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Z. Phys. Chem. 226 (2012) 341–353 / DOI 10.1524/zpch.2012.0215 © by Oldenbourg Wissenschaftsverlag, München Bombardment Induced Potassium Ion Transport Through a Sodium Ion Conductor: Conductivities and Diffusion Profiles By Lisa Rossrucker, Pramod V. Menezes, Julia Zakel, Martin Schäfer, Bernhard Roling, and Karl-Michael Weitzel∗ Philipps-Universität Marburg, Fachbereich Chemie, Hans-Meerwein-Straße, 35032 Marburg, Germany Dedicated to Paul Heitjans on the occasion of his 65th birthday (Received January 26, 2012; accepted in revised form March 15, 2012) (Published online May 14, 2012) Ion Conductivity / Temperature Dependence / Mixed Alkali Effect / Concentration Dependence of Diffusion Coefficient / Tof-SIMS / Migration Ion transport through a Ca30 glass, a sodium ion (Na+ ) conductor, has been induced by bombardment with a potassium ion (K+ ) beam. The measurement of back side ion currents as a function of the ion beam kinetic energy by means of the recently developed BIIT (bombardment induced ion transport) approach allows determining the conductivity of the material. Measurement of this conductivity as a function of the temperature allows deriving the activation energy for ion transport as 0.99 eV ± 0.01 eV in perfect agreement with impedance spectroscopy. While the conductivity as well as the activation energy clearly correspond to the bulk property, i.e. the transport of Na+ , depth profiling of the glass sample after the BIIT experiment exhibits K+ profiles reaching up to 100 nm into the glass. Ultimately, modeling of the experimental data by means of the Nernst–Planck–Poisson theory provides access to a quantitative understanding of the conductivities and the diffusion profiles under the condition of competing Na+ /K+ ion transport. 1. Introduction The transport of ions through solid electrolytes is a core ingredient to the fields of energy conversion and energy storage [1–3]. A broad spectrum of methods for measuring and modeling ion transport is available today, including impedance spectroscopy (IS) [4,5], nuclear magnetic resonance spectroscopy (NMR), in particular pulsed field gradient NMR (PFG-NMR) [6–9] and tracer diffusion (TD) techniques [10, 11] on the experimental side, hopping models [4] including random free energy barrier models [12], molecular dynamics models [13,14] and macroscopic electrodiffusion models [15] on the theoretical side. While the focus was directed at ionic conductivities in the past, concentration profiles induced in solid state ion conductors have attracted increasing interest in recent * Corresponding author. E-mail: [email protected] 342 years. Concentration gradients together with potential gradients form the basis for what is usually referred to as electrodiffusion [16]. Very pronounced concentration profiles can e.g. be generated by electro-poling, where a solid electrolyte is exposed to an electric field at elevated temperature leading to migration of the charge carrier [17,18]. This in turn generates a depletion zone, in other words a characteristic concentration profile, which can be literally frozen by decreasing the temperature to a value where migration is effectively stopped. This electro-poling is e.g. often employed in the context of bioactive glasses [19,20]. It has also been demonstrated to facilitate non-linear properties of materials [17,21–23]. Pronounced concentration profiles of a charge carrier further occur in the tracer diffusion studies mentioned above. More generally, concentration profiles must occur where molecules of a certain sort are deposited on a solid sample into which these molecules can diffuse. In extension of the techniques available for ionic conductivity measurements, we have recently developed the bombardment induced ion transport (BIIT) technique, where a solid electrolyte sample is connected to a backside electrode allowing for a current measurement. The sample is bombarded from the front side by a c.w. alkali ion beam. Attachment of the ions to the front side of the sample causes a well defined surface potential and consequently a potential gradient over the material but at the same time also a concentration gradient inside the material. Both form the basis of what we term electrodiffusion. This induces a neutralization current at the backside electrode. Measuring this backside current as a function of the temperature ultimately provides access to the bulk activation energy for ion transport. If we bombard e.g. a potassium ion (K+ ) conductor with a K+ ion beam the excess charges are located at the surface of the sample. Here, ion conduction ultimately implies that one K+ ion entering the sample at the front side leads to another K+ ion being discharged at the backside of the sample, which is detected by an electrometer. Consequently, the K+ ion profile remains flat everywhere inside the sample. A very different situation is expected when we e.g. bombard a sodium (Na+ ) ion conductor with a K+ ion beam. Intuitively, one would expect that the effective conductivity measured should still be dominated by the conductivity of the bulk Na+ . However, a finite amount of K+ ions should be present in the front layers of the sample and the effective conductivity of the sample could be different from that of the pure Na+ ion conductor. It is the aim of this work to present experimental data and a theoretical analysis of K+ ion transport into/through a Na+ ion conductor. We demonstrate that the macroscopic effective conductivity is dominated by the bulk properties of the material. Ultimately, the number density of various relevant elements will be investigated by means of a well established depth profiling technique. Here, we employ time-of-flight secondary-ion-mass-spectrometry (TOF-SIMS) [24,25], which has been successfully applied in a large number of depth profiling studies [26]. 2. Experimental approach The experimental setup used for the BIIT investigations consists of an ion source, an electrostatic ion optics and a sample holder with detection electrode that is connected to an electrometer amplifier. The entire setup is housed in a high vacuum chamber at BIIT of Ca30 343 Fig. 1. Sketch of the sample holder (color online). an operating pressure of 10−6 mbar. We have employed a home made synthetic leucite ion source [27] that is heated such that an ion beam is thermionically emitted [28]. The ions are repelled by a positive potential UR applied to a repeller lens and accelerated towards the sample. A set of electrostatic lenses and flight tubes is used to guide and focus the ion beam towards the sample. After leaving the ion optics, the ions pass a 20 mm thick grounded tube with 10 mm central opening that is positioned 3 mm in front of the sample. Both sides of the tube are covered with copper meshes such that a homogeneous field is created in front of the sample surface and field penetrations are avoided. Eventually, an ion current of 8.7 nA reaches the sample position. The ions are deposited at the sample surface such that an electrostatic potential builds up at the sample surface whereas the backside of the sample is glued on a copper electrode. Thus, a potential gradient develops that leads to the electrodiffusion of ions through the sample towards the backside electrode where the ion current is detected with a home made electrometer amplifier. In order to keep contact potentials between backside electrode and sample small, we use an excellently conducting epoxide glue (Loctite 3880) to attach the electrode to the sample. The ion current is A/D-converted and processed in a personal computer. The front side of the sample is masked by a metal ring with 8 mm inner diameter to define the bombarded area A. The electric contact between the glass and the front side mask is desired to be “bad” to avoid errors in the conductivity measurement. Therefore, the mask is not glued but just loosely pressed. The influence of the mask on the conductivity measurements has been tested by detecting the backside current once with grounded mask and the second time without any electric contact to the mask and otherwise unchanged parameters. Both measurements showed the same ion current at the backside electrode implying that there is no influence of the mask on the bulk ion transport. The sample holder (Fig. 1) is mounted on a temperature controlled heating device that permits us to define the sample temperature to an accuracy of 0.1 K. The entire device can be moved using an ultrasonic motor such that the sample is shifted off the ion beam and the ion current reaching the sample surface can be detected in a blind measurement. The glass sample investigated was prepared by heating a stoichiometric mixture of Na2 CO3 , CaCO3 and (NH4 )2 HPO4 . The two carbonates have been heated to 393 K to re- 344 move water and adsorbed gases. After pestling, the educts have been heated to 1423 K for 1 h in a platinum pot. The molten mixture has been poured into a preheated steel cylinder with inner diameter of 20 mm. Subsequently, the melt was kept 40 K below the glass transition temperature (Tg = 603 K) for 10 h before cooling to room temperature. The actual sample is obtained by cutting thin discs from the glass cylinder and polishing down to the desired thickness, in the current case 1.219 mm. The final composition of the glass is 25% Na2 O – 30% CaO – 45% P2 O3 . In the rest of the paper, we will refer to this Na+ ion conducting glass as Ca30. Depth profiles of the sample have been recorded by means of ToF-SIMS employing a TOF.SIMS 5 device (IONTOF GmbH, Münster, Germany). As a primary ion source, Bi+ has been used in high current bunched mode (pulsed target current: 0.1 pA). The dual source column (DSC-S) sputter gun, has been operating with O+2 as the sputter species (target current: 170 nA). The sputter crater dimension has been 300 × 300 μm2 and the Bi+ ions were scanned over an area of 100 × 100 μm2 for analysis. All depth profiles were acquired in non-interlaced mode (1.0 s sputter time, 0.5 s pause) and a low energy electron gun (20 eV) was used for charge compensation. The crater depth was determined post-analysis with as Sloan Dektak 3ST surface profilometer. 3. Theory The demonstration of the diffusion profiles in the second part of this manuscript is accompanied by numerical simulations. For these simulations, we employ the theory introduced in [15] and calculate the coupled set of Nernst–Planck and Poisson equations [29] for the given experimental setup. The experimentally investigated glass is thin compared to its radial extension such that radial transport can be neglected. The ion beam hits a circular area and shows circular symmetry in a very good approximation. Hence, angular transport can be neglected. As a consequence, we may concentrate on the ion transport alongside the axis perpendicular to the glass surface; the z-axis. Prior to the bombardment, the only mobile ion species in the Ca30 glass is Na+ . The initial concentration of the Na+ ions is 7.16 × 109 ions/μm3 given by the stoichiometry and the density of the glass. The initial K+ content is set to zero, neglecting the small amount of impurity. However, once the bombardment is started K+ ions are deposited on the glass surface and a potential gradient builds up. In this situation, both ion species contribute to the electrodiffusion and the Nernst–Planck equations need to be formulated for two mobile ion species. Ion species other than K+ and Na+ are neglected. Generally, one expects that the diffusion coefficients of the two ion species are different from each other connected to the difference in the ion sizes. Moreover, the effective diffusion coefficient Dν (ν = Na+ or K+ ) may depend on the local environment in particular the concentration of both charge carriers Na+ and K+ . As we will demonstrate below the sum of the Na+ and K+ concentration is uniform throughout the sample (except directly at the surface, see [27]), hence, it is sufficient to discuss Dν as a function of one of the two species. The dielectric constant is assumed to be space and concentration independent. It is set to εr = 10 everywhere in the glass. BIIT of Ca30 345 Accounting for these approximations, the Nernst–Planck equation for the two ions species reads ∂n ν ∂ϕ e Jν = −Dν (n Na+ ) + nν , (1) ∂z ∂z kB T where ν is the ion species index, Jν is the ion flux densities, Dν (n Na+ ) is the diffusion coefficients of the mobile ions that depends on the local concentrations of both ions. The ion concentration is n ν whereas the electrostatic potential is given by φ. The charge of the ion species is e and kB T is Boltzmann’s constant times the temperature. The concentrations of both ions species also enter the Poisson equation that is then given by ε0 εr ∂2ϕ = −e n K+ + n Na+ − n 0Na+ , ∂z 2 (2) with the vacuum dielectric permittivity ε and εr the relative dielectric constant. Because the Na+ ions that belong to the Ca30 glass are explicitly treated in Eq. (3), we also need to take into account the immobile negative charge of the glass matrix. We assume that initially the Na+ ions are homogeneously distributed inside the glass and the glass is electrically neutral such that the immobile negative charge q− of the glass matrix can be written in terms of the space and time independent constant n 0Na+ , q − = (−e) · n 0Na+ . Finally, the time evolution of the ion distributions is given by Fick’s second law ∂Jν ∂ nν = − , ∂t ∂z (3) We discretize the z-axis into space elements that may have different sizes Δz i and rewrite the Eqs. (1)–(3) n ν,i+1 − n ν,i ϕi+1 − ϕi e i+1 i+1 Jν,i = −Dν,i + n i+1 , (4) ν,i Δz i Δz i kB T ⎛ en i ⎞ Δz i Δz i+1,i Δz i,i−1 + (ϕi+1 Δz i,i−1 + ϕi−1 Δz i+1,i ) ⎜ε ε ⎟ ϕi = ⎝ 0 r (5) ⎠, (Δz i,i−1 + Δz i+1,i ) i+1 i − Jν,i−1 Jν,i ∂ , n ν,i = − ∂t Δz i (6) where n i is n K+ ,i + n Na+ ,i − n 0Na+ is the excess ion density in the space element i and Δz i,i+1 = 1/2(Δz i + Δz i+1 ). The ion flux density between the adjacent space elements i+1 i+1 while Dν,i and n i+1 = (n i Δz i+1 + n i+1 Δz i )/(Δz i+1 + Δz i ) i and i + 1 is given by Jν,i i are the diffusion coefficient and the ion density at the boundary of these two space elements. Please note that the electric potential (Eq. 5) depends on the exact charge distribution inside the glass as well as on the potential in the neighboring space elements. Therefore, we calculate the potential recursively using the potential of the previous recursion step as an input for the actual recursion step. The converged potential subsequently enters the Nernst–Planck equation (4) where the electrodiffusion of the carriers 346 Fig. 2. Backside current, Iback , as function of the applied repeller voltage. Symbols: experimental data; solid line: linear regression. is calculated. The so calculated ion fluxes enter Fick’s second law such that the ion distribution is modified. In the following time step, the potential is calculated again to match the modified ion distribution and so forth. In order to solve equations (4)–(6), it is essential to use the correct boundary conditions for the potential. Due to the grounding of the backside electrode, we use ϕ(L) = 0, where L is the thickness of the sample. The potential directly in front of the sample surface is defined by a linear potential gradient between the charged glass surface and the grounded tube in front of the glass. A detailed discussion of the boundary conditions can be found in [15]. 4. Results We have bombarded a 1.219 nm thick Ca30 glass with a K+ ion beam. The ion beam has been focused such that the ion current obtained at the backside electrode is maximal. Under theses conditions the inhomogeneities of the ion beam are minimal and the overall blind current is about 8.7 nA. The temperature of the sample has first been set to 326.2 ± 0.1 K. Under these conditions, the backside current, Iback , has been detected as a function of the applied repeller voltage. The repeller voltage has always been ramped slowly compared to the surface charging. Consequently the ions are rather gently attached to the surface; implantation of ions into the sample does not play a major role. Please note, that although modifying U R we have kept the electric field in front of the emitter constant. This is provided by appropriately adjusting the voltage applied to the first electrostatic lens behind the repeller. The abstracting field in front of the emitter has been 2000 V/cm. As shown in Fig. 2, the obtained backside current increases linearly with the repeller voltage in a range between 10 and 600 V. A linear regression of these data points yields a slope of 0.00195 nA/V and a small offset of 0.025 nA that is mainly caused by the electronics of the setup. For voltages larger than 600 V, the observed backside BIIT of Ca30 347 Fig. 3. Arrhenius plot of the temperature dependence of the conductivity. Black squares: experimental IS data, red circles: BIIT data. The solid line represents in each case the result of a linear regression to the experimental data (color online). current is smaller than the values extrapolated by the linear regression – an indication for the onset of the transition regime which is caused by the inhomogeneities of the ion beam [27]. Using the slope of the linear regression, we may calculate the actual conductance of the sample G = ΔIback /ΔUR = 1.95 × 10−12 S and conclude a specific conductivity of σ = G L/A = 4.73 × 10−13 S/cm. It is well established that the dominant transport mechanism in disordered solids is given by thermally activated hopping. Because the experiment operates under conditions where the migration contribution to the conductivity strongly dominates over the concentration gradient driven diffusion, the temperature dependence of the conductivity can be described via σ= S0 −E act e kB T . T (7) Here, σ is the conductivity, E act is the activation energy for the DC transport and S0 is the pre-exponential factor. Consequently, E act can be detected by measuring σ at different sample temperatures. The slope of an Arrhenius plot where ln(σT ) is plotted as a function of the inverse temperature then yields the activation energy. Thus, we have measured the conductivity in a temperature range between 306.2 K and 334.2 K. The corresponding Arrhenius plot is shown in Fig. 3, where the BIIT data are shown as red dots. For comparison, IS measurements with the same glass batch have been performed in a temperature range between 333 K and 423 K. The corresponding data are presented as black squares. For both data sets, linear regressions have been performed showing that Eq. (7) is fulfilled in the investigated temperature range. Moreover, the analysis of the slopes of the two linear regressions shows that the activation energy determined by BIIT (0.99 eV ± 0.01 eV) and by IS (0.98 eV ± 0.02 eV) perfectly match. Even the overall conductivity determined by the two methods agrees very well. Nevertheless, we observe a small difference. The conductivities determined by BIIT are about 15 percent smaller compared to the ones determined by IS. 348 Fig. 4. Depth profiles of the most relevant elements in the sample. Depth = 0 refers to the surface of the glass (color online). In principle, part of this difference may originate from the injection of K+ ions in the Ca30 glass during the bombardment process. Prior to the bombardment, the only mobile ion species is Na+ while the K+ content is negligible. With proceeding bombardment more and more K+ is deposited at the surface and subsequently transported into the material. As already mentioned, we expect that this modification should affect the average diffusion coefficient of the entire glass and therefore the conductivity of the sample. We can demonstrate that even for an experiment operated for about a week the decrease in the effective conductivity is only on the order of 5%. The major part of the difference between the BIIT and the IS conductivity (approximately 10%) must be attributed to remaining differences between the two methods. Given the typical uncertainties of conductivity measurements, including uncertainties in sample preparation, this agreement may still be considered very satisfying. Obviously, the alteration of conductivities of a sample could be avoided by using Na+ for the ion bombardment. A similar experiment with a borosilicate glass [27] performed in our laboratory showed excellent agreement between IS and BIIT regarding the absolute value of the conductivity. Yet, in this manuscript we are also interested in the answer to the question how the introduction of the K+ influences the structure and therefore the conduction properties of the Ca30 glass. Therefore, a long term measurement has been performed where a 1.543 mm thick Ca30 sample has been bombarded for a period of 24 days with an average ion current of 1.5 nA. The ion beam hitting the sample showed a Gaussian like ion flux density profile. As a consequence, the ion beam intensity has been larger than the average ion flux density 1.5 nA/0.785 cm2 in the center and lower in the outskirts of the bombarded area. The repeller voltage has been set to 100 V and the temperature was kept at 373 K during the entire bombardment time. Subsequent to the bombardment, the sample has been analyzed by time-of-flight secondary-ion-mass-spectrometry. Fig. 4 shows the first 150 nm of the depth profiling in the centre of the bombarded area where the ion beam current has been largest. The point z = 0 has been defined at the onset of the phosphorus and the oxygen profiles. BIIT of Ca30 349 The relative signal of the Na+ ions is shown as blue dots whereas the K+ signal is presented by the red squares. The calcium content is given by the green triangles whereas the orange diamonds and the light blue triangles yield the phosphorus and the oxygen distribution, respectively. The Na+ and the calcium signals have been normalized to the average value deep inside the material where no K+ is present. The K+ signal has been normalized to the maximum value directly below the front surface of the glass. For better visibility, the oxygen and the phosphorus signal have been normalized such that their average value is one third. Analyzing the depth profiles, one observes a diffusion front about 100 nm below the glass surface. Between this front and the surface of the glass, most of the Na+ has been replaced by K+ . However, the Na+ concentration is not completely zero but between 10% and 20% of the Na+ remains in this zone. The sum of the K+ and the Na+ distributions is close to one everywhere in the sample, except in the region of the diffusion front itself where the sum is smaller than one. Interestingly, the calcium signal shows an opposite feature at the same position and is space independent elsewhere. Phosphorus and oxygen exhibit a constant distribution through the entire material. Note, that the rise of the phosphorus and oxygen signals defines the front of the sample. The depth profiles clearly show that the composition of the glass has been substantially modified in an extended zone below the surface by the BIIT experiment. This zone, on the other hand, accounts for approximately 0.008% of the sample thickness. In order to gain more insights into the transport process, numerical simulations on the basis of the coupled set of the Nernst–Planck and the Poisson equation have been performed to complement the experiment. To this end, Eqs. (4)–(6) were solved with an input current of 2.12 nA corresponding to 1.4 times the average ion flux reaching the sample, a typical value for the Gaussian beam profile in the centre of the bombarded zone in the used experimental setup. In these calculations the only free parameters are the diffusion coefficients of Na+ and K+ . All other quantities are self-consistently calculated or defined by the experimental setup. The diffusion coefficient of Na+ in the pure Na+ glass at 373 K can be determined by matching the calculated conductivity of the glass to the experimentally measured conductivity. The comparison between experiment and theory yields DNa+ = 1.03 × 10−15 cm2 s−1 . Test calculations with concentration independent diffusion coefficients show that the slope of the diffusion profile at the position of the diffusion front depends on the ratio between K+ and Na+ diffusion coefficient. Therefore, the K+ diffusion coefficient in a Ca30 glass can be estimated. It is predicted to be DK+ = 2 × 10−18 cm2 s−1 . Generally, the simulations with homogeneous diffusion coefficient provide already some of the features obtained in the diffusion profiles of K+ and Na+ in Fig. 4, such as a diffusion front, and the slope of the diffusion profile at the diffusion front. However, these simulations also predict that all Na+ should be replaced in the first nanometers below the surface, which is contradicting the experimental observations where about 10%–20% of the Na+ remain in the diffusion zone. In order to resolve this discrepancy, we allow the diffusion coefficients to be concentration dependent. Generally, one may expect that both coefficients could be concentration dependent. Yet, since the diffusion coefficient of Na+ is larger than the one of K+ , we expect most of the effect to originate 350 Fig. 5. Concentration dependence of the Na+ diffusion coefficient. Fig. 6. Potassium and sodium depth profiles: Symbols: experimental data; solid lines: numerical simulation (color online). from the concentration dependence of the Na+ diffusion coefficient. Hence, we keep the diffusion coefficient of K+ constant. The functional form of the concentration variation of DNa+ (n Na+ ) used for the simulations is shown in Fig. 5. The form follows the sigmoid equation DNa+ (n Na+ ) = 1.0 × 10−20 cm2 s−1 + 1.03 × 10−15 cm2 s−1 1 (8) , n + 1 + 2.0 × 104 exp −12.5 Na n0 Please note, that the first term of the sum in Eq. (8) reflects the limit of the Na+ diffusion coefficient in a Ca30 glass where all Na+ is replaced by K+ . The prefactor of the sigmoid function is the diffusion coefficient of the Na+ in the pure Na+ glass. The result of the simulations performed with these parameters is shown as red line (K+ BIIT of Ca30 351 profile) and blue line (Na+ profile) in Fig. 6 and compared to the experiment. We observe excellent overall agreement between experiment and theory. Note, that agreement is not only observed for the position of the diffusion front but also for the slopes of this front and even the slopes in the depletion region. A very detailed inspection of the data between about 80 nm and 120 nm indicates that the experimental Na+ signal is slightly smaller than the calculated one. Most likely this difference is connected to the small excess of calcium in this region, a species not included in the calculations (see Fig. 4) 5. Discussion and summary We have investigated the transport of ions in a Na+ ion conductor by means of K+ ion bombardment by the BIIT approach. The measured conductivities are shown to be in nice agreement with impedance spectroscopy. The activation energy is clearly that of the bulk Na+ transport. The BIIT result is E A = 0.99 eV ± 0.01 eV, the IS value is E A = 0.98 eV ± 0.02 eV. However, the absolute BIIT conductivity is about 15% below the IS values. The discrepancy is in part (up to 5%) due to the incorporation of the K+ into the material, which decreases the diffusion coefficient. There appear to remain, however, differences between the current IS and BIIT measurement on the order of 10%. Given the common view on the precision of conductivity measurement, these numbers may be considered as very good agreement. Inducing Na+ transport by bombardment with K+ inevitably creates the prospect of + a K zone in the sample. This K+ profile has been quantitatively analyzed by means of TOF-SIMS. Basically the BIIT experiment has led to a depletion of Na+ down to approximately 100 nm below the surface of the material. In this zone between 80% and 90% of all Na+ ions have been replaced by K+ . This diffusion profile has been quantitatively modeled by means of the Nernst–Planck–Poisson equation. Quantitative agreement between experimental and calculated data can only be achieved by assuming that the diffusion coefficient of the Na+ is concentration dependent. Clearly, the diffusion coefficient for K+ is orders of magnitude smaller than that for Na+ . As the Na+ , which are more mobile than the K+ , move towards the detector, they leave temporary vacancies behind, which are immediately filled by K+ , in other words the Na+ are dragging the K+ behind them. One major result of the current work is the evidence for concentration dependent diffusion coefficients. A similar effect has been discussed by Furini et al. [30]. For the transport of K+ through a KcsA ion channel, where agreement between experiments and Nernst–Planck–Poisson theory was only obtained, if the K+ ions were assumed to be slowed down inside the channel, effectively represented by a smaller diffusion coefficient. As mentioned earlier diffusion profiles of alkali ions are also operative in voltage assisted ion exchange [31]. E.g., voltage assisted 18 O tracer incorporation into oxides leads to electrodiffusion profiles qualitatively similar to the ones discussed in the current work [32]. That experiment again employs two electrodes to define the voltage drop across the sample. In contrast, our current experiment may be considered as voltage assisted ion exchange without the anode. 352 The concentration profiles discussed in this work clearly demonstrate that two alkali ions coexist in certain regions of the sample. The ratio of number densities even varies along the profile. This stimulates thoughts, whether the conductivities observed here might be related to the elusive mixed alkali ion effect [33–35]. In fact studies of the mixed alkali effect also involves the discussion of concentration dependent diffusion coefficients [36,37]. It appears possible that the current experiment eventually contributes to the understanding of the mixed alkali effect. However, significantly more studies are required before reaching there. What are the prospects of the current approach and what are the limitations? We wish to stress the astonishing accuracy of our BIIT experiments, in terms of absolute conductivities and activation energies, which is now comparable to IS. So far the BIIT approach works best for extremely small diffusion coefficients. However, this is not a limitation of the concept, but a limitation of the implementation. 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