Libraries of (La_(0.8)Sr_(0.2))_(0.95)MnO_(3+δ) (LSM) thin film 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 diffusion through the film 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 film thickness (at constant growth temperature) or increasing film growth temperature (at constant thickness). These findings suggest that exposed grain boundaries in LSM films are more active than exposed grains towards the rate-limiting surface process, and that oxygen ion diffusion through polycrystalline LSM films is faster than many prior studies have concluded

Haile, Sossina M.

Kucharczyk, Chris J.

Maruyama, Shingo

Takeuchi, Ichiro

Usiskin, Robert E.

Caltech Authors - Main

Probing the reaction pathway in (La_(0.8)Sr_(0.2))_(0.95)MnO_(3+δ) using libraries of thin film microelectrodes

1
Title
Probing the Reaction Pathway in (La0.8Sr0.2)0.95MnO3+δ Using Libraries of Thin Film 
Microelectrodes
Authors
Robert E. Usiskin1, Shingo Maruyama2, Chris J. Kucharczyk1, Ichiro Takeuchi2, Sossina 
M. Haile1, 3
1. Applied Physics & Materials Science, California Institute of Technology, Pasadena, CA, United 
States. 
2. Materials Science and Engineering, University of Maryland, College Park, MD, United States.
3. Chemical Engineering, California Institute of Technology, Pasadena, CA, United States.
Supplemental Information
Figure S1. Primary chamber of the automated impedance microprobe used for 
electrochemical testing. Left: external photo. Right: computer model cross-section 
showing the chamber interior. For scale, the heated stage has a diameter of 5 cm.
Figure S2. Optical photograph of the asymmetric support used to heat the substrate 
during pulsed laser deposition of the growth temperature library, Library 2.
Electronic Supplementary Material (ESI) for Journal of Materials Chemistry A.
This journal is © The Royal Society of Chemistry 2015
2
 
Figure S3. Typical edge profile of an LSM microelectrode prepared by dry etching. 
This particular profile was acquired from an 80 μm diameter microelectrode in 
Library 1.
Temperature calibration
Opitz and Fleig have observed1 that in a typical microelectrode measurement the 
metal probe tip is cooler than the sample, and thus the probe tip cools the 
microelectrode by conduction during each impedance measurement. They measured 
that the resulting temperature drop between the counter electrode and the 
microelectrode can generate a Seebeck voltage of tens of millivolts, and they pointed 
out that the smaller the microelectrode diameter, the more the average 
microelectrode temperature is expected to be lowered by tip cooling. To determine 
an effective (average) temperature for the microelectrode, they considered an 
approach that uses the measured YSZ ionic conductivity and prior knowledge of the 
one-to-one relationship between YSZ ionic conductivity and temperature. A recent 
analysis indicated that this approach may be suitable for estimating the temperature 
at the microelectrode edge, but that it may overestimate the average temperature 
over the microelectrode surface.2
The current work employed a somewhat different procedure. First, a thin 
thermocouple was used to measure the temperature underneath the sample, i.e., the 
temperature of the counter electrode. This temperature closely matched the setpoint 
of the heated stage. Then the thermocouple was removed, and in a separate 
experiment, representative oxide microelectrodes of various diameters were 
contacted by a metal probe tip, and the induced thermovoltage Vcounter electrode - 
Vmicroelectrode was measured at various stage temperatures using a nanovoltmeter. The 
corresponding temperature drop Tcounter electrode - Tmicroelectrode was then calculated 
from the expression /Vcounter electrode - Vmicroelectrode), where  is the substrate 
Seebeck coefficient (~0.5 mV/K for YSZ3). Typical results are shown in Figure S3. 
From this temperature drop, the average microelectrode surface temperature was 
determined.
3
For example, with a stage temperature setpoint of 750 ˚C the average actual 
temperature of the microelectrodes under test was estimated as ranging from ~700 
˚C (for 100 μm diameter) up to ~720 ˚C (for 500 μm diameter).
In Figures 11a and 11c the deviations in the log-log relationships from the expected 
slope of -2.0 are attributed primarily to the temperature effects described above. Note 
that this tip cooling effect is not expected to significantly distort any of the other 
impedance trends reported in this work, since in all figures except for Figure 11, only 
results from 200 μm diameter microelectrodes were measured.
Upon touching the probe tip to a microelectrode, the thermovoltage typically took 5 - 
180 s to stabilize, with the faster times corresponding to the higher temperatures or 
larger diameters. The observed thermovoltages varied slightly between 
measurements, and larger thermovoltages were observed when contacting metal 
microelectrodes than when contacting the oxide microelectrodes used in this study. 
These effects are likely both explained by differences in thermomechanical contact 
and thermal resistance at the contact point. The thermovoltages measured here are 
somewhat smaller than those reported by Opitz, Fleig, and their colleagues.1 It may 
be that the larger stage here resulted in more radiative and convective heating of the 
probe, thus reducing somewhat the extent to which the probe locally cools a 
contacted microelectrode.
0 100 200 300 400 500
0
10
20
30
 750°C
 650°C
 550°C
V
co
un
te
r e
le
ct
ro
de
 - 
V
m
ic
ro
el
ec
tro
de
 / 
m
V
Microelectrode diameter / m
Heated stage setpoint
0
20
40
60
T c
ou
nt
er
 e
le
ct
ro
de
 - 
T m
ic
ro
el
ec
tro
de
 / 
C
Figure S4. Seebeck voltage measured between the counter electrode and an oxide 
microelectrode contacted by a Paliney7 probe tip. Rescaling the voltage by the 
Seebeck coefficient of YSZ yields an estimate for the associated temperature drop 
between the electrodes, also shown. Curves are power-law fits to the data at each 
temperature.
Sources of uncertainty in tip position
4
The total error in the position of the probe tip relative to the center of the target 
microelectrode has several contributions with the following estimated magnitudes: 
creep of the Paliney7 probe tip at high temperatures (±10 μm); deflection of the tip 
due to contact forces with the substrate (±10 μm); the manual process of visually 
identifying reference points (±10 μm); the photolithography method used to pattern 
the films (±5 μm); and the stepper motor positioning accuracy (±1 μm). The resulting 
total tolerance in tip position motivated the use of microelectrodes with sufficiently 
large diameter (≥ 100 μm) so as to ensure that reliable electrical contact could be 
achieved throughout the study. Probe tips made of Pt0.7Ir0.3 exhibited reduced creep 
and deflection but typically scratched the films at elevated temperature. Overall, it is 
likely possible to reduce the above tolerances in future studies and thereby reliably 
contact microelectrodes with smaller diameters.
Fitting routine: Choosing the initial values
Depending on the initial values chosen for the fit parameters, the fitting routine 
sometimes either failed to converge or converged to a solution with unreasonably 
large confidence intervals for all parameters. It was found that these convergence 
problems could largely be avoided by taking as the initial value of each fit parameter 
the median result for that parameter from preliminary fits to the same spectra that 
were performed using plausible but otherwise somewhat arbitrary initial values.
Additional Figures
20 30 40 50 60 70 80
30 nm
165 nm
*
22
0
02
42
02
01
2
In
te
ns
ity
 / 
a.
u.
2 / 
Thickness
11
0
*
300 nm
Figure S5. XRD patterns acquired from the supplemental library. The corresponding 
film thickness is listed to the right of each pattern. The orientation of each LSM 
reflection is also indicated. Reflections marked with an asterisk are from the YSZ 
substrate.
5
    
550 600 650 700 750
0
1
2
3
4
5
su
rfa
ce
 ro
ug
hn
es
s
/ n
m
 R
M
S
Tgrowth / C
2.740
2.745
2.750
2.755
2.760
2.765
ou
t-o
f-p
la
ne
(1
10
) s
pa
ci
ng
 / 
Å
Figure S6. Surface roughness and out-of-plane (110) plane spacing measured from 
Library 2 using AFM and XRD, respectively.
  
550 600 650 700 750
0.0
0.2
0.4
0.6
0.8
Sharper component
FW
H
M
 / 

Tgrowth / C
Broader component
Figure S7. Typical rocking curve data acquired from Library 2. Left: Raw data and fits 
acquired in a region where the growth temperature was 725 ˚C. The two fit 
components are shown in red at bottom; the fit residual is shown in green at top. 
Right: Full width at half maximum (FWHM) values as a function of growth 
temperature.
6
Figure S8. Secondary ion mass spectrometry measurement from a microelectrode in 
Library 2 grown at 627 ˚C.
Figure S9. AFM images acquired after patterning from the supplemental library. The 
corresponding film thickness and root-mean-squared roughness are listed under 
each micrograph.
7
Figure S10. SEM images from Library 2 after impedance testing for 2 days at ~710 ˚C. 
Some of the observed contrast is due to mild sample charging.
 
Figure S11. Typical images used to estimate the exposed grain boundary length. Films 
from Library 2 grown at two different temperatures are shown. Left: AFM 
micrographs. Right: Same micrographs after image processing. The exposed grain 
boundary length was estimated by summing the length of the borders between the 
green regions.
8
0 100 200 300
0.0
0.2
0.4
0.6
0.8
1.0
~ R
io
n /
 k

c
m
2
Thickness / nm
 0.01
 0.03
 0.1
 0.2
 1
pO2 / atm
Figure S12. Thickness dependence of the bulk ionic resistance obtained from fits to 
impedance spectra from 200 m diameter microelectrodes in Library 1 at ~710 ˚C 
under various oxygen partial pressures as indicated. This plot is identical to Figure 
13c, except here all seven parameters were free to vary in all fits, including the 0.2 
atm and 1 atm fits. 95% confidence intervals are shown.
 
0 100 200 300
0
1x106
2x106
3x106
4x106
5x106
R
s io
n /
 
Thickness / nm
 Library 1
 Supplemental library, initially
 Supplemental library, after 2 days
Figure S13. Surface resistance Rions extracted from impedance spectra from both 
Library 1 and the supplemental library at ~710 ˚C in 0.2 atm O2 using 200 μm 
diameter microelectrodes. 95% confidence intervals are shown.
9
0 20 40 60 80 100
0.0
5.0x10-3
1.0x10-2
1.5x10-2
2.0x10-2
~
Library 1(
R
io
n)
-1
 / 


c
m
2
surface g.b. length / m m-2
Library 2
(a)
0 20 40 60 80 100 120
0
1x10-4
2x10-4
3x10-4
4x10-4
5x10-4
~ Library 1C
ch
em
 / 
F 
cm
2
surface g.b. length / m m-2
Library 2
(b)
0 20 40 60 80 100
1x10-10
1x10-9
1x10-8
1x10-7
1x10-6
Library 1D
ch
em
 / 
cm
2  s
-1
surface g.b. length / m m-2
Library 2
(c)
Figure S14. Dependence of bulk electrochemical parameters on surface-terminated 
grain boundary length as measured from 200 μm diameter microelectrodes in 
Libraries 1 and 2 (varied thickness for Library 1 and varied growth temperature for 
Library 2) under 0.01 bar O2 (T ~ 710 C). (a) through-film conductance (inverse of 
the through-film resistance), (b) chemical capacitance, and (c) through-film 
ambipolar diffusivity. All parameters are area-normalized, and 95% confidence 
intervals propagated from the impedance analysis are shown, except where they are 
smaller than the data points.
10
Derivation of Equation 1
An analytical expression for the equivalent impedance Z of the circuit shown in 
Figure 8 can be derived following the method described in the appendix of a paper 
by Lai and Haile.4 First, the circuit is recast using generalized impedance elements 
ZA, Z1, Z3, and ZD, as shown below in Figure S15. V1(x) and I1(x) are defined as the 
voltage and the current for the branch point in the top rail of the circuit, V2(x) and 
I2(x) are analogous values for the bottom rail, Va is the input voltage, Vb is the output 
voltage, and I is the total current. The value of x varies from 0 at one end of the MIEC 
(the top face of the microelectrode) to L at the other end of the MIEC (the MIEC/YSZ 
interface). Additional definitions are that there are N branch points, , 

Z1
Total  Z1N
, and dx = L/N.

Z3
Total  Z3 /N
Figure S15. Generalized circuit.
From these definitions it follows that
(2)

Z1  Z1
Total dx
L
(3)

Z3  Z3
Total L
dx
Ohm's law implies
(4)

dV1(x)
dx
 
Z1
Total
L
I1(x)
Kirchoff's law implies
(5)
LZ
VxV
dx
xdI
dx
xdI
Total
a
3
121 )()()( 
(6)

I  I1(x)  I2(x)
The boundary conditions are
(7)

Va V1(0)  ZA I1(0)
(8)

V1(L) Vb  0
11
(9)ZILIZVV Dba  )(2
From equations 4 - 5, one obtains
 (10)

Z3
TotalL2I1' 'Z1
TotalI1  0
The solution to equation 10 is
(11)

I1(x)  C1e
kx C2e
kx
with 
(12)

k 
Z1
Total
L2Z3
Total
The solutions to the other parameters are
(13)

I2(x)  C1e
kx C2e
kx
(14)

V1(x)  
Z1
Total
L
C1
k
ekx 
C2
k
ekx




Applying the boundary conditions, the desired expression is obtained:
(15)
)coth(*)(
)(
)coth(*
2
kLkLZZ
R
kLZZR
kLkLZZZR
Z
DA
ion
DA
ion
DADion



where the generalized impedance elements are defined as
(17)

Z3
Total 
1
jwCchem
(18)

ZD 
1
jwCeon

(19)

ZA 
Rion
s
1 Rion
s Yion
s ( jw)n
and the argument of the coth can be evaluated from equation 12 to obtain
(20)

kL  jwRionCchem
12
Supplemental references
1 Opitz, A. K. & Fleig, J. Investigation of O-2 reduction on Pt/YSZ by means of thin 
film microelectrodes: The geometry dependence of the electrode impedance. 
Solid State Ion. 181, 684-693, doi:Doi 10.1016/J.Ssi.2010.03.017 (2010).
2 Huber, T. M., Opitz, A. K., Kubicek, M., Hutter, H. & Fleig, J. Temperature 
gradients in microelectrode measurements: Relevance and solutions for 
studies of SOFC electrode materials. Solid State Ion. 268, 82-93, 
doi:10.1016/j.ssi.2014.10.002 (2014).
3 Ahlgren, E. O. & Poulsen, F. W. Thermoelectric power of stabilized zirconia. 
Solid State Ion. 82, 193-201, doi:Doi 10.1016/0167-2738(95)00201-3 (1995).
4 Lai, W. & Haile, S. M. Impedance Spectroscopy as a Tool for Chemical and 
Electrochemical Analysis of Mixed Conductors: A Case Study of Ceria. J 
American Ceramic Society 88, 2979-2997, doi:10.1111/j.1551-
2916.2005.00740.x (2005).


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Probing the reaction pathway in (La_(0.8)Sr_(0.2))_(0.95)MnO_(3+δ) using libraries of thin film microelectrodes

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