in automated fashion.
2.1. Experimental procedures
A sintered pellet (26 mm in diameter, 6 mm in thickness) of
(La
0.8
Sr
0.2
)
0.95
MnO
3+
d
(LSM) was fabricated as follows for use as
a pulsed laser deposition target. Polyvinylpyrrolidone, 0.2 g
dissolved in 4 mL isopropanol, served as a binder and was
mixed dropwise into 20 g commercial powder (Fuel Cell Mate-
rials, 99.5% pure). This mixture was placed in a 32 mm diameter
die and subjected to a uniaxial pressure of 20 MPa for 10 min,
then transferred to a sealed latex sheath and subjected to
isostatic pressure of 350 MPa for 20 min. For sintering, the
green body was placed on an alumina support onto which a bed
of loose excess LSM powder had been applied to serve as a
reaction barrier. Sintering was carried out at 1450

C for 5 h in
Fig. 1
Schematic of the test con
fi
guration in the automated imped-
ance microprobe. Dimensions are not to scale.
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stagnant air in a dedicated alumina tube. The resulting pellet
was polished on all sides and then sonicated in water to remove
residual grit generated by polishing. X-ray di
ff
raction (XRD,
Philips X'Pert Pro, Cu K
a
) patterns acquired from both faces of
the pellet showed good agreement with pattern #90422 reported
in the Inorganic Crystal Structure Database for a similar
composition, La
0.8
Sr
0.2
MnO
3
.
16
Using this target, (La
0.8
Sr
0.2
)
0.95
MnO
3+
d
lms were grown on
(100)-oriented single crystal Y
0.15
Zr
1.85
O
1.93
substrates (YSZ, 8
mol% Y
2
O
3
-stabilized ZrO
2
,5

10

0.5 mm, MTI Corporation)
by pulsed laser deposition with a KrF excimer laser (248 nm, 0.8
Jcm

2
). Growth temperatures were determined by optical
pyrometry from relevant locations on the substrate immediately
prior to growth. During
lm growth, each substrate was adhered
to a heated support with silver paste. The paste was subse-
quently scraped o
ff
.
Three libraries of LSM microelectrodes were prepared,
Table 1. For the
rst, the thickness of the LSM
lm was
systematically varied by using a motor to slowly draw an
Inconel shutter held above the substrate across the deposition
plume during growth.
17
This procedure created a
thickness
library
, Library 1, in which the
lm thickness varied
continuously from 30 to 300 nm across the substrate. Other
relevant deposition conditions are summarized in Table 1.
The 1 Hz ablation laser pulse frequency resulted in a 0.7 nm
min

1
deposition rate, determined by prior calibration using
atomic force microscopy (AFM, Digital Instruments Nano-
scope III and Dimension 5000) pro
les from test
lms
prepared with the same target and deposition parameters.
The majority of data related to scaling with geometric features
were obtained from Library 1. Selected validations were per-
formed using a supplemental thickness library, which was
prepared on a separate substra
te with identical processing
parameters,exceptforuseofaslightlyhigherO
2
working
pressure during growth. On another substrate, the growth
temperature of the LSM
lm was systematically varied using
an asymmetric substrate support (shown in Fig. S2
)heatedat
one end with infrared radiation.
18
This procedure created a
growth temperature library
, Library 2, in which the growth
temperature varied continuously from 555 to 725

Cacross
the substrate.
As grown
lms were characterized by atomic force micros-
copy (AFM, Digital Instruments Nanoscope III and Dimension
5000) and X-ray di
ff
raction (Bruker D8 Discover with 4 bounce
monochromator, Cu K
a
) in both a
q

2
q
geometry and, in
selected cases, using a rocking curve geometry. Each
lm was
then patterned into a library of microelectrodes using photoli-
thography and ion milling. Speci
cally, two coats of photoresist
(Shipley 1813) were applied by spin coating on top of each
lm
(4000 rpm for 50 s a
er pre-baking at 90

C for 2 min), exposed
to UV radiation for 12 s through a photomask, and then
developed in Shipley 352 developer for 40 s. The
lm then
underwent ion milling for 45 min, resulting in a milling depth
of

350 nm. In the
nal step, the residual photoresist was
stripped using acetone. This patterning procedure yielded
microelectrodes with sharp edges (Fig. S3
), thus avoiding
complications that may arise from edges with a substantial
taper, and it involves no exposure to an acid; in related systems,
acid exposure has been shown to enhance activity.
19,20
In this way, each
lm was converted into a library of 337
circular microelectrodes with layout as shown in Fig. 2. Within
each library, eleven distinct values of microelectrode diameter
spanning the range 30
500
m
m were created, with the six values
in the range 100
500
m
m ultimately proving useful. The thick-
ness libraries included twenty-one di
ff
erent values of
lm
thickness, evenly spaced from 30
300 nm, with impedance
measurements restricted to
lms 44 nm and greater in thick-
ness; the growth-temperature library included twenty-one
di
ff
erent values of growth temperature, unevenly spaced from
555
725

C. Because the thickness or growth temperature
varied continuously across each library, it also varied slightly
across each microelectrode. However, the microelectrodes had
small enough diameter that a single value of thickness or
growth temperature (the local average value) could be assigned
to each microelectrode with minimal loss of accuracy. Speci
-
cally, for Library 1 the di
ff
erence in thickness across the largest
(500
m
m diameter) microelectrode probed was 15 nm, whereas
for Library 2 the di
ff
erence in growth temperature across the
largest (200
m
m diameter) microelectrode for which data are
reported in this work was

5

C. The microelectrode diameters,
as measured by digital optical microscopy, were found to be
within 5% of the nominal values. Optical microscopy (Keyence
Table 1
Geometry and growth characteristics of the (La
0.8
Sr
0.2
)
0.95
MnO
3+
d
microelectrodes that underwent impedance testing in this study
Characteristic
Library 1
Library 2
Supplemental library
Number of diameters
6
6
6
Range
100
500
m
m
100
500
m
m
100
500
m
m
Number of thicknesses
18
1
18
Range
44
287 nm
135 nm
44
287 nm
Number of growth
temperatures
1191
Range
650

C
556
692

C
650

C
Growth pressure
10 mTorr O
2
30 mTorr O
2
30 mTorr O
2
Laser pulse rate
1 Hz
5 Hz
1 Hz
Growth rate
0.7 nm min

1
2.7 nm min

1
0.7 nm min

1
Cooling rate
100

C min

1
20

C min

1
100

Cmin

1
19332
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,2015,
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, 19330
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VW-9000) and AFM were employed to characterize the surfaces
of the patterned
lms. Features observed in AFM images were
quanti
ed by image analyses using the so
ware program
Gwyddion.
21
Library 2 was further characterized a
er electro-
chemical measurements by optical pro
lometry (New View
6000), to con
rm the microelectrode thickness was uniform
across the library. Secondary ion mass spectrometry (SIMS,
Physical Electronics PHI TRIFT III) was performed, again,
subsequent to electrochemical characterization, to evaluate the
uniformity of the cation concentrations through the
lm
thickness.
In preparation for impedance measurements, each substrate
was adhered to a

10

20

0.6 mm alumina sheet using silver
paste (DAD-87, Shanghai Research Institute). Heat treatment in
a quartz tube under stagnant air at 600
700

C for 1 h converted
the paste into a porous counter electrode. Thus prepared, each
library was installed in the automated impedance microprobe
and heated to a stage temperature of 750

C, resulting in a
temperature of 735

C at the microelectrodes due to the
temperature gradient across the YSZ substrate. When a partic-
ular microelectrode was contacted by the probe tip, its average
temperature decreased further (due to cooling by the probe tip)
to

710

C, with the exact value depending on the microelec-
trode diameter. A detailed discussion of the temperature cali-
bration is given in the ESI.
The oxygen partial pressure (
p
O
2
)in
the chamber was varied over the range 10

3
to 1 bar by
owing
bottled oxygen or oxygen
nitrogen mixtures through the
chamber and then past a zirconia-based oxygen sensor (Setnag)
housed in a quartz tube in a separate furnace. The
p
O
2
was
allowed to stabilize at each condition prior to the acquisition of
impedance data; typical stabilization times were 0.5
3 h. The
total pressure in the chamber was always 1 bar. The micro-
electrodes were contacted using a probe tip made of Paliney7, a
commercial alloy containing 35% Pd, 30% Ag, 14% Cu, 10% Au,
10% Pt, 1% Zn (American Probe & Technologies, 20
m
m tip
radius). Several measurements were repeated using a probe tip
made of Pt
0.7
Ir
0.3
(Moser, 10
m
m tip radius); identical results
were obtained. The former probe material was preferred
because it did not scratch the microelectrodes and thus enabled
multiple measurements over the range of conditions of interest.
Uncertainty in the tip position, the sources of which are dis-
cussed in the ESI,
precluded reliable measurement of micro-
electrodes less than 100
m
m in diameter. The use of silver as a
counter electrode creates a contamination concern, and indeed,
in other, longer term studies, it was observed that silver can
migrate from the back of the electrolyte substrate to the
microelectrode surface. In the present work, the contamination
concern was mitigated by completing the measurement of each
library in two days or less. To con
rm the adequacy of this
approach, some impedance spectra were collected under iden-
tical conditions at both the beginning and the end of the study
(for Library 2 and the supplemental library); the resulting
spectra were found to be nearly identical.
Impedance spectra were acquired using a frequency response
analyzer (Solartron Modulab) with an applied a.c. voltage of
30 mV, no applied d.c. bias, and a typical frequency range of
10kHzto32mHz.AsdescribedintheESI,
coolingofthesample
by the probe tip generated a 10
50

C temperature drop between
the top (measurement) and bottom (counter) electrodes, detected
in the form of a 5
25 mV Seebeck voltage (with the exact value
depending on the microelectrode diameter (Fig. S4
)). Conse-
quently, each impedance spectrum was e
ff
ectively measured
under 5
25 mV anodic d.c. bias (with oxygen ions being driven
from the electrolyte into the microelectrode). Selected measure-
ments were repeated with an applied a.c. voltage of only 10 mV,
and identical results were obtained, indicating that all measure-
ments remained in the linear regime and thus that the Seebeck
voltage had negligible impact on the electrochemical response.
The analyzer calibration was veri
ed in advance by acquiring
impedance spectra from test circuits containing precision mega-
ohm resistors and nanofarad capacitors;
ts to these spectra
reproduced the expected resistance and capacitance values with
<3% error. Impedance spectra acquired from the LSM micro-
electrodes were
tbyanexpressionsimilartothat
rst proposed
by Fleig
et al.
,
6
as described in detail below.
Morphological features were reexamined a
er impedance
measurements. The sample surfaces were coated with a conduc-
tive layer of

10 nm carbon (Cressington 108) and/or

10 nm
osmium and then characterized by scanning electron microscopy
(SEM, Zeiss 1550 VP). Additionally, cross-sections of selected
regions were prepared and imaged using focused ion beam (FIB)
milling and SEM (FEI Helios Nanolab 600) a
er application of a
protective layer of several hundred nm platinum.
3. Results of physical characterization
X-ray di
ff
raction patterns acquired prior to patterning are
shown in Fig. 3 (for Libraries 1 and 2) and Fig. S5
(for the
Fig. 2
Layout of a library of (La
0.8
Sr
0.2
)
0.95
MnO
3+
d
thin
fi
lm microelectrodes grown on a 5

10 mm substrate. Left: Schematic. Right: Optical
microscope image of Library 1 during impedance testing.
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supplemental library). The patterns from the thickness libraries
(Library 1 and supplemental) exhibit re
ections that corre-
spond primarily to (110)-oriented grains. Some intensity from
(012) and (202) re
ections is also evident. The graded thickness
of these libraries was visible by optical microscopy, with thinner
regions giving rise to a lighter color (Fig. 2). The patterns from
the growth temperature library, Library 2, show no re
ections at
growth temperatures of

580

C and below, indicating those
regions of the
lm were largely amorphous and/or had grains
too small to yield sharp di
ff
raction peaks with intensity above
the background. At growth temperatures of

615

C and higher,
the
lms appeared crystalline with similar orientations as
measured from the thickness library and an out-of-plane (110)
spacing that decreased slightly with increasing growth
temperature (Fig. S6
). A transition from XRD-amorphous to
crystalline growth has been observed over a similar range of
growth temperatures for La
0.6
Sr
0.4
CoO
3

d
(ref. 22) and
La
0.58
Sr
0.4
Co
0.2
Fe
0.8
O
3

d
.
23
Rocking curves obtained from Library 2 revealed pro
les
about the (110) di
ff
raction intensity that were best
t using two
Voigt peaks, yielding two sets of values for the full width at half
maximum (FWHM, Fig. S7
). The FWHM of the sharper
component remained constant with growth temperature,
whereas that of the broader component decreased, suggesting
that the
lms had a thin, near-perfect epitaxial layer adjacent to
the substrate overlaid with a thicker, slightly misoriented
layer.
24
Cross-sectional FIB-SEM images acquired a
er imped-
ance measurements indicated that the
lms were dense. A
representative image is shown in Fig. 4. It can be presumed that
the
lms were also dense as grown. Optical pro
lometry and
FIB-SEM images con
rmed the
lm thickness was uniform
across Library 2, and the
lm color appeared uniform across
that library (not shown), consistent with a uniform thickness.
The surface roughness was 1
2 nm RMS throughout (Fig. S6
).
The SIMS measurement (Fig. S8
) indicated the cation
concentrations were uniform through the bulk of the
lm.
AFM micrographs collected a
er patterning but before
electrochemical characterization are shown in Fig. 5 (Library 1),
Fig. 6 (Library 2), and Fig. S9
(supplemental library). These
images are indistinguishable from corresponding images that
were collected before patterning (not shown). The features are
interpreted as corresponding to grains resulting from columnar
growth.
25
The grain size is seen to increase with increasing
thickness (Fig. 5 and S9
) or increasing growth temperature
Fig. 3
X-ray di
ff
raction patterns acquired from various regions of (a)
Library 1, and (b) Library 2 (Table 1). The Miller indices of each LSM
re
fl
ection are indicated. Re
fl
ections marked with an asterisk are from
the YSZ substrate.
Fig. 4
FIB-SEM cross-section acquired from Library 2 after imped-
ance measurements. The sample was coated with conductive and
protective layers of carbon and platinum prior to FIB milling to facilitate
imaging. The top surface is tilted 52

away from the viewer.
Fig. 5
Atomic force micrographs of selected microelectrodes from Library 1 acquired after patterning. The corresponding thickness and root-
mean-squared roughness values are listed below each image.
19334
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(Fig. 6 and S10
), and nanometer-sized grains are apparent for
all
lms. Such growth characteristics are again typical. Quan-
ti
cation of these trends by image analysis (Fig. S11
) revealed a
largely monotonic variation in grain boundary density across
the thickness library, spanning from 45 to 95
m
m
m
m

2
(Fig. 7a).
For the growth temperature library, the range was wider,
spanning from 10 to 100
m
m
m
m

2
(Fig. 7b). Importantly, SEM
micrographs acquired a
er impedance testing indicate that
these grain size di
ff
erences persisted through the two days of
high-temperature exposure at 735

C (Fig. S10
). In short, the
thickness libraries and growth temperature library prepared in
this work were also e
ff
ectively
grain size libraries
with grain
sizes that remained stable during the electrochemical imped-
ance measurements.
4. Results of electrochemical
characterization
Before presenting electrochemical impedance results, it is
valuable to consider the nature of the system under investiga-
tion and the likely reaction pathway. Consistent with what has
been previously suggested in the literature, it is posited here
that the dominant pathway proceeds as shown in Fig. 8: oxygen
gas reacts with electrons over the entire surface of the LSM
microelectrode; electrons arrive at the reaction sites by traveling
laterally through the LSM from the probe tip; and the oxygen
ions created in the reduction reaction are incorporated into and
migrate through the mixed conducting LSM
lm and then into
the YSZ electrolyte.
A model for this sequence of steps, producing the result
shown in Fig. 9, can be postulated by
rst treating transport
through the LSM. It has been shown elsewhere that the elec-
trochemical impedance response arising from 1D di
ff
usion
through a generic mixed ionic and electronic conductor (MIEC)
can be rigorously mapped to an equivalent circuit based on a
generalized transmission model.
26,27
Under the condition of
electroneutrality, this generic MIEC equivalent circuit reduces
(as also shown previously) to an electronic path in parallel with
an ionic path, with the paths linked
via
what is termed the
chemical capacitance. In the case of LSM, the high electronic
conductivity suggests the resistance along the electronic path
(in the through-plane direction) is negligible. Accordingly, it is
omitted from the circuit in the present analysis. The termina-
tion of the MIEC circuit at the LSM/gas/probe interface is
assumed here to be reversible to electrons but to display a
nite
electrochemical reaction resistance with respect to incorpora-
tion/release of oxygen ions. This reaction is further taken to be
associated with a surface ionic capacitance term. The buried
LSM/YSZ interface is assumed here to be reversible to ions and
blocking to electrons, and thus is modeled by a simple (double-
layer) electronic capacitance. To describe the entire cell, this
MIEC system is placed in series with a single resistor that
accounts for bulk ion di
ff
usion through the YSZ electrolyte as
well as any lateral electron migration resistance (sheet resis-
tance) from the probe tip to the surface reaction sites. Finally, as
is common in impedance spectroscopy, dispersion e
ff
ects are
captured here by replacing (selected) ideal capacitors by a
constant phase element (CPE) with impedance
Z
CPE
¼
Q

1
(
j
u
)

n
, where
Q
is a constant,
j
¼
ffiffiffiffiffiffiffi

1
p
,
u
is the frequency of
Fig. 6
Atomic force micrographs of selected microelectrodes from Library 2 acquired after patterning. The corresponding growth temperature
and root-mean-squared roughness values are listed below each image.
Fig. 7
Exposed grain boundary length per unit surface area, estimated
using AFM images from microelectrodes
in (a) Library 1, and (b) Library 2.
This journal is © The Royal Society of Chemistry 2015
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,2015,
3
, 19330
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the applied a.c. signal, and
n
is a constant between 0 and 1.
28
Speci
cally, it was observed during data analysis that such a
substitution for the ionic surface capacitance signi
cantly
improved the quality of the
ts, so this substitution was
implemented throughout.
The complex impedance of the resulting equivalent circuit
(with analytical derivation provided in the ESI
) is:
Z
¼
R
ion
Z
D
þ
Z
D
Z
A
a
coth
ð
a
Þ
R
ion
þ
Z
A
Z
D
a
2
=
R
ion
þð
Z
A
þ
Z
D
Þ
a
coth
ð
a
Þ
þ
R
0
(1)
where
Z
D
¼
1
j
u
C
t
eon
,
Z
A
¼
R
s
ion
1
þ
R
s
ion
Y
s
ion
ð
j
u
Þ
n
,
and
a
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
j
u
R
ion
C
chem
p
. The seven
t parameters in this model are
R
s
ion
,
Y
s
ion
,
n
,
R
ion
,
C
chem
,
C
eon
, and
R
0
, which correspond,
respectively, to the LSM surface reaction resistance, the LSM
surface ionic capacitance (in the form of a constant phase
element magnitude and exponent), the LSM through-
lm
oxygen ion di
ff
usion resistance, the LSM chemical capacitance,
the LSM/YSZ interfacial electronic capacitance, and the sum of
the YSZ oxygen ion di
ff
usion resistance and the small LSM
electronic sheet resistance. This result is virtually identical to
that presented in brief previously by Fleig
et al.
,
6
except in the
use of CPEs. In that earlier work, a CPE was employed to
describe the interfacial electronic capacitance, whereas in the
present study a CPE was used to describe the surface ionic
capacitance, as noted above. The
ts were performed using a
complex nonlinear least squares
tting routine implemented in
a custom Matlab code. The residual of each complex impedance
datum was weighted by the complex modulus of the datum,
which is commonly used as a proxy for the variance of that
datum.
28
To validate the routine, impedance spectra from vali-
dation samples were
t to relevant equivalent circuits using
both this custom code and a commercial code (Zview), with
identical results obtained. From the CPE
t parameters, the
e
ff
ective surface ionic capacitance
C
s
ion
was calculated using the
standard expression
C
s
ion
¼
(
Y
s
ion
)
1/
n
(
R
s
ion
)
(1/
n
)

1
.
28
Selected raw impedance spectra and the corresponding
t
curves from a microelectrode in Library 1 (200
m
m diameter, 192
nm thick), are shown in Fig. 10 for a representative measure-
ment at two di
ff
erent oxygen partial pressures (
T

710

C). As
presented in the complex plane, Fig. 10a, the spectra are formed
of a large arc at lower frequencies, an additional smaller feature
at higher frequencies, and a relatively small o
ff
set from the
origin along the real direction appearing at the high frequency
limit. These spectral features are similar to those observed by
Fleig
et al.
,
6
and they are broadly akin to the spectra observed in
other reports as well.
7
9
Signi
cantly, the features are precisely
captured by the proposed model, as indicated by the corre-
spondence between the measured and
t spectra. The quality of
the
ts is particularly evident in the magnitude and phase plots
shown in Fig. 10d and e, respectively. The model parameters
extracted from these
ts are listed in Table 2 along with 95%
con
dence intervals. While (as is widely appreciated) an excel-
lent
t with reasonably small con
dence intervals does not,
alone, validate a model, it does give con
dence in the approach.
Fig. 8
Schematic of the posited through-
fi
lm reaction pathway.
Fig. 9
Equivalent circuit corresponding to the reaction pathway shown in Fig. 8.
19336
|
J.Mater.Chem.A
,2015,
3
, 19330
19345
This journal is © The Royal Society of Chemistry 2015
Journal of Materials Chemistry A
Paper
Open Access Article. Published on 27 August 2015. Downloaded on 15/10/2015 23:39:47.
This article is licensed under a
Creative Commons Attribution-NonCommercial 3.0 Unported Licence.
View Article Online