1
Title
Probing
the
Reaction
Pathway
in (La
0.8
Sr
0.2
)
0.95
MnO
3+δ
Using
Libraries
of Thin
Film
Microelectrodes
Authors
Robert
E.
Usiskin
1
,
Shingo
Maruyama
2
,
Chris
J. Kucharczyk
1
,
Ichiro
Takeuchi
2
,
Sossina
M.
Haile
1,
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
observed
1
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
V
counter
electrode
-
V
microelectrode
was
measured
at various
stage
temperatures
using
a nanovoltmeter.
The
corresponding
temperature
drop
T
counter
electrode
-
T
microelectrode
was
then
calculated
from
the
expression
/
V
counter
electrode
-
V
microelectrode
),
where
is
the
substrate
Seebeck
coefficient
(~0.5
mV/K
for
YSZ
3
).
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
1
0
0
2
0
0
3
0
0
4
0
0
5
0
0
0
1
0
2
0
3
0
7
5
0
°
C
6
5
0
°
C
5
5
0
°
C
V
c
o
u
n
t
e
r
e
l
e
c
t
r
o
d
e
-
V
m
i
c
r
o
e
l
e
c
t
r
o
d
e
/
m
V
M
i
c
r
o
e
l
e
c
t
r
o
d
e
d
i
a
m
e
t
e
r
/
m
H
e
a
t
e
d
s
t
a
g
e
s
e
t
p
o
i
n
t
0
2
0
4
0
6
0
T
c
o
u
n
t
e
r
e
l
e
c
t
r
o
d
e
-
T
m
i
c
r
o
e
l
e
c
t
r
o
d
e
/
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
Pt
0.7
Ir
0.3
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
2
0
3
0
4
0
5
0
6
0
7
0
8
0
3
0
n
m
1
6
5
n
m
*
2
2
0
0
2
4
2
0
2
0
1
2
I
n
t
e
n
s
i
t
y
/
a
.
u
.
2
/
T
h
i
c
k
n
e
s
s
1
1
0
*
3
0
0
n
m
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
5
5
0
6
0
0
6
5
0
7
0
0
7
5
0
0
1
2
3
4
5
s
u
r
f
a
c
e
r
o
u
g
h
n
e
s
s
/
n
m
R
M
S
T
g
r
o
w
t
h
/
C
2
.
7
4
0
2
.
7
4
5
2
.
7
5
0
2
.
7
5
5
2
.
7
6
0
2
.
7
6
5
o
u
t
-
o
f
-
p
l
a
n
e
(
1
1
0
)
s
p
a
c
i
n
g
/
Å
Figure
S6.
Surface
roughness
and
out-of-plane
(110)
plane
spacing
measured
from
Library
2 using
AFM
and
XRD,
respectively.
5
5
0
6
0
0
6
5
0
7
0
0
7
5
0
0
.
0
0
.
2
0
.
4
0
.
6
0
.
8
S
h
a
r
p
e
r
c
o
m
p
o
n
e
n
t
F
W
H
M
/
T
g
r
o
w
t
h
/
C
B
r
o
a
d
e
r
c
o
m
p
o
n
e
n
t
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
1
0
0
2
0
0
3
0
0
0
.
0
0
.
2
0
.
4
0
.
6
0
.
8
1
.
0
~
R
i
o
n
/
k
c
m
2
T
h
i
c
k
n
e
s
s
/
n
m
0
.
0
1
0
.
0
3
0
.
1
0
.
2
1
p
O
2
/
a
t
m
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
1
0
0
2
0
0
3
0
0
0
1
x
1
0
6
2
x
1
0
6
3
x
1
0
6
4
x
1
0
6
5
x
1
0
6
R
s
i
o
n
/
T
h
i
c
k
n
e
s
s
/
n
m
L
i
b
r
a
r
y
1
S
u
p
p
l
e
m
e
n
t
a
l
l
i
b
r
a
r
y
,
i
n
i
t
i
a
l
l
y
S
u
p
p
l
e
m
e
n
t
a
l
l
i
b
r
a
r
y
,
a
f
t
e
r
2
d
a
y
s
Figure
S13.
Surface
resistance
R
ion
s
extracted
from
impedance
spectra
from
both
Library
1
and
the
supplemental
library
at
~710
̊C
in 0.2
atm
O
2
using
200
μm
diameter
microelectrodes.
95%
confidence
intervals
are
shown.
9
0
2
0
4
0
6
0
8
0
1
0
0
0
.
0
5
.
0
x
1
0
-
3
1
.
0
x
1
0
-
2
1
.
5
x
1
0
-
2
2
.
0
x
1
0
-
2
~
L
i
b
r
a
r
y
1
(
R
i
o
n
)
-
1
/
c
m
2
s
u
r
f
a
c
e
g
.
b
.
l
e
n
g
t
h
/
m
m
-
2
L
i
b
r
a
r
y
2
(
a
)
0
2
0
4
0
6
0
8
0
1
0
0
1
2
0
0
1
x
1
0
-
4
2
x
1
0
-
4
3
x
1
0
-
4
4
x
1
0
-
4
5
x
1
0
-
4
~
L
i
b
r
a
r
y
1
C
c
h
e
m
/
F
c
m
2
s
u
r
f
a
c
e
g
.
b
.
l
e
n
g
t
h
/
m
m
-
2
L
i
b
r
a
r
y
2
(
b
)
0
2
0
4
0
6
0
8
0
1
0
0
1
x
1
0
-
1
0
1
x
1
0
-
9
1
x
1
0
-
8
1
x
1
0
-
7
1
x
1
0
-
6
L
i
b
r
a
r
y
1
D
c
h
e
m
/
c
m
2
s
-
1
s
u
r
f
a
c
e
g
.
b
.
l
e
n
g
t
h
/
m
m
-
2
L
i
b
r
a
r
y
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
O
2
(
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
Z
A
,
Z
1
,
Z
3
,
and
Z
D
,
as
shown
below
in
Figure
S15
. V
1
(x)
and
I
1
(x)
are
defined
as
the
voltage
and
the
current
for
the
branch
point
in
the
top
rail
of the
circuit,
V
2
(x)
and
I
2
(x)
are
analogous
values
for
the
bottom
rail,
V
a
is
the
input
voltage,
V
b
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,
,
Z
1
T
o
t
a
l
Z
1
N
, and
dx
= L/N.
Z
3
T
o
t
a
l
Z
3
/
N
Figure
S15.
Generalized
circuit.
From
these
definitions
it follows
that
(2)
Z
1
Z
1
T
o
t
a
l
d
x
L
(3)
Z
3
Z
3
T
o
t
a
l
L
d
x
Ohm's
law
implies
(4)
d
V
1
(
x
)
d
x
Z
1
T
o
t
a
l
L
I
1
(
x
)
Kirchoff's
law
implies
(5)
L
Z
V
x
V
d
x
x
d
I
d
x
x
d
I
T
o
t
a
l
a
3
1
2
1
)
(
)
(
)
(
(6)
I
I
1
(
x
)
I
2
(
x
)
The
boundary
conditions
are
(7)
V
a
V
1
(
0
)
Z
A
I
1
(
0
)
(8)
V
1
(
L
)
V
b
0
11
(9)
Z
I
L
I
Z
V
V
D
b
a
)
(
2
From
equations
4 - 5,
one
obtains
(10)
Z
3
T
o
t
a
l
L
2
I
1
'
'
Z
1
T
o
t
a
l
I
1
0
The
solution
to
equation
10
is
(11)
I
1
(
x
)
C
1
e
k
x
C
2
e
k
x
with
(12)
k
Z
1
T
o
t
a
l
L
2
Z
3
T
o
t
a
l
The
solutions
to
the
other
parameters
are
(13)
I
2
(
x
)
C
1
e
k
x
C
2
e
k
x
(14)
V
1
(
x
)
Z
1
T
o
t
a
l
L
C
1
k
e
k
x
C
2
k
e
k
x
Applying
the
boundary
conditions,
the
desired
expression
is
obtained:
(15)
)
c
o
t
h
(
*
)
(
)
(
)
c
o
t
h
(
*
2
k
L
k
L
Z
Z
R
k
L
Z
Z
R
k
L
k
L
Z
Z
Z
R
Z
D
A
i
o
n
D
A
i
o
n
D
A
D
i
o
n
where
the
generalized
impedance
elements
are
defined
as
(17)
Z
3
T
o
t
a
l
1
j
w
C
c
h
e
m
(18)
Z
D
1
j
w
C
e
o
n
(19)
Z
A
R
i
o
n
s
1
R
i
o
n
s
Y
i
o
n
s
(
j
w
)
n
and
the
argument
of
the
coth
can
be
evaluated
from
equation
12
to
obtain
(20)
k
L
j
w
R
i
o
n
C
c
h
e
m
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).