Three-dimensional vector electrochemical strain microscopy
N. Balke, E. A. Eliseev, S. Jesse, S. Kalnaus, C. Daniel, N. J. Dudney, A. N. Morozovska, and S. V. Kalinin
Citation: Journal of Applied Physics 112, 052020 (2012); doi: 10.1063/1.4746085
View online: http://dx.doi.org/10.1063/1.4746085
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/112/5?ver=pdfcov
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JOURNAL OF APPLIED PHYSICS 112, 052020 (2012)
Three-dimensional vector electrochemical strain microscopy
N. Balke,1,a) E. A. Eliseev,2 S. Jesse,1 S. Kalnaus,3 C. Daniel,3 N. J. Dudney,3
A. N. Morozovska,4,a) and S. V. Kalinin1
1
The Center for Nanophase Materials Science, Oak Ridge National Laboratory, Oak Ridge,
Tennessee 37831, USA
2
Institute for Problems of Materials Science, National Academy of Science of Ukraine, Ukraine 3,
Krjijanovskogo, 03142 Kiev, Ukraine
3
Materials Sciences and Technology Division, Oak Ridge National Laboratory, Oak Ridge,
Tennessee 37831, USA
4
Institute of Semiconductor Physics, National Academy of Science of Ukraine, Ukraine 41,
pr. Nauki, 03028 Kiev, Ukraine
(Received 19 December 2011; accepted 27 July 2012; published online 4 September 2012)
Three-dimensional vector imaging of bias-induced displacements of surfaces of ionically
conductive materials using electrochemical strain microscopy (ESM) is demonstrated for model
polycrystalline LiCoO2 surface. We demonstrate that resonance enhanced imaging using band
excitation detection can be performed both for out-of-plane and in-plane response components at
flexural and torsional resonances of the cantilever, respectively. The image formation mechanism
in vector ESM is analyzed and relationship between measured signal and grain orientation is
C 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4746085]
discussed. V
I. INTRODUCTION
The growing use of renewable energy sources is strongly
tied to the need for development of advanced energy storage
technologies.1–3 The functionality of energy storage systems,
such as Li-ion and Li-air batteries, is based on and ultimately
limited by the rate and localization of ion flows through the
device on different length scales ranging from atoms and
interfaces to mesoscopic grains and macroscopic grain assemblies.4–7 The improvement of existing and development of
future battery technologies are strongly hindered by the fundamental gap in understanding ionic transport processes on the
sub-micron length scales, necessitating development of local
characterization techniques capable of probing local electrochemical reactions and ionic transport.8–11
Recently, a scanning probe microscopy (SPM) based
method referred to as electrochemical strain microscopy
(ESM) was developed to probe Li-ion transport dynamics on
the nanoscale. The ESM was demonstrated on Li-ion battery
cathode materials and thin film battery devices.12,13 During
ESM, a high-frequency electrical bias Vac is applied to the
SPM tip in contact with Li-containing material. The applied
bias results in bias-induced Li-ion transport in the local volume proximal to the tip. The change in local Li-ion concentration is accompanied by a surface deformation induced due to
the intrinsic link between Li-ion concentration and molar volume of electrode materials. This deformation can be measured
with the SPM tip as surface displacement. The measurement
of the ion-flow induced strain, as opposed to Faradaic currents,
allows to reduce the probing volume size by a factor of
106–108 compared to existing electrochemical methods, and
perform imaging in a spatially resolved manner.14,15 The ESM
can be further extended to a broad range of spectroscopic techa)
Authors to whom correspondence should be addressed. Electronic
addresses: n2b@ornl.gov and morozo@voliacable.com.
0021-8979/2012/112(5)/052020/7/$30.00
niques that allow probing time16 and voltage dynamics of
ionic transport and separate transport and reaction stages.17
Commonly used electrode materials exhibit strong anisotropy both in Li-ion transport and chemical expansion.
Exemplarily, layered LiCoO2 show enhanced ionic diffusivity in the CoO2 planes perpendicular to the crystallographic
c-axis, whereas the volume change upon Li insertion/extraction occurs mainly along c-axis.18 As a result, the ESM
response will differ greatly between differently oriented
grains or single crystals. Correspondingly, it is of high interest to detect the full surface displacement vector during
ESM, as it has been previously achieved for ferroelectric material (Vector Piezoelectric Force Microscopy).19
Here, we demonstrate that ESM can be performed in the
vector mode by measuring out-of-plane (OP) and in-plane
(IP) components of the surface displacement on a polycrystalline LiCoO2 thin film. We further demonstrate that vector
ESM can be performed in the resonance enhanced mode,
i.e., at the frequencies corresponding to flexural and torsional
cantilever oscillations. The image formation mechanism in
ESM for system with anisotropic Vegard and diffusion constant tensors is analyzed. Analytical expressions for OP and
IP ESM signal for transversally isotropic material in general
orientation are derived. The potential of vector-ESM to
probe crystallographic orientation and electrochemical activity of individual electroactive grains is discussed.
II. EXPERIMENTAL
Layered LiCoO2 was selected as a model system, due to
the fact that it is most widely used cathode materials in
rechargeable Li-ion batteries and is also relatively stable
when in contact with ambient and aqueous environments.20
Due to the layered structure, LiCoO2 shows a strong anisotropy in Li-ion diffusivity and volume expansion upon Li removal.18 Therefore, we expect a strong variation in ESM for
112, 052020-1
C 2012 American Institute of Physics
V
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Balke et al.
differently oriented grains. Here, LiCoO2 thin films were fabricated by radio frequency sputtering on ceramic Al2O3 substrates with a thin Au film as bottom current collector.6 The
roughness of the substrate was measured by AFM to be
around 100 nm. The LiCoO2 was annealed at 800 C for 2 h in
O2. The cathode area was 1 cm2 and the film thickness was
about 530 nm.
Electrochemical strain microscopy measurements were
performed with a commercial atomic force microscopy system (Cypher, Asylum Research) additionally equipped with
LABVIEW/MATLAB based band excitation controller implemented on a National Instrument NI-6115 fast data acquisition (DAQ) card.21 All measurements were performed with
the biased tip in direct contact with the LiCoO2 surface in air
without any additional protective coating. Note that the use
of the band excitation (BE) method allows the surface
response and variations of resonant frequency to be
decoupled, obviating indirect topographic cross-talk.22
ESM imaging was performed at high (0.1–1 MHz) frequencies with 2Vac band excitation signal applied to a metal
coated tip (Nanosensors, Pt/Ir coating). These high frequencies allow us to utilize the contact resonance enhancement of
the surface oscillation amplitude with minimal Li-ion motion
to keep changes in the material reversible. The applied bias
between the SPM tip as a point contact and the bottom electrode results in a heterogeneous field distribution around the
tip with field components perpendicular and parallel to the
sample surface. Li-ions move under the influence of this field
which results in a change in sample volume, and thus a
change in surface height. To be able to measure the threedimensional surface displacement, the cantilever deflection
and torsion are measured independently. The deflection and
torsion signals corresponds to the vertical (OP) and lateral
(IP) component of the surface displacement. Here, the OP
and IP ESM signals are recorded around the deflection and
torsional resonance frequencies of the cantilever at 360 KHz
and 710 kHz, respectively. These frequencies are determined
by the mechanical properties of the cantilever and the
cantilever-sample contact and were established experimentally by using the band excitation method.21 The measured
parameters are the maximum surface oscillation (height of
the contact resonance peak) which forms the ESM signal,
and corresponding resonance frequencies and Q-factors that
define mechanical properties of the tip-surface junction and
energy dissipation, respectively.
III. RESULT AND DISCUSSION
Due to the strong anisotropy of the Vegard and diffusion
tensors in layered materials, the OP and IP ESM response is
expected to depend strongly on the grain orientation.23 This
behavior is schematically shown in Fig. 1. If the c-axis of
layered LiCoO2 is aligned parallel to the sample surface, the
strong OP field component is aligned directly with the Liion/CoO2 planes, resulting in a strong Li-ion concentration
change within the probed volume underneath the tip due to
high mobility and possible surface reaction. However, the
direction of maximum volume change is along c-direction,
and is thus purely in-plane. In this case we expect a high IP
J. Appl. Phys. 112, 052020 (2012)
FIG. 1. Correlation between OP and IP ESM response and the grain
orientation.
ESM signal and a zero or low OP ESM signal. Note that mechanical clamping can strongly reduce the IP volume change
due to mechanical constraints within the film. The opposite
behavior is expected if the c-axis is aligned normally to the
sample surface. In this case, only minimal changes in Li-ion
concentration are expected since only the weaker IP field
components give rise to electromigrative Li-ion motion and
surface reaction is minimized. However, in this case even
small changes in Li will result in strong OP ESM signals
since the direction of maximum volume change is OP and
mechanical clamping will play a smaller role than for the
purely IP volume change. In other grain orientations, nonzero OP and IP ESM signals are expected, with relevant signal strength dependent on exact grain orientation.
Figure 2 displays the correlation between topography
and the measured OP and IP ESM amplitude and phase
signals. To demonstrate the surface characteristics of the
LiCoO2 film, topography and deflection signal are shown in
Figs. 2(a) and 2(b), respectively. Small grains of LiCoO2
with a diameter of approximately 200-300 nm can be identified. The maximum OP and IP ESM amplitudes are displayed in Figs. 2(c) and 2(d). Both images show strong
variations in the ESM response across the scanned area. In
addition, the contrast in OP and IP ESM amplitude maps is
highly complementary and images show dissimilar features,
indicative of no or minimum cross-talk between the cantilever deflection and torsion signals. If Figs. 2(c) and 2(d) are
compared, grains with both OP and IP response (#1), no OP
but strong IP response (#2), and strong OP but zero IP
response (#3) can be identified. It can also be seen that the
lowest OP ESM response is non-zero as it is the case for IP
ESM. We further note that the cantilever deflection and torsion have different sensitivities and noise levels, making
direct comparison of absolute values difficult.
2D-ESM as shown in Fig. 2 can be used to extract information about the OP and IP volume changes. However, the
measured IP volume change is only sensitive to the direction
perpendicular to the cantilever axis. If the IP volume change
occurs parallel to the cantilever axis, the cantilever deformation is pure buckling and no torsion (i.e., IP ESM signal) is
recorded. Thus, to realize full 3D-ESM imaging collecting
information on all three components of surface displacement
vector, it is necessary to physically rotate the sample by 90
and image the same area again.
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FIG. 2. (a) Topography, (b) deflection, (c) OP ESM
map, and (d) IP ESM map for a 2 2 lm area on a
LiCoO2 thin film.
The V-ESM imaging of LCO surface is illustrated in
Fig. 3 exhibiting IP ESM amplitude map for the same area as
in Fig. 2 under different sample rotations. In order to find the
same area again after sample rotation, focused ion beam was
used to mark regions on the surface. The images were rotated
to show the same orientation. First, it can be seen that the
images for 0 and 90 look different. Some areas with a high
IP ESM signal under 0 show up as low signal areas under
90 and vice versa. This can be nicely seen in the upper right
corner of the image. In contrast, if 0 and 180 (or 90 and
270 ) images are compared, they look almost identical. This
was expected since the contrast is given by the relative orientation of the cantilever axis to the sample which is the same
for a 180 rotation between the two image pairs.
The essential condition for the existence of well-defined solution existence is the absence of dC at the infinity, well satisfied in an SPM experiment with local excitation. GSij is
appropriate tensorial Green function.27 Here, we approximate the symmetry of elastic properties as isotropic (well
justified to 3D compounds such as spinels and olivines),
albeit numerical schemes for Eq. (1) can be developed for
lower symmetries in straightforward fashion.28
We consider diagonal Vegard tensor bij ¼ dij bi with b1
6¼ b2 6¼ b3 (dij is the Kroneker delta symbol), but with the
general orientation of principal axes. In laboratory coordinate system the tensor components will be:
0
^ ¼B
b
@
A. Analytical calculation of ESM signals
for flat surfaces
cos / 0 sin/
0
1
0
(1)
0
B
¼@
b1 0
0
10
cos / 0 sin/
CB
CB
0 A@ 0 b2 0 A@ 0
sin/ 0 cos /
In the following section, we analyze image formation
mechanisms for the OP and IP ESM response and derive signal dependence on frequency of the applied electric field and
crystallographic orientation of LiCoO2. The general solution
of the problem for the elastic displacement of the sample surface is24–26
1
ð
e 1 ;k2 ;n3 ;tÞ:
es ðk1 ;k2 ;x3 ;n3 ÞdCðk
uei ðk1 ;k2 ;x3 Þ ¼ dn3 bkl cjmkl G
ij;m
10
0
0 b3
1
b2
C
A
0
sin/ 0 cos /
b1 cos2 / þ b3 sin2 / 0 ðb1 b3 Þcos /sin /
0
1
0
1
C
A
ðb1 b3 Þcos /sin / 0 b3 cos2 / þ b1 sin2 /
1
b11 0 b13
B
C
@ 0 b22 0 A
0
b13
0
b33
(2a)
FIG. 3. IP ESM map for a 2 2 lm area
on a LiCoO2 thin film for a sample rotation angle of (a) 0 , (b) 90 , (c) 180 ,
and (d) 270 for the area shown in Fig.
2. The images were rotated to show the
same orientation.
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Balke et al.
J. Appl. Phys. 112, 052020 (2012)
Using Eq. (2a) the OP ESM response ui (1) could rewritten as
1
u3 ðx1 ; x2 ; 0; tÞ ¼ 2p
1
ð
1
ð
dk2
1
1
ð
e 1 ; k2 ; n3 ; tÞ
dk1 dn3 expðik1 x1 ik2 x2 k n3 ÞdCðk
1
0
2k12 þ k22 ð1 k n3 Þ
2k22 þ k12 ð1 k n3 Þ
b33 ð1 þ k n3 Þ 2ik1 n3 b13 þ b22
þ b11
k2
k2
1
u1 ðx1 ; x2 ; 0; tÞ ¼
2p
1
ð
1
ð
dk2
1
1
1
ð
e 1 ; k2 ; n3 ; tÞ
dk1 dn3 expðik1 x1 ik2 x2 k n3 ÞdCðk
0
2k2 ð1 þ Þ þ k12 ð2 k n3 Þ
k k12 n3
2k12 k22 k n3
ik1 b11 2
b
2
þ
ik
b
þ
ik
n
b
1
1
3 33 :
13
22
k
k3
k3
e 1 ; k2 ; n3 ; tÞ is the 2D Fourier image
Here k2 ¼ k12 þ k22 , dCðk
of the concentration field dCðx1 ; x2 ; n3 ; tÞ. Note, that the
e 1 ; k2 ; n3 ; tÞ is an even
probe potential and consequently dCðk
function with respect of both k1 and k2 , and thus
u2 ð0; xÞ 0.
Here, we consider the case of the purely diffusion driven
process, in which electrochemical reaction at the tip-surface
junction creates modulates concentration or flux of mobile
ions, and the ionic transport in the material is dominated by
diffusion (corresponding to the presence of supporting electrolyte in solution-based electrochemistry). Here, the concentration dynamics is described by
@
@ 2 dCðx; tÞ
dCðx; tÞ ¼ Dij
;
@t
@xi @xj
B
B
D^ ¼ B
@
D1 cos2 / þ D3 sin2 / 0 ðD1 D3 Þcos/sin/
0
D2
0
ðD1 D3 Þcos/sin/ 0 D3 cos2 / þ D1 sin2 /
1
D11 0 D13
B
C
B
C
B 0 D22 0 C:
@
A
D13 0 D33
1
@
@ 2 dCðx;tÞ
dCðx;tÞ ¼ Dij
@t
@xi @xj
@2
@2
@2
@2
þD11 2 þD22 2 dCðx;tÞ
D33 2 þ2D13
@z
@z@x
@x
@y
(6)
one should solve the characteristic equation in FourierLaplace representation sdCe ðD33 q2 þ 2iD13 k1 q D11 k12
D22 k22 ÞdCe for a z-wave number, q, defined as
iD13 k1 6
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
D33 ðs þ D11 k12 þ D22 k22 Þ ðD13 k1 Þ2
D33
(7a)
(4)
Boundary conditions to Eq. (3) are (a) the absence of the
time-dependent part dCðx; tÞ at infinity and (b) the general
third kind boundary conditions in the contact area:29
@
dCðx1 ; x2 ; 0; tÞ gdCðx1 ; x2 ; 0; tÞ ¼ V0 ðx1 ; x2 ; tÞ;
@x3
(5)
dCðx1 ; x2 ; x3 ! 1; tÞ ! 0; dCðx; 0Þ ¼ 0:
Here V0 ðx1 ; x2 ; tÞ is the electrostatic potential distribution
at the tip electrode x3 ¼ 0. This boundary conditions reduces
to the case of either fixed concentration or fixed ionic flux
at phenomenological exchange coefficient k ¼ 0 or g ¼ 0,
correspondingly.
Rewriting Eq. (3) for the tensor Eq. (4) as
qðs; kÞ ¼
C
C
C
A
0
k
(2c)
(3)
where diffusion tensor is Dij . Similarly to Vegard tensor, in
the laboratory coordinate systems the diffusion tensor can be
written as
0
(2b)
Only negative term is relevant for a semi-infinite problem.
Here the vector k ¼ fk1 ; k2 g.
Using Laplace transformation on time t, and Fourier
transformation on transverse coordinates, the solution of
problem (3), Eq. (5) was found as Mellin integral:
e 1 ; k2 ; x3 ; tÞ ¼
dCðk
1
2ip
Aþi1
ð
ds exp x3 qðs; kÞ þ st
Ai1
Ve0 ðk1 ; k2 ; sÞ
:
kqðs; kÞ þ g
(7b)
Here Ve0 ðk; sÞ is the Fourier-Laplace image of V0 ðx1 ; x2 ; tÞ.
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Balke et al.
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Using Fourier transformation on time t, and Fourier
transformation on transverse coordinates, the solution of
problem (3), Eq. (5) was found as
e 1 ; k2 ; x3 ; xÞ ¼ exp x3 qðx; kÞ þ ixt
dCðk
qðx; kÞ ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
iD13 k1 6 D33 ðix þ D11 k12 þ D22 k22 Þ ðD13 k1 Þ2
D33
(8b)
Ve ðk ; k ; xÞ
0 1 2
:
kqðx; kÞ þ g
(8a)
:
Using the solution (8a) and Eqs. (2b) and (2c), the maximal
value of response can be written in the following form:
1
1
ð
ð
1
Ve0 ðk1 ; k2 ; xÞexpðixtÞ
dk2 dk1 u1 ð0; xÞ ¼
2p
kqðx;
kÞ
þ
g
k
þ
qðx;
kÞ
1
1
0
1 1
0 2
ik1
k22
k12
k
k
1
Ab13 C
B
2 2 ð1 þ Þ þ 2 2 b11 2@1 B k
C
k
k
k
þ
qðx;
kÞ
k k þ qðx; kÞ
B
C
B
C
0
1
B
C
2
2
B
C
k
@ þ ik1 @2 k1 k2 A
Ab22 þ ik1 b33 k
k2
k2 k þ qðx; kÞ
k þ qðx; kÞ
(9a)
and
1
ð
1
ð
expð ixtÞVe0 ðk1 ; k2 ; xÞ
kqðx;
kÞ
þ
g
k
þ
qðx;
kÞ
1
1
0 1
k
2ik1 b13
k12 k22
k
þ
b
b
1
þ
2
þ
1
22
B 33
C
k þ qðx; kÞ
k2 k 2
k þ qðx; kÞ
k þ qðx; kÞ
B
C
B
C:
@
A
k22 k12
k
þ b11 2 2 þ 2 1 k
k
k þ qðx; kÞ
1
u3 ð0; xÞ ¼ 2p
dk2
dk1 e
R0 qðx; kÞ qeðw; kÞ
Results for localized excitation
Ve0 ðk1 ; k2 ; xÞ ¼ V0 R20 exp ðk R0 Þ2 =2 ;
(10)
using dimensionless variables
k R0 ¼ ke and w ¼ x R20 =D1 ;
(11a)
¼
iD13 ke1 þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
2
iwD1 D33 þ D1 D3 ke1 þ D22 D33 ke2
:
D33
(11b)
In deriving Eq. (11b), the identity D33 D11 ðD13 Þ2 ¼ D1 D3
was used. After trivial transformations, the response acquires
the dimensionless form:
e 2 =2
V0 exp ðkÞ
dke2 dke1 e
e
ke þ qeðw; kÞ
ke
q ðw; kÞ=R
0þg
1
1
0
1 1
0
!!
2
2
2
~
e
e
e
e
ik
k
k
k
k1
Ab13 C
B 1 2 22 ð1 þ Þ þ 12 2 b11 2@1 B k~
C
e
e
e
e
e
e
e
e
k
þ
q
ðw;
kÞ
k k þ qeðw; kÞ
k
k
B
C
C
0
1
B
B
C
2
2
~1
e1 b33
e
e
e
B
C
i
k
i
k
k
k
k
1
2
@
A
@
A
b22 þ
2 2 2
þ
~
e
e
k
e
k þ qeðw; kÞ
ke
ke ke þ qeðw; kÞ
R0
u1 ð0; xÞ ¼
2p
1
ð
(9b)
1
ð
(12)
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J. Appl. Phys. 112, 052020 (2012)
and
2
e
V
exp
ð
kÞ
=2
0
1
d ke2 dke1 u3 ð0; xÞ ¼ R0
2p
e
e
ke þ qeðw; kÞ
ke
q ðw; kÞ=R
0þg
1
1
!
0
1
2ike1 b13
ke
B b33 1 þ e
C
e
e
B
C
ke þ qeðw; kÞ
k þ qeðw; kÞ
B
C:
!
!
!
!
B
2
2
2
2
C
e
e
e
e
e
e
k1 k2
k
k2 k1
k
@
A
þ b11 2 2 þ 2 1 þb22 2 2 þ 2 1 e
e
e
e
k þ qeðw; kÞ
k þ qeðw; kÞ
ke
ke
ke
ke
1
ð
1
ð
High-frequency limit of Eq. (12) is
u3 ð0; xÞ ¼ V0
ðb11 þ b22 Þð1 þ 2Þ þ 2b33
rffiffiffiffiffiffiffiffi
ix
ix
2
kþg
D33
D33
(14)
and u2 ð0; xÞ 0.
Note that for the case D1 ¼ D2 D3 , b1 ¼ b2 b3 the
dimensionless response is a universal function of the dimensionless frequency w ¼ x R20 =D1 and rotation angle /, and is
virtually independent on the tip radius and material properties
(except for Poisson ratio). Similar calculations can be made to
derive the IP ESM response u1/u2 and are not shown here.
(13)
Figures 4(a) and 4(b) demonstrate the frequency dependent OP and IP ESM signal (from Eq. (12)) for the cases
of fixed concentration boundary condition (k ¼ 0) for differently oriented grains, respectively. Here, we assume that
D1 ¼ D2 ¼ 100D3 and b1 ¼ b2 ¼ 0. The highest OP ESM
response is predicted in the low frequency region, defined as
that with probing frequencies smaller than the diffusion frequencies of the Li-ions. At the dimensionless frequency
w ¼ 1 the probing frequency is equal to the diffusion frequency and the ESM signal starts to drastically decrease
with increasing measurement frequency.
To demonstrate the correlation of the ESM signal and the
crystallographic orientation more clearly, Fig. 3(c) shows the
OP ESM signal for different crystallographic orientations for
FIG. 4. (a) Absolute amplitude normalized OP ESM responses dependence on the dimensionless frequency
w ¼ x R20 =D1 for D1 ¼ D2 ¼ 100D3 ,
b1 ¼ b2 ¼ b3 =100 and the different values of angle / ¼ 0 , 10 , 30 , 45 , 60 ,
75 , 85 , 90 (specified near the curves)
for the boundary conditions of fixed
concentration (k ¼ 0). (c) Absolute
value of OP ESM response as a function
of angle for low frequency, close to
cross-over frequency, and very high frequency (w ¼ 102, 1, 102, respectively)
for the boundary conditions of fixed
concentration. (b) Absolute amplitude
normalized IP ESM response under the
same conditions as (a) and the different
values of angle / ¼ 1 , 10 , 30 , 45 ,
60 , 75 , 85 , 89 (specified near the
curves). (d) Absolute value of IP ESM
response as a function of angle for different frequencies as shown in (c).
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052020-7
Balke et al.
low frequency, close to cross-over frequency, and very high
frequency. The latter case is the one corresponding to the experimental conditions, where since the frequencies used to
measure the ESM signal (0.1–1 MHz) are estimated to b much
higher than the diffusion frequencies in the probed volume
(1 Hz for 1 nm diffusion length). Figure 4(d) shows the same
calculations for IP ESM. In the case of OP ESM, the measured
signal becomes higher with rotation of the Li-ion planes parallel to the surface, i.e., for the c-axis perpendicular to the surface, but never becomes zero. This shows, even if the easy
diffusion direction for Li-ions is not aligned with the applied
field, the highest surface displacements can be measured due
to the strong changes of the c-axis upon deintercalation. For
IP ESM, the response is zero (non-detectable) for / ¼ 0 and
90 grain orientations. The difference in OP and IP ESM as
function of grain orientation can now be used to make conclusion about the texture of the film. Exemplarily, if OP ESM is
low (but non-zero) and IP ESM is zero, then / ¼ 0 is the
most likely grain orientation. If OP ESM is high and IP ESM
is zero, / ¼ 90 is the most likely grain orientation.
Here we note that the calculations shown above are valid
only for flat surfaces. The influence of surface morphology,
i.e., roughness and features like step edges, are not discussed
and may lead to the non-trivial dependence of ESM signal on
topography. The first leads to rotated surface normal vectors
which are different on different sides of the grain which can
lead to additional offsets in the measured OP and IP ESM values.30–33 For the latter, step edges or other topographical features can lead to an enhanced Li-ion extraction and thus an
enhanced ESM signal which is not considered in the analytical
calculations. This will be subject to future studies as well as
the influence of an asymmetric tip shape on the ESM signal.
IV. CONCLUSION
Vector-ESM can be used to investigate local volume
changes in Li-ion battery materials with strong anisotropy in
Li-ion conduction as well as volume changes. The cantilever
deflection and torsion are measured independent of each
other at flexural and torsional resonances respectively, forming the out-of-plane and in-plane components of the volume
change due to bias-induced changes in the local Li-ion concentration. Vector-ESM is demonstrated on LiCoO2 thin
films sputtered on Al2O3 substrates. Comparison with analytical calculations have shown, that the comparison of OP and
IP ESM signals for individual grains can be used to make
conclusions about single grain orientations.
ACKNOWLEDGMENTS
The experiments were performed with support provided
by the U.S. Department of Energy, Basic Energy Sciences,
Materials Sciences and Engineering Division through the
Office of Science Early Career Research Program. Experimental capabilities and part of the data analysis were supported by
the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User
J. Appl. Phys. 112, 052020 (2012)
Facilities Division, Office of Basic Energy Sciences, U.S.
Department of Energy. The samples were provided through
the Vehicle Technologies Program for the Office of Energy
Efficiency and Renewable Energy at Oak Ridge National Laboratory, managed by UT Battelle, LLC, for the U.S. Department of Energy under contract DE-AC05-00OR22725.
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