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. 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. 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]: 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. 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 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. 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 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. 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 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. 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. 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. 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- 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. 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 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. 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 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. 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- 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. 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: 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. 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 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. 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 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. 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- [1] T. Stockhoff, T. Gallasch, F. Berkemeier, G. Schmitz: Thin solid films 520 (2012) 3668 – 3674. DOI:10.1016/j.tsf.2011.12.065 [2] F. Wunde, F. Berkemeier, G. Schmitz: J. Power Sources 215 (2012) 109 – 115. DOI:10.1016/j.jpowsour.2012.04.102 [3] M. Köhler, F. Berkemeier, T. Gallasch, G. Schmitz: J. Power Sources 236 (2013) 61 – 67. DOI:10.1016/j.jpowsour.2013.02.043 [4] S. Nowak, F. Berkemeier, G. 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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 # Carl Hanser Verlag GmbH & Co. KG ISSN 1862-5282 15

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