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F. Wunde et al.: Ion transport and phase transformation in thin film intercalation electrodes
Fabian Wunde, Susann Nowak, Juliane Mürter, Efi Hadjixenophontos, Frank Berkemeier,
Guido Schmitz
Institut für Materialwissenschaft, Universität Stuttgart, Stuttgart, Germany
International Journal of Materials Research downloaded from www.hanser-elibrary.com by University of New South Wales on October 28, 2017
For personal use only.
Ion transport and phase transformation
in thin film intercalation electrodes
Thin film battery electrodes of the olivine structure LiFePO4 and the spinel phase LiMn2O4 are deposited through
ion-beam sputtering. The intercalation kinetics is studied
by cyclo-voltammetry using variation of the cycling rate
over 4 to 5 orders of magnitude. The well-defined layer
geometry allows a detailed quantitative analysis. It is
shown that LiFePO4 clearly undergoes phase separation
during intercalation, although the material is nano-confined
and very high charging rates are applied. We present a modified Randles–Sevcik evaluation adapted to phase-separating systems. Both the charging current and the overpotential depend on the film thickness in a systematic way. The
analysis yields evidence that the grain boundaries are important short circuit paths for fast transport. They increase
the electrochemical active area with increasing layer thickness. Evidence is obtained that the grain boundaries in
LiFePO4 have the character of an ion-conductor of vanishing electronic conductivity.
Keywords: Intercalation compounds; Thin films; Elastic
interaction; Ionic transport; Grain boundary transport
1. Introduction
Li ion batteries are presently the preferred technical solution
for storage of electric energy in mobile applications. Improving their storage or power density, as well as their cycle stability requires a detailed physical understanding of the intercalation kinetics. The priority program SPP1473 motivated
experimental studies that focused on Li transport in well-defined model structures as they are provided by thin films of
controlled thickness and outstanding surface and interface
quality. In contrast to conventional particle electrodes, thin
films allow studying the pure battery function without any
disturbance by conductivity additives or complicated polymeric binders. Transport pathways become comparably simple.
In a series of projects, we studied deposition of various
active thin film materials, characterized their properties
and studied various kinetic aspects [1 – 4]. Furthermore,
the variation of optical properties during de/charging was
investigated [5]. Possibilities to exploit this function in optical switching were explored [6]. We also studied the composition and the growth of solid-electrolyte-interfaces (SEI)
at the surface of thin films using in-situ quartz-balance
micro-gravimetry [7].
Here, we report a recent not yet published study on the
intercalation kinetics in LiFePO4 and LiMn2O4 thin films,
which represents the final experimental effort triggered by
the SPP 1473. Both oxides are well-known and particularly
attractive as cathode battery materials, as they comprise exclusively non-toxic abundant components. LiFePO4 stands
out due to its low costs, while LiMn2O4, also not very expensive, offers a particularly high open-circuit potential of
about 4 V. Both materials were also studied by other teams
within the SPP 1473, albeit with a focus on equilibrium
thermodynamics. The heat capacity of LiFePO4 has been
measured in a rather broad range of temperatures [8]. Several studies explored the Li–Mn–O systems, however in a
different concentration range than relevant in this work
[9 – 11]. Two further studies addressed the deposition of
Li–Mn–O thin films by the alternative methods magnetron
sputtering and pulsed laser deposition [12, 13].
The possible electrochemical function of the spinel
LixMn2O4 (x = 0. . .1) was first reported by Thackeray
et al. [14]. Due to short-ranged repulsion between the Li
atoms, the Li intercalation proceeds in two steps. First,
only half of the tetrahedral sites are homogeneously filled.
Then in a second step, at slightly higher potential, the
other half is occupied to reach one Li per molecular unit
[15]. LiMn2O4 has been already very early integrated in
all-solid-state thin film batteries along with LiPON electrolyte and Li metal anodes [16]. This has initiated intensive research on thin film deposition of the material by
electron beam evaporation [17], magnetron sputtering
[18] and pulsed laser deposition (PLD) [19, 20]. To our
knowledge, however, the ion-beam sputtering technique,
which is applied in this study, has not been reported on
before. Li diffusivity in the thin films (mostly produced
by PLD) has already been investigated using various electrochemical methods, such as GITT, PITT, CV, EIS [19 –
21]. In the majority of cases, a diffusion coefficient of
10–11 to 10–12 cm2 s–1 at room temperature is reported with
a few exceptions mentioning up to two orders of magnitude lower or higher values [21, 22] which was presumably due to deviation from stoichiometry, impurities or
particular microstructural effects.
The olivine structure LiFePO4 demonstrates a high reversibility in intercalation. The material allows full delithiation
without degrading the FePO4 host lattice. During intercalation, the material experiences a phase separation into an
Li-poor a and an Li-rich b phase [23, 24], which hinders
the application of classical electrochemical techniques
[25] in the evaluation of the diffusivity. Presently, however,
1
F. Wunde et al.: Ion transport and phase transformation in thin film intercalation electrodes
there are controversial discussions as to which extent the
phase separation may be suppressed due to nano-confinement, elastic stress or fast intercalation [24, 26, 27]. This
question represents the starting point of our investigation.
By performing a careful comparison of the intercalation behaviour of the two materials that differ in their respective
phase diagram, we try to clarify the specific situation in nanometric LiFePO4 thin films.
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2. Elasticity of interstitial solutions
Intercalation compounds such as the studied LiMn2O4 and
LiFePO4 represent interstitial solutions. Fundamental features of such solutions have previously been considered in
the field of hydrogen solution and formation of hydrides in
transition metals. Hydrogen molecules are split at the metal
surface and enter the host as single atoms to occupy available interstitial sites. Since hydrogen atoms are slightly larger than the offered interstices, the uptake of hydrogen induces an expansion of the host lattice, which increases in
proportion to the total hydrogen content. Elastic interaction
then leads to formation of dense hydride phases. The latter
features of lattice expansion and decomposition are reminiscent of central aspects of Li intercalation. It is, therefore,
attempting to transfer the elastic concepts that were developed in the context of metal hydrides to the battery materials.
In view of elasticity, Li atoms solved on specific interstitial sites represent dilatational centres, which interact via
their elastic fields. Since the insertion of an Li atom requires more space than that offered by the respective host
site, the Li interstitials are located in a compressive stress
field. In a superficial view, one could assume that these
compressive fields repel each other and so a repulsive interaction between the Li atoms would result. However, it has
been shown in the example of hydrogen in metals that just
the opposite is the case (e. g. [28, 29]). Overall, a thermodynamically attractive interaction is predicted, which interestingly depends on the boundary condition at the material
surfaces. For a finite sample with free boundaries, the solution of a dilatational centre leads to an average increase of
the lattice spacing, which then makes it easier to insert
further interstitials. Formally, this is described by the action
of tensile surface stress, image forces that are required to
satisfy the boundary condition (see [30] for an exact theoretical derivation).
Let us assume a spherical particle of an intercalation
compound of volume Vp. Frequent experience in intercalation is that the lattice expands in proportion to the concentration of the inserted species (see, e. g. Refs. [33, 34]).
Thus, each interstitial increases the volume by an almost
constant excess DVLi. To induce the volume increase of nLi
intercalated atoms, the tensile image stress (negative pressure) at the surface must amount to
r¼B
nLi DVLi
nLi DVLi
DVLi
¼B
¼B
cLi
Vp
NVsite
Vsite
ð1Þ
in which B, N, Vsite, and cLi represent the bulk modulus, the
number of available interstitial sites, the total volume per
interstitial site, and the concentration (atomic ratio) of Li.
2
The interaction energy of the interstitials with this (homogeneous) stress field is
DwðcLi Þ ¼ r DVLi ¼ B
2
DVLi
cLi ¼ : 2X cLi
Vsite
ð2Þ
in which we defined the elastic interaction parameter X. By
integration on the concentration, we determine the total
elastic energy of all intercalated species to express the
Gibbs energy as a regular solution
gðcLi Þ ¼ cLi l0 þ 2 kB T fcLi ln cLi
þ ð1 cLi Þ lnð1 cLi Þg X c2Li
ð3Þ
in which l0 denotes the Gibbs solution energy of a single Li
atom in infinite dilution. The unusual factor 2 in front of the
mixing entropy accounts for additional electronic contributions to the entropy [31]. Analysis of Eq. (3) predicts a
miscibility gap for any temperature below Tc ¼ X=4kB . It
should be noted that Eq. (3) neglects any coherency strain
inside the sample. Furthermore, its derivation is based on
free surfaces. If the sample were prevented from expansion,
the attractive interaction would vanish. So any constraint
that hinders the free expansion at least partially has a significant effect on the phase boundaries or the phase separation
at all.
In thin film geometry, such constraints could stem from
the fixation to the substrate. If volume expansion and
elastic constants are isotropic, one can presume to a first
approximation that the elastic energy X gets reduced by
one third per constraint dimension (in film geometry the
two lateral dimensions). The elastic effects on the intercalation might be quite different in both studied materials
as the volumetric expansion of LixMn2O4 (x = 0. . .1)
amounts to only slightly more than 3 % [32], while the
expansion of LixFePO4 (x = 0. . .1) reaches up to 7 % [27].
Let us study the probably larger effects in LFP quantitatively. Given the olivine structure of LiFePO4, both expansion and elastic moduli are anisotropic, so that the tensor
algebra of linear elasticity must be applied for concrete
statements.
The total elastic energy of free expansion is calculated
as
3
X
1
X ¼ Vsite
ei Cij ej
2
i;j¼1
ð4Þ
Here, Cij and ei represent the tensor of elastic moduli and
the strains into the three main axes directions when the system is fully charged to cLi = 1. (Following from experiment,
shear terms can be neglected.) If fixed to a rigid substrate,
additional compressive stress evolves in the two lateral dimensions, which counteracts the free expansion, while the
expansion in the perpendicular free direction even enlarges
due to transverse contraction. Assuming an (100) uniaxial
texture of the thin film, we determine the additional expansion along the stress-free 1-axis as
e01 ¼
C12 e2 þ C13 e3
C11
ð5Þ
F. Wunde et al.: Ion transport and phase transformation in thin film intercalation electrodes
The additional constraint contribution to the elastic energy
amounts to
1
Xð100Þ ¼ Vsite C~22 e22 þ C~33 e23 þ 2C~23 e2 e3
2
ð6Þ
with appropriately defined elastic constants [33]:
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Ci1 C1j
C~ij :¼ Cij C11
ð7Þ
Analogous equations for the other main texture orientations
follow by cyclic permutation.
Required input parameters and results of the calculation
are summarized in Table 1. All strains are considered relative to the lattice parameters of the Li-free a phase [27].
Tensor components of the elastic moduli were derived from
density functional theory [34]. The two most remarkable results are seen in the last rows of Table 1: i) The elastic interaction X of the free system is way larger than 4kBT at room
temperature. So, the elastic effects let expect a miscibility
gap of DcLi = 87 at.%, which corresponds closely to the experimentally observed phase boundaries in the LixFePO4
system. Obviously, we can understand the essential phase
diagram of the incoherent heterogeneous system already
by elasticity without discussing the chemical interactions
in detail. ii) If a thin film is fixed to a substrate and plastic
relaxation prevented, the miscibility gap at room temperature will become significantly narrowed or will even vanish
for the main axes of possible film orientation (hkl) = (100),
(010), (001), respectively.
For coherent interfaces between the a and b phase, the situation is more complex as the elastic energy not only depends on the total Li content,
but also on the fraction of
the b phase c ¼ cLi cðaÞ = cðbÞ cðaÞ , a function of
the solubility limits c(a) and c(b) of both phases. Parallel to
the interphase boundary, the lattice constants of both phases
are forced to become equal through additional elastic strain.
So, these shared lattice constants become a function of the
phase fraction, too. Assuming the interface perpendicular
to a given coordinate axis, we derive for the additional elastic strains in the two other directions parallel to the interphase boundary:
ðaÞ
ei
ðbÞ
ei
¼
ðaÞ
ai ai
ðaÞ
ai
¼
ðbÞ
ðaÞ
ai ai
ðaÞ
ai
c ei c
ð8aÞ
ei ð1 cÞ
ð8bÞ
The total elastic energy comprises the weighted contributions of both phases according to
ðhklÞ
ðhklÞ
Xcoh ¼ ð1 cÞ XðhklÞ
þ c Xb
a
ð9Þ
which leads by combination of Eqs. (6, 8) and regarding
Vegards law to
h
i
ðhklÞ
Xcoh ¼ XðhklÞ ð1 cÞc2 þ cð1 cÞ2 ¼ XðhklÞ cð1 cÞ
ð10Þ
Accordingly, the Gibbs energy of the coherent system becomes a function of the total content cLi and in addition to
the solubility limits cðaÞ ; cðbÞ of the two phases in constraint
equilibrium:
gðcLi ; cðaÞ ; cðbÞ Þ ¼ ð1 cÞghom ðcðaÞ Þ þ cghom ðcðbÞ Þ
þ cð1 cÞXðhklÞ
ð11Þ
Minimizing this function, with respect to cðaÞ and cðbÞ at
given Li content cLi, determines the Gibbs energy as well
as its strain part in thermodynamic equilibrium, as shown
in Fig. 1. The graphs are plotted for different strengths of
the elastic effect as controlled by the respective moduli
and stress free expansions. If elastic effects are nil
(XðhklÞ ¼ 0), the conventional double tangent construction
is reproduced. With increasing elastic effect (XðhklÞ > 0)
however, the Gibbs energy in the miscibility gap is not de-
Table 1. Elastic calculations according to Eqs. (4 – 7). Values of lattice parameters were taken from [27]. Strains are estimated based on
Vegards law. DFT-based elastic moduli were obtained by averaging various approximations and the values for the a and b phase in [34].
a1 (Å)
9.826
10.334
a2 (Å)
5.794
6.002
a3 (Å)
4.784
4.695
Vsite (Å3)
68.09
strain
e1
0.052
e2
0.036
e3
–0.019
e1 + e2 + e3
0.069
moduli
C11 (GPa)
154
C23 (GPa)
35
C22 (GPa)
171
C31 (GPa)
54
C33 (GPa)
150
C12 (GPa)
52
elastic energy
X(100) (10–20J)
0.75
X(100)/kBTR.T.
–1.81
X(010) (10–20J)
1.13
X(010)/kBTR.T.
–2.74
X(001) (10–20J)
2.43
X(001)/kBTR.T.
–5.88
X (10–20J)
–2.47
X /kBTR.T.
+5.97
effective (X + X(hkl))/kB TR.T.
+4.16
+3.23
+0.09
+5.97
width of miscibility gap
44 at.%-Li
–
–
87 at.%-Li
Lattice constants
a
b
3
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F. Wunde et al.: Ion transport and phase transformation in thin film intercalation electrodes
Fig. 1. Calculation of the two-phase equilibrium by minimizing
Eq. (11) for different strength of coherency constraint: elastic energy
(top) and total Gibbs energy (bottom). In the bottom figure, the Gibbs
energy before phase separation is shown by a thick solid line, after
phase separation by dashed lines. (The driving force to phase separation is represented by the difference between the thick solid and the respective dashed line.) Without elastic constraint (X(coh) = 0), the Gibbs
energy after phase separation is conventionally predicted by the double
tangent (straight dashed line).
a linear superposition anymore. Remarkably, for
fined by
ðhklÞ X ¼ kB TR:T: , the gain in Gibbs energy due to phase separation becomes very small and the miscibility gap is diminished considerably. With only a slight further increase
of the elastic effect, the miscibility gap would even vanish.
Thus, be it the fixation to the substrate or the coherency
between matrix and precipitate phase, the LiFePO4 layers
could not show any phase separation, except that sufficient
relaxation by e. g. plastic deformation or roughening of interfaces (similar as in the Stranski-Krastanov thin film
growth mechanism) would take place. It is anything but
natural to observe the phase separation in nanometric
LiFePO4.
3. Performed experiments
The goal of the presented study is to clarify to which extent
phase separation and thin film microstructure may affect
the (de-)intercalation kinetics of sputter-deposited nanometric cathode films. In order to demonstrate possible effects, we compare the kinetics of LiFePO4 with that observed in LiMn2O4 layers, varying layer thickness and
charging rate. Both materials were deposited as thin films
by an ion beam sputtering technique in a self-constructed
UHV chamber, offering a background pressure of less than
1 107 mbar. The Ar beam of the ion gun is accelerated
to 850 – 1 000 eV. Its current density amounts to 1 –
2 mA · cm–2. Electric charging of the targets and films is
prevented by an additional electron shower. Thermally oxidized Si was used as substrate, initially coated by a current
collector of platinum, 50 or 100 nm in thickness. Targets
of both active materials were produced from carbon-free
LiFePO4 powder (Südchemie) and electrochemical grade
LiMn2O4 powder (Sigma-Aldrich Co. LLC) by cold pressing to a disc of 8 cm diameter and a few millimetres in
4
thickness. In the case of LiMn2O4, sufficient mechanical
stability of the powder target was only achieved through
subsequent sintering for 10 h at 900 8C in ambient air.
The sputtering conditions must be carefully chosen to obtain active thin films of sufficient electrochemical capacity
and well reversible intercalation function. The optimum parameters were determined in an extended series of experiments [3, 35]. In the case of LiFePO4, over-oxidation must
be carefully avoided in all production steps. So, sputtering
is performed in a pure Ar atmosphere (10–4 mbar) at room
temperature, and the required post-deposition annealing at
500 8C for 3 h is also performed under an Ar protecting atmosphere. In contrast, LiMn2O4 was sputter-deposited in
an Ar:Oxygen mixture (1 : 10, 4 104 mbar total pressure)
and likewise, the post treatment to establish the correct lattice structure was done under ambient air at 750 8C for 1 h.
The correct lattice structure of the deposited thin films was
confirmed in both materials applying X-ray diffraction.
Quality, film thickness and microstructure were proven by
transmission electron microscopy at cross-sections of the
layer stack. Required electron transparent samples were
prepared via the \lift-out" process using a dual beam scanning microscope SCIOS (FEI). They were investigated
using a CM200FEG (Philips) transmission microscope
equipped with an EDX system.
Overviews of the microstructural features of produced
LiMn2O4 and LiFePO4 are presented in Figs. 2 and 3, respectively. In both cases, cross-sections are shown of the
layer stack in the as-deposited state and, with two different
thicknesses, after the post-sputter annealing. The diffraction pattern of the LiMnO4 layer confirms the expected spinel structure. For the LiFePO4 layers, the result of the
chemical analysis by EDX is shown. Li cannot be detected
using this method. However, keeping the limited accuracy
in mind, the content of Fe and P matches closely, and the intended under-oxidation is confirmed. Pt and C impurities
stem from the current collector underneath the active material, the additional PtC protective coating deposited before
the lift-out, and an unavoidable hydrocarbon contamination
on the surface of the electron transparent thin films. Cu
stems from the TEM grid, while Cr is a slight contamination of the used sputter chamber.
In our experience, structural analysis using XRD and
chemical analysis by means of EDX can prove that the
layers represent, the intended material and lattice structure.
But, they do not allow a reasonable prediction of whether
or not the produced materials will perform well in battery
function. This must be checked in real electro-chemical cycling.
In the context of this study, the different microstructures
of both active materials must be pointed out. In the case of
LiMn2O4, the as-deposited material is already crystalline,
with a columnar grain structure, where the lateral grain size
typically increases with the deposited thickness. During the
subsequent annealing at a comparatively high temperature,
significant grain growth appears and the grains develop a
brick-like shape. By comparing Fig. 2b and c, it becomes
obvious that the final grain size depends significantly on
the layer thickness, though the increase in size is clearly
less than proportional to the layer thickness.
In the case of LiFePO4, the quality of the micrographs is
poor, since the material is beam-sensitive in the preparation
and the subsequent TEM investigation. Nevertheless, the
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F. Wunde et al.: Ion transport and phase transformation in thin film intercalation electrodes
Fig. 2. TEM investigation of the LiMn2O4
(LMO) electrode stacks deposited on oxidized Si wafer substrates: (a) Pt50 nm/
LMO300 nm in as-deposited state, (b) Pt50 nm/
LMO100 nm annealed, (c) Pt50 nm/LMO500 nm
annealed, (d) electron diffraction pattern of
the LMO layer after annealing. The expected
ring pattern of the spinel structure is marked.
Fig. 3. TEM investigation of the LiFePO4
(LFP) electrode stacks deposited on oxidized
Si wafer substrates: (a) Pt100 nm/LFP200 nm in
as-deposited state, (b) Pt100 nm/LFP200 nm annealed; inset shows electron diffraction pattern of crystalline LFP layer, (c) Pt100 nm/
LFP400 nm annealed, (d) EDX spectrum of the
LFP layer after annealing and quantitative
evaluation (concentrations in at.%).
5
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F. Wunde et al.: Ion transport and phase transformation in thin film intercalation electrodes
evolution of the grain structure can still be qualified. During
the annealing, the microstructural development starts from
an amorphous state, which can explain that the layer thickness has only negligible impact on the grain structure.
Small globular grains develop with a local variation in the
average size, but without any unambiguous correlation to
the layer thickness (compare Fig. 3b and c).
The thin film cathodes were electrochemically cycled in
a half-cell configuration that consisted of the studied film
(working electrode) and two Li foils (reference and counter
electrode) immersed into a water-free liquid electrolyte of
DMC/EC (1 : 1) with 1 mol l–1 LiClO4. Electrical measurements were controlled by a Bio-Logic potentiostat VSP300. To prevent any contamination by oxygen or water, all
measurements were performed in self-designed argon-filled
test cells, which are assembled in a glove box. After cell assembly, cyclic voltammetry is executed under variation of
the scan rate over a very broad range of v = 0.004 mV s–1
to 400 mV s–1.
A few key-results to document the performance of the
produced thin films are presented in Fig. 4 and Fig. 5 for
LiMn2O4 and LiFePO4, respectively. Voltage ranges of 3.7
to 4.25 V (LiMn2O4) and 2.8 to 4.2 V (LiFePO4) were used
for cycling. For the kinetic studies presented below, the cycle stability is most important to allow multiple repetition
of de/charging cycles without changing the sample. Therefore, for the LiMn2O4, we decided to use the material annealed at 750 8C. It has a slightly less initial capacity than
samples annealed at higher temperature, but offers the better cycling stability and less rate-dependence in capacity.
The produced LiFePO4 thin films show an excellent cycling
stability (see also [3] for data of X-ray diffractometry and
electrochemical cycling to higher cycle numbers). After a
few \running-in" cycles, the capacity fading is less than
10 % per 1 000 cycles. As the first cycles still show some
equilibration effects to establish the full efficiency close to
100 %, all kinetic investigations were started after the first
10 cycles.
(a)
Fig. 4. (a) Electrochemical capacity of the produced LiMn2O4 thin
films determined in cyclo-voltametry of the first 50 cycles. The influence of the annealing temperature of the post-deposition treatment
and the dependence on the scanning rate are shown. At the end of each
series of increasing rates, ten further slow cycles demonstrate the degree of reversibility. (b) Cycling stability of ion-beam sputter-deposited LiMn2O4 after annealing at 750 8C/1 h. Inset shows the first 500 cycles with less than 10 % capacity fade although cycled a high rate (20 C
(!), i. e. full charge within 3 min).
6
(b)
Fig. 5. De/intercalation of LiFePO4 films: (a) Chrono-potentiometry
in half-cell configuration after first, 10th and 20th cycles. (b) Capacity
measured in the first 20 charging cycles.
F. Wunde et al.: Ion transport and phase transformation in thin film intercalation electrodes
The observed remarkable reversibility in cycling is primarily a consequence of the thin layer geometry that prevents crack formation. In our experience, the more serious
issue is delamination, which appears when the layer thickness increases. Therefore, we restricted the maximum
thickness to 200 nm in the case of LiFePO4 and to about
500 nm in the case of LiMn2O4.
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4. Kinetic studies
Both layer materials were investigated by cyclo-voltammetry under variation of the scanning rate over several orders
of magnitude. Plots of the measured charging currents versus the voltage (cyclograms) are presented in Fig. 6. The
cyclograms of the materials differ significantly, which is,
however, in line with previously published reports. While
LiFePO4 reveals a single, sharply defined current peak
(see Fig. 6a), two overlapping peaks shifted with respect
to each other by 0.15 V are observed in LiMn2O4 (see
Fig. 6b). Intercalation in LixMn2O4 up to x = 1 is known to
appear in two consecutive steps [15]. In both systems, the
currents vary systematically depending on the scanning
rate. Thus, the peak current density can be used as a characteristic measure of the kinetic behaviour as suggested by the
classic Randles–Sevcik analysis [36]. In its original form,
this analysis assumes an ideal solution of Li in the electrode
materials and a semi-infinite bulk diffusion regime. By contrast, in the case of thin films, phase separating systems,
nano-crystalline microstructures, or diffusion-induced
stress, essential assumptions of the derivation are not fulfilled and a more complex behaviour must be expected,
which represents the topical focus of this report.
In the following quantitative study, we evaluate the peak
currents and the relative shift of the peaks, between intercalation and deintercalation as functions of the scanning rate.
Investigated rates ranged from 0.005 mV s–1 to 768 mV s–1
in the case of LiMn2O4, and from 0.004 mV s–1 to
40 mV s–1 in the case of LiFePO4.
The central kinetic result of the LixMn2O4 layers is presented in Fig. 7. The peak current density of the first de/intercalation peak (x ¼ 0:5 . . . 1:0) is plotted versus the scanning rate. The double logarithmic plot in Fig. 7a clearly
reveals a linear dependence of the peak current density on
the rate for slow scanning, while the plot of current versus
the square root of rate in Fig. 7b demonstrates a parabolic
dependence for the fast scanning rates. This transition in
the kinetic exponent agrees to the continuum approximation of the thin film diffusion regime as suggested by Aoki
et al. [37]
pffiffiffi
D pffiffiffi
jp ¼ 0:446 e cmax
v~ tanh 0:56 v~ þ 0:05 v~
ð12Þ
d
in which ~m represents the dimensionless rate
v~ :¼
e d2
v
D kB T
ð120 Þ
and e, cmax, v, d, and D the elementary charge, the maximum intercalated Li content, the scanning rate (dU/dt), the
maximum diffusion width (thickness of the film), and the
(composition-independent) diffusion coefficient, respectively. Equation (12) may be considered in two limiting
cases. As tanhðxÞ 1 for large x, we find the classic Randles–Sevcik solution
rffiffiffiffiffiffiffiffi
eD pffiffiffi
jp ¼ 0:446 e cmax
v
ð13Þ
kB T
in the limit of thick films, slow diffusion, or fast scanning.
On the other hand, for small ~m, the tanh(x) function can be
replaced by its argument, in which furthermore the square
root term dominates so that one expects
jp ¼ 0:25 e2 cmax
Fig. 6. Cyclo-voltammetry of (a) LiFePO4 layer (thickness 100 nm)
and (b) LiMn2O4 layer (thickness 300 nm) at various scanning rates as
indicated. (Voltage with respect to Li reference. De-intercalation peaks
at positive currents).
d
v
kB T
ð14Þ
in the case of very thin layers, fast diffusion or slow scanning. The latter relation is intuitively understood. In the
case of slow scanning, the composition stays practically
homogeneous. At any moment the voltage corresponds to
the chemical potential which has a minimum slope of
7
F. Wunde et al.: Ion transport and phase transformation in thin film intercalation electrodes
kB T
and so even explains the numerical pre0:25
factor in Eq. (14).
With Eqs. (13, 14), we understand the transition between
the linear and the square root dependence on the scanning
rate that is experimentally observed in LiMn2O4. In addition, however, we observe in Fig. 7 that the peak currents
increase with the layer thickness. This becomes particularly
clear, if the diffusivities are calculated from the slopes of
the graphs in Fig. 7b (based on Eq. (13)) as presented in Table 2. While such an increase would be naturally expected
in the linear regime of slow scanning, it is an absolute surprise for the Randles–Sevcik regime at higher scanning
rates, since this assumes an infinite diffusion space and
therefore excludes any influence of a finite sample thickness. At present, the exact functional relation between the
peak current and the thickness may not be finally clarified,
as the capacity and so the peak current densities and derived
diffusivities of individual samples still show an experimental scatter of 10 to 20 %. However, from the data presented
in Table 2, it is at least indicated that the apparent diffusion
coefficient varies approximately proportionally to the layer
thickness. Consequently, the peak current density increases
approximately with the square root of the thickness. This
dependence is physically difficult to understand and provokes further considerations (see below). Interestingly, the
overpotential, as derived from the peak shift, reveals exactly the same dependence, as shown in Fig. 8. The overpotential appears proportionally to both the square root of the
rate and the square root of the thickness.
The analogous analysis was also performed for a series
on LiFePO4 thin films. A summary of obtained experimental data, peak current densities and peak shifts (overpotentials) is presented in Fig. 9. Data of three different layer
thicknesses (100, 150, and 200 nm) are compared to each
other. Figure 9a presents the peak current density for the
de- and intercalation peaks, similar to those shown in
Fig. 7a for the previous spinel layers. However, here the yaxis is already scaled by the layer thickness as stated in the
axis label. Furthermore, the data of the intercalation are
multiplied by ten for clarity. Noteworthy, by normalizing
to the thickness, the peak currents densities of films of different widths match, which makes clear that in the case of
LiFePO4, the peak current scales in proportion to the layer
thickness.
As before, the scanning rate was varied over several orders of magnitude. However, in contrast to what has been
stated for LiMn2O4, now the data demonstrate a continuous
Randles–Sevcik regime proportional to the square root of
rate, even at very low scanning rates. In the double logarith-
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dl=dcjmin ¼
Fig. 7. Peak current density of the first de/intercalation peak (\I." as
defined in Fig. 6b) of LiMn2O4. Different layer widths as labelled: (a)
Double logarithmic plot indicates current proportional to the rate at
slow scanning. (b) Current density versus square root of rate indicates
Randles–Sevcik behaviour at fast scanning. Peak currents are clearly
dependent on the layer thickness.
Table 2. Apparent diffusion coefficients for the first peak pair (peaks \I." as defined in Fig. 6b) calculated by means of the Randles–
Sevcik relation, Eq. (13). By normalization to the layer thickness (last column), a proportionality between diffusivity and thickness is indicated.
8
Layer thickness d (nm)
D (Intercalation) (cm2 s–1)
D (Deintercalation) (cm2 s–1)
D (Deintercalation)/d
(10–14 cm2 s–1 nm–1)
55
110
300
515
1.14 · 10–12
3.60 · 10–12
7.31 · 10–12
1.20 · 10–11
1.21 · 10–12
3.63 · 10–12
7.99 · 10–12
1.18 · 10–11
2.2
3.3
2.7
2.3
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F. Wunde et al.: Ion transport and phase transformation in thin film intercalation electrodes
mic plot, all data points fall on straight lines, of which the
slopes represent exponents of n = 0.62 and n = 0.56 for the
intercalation and the deintercalation peak, respectively.
The voltages at which the current peak appears are plotted
in Fig. 9b. The overpotential may be defined as half of the
voltage shift between the intercalation and deintercalation
peak. Naturally, the overpotential increases with the scanning rate since stronger driving force is required to accelerate the transfer of the ions from the electrolyte into the solid
materials. In comparison to Fig. 9a, it is remarkable that the
overpotential is obviously independent of the layer thickness. Since the peak currents depend on the thickness, it follows that the same peak current density (per film area) is
obviously obtained in thicker films with lower driving
forces, which is clearly worked out at the two example
peaks shown in Fig. 10.
Performing a naïve Randles–Sevcik analysis of the peak
currents of LiFePO4 by Eq. (13) (see Fig. 9), yields diffusion coefficients of about 0:4 1012 cm2 s–1. Thus, the diffusivity of LiFePO4 might be at most two orders of magni-
tudes less than that of LiMn2O4. In the latter however, the
described transition between the linear and the square root
regime appears at a scanning rate of about 10 mV s–1,
which is close to the right margin of the range shown in
Fig. 9a. In consequence, the analogous transition in LiFePO4 should certainly lie inside the evaluated measurement
window if it existed. The fact that such a transition is not
observed must be accepted as evidence that LiFePO4 does
not show any linear regime in the peak current at all.
At this point, the important experimental observations on
the intercalation kinetics may be summarized as
. both oxides, LiMn2O4, as well as LiFePO4, reveal a Randles–Sevcik regime in which the peak current is proportional to the square root of the sweeping rate. This
allows estimating the diffusivity. The diffusion coefficients of both materials in all studied phases are quite
similar and amount to 1013 to 1011 cm2 s1 at room
temperature. (In order to be of practical use, any reasonable battery material needs a diffusivity in the range of
1014 to 1010 cm2 s1 );
(a)
(a)
(b)
(b)
Fig. 8. Evaluation of the overpotential (shift of the current peaks) in
cyclo-voltametry of LiMn2O4 films: (a) dependence on the scanning
rate, (b) dependence on the layer thickness. (Peak I. and peak II. as defined in Fig. 6b).
Fig. 9. Analysis of the (de-)intercalation kinetics of LiFePO4 films,
100 nm, 150 nm, and 200 nm in thickness. (a) Peak current density versus scan rate. (Currents normalized to the film thickness, data of intercalation multiplied by a factor of ten for clarity). The normalized data
merge on a common master line. (b) Voltage positions of the current
peaks. The shift between the inter- and deintercalation peaks (overpotential) is practically independent of the layer thickness.
9
F. Wunde et al.: Ion transport and phase transformation in thin film intercalation electrodes
tails of the performed calculations are found in [40]). For
this, the volume is subdivided into discrete lattice planes,
perpendicular to the presumed fast diffusion direction
(usually the a2 axis, distance between the Li planes and thus
the jump length k 0:3 nm). The transport flux of the Li
atoms between neighboured planes is described as
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ji;iþ1 ¼ ci ð1 ciþ1 ÞCi!iþ1 ciþ1 ð1 ci ÞCiþ1!i
ð15Þ
which considers the concentration ci of Li atoms in the
plane (i) before the jump and that of vacant sites in the
plane (i+1) after the jump. The jump rates Ci!j are thermally activated as described by Boltzmann factors. By
drawing a part of the concentration factors of Eq. (15) into
the exponents of the Boltzmann factors, we finally arrive at:
ji;iþ1 ¼
Fig. 10. Comparison of deintercalation peaks in cyclo-voltametry of
LiFePO4 films, 100 nm (top) and 200 nm (bottom) in thickness, at various scanning rates. The equilibrium peak voltage (left dashed line at
3.435 V) was derived from the data in Fig. 9b. A film of double thickness, needs four times less rate to achieve the same peak current density. Even more remarkable, the same peak density of about 0.3 A m–2
is achieved in the thicker film with significantly less overpotential as
marked by the pairs of dashed lines.
. at low rates, only the LiMn2O4 layers reveal a linear kinetic regime between peak current and square root of
rate;
. in both materials, the peak currents increase with the
thickness;
. at constant peak current, the overpotential in LiFePO4
does vary reciprocally to the layer thickness.
5. Kinetic simulation of the Li transport
The presented experimental study on the intercalation kinetics in thin film cathodes has revealed significant deviations from the classical continuum solution of the diffusion
equations as it was proposed by Aoki et al. [37]. Since this
assumes an ideal thermodynamic solution of Li and neglects any surface effects, it cannot handle phase separation
and overpotentials appropriately. So, to interpret the data on
a sound basis, we performed simulations of the intercalation
in a discrete, kinetic mean field model (for general information on this kind of modelling see, e. g. [38, 39]. Further de10
m0 pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ci ciþ1 ð1 ci Þð1 ciþ1 Þ
Vsite
liþ1 li
liþ1 li
exp exp
2kB T
2kB T
ð16Þ
with the attempt frequency m0 . The electronic conductivity
of the mixed ionic conductors is assumed to be so large that
the electrical potential stays homogeneous inside the material. Thus, no electrostatic driving forces appear in the diffusion equation. This is different at the surface to the electrolyte, where a significant drop in the potential appears.
Here, we use a Buttler–Volmer Ansatz that considers the
jump across the kinetic barrier, between inside of (plane
i = 0) and outside of the electrode:
jsurf pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
l þ eð U U 0 Þ
jsurf ¼
c0 ð1 c0 Þ exp 0
Vsite
2kB T
l0 þ eðU U0 Þ
ð17Þ
exp
2kB T
The coefficient jsurf denotes the respective attempt-frequency, which we may interpret as the surface permittivity,
and U0 represents the open circuit voltage. Finally, the required chemical potentials are derived from Eq. (3)
cLi
l ¼ 2Xð1 2cLi Þ þ 2kB T ln
þ 2j r2 cLi
1 cLi
ð18Þ
In comparison to Eq. (3), we added a concentration gradient
term in Eq. (18) (last term on the right hand side) and chose
the respective coefficient sufficiently large (j ¼ X=8) to
warrant the stability of the hetero-phase interfaces. However, its exact choice is not critical for the simulation results
presented below. Simulations were performed for two different choices of the interaction parameter, (i) X ¼ 0 for
an ideal solution and (ii) X ¼ 5:5 realizing a miscibility
gap of about Dc = 80 at.% Li at room temperature.
The essential outcome of the simulation is presented in
Fig. 11, which shows (a) a typical current trace of a cyclovoltammetry cycle, (b) the evaluated peak current densities
versus the voltage scanning rate for different layer thicknesses and interaction parameters, as well as (c) the typical
Li concentration profiles across the thin film. As seen by
Fig. 11a, the simulation is well suited to describing the cur-
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F. Wunde et al.: Ion transport and phase transformation in thin film intercalation electrodes
(a)
(b)
(c)
Fig. 11. Kinetic mean-field simulation of Li intercalation on a simple
cubic lattice of interstices during cyclo-voltametry (used parameters: D ¼ m0 k ¼ 7 1013 cm2 s1 , jsurf ¼ 1:65 107 cm s1 , cmax ¼
20 lAh cm2 lm1 . Interaction energy adjusted to establish a miscibility of 80 at.% at room temperature): (a) current versus voltage (voltage
as difference to the open circuit value); (b) peak current density versus
voltage scanning rate. Results of the ideal solution in comparison to decomposing regular solutions in films of various thicknesses (marked by
different symbols); (c) Li concentration profiles perpendicular to layer
surface during deintercalation in the case of an ideal solution at slow
scanning (left), ideal solution at fast scanning (center), and the simulated phase separating system (right). (Surface to the electrolyte at the
left, current collector at the right side. The arrows indicate the further
temporal evolution of the profile.) While the left composition profile
leads to a kinetic exponent of n = 1.0, the centre and right profiles lead
to an exponent of n = 0.5.
rent in a cyclo-voltametry experiment so that the current
peaks and the overpotential (measured as the shift between
the intercalation and deintercalation peak) can be evaluated. The simulation result for an ideal solution (Fig. 11b,
green curve) convincingly confirms the continuum solution
Eq. (12). As a function of the scanning rate (jp / vn ), the
peak current reveals a clear transition between a regime
with the exponent n ¼ 1 and a regime with the exponent
of n ¼ 0:5. Such transition is indeed observed for the
LiMn2O4 films. But it stands in obvious contrast to the experimental behaviour of the LiFePO4 thin films. For the
phase separating system, on the other hand, the simulation
predicts the kinetic exponent being constant at n = 0.5 over
the experimentally studied range of scanning rates, which
is in perfect agreement with the experimental observation
at the LiFePO4 films.
The different behaviour of the ideal and the phase separating system is well understood with regard to the corresponding concentration profiles derived perpendicular to
the film surface. Profiles simulated at about 50 % deintercalation are shown in Fig. 11c. Given an ideal solution at slow
scanning, the concentration is almost homogeneous across
the film and so, during deintercalation, the concentration
profiles develop from top to bottom. For fast scanning however, the profiles show a continuous slope and shift from
left to right. So the required diffusion width of the Li atoms
increases with time, which has the immediate consequence
of a square root relation between peak current and rate.
The composition profiles of the phase separating system resembles this latter case. The phase boundary provokes an
infinite slope of the profile even for arbitrary slow rates
and the concentration profile always shifts from left to
right. Thus again, the diffusion width increases in time and
in consequence, a square root relation is observed at any
scanning rate.
In reversed conclusion: The fact that we do observe a
transition from a linear to a square root regime in LiMn2O4
provides strong evidence that intercalation happens in these
films without any significant phase separation in diffusion
direction. The absence of any such transition in LiFePO4
proves, on the contrary, that the (de-)intercalation in this
system appears heterogeneously via the migration of a
phase boundary. Thus, in the studied nanometric thin films,
LiFePO4 does clearly decompose in spite of the expected
elastic depression of phase separation by geometric constraints. Obviously, major plastic relaxation takes place
even on the nanoscale and under very fast scanning.
Having confirmed in this way that the LiFePO4 films indeed undergo a phase separation during the intercalation,
the application of the classical Randles–Sevcik analysis to
determine the diffusion coefficient (based on Eq. (13)) becomes questionable. However, by simulating the kinetics
for the phase separating system of 80 at.% miscibility gap,
we can show that the procedure of the classical evaluation
is nevertheless not that bad. As shown in Fig. 12a, the linear
relation between the peak current density and the square
root of the scanning rate is preserved although the material
decomposes. Only the slope, i. e. the pre-factor in Eq. (13),
needs to be modified. This modification does depend on
the surface permittivity (expressed by jsurf), but this unknown parameter can be determined by evaluation of the
overpotential under variation of the scanning rate, as confirmed by the simulation results presented in Fig. 12b.
11
F. Wunde et al.: Ion transport and phase transformation in thin film intercalation electrodes
With the following considerations, an accurate evaluation of experimental data in terms of the diffusivity can be
achieved. A scaling analysis demonstrates that the simulated cyclograms all fall on a common master curve, if aside
from the voltage, only the following scaled dimensionless
variables are used:
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j~ :¼
d
j;
D e cmax
v~ :¼
e d2
v;
D kB T
~surf :¼
j
d
jsurf
D
ð19Þ
One can suggest the following procedure. First, according
to the simulation, peak shift and scanning rate (slopes in
Fig. 12b) are related by
pffiffiffi
rffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffi
ed
v
v~
DU ¼ ð0:0721 VÞ pffiffiffiffiffiffiffiffiffi ¼ ð0:0721 VÞ kB T
jsurf
~surf
j
ð20Þ
(a)
Therefore, a plot of the peak shift versus the square root of
the scanning rate v delivers the surface permittivity jsurf.
Second, in analogy to Eq. (13), the relation between peak
current density and rate is formulated as
pffiffiffi
j~p ¼ cR:S: v~
rffiffiffiffiffiffiffiffi
ð21Þ
eD pffiffiffi
v
jp ¼ cR:S: e cmax kB T
Yet, the dimensionless Randles–Sevcik coefficient c R.S.
still depends on the surface permittivity. By evaluating the
slopes of the graphs in Fig. 12a, we derive:
rffiffiffiffiffiffiffiffiffi
1
cR:S: ¼ 0:272 0:028 ð22Þ
~surf
j
Inserting this expression into Eq. (21), we arrive at a quadratic equation for the square root of the diffusion coefficient
rffiffiffiffiffiffiffiffiffi pffiffiffiffi
jp
e
D
pffiffiffi ¼ e cmax 0:272 D 0:028 pffiffiffiffiffiffiffiffiffiffiffiffiffi
kB T
v
d jsurf
ð23Þ
that can be equated to the experimentally determined ratedependence of the peak current density and numerically
solved for the diffusion coefficient, if the maximum diffusion length d is known.
6. Interpreting the dependency
on the layer thickness
As a decisive advantage in comparison to conventional particle compound electrodes, thin films allow the exact control of the geometry. So the layer thickness can be used as
a control parameter to discover fundamental features of
the intercalation transport. As an unambiguous result, the
simulation for a phase separating system predicts the
peak currents being independent of the layer thickness
(Fig. 11b), since the maximum of the current appears way
before the phase boundary has reached the back side at the
current collector. The same independence is also expected
for the classical Randles–Sevcik condition under fast scanning. In remarkable contrast, the presented experimental
data demonstrate that this is not the case, either for LiFePO4
12
(b)
Fig. 12. Kinetic mean field simulation of (a) the peak current and (b)
peak shift (with respect to the open circuit voltage) during deintercalation of a phase separating system of 80 at.% miscibility gap.
or LiMn2O4, though the dependencies on the thickness may
differ in detail. In LiFePO4, we revealed the peak current
being proportional to the thickness, while in LiMn2O4, the
increase of current probably better agrees with a square root
dependence. Although we varied the parameter set widely,
we failed to reproduce this experimentally observed variation with thickness in the simulation. This leads to the conclusion that the layer-like transport geometry used in the
simulation is too simple to understand the real intercalation
kinetics.
In Fig. 13, a cross-section TEM micrograph of the produced LiFePO4 layer, after the necessary heat treatment, is
shown in higher resolution. The material consists of equiaxed grains, about 50 nm in average grain diameter. In the
case of LiFePO4 the observed microstructure is formed only
during the post-annealing treatment after film deposition.
Consequently, the grain size is found to be almost independent of the deposited thickness (compare also Fig. 4). This
strongly suggests a natural solution to the unexplained dependence of the peak currents on the layer thickness. If the
transport of Li along the grain boundaries were significantly faster than inside the grain volume, intercalation
would appear from the grain boundaries towards the grain
interior. Thus, the controlling area for the total current is
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F. Wunde et al.: Ion transport and phase transformation in thin film intercalation electrodes
ways of deep intercalation as illustrated in Fig. 13b. In this
context, it should be mentioned that Quan et al. [22] produced LiMn2O4 films by sintering of electrodeposited particles. For these films, they found superfast intercalation,
which they also explained via short circuit transport along
the less dense sintering boundaries.
Having discovered the important role of short-circuit
transport along the grain boundaries, we laid the basis to
quantify the correct depth of diffusion transport required to
evaluate Eqs. (20) and (23). Assuming diffusion from the
GBs into globular grains, the maximum diffusion depth is
naturally given by the grain radius, i. e. d = rgrain. Also, with
constant grain size in the LiFePO4 films, the total
reactive
area amounts to Atot ¼ ð3=2Þ Afilm dfilm =rgrain .
With these corrections, we now use Eqs. (20) and (23) to
determine the correct diffusion coefficient of Li in LiFePO4. For example, with the experimental data of Fig. 9, we
evaluate for the de-intercalation
DU pffiffiffi ¼ 1:65 V1=2 s1=2 ;
v exp
(a)
jp Afilm
pffiffiffi ¼ 3:91 108 A s1=2 m3 V1=2 dfilm
Atot
v exp
¼ 6:77 A s1=2 m2 V1=2 ;
and so determine
jsurf ¼ 2:0 nm s1 and DLi ¼ 3:6 1013 cm2 s1
Naturally, jsurf has to be interpreted here as the kinetic constant for Li transfer from the grain volume into the GBs.
Since the evaluation was based on the deintercalation peak,
the derived diffusion coefficient is relevant to the transport
inside the Li-poor a phase. The same analysis may also be
done for the intercalation peak, although here, the kinetic
exponent deviates slightly more from the expected square
root behaviour (n = 0.62 instead of n = 0.5, see Fig. 9a).
For intercalation, the kinetic parameters are determined by
jsurf ¼ 4:6 nm s1 and DLi ¼ 2:3 1013 cm2 s1
(b)
Fig. 13. Microstructure of the studied LiFePO4 films: (a) TEM crosssectional micrograph shows equi-axed grains of on average 52 nm in
diameter, independent of the layer thickness. (b) Sketch of presumed
transport geometry in LFP thin films. Light grey: Li in ionic form, thin
arrows: ionic transport, thick arrows: intercalation transport in preferred 1D channels.
not the thin film surface anymore, but the total grain boundary area. At constant grain size, we expect the total GB area
increasing proportionally to the thickness, which clearly explains the dependence of the peak currents in LiFePO4.
If on the other hand, the grain size depends on the layer
thickness, as is often observed in columnar grain structures
of thin films, the increase in the GB area and, thus, the current would become under-proportional to the thickness,
which is experimentally demonstrated by the LiMn2O4
films. Thus, we conclude from our kinetic study, that the
grain boundaries probably represent decisive quick path-
It is indicated that the Li transport inside the Li-rich b phase
is only slightly slower than in the a phase, while interestingly the transport across the interfacial barrier, between
the GBs and the grain volume, is significantly faster for
the b phase. It should be noted that these stated kinetic parameters are obtained for LiPO4 material without any binders and conductivity additives, and so are believed to represent the pure material properties.
As a second important aspect, it is insightful to evaluate
the behaviour of the overpotential as a function of the layer
thickness. In LiMn2O4, both peak current and overpotential
reveal the same dependence on the layer thickness. Thus,
the current density (per area of the thin film) is proportional
to the overpotential. In consequence, atomic fluxes are proportional to the driving force, as is conventionally assumed,
which is also in line with Eq. (17) if expanded to first order.
In LiFePO4 however, the situation is surprisingly different. While the peak currents at a given scanning rate increase in proportion to the layer thickness (Fig. 9a), the
overpotential is hardly influenced (Fig. 9b). Thus, the over13
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F. Wunde et al.: Ion transport and phase transformation in thin film intercalation electrodes
potential required to drive a given current density (per area
of film) is inversely proportional to the thickness. This
may be illustrated by a direct comparison between two different layer widths, 100 nm and 200 nm, as shown in
Fig. 10. We know from the data presented in Fig. 9, that
the peak current is proportional to the product d · m1/2. Thus
in order to produce the same peak current, we have to apply
a four-fold higher scanning rate to the thinner layer. Compare, for example, the curves to 0.08 mV s–1 and
0.02 mV s–1 of the 100 nm and the 200 nm thick film, respectively. In both cases, a peak current of slightly less than
0.3 A m–2 is established, but the overpotential necessary for
the thicker layer (marked by a pair of dashed lines) is only
half of that necessary for the thinner layer. Obviously, less
electrical driving force is required in the thicker layer to
force the same current per film area. On the other hand, we
know that the GB area increases proportional to the thickness and so do the absolute fluxes.
To end in a consistent explanation of these facts, the natural proposition is that in the case of LiFePO4, the grain boundaries represent the important electroactive interface at which
the overpotential appears. This suggests that the grain boundaries in LiFePO4 have the character of an ion conductor,
meaning they are electronic insulators, as indicated in the
sketch of Fig. 13b. To its dominant part, the overpotential is
required to drive the ions from the grain boundary into the
grain volume. Quantitatively, we may express
j/
AGB
dfilm
ðU U 0 Þ /
ðU U 0 Þ
Afilm
Afilm
ð24Þ
In literature and also in our TEM micrographs, we see hints
that the grain boundaries of LiFePO4 tend to form an amorphous interlayer, which would make such remarkable character of the grain boundary region understandable. Alternatively, space charge zones along the GB could also justify a
different electrical and diffusional behaviour of a finite region along the GBs. The nature of the grain boundaries in
LiFePO4 definitely represent an interesting subject of future
research.
pectation that geometric constraints in nanostructures,
either by coherent fixation to a substrate or coherent interphase boundaries, would fully suppress the phase separation. In contrast, the volume expansion in LiMn2O4
is too small to stabilize a miscibility gap at room temperature.
. In thin films, the materials demonstrate contrasting kinetic behaviour in cyclo-voltammetry. While the current peaks in LiMn2O4 reveal a systematic transition between a linear kinetic regime and a square root Randles–
Sevcik regime, only the latter regime is observed in
LiFePO4. Based on a computational simulation of the
Li intercalation in ideal solutions and phase separating
systems, this characteristic difference proves that intercalation in LiFePO4 films happens heterogeneously by
migration of a phase boundary. Thus, in spite of possible
geometric constraints in the nanometric films, phase separation does clearly appear and so, major plastic relaxation is proven even for the nanosystem.
. In both materials, the intercalation currents in the Randles–Sevcik regime reveal an unexpected dependence
on the layer thickness. It is shown that this dependence
is well understood by the nanocrystalline microstructure, if grain boundaries represent fast conduction paths.
By short-circuit transport along the grain boundaries the
effective cross-sectional area for the intercalation current increases with the thickness of the layers.
. Also, the overpotential to drive the intercalation current
at fast rates does depend on the layer thickness. However, while this dependence in LiMn2O4 is balanced so
that the driving force remains proportional to the total
current, the driving force at given total current does decrease with the layer thickness in LiFePO4. It has been
shown that this peculiarity is probably due to the fact
that the grain boundaries in LiFePO4 represent a purely
ionic conductor, while grain boundaries in LiMn2O4
show mixed ionic/electronic conductivity.
Financial support by the German Science Foundation (DFG, SPP 1473)
is gratefully acknowledged.
7. Conclusions
References
Nanometric thin films of the olivine structure LiFePO4 and
the spinel LiMn2O4 were ion-beam sputter-deposited upon
suitable current collectors to act as the cathode of thin film
batteries. Deposition conditions and heat treatment were
optimized to achieve a high reversibility in de/intercalation.
The intercalation of LixFePO4 (x = 0. . .1) and LixMn2O4
(x = 0. . .1) was studied in cyclo-voltammetry over a several
orders of magnitude broad range of cycling rates. Also, the
thickness of the thin films was systematically varied. In order to more deeply understand the intercalation kinetics,
the experimental investigation was corroborated by a theoretical analysis of elastic driving forces and a simulation
by a kinetic mean field model. As the key results the following can be stated:
. Elastic models previously derived to explain the solubility in metal–hydrogen systems can be transferred to intercalation compounds. In so doing, the known miscibility gap of free-standing LiFePO4 at room temperature is
almost completely understood by elastic interaction.
This elastic origin of the miscibility gap leads to the ex-
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(Received December 20, 2016; accepted May 22, 2017)
Correspondence address
Prof. Dr. Dr. h.c. Guido Schmitz
Institute for Materials Science
University of Stuttgart
Heisenbergstr. 3
70569 Stuttgart
Germany
Tel.: +49-711-685-61901
E-mail: matphys@imw.uni-stuttgart.de
Web: www.uni-stuttgart.de/imw/mp
Bibliography
DOI 10.3139/146.111549
Int. J. Mater. Res. (formerly Z. Metallkd.)
108 (2017) E; page 1 – 15
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