In an all-solid-state battery, the electrical contact between its individual components is of key relevance in addition to the electrochemical stability of its interfaces. Impedance spectroscopy is particularly suited for the non-destructive investigation of interfaces and of their stability under load. Establishing a valid correlation between microscopic processes and the macroscopic impedance signal, however, is challenging and prone to errors. Here, we use a 3D electric network model to systematically investigate the effect of various electrode/sample interface morphologies on the impedance spectrum. It is demonstrated that the interface impedance generally results from a charge transfer step and a geometric constriction contribution. The weights of both signals depend strongly on the material parameters as well as on the interface morphology. Dynamic constriction results from a non-ideal local contact, e.g., from pores or voids, which reduce the electrochemical active surface area only in a certain frequency range. Constriction effects dominate the interface behavior for systems with small charge transfer resistance like garnet-type solid electrolytes in contact with a lithium metal electrode. An in-depth analysis of the origin and the characteristics of the constriction phenomenon and their dependence on the interface morphology is conducted. The discussion of the constriction effect provides further insight into the processes at the microscopic level, which are, e.g., relevant in the case of reversible metal anodes.

A non-ideal contact at the electrode/solid electrolyte interface of a solid-state battery arising due to pores (voids) or inclusions results in a geometric constriction effect that severely deteriorates the electric transport properties of the battery cell. The lack of understanding of this phenomenon hinders the optimization process of novel components, such as reversible and high-rate metal anodes. Deeper insight into the constriction phenomenon is necessary to correctly monitor interface degradation and to accelerate the successful use of metal anodes in solid-state batteries. Here, we use a 3D electric network model to study the fundamentals of the constriction effect. Our findings suggest that dynamic constriction as a non-local effect cannot be captured by conventional 1D equivalent circuit models and that its electric behavior is not ad hoc predictable. It strongly depends on the interplay of the geometry of the interface causing the constriction and the microscopic transport processes in the adjacent phases. In the presence of constriction, the contribution from the non-ideal electrode/solid electrolyte interface to the impedance spectrum may exhibit two signals that cannot be explained when the porous interface is described by a physical-based (effective medium theory) 1D equivalent circuit model. In consequence, the widespread assumption of a single interface contribution to the experimental impedance spectrum may be entirely misleading and can cause serious misinterpretation.

We present a technique for systematically investigating electronic and ionic charge transport in single Li­(Ni1/3Co1/3Mn1/3)­O2 (NCM 111) secondary particles as a function of size. We perform electrochemical impedance spectroscopy employing ion-blocking electrodes. Micrometer-sized spherical particles are arranged in cylindrical particle traps on a patterned substrate. A specially designed electrochemical cell is used to contact and measure individual immobilized particles in a defined contact geometry. The obtained electronic and ionic resistances of the particles as a function of size are compared with model calculations based on a homogeneous sphere with finite contact areas. The modeling reveals that electronic transport mainly occurs in the bulk of the NCM 111 particles, whereas ionic transport takes place along the particle surface. The extracted material parameters are in good agreement with literature values, showing the reliability of our measurement technique and its potential for systematic studies on the single-particle level.

Charge transport in polycrystalline electronic or ionic conductors is usually analyzed by serial macroscopic equivalent circuits, e.g., the brick layer model, which assume a homogeneous electric potential distribution across the sample. In such analyses, the microstructure is highly idealized and usually not representative of the actual microstructure. Here, we use a network model approach to investigate the impact of the sample’s microstructure on the impedance. We find that this influence can be severe and should not be ignored. The interplay between microscopic transport paths affects the impedance response, which is reflected in both the frequency and the time domain. Especially in the distribution of relaxation times additional signals are identified and studied systematically. These additional contributions cannot be assigned to a microscopic transport process as usually done in a conventional analysis based on an equivalent circuit model fitted to the impedance data. The neglect of the peculiarities of the real microstructure in impedance analyses based on the brick layer model may yield deviations in the order of 100 % in terms of the derived microscopic transport parameters. The microstructures used as input for the modelling are digitalized electron microscope images of polycrystalline samples.

In recent years, many efforts have been made to introduce reversible alkali metal anodes using solid electrolytes in order to increase the energy density of next‐generation batteries. In this respect, Na3.4Zr2Si2.4P0.6O12 is a promising solid electrolyte for solid‐state sodium batteries, due to its high ionic conductivity and apparent stability versus sodium metal. The formation of a kinetically stable interphase in contact with sodium metal is revealed by time‐resolved impedance analysis, in situ X‐ray photoelectron spectroscopy, and transmission electron microscopy. Based on pressure‐ and temperature‐dependent impedance analyses, it is concluded that the Na|Na3.4Zr2Si2.4P0.6O12 interface kinetics is dominated by current constriction rather than by charge transfer. Cross‐sections of the interface after anodic dissolution at various mechanical loads visualize the formed pore structure due to the accumulation of vacancies near the interface. The temporal evolution of the pore morphology after anodic dissolution is monitored by time‐resolved impedance analysis. Equilibration of the interface is observed even under extremely low external mechanical load, which is attributed to fast vacancy diffusion in sodium metal, while equilibration is faster and mainly caused by creep at increased external load. The presented information provides useful insights into a more profound evaluation of the sodium metal anode in solid‐state batteries.

Impedance spectroscopy is widely used in operando studies of solid‐state batteries for characterizing charge transport and correlating it with structural features. A typical impedance spectrum reveals, in addition to transport signals of the solid electrolyte, one or more contributions due to processes taking place at the electrode interfaces. The focus of this study is on reversible (parent) metal anodes and a 3D electric network model is used to analyze the variation of their impedance as a function of pressure, temperature, or aging during cycling. This provides a recipe for experimentalists on how to identify impedance contributions arising from different interface effects, such as, charge transfer, dynamic current constriction, and solid electrolyte interphase formation. Rules are derived for assigning the different interface signals or identifying the dominant contribution in case of similar frequency‐dependence and a standard procedure for analysis is proposed. The suggested procedure is applied to experimental data of half cells where lithium metal is in contact with garnet‐type Li6.25Al0.25La3Zr2O12. This case study yields unambiguously that geometric current constriction due to morphological instabilities at the metal anode interface during cycling is the rate‐limiting step for this type of metal anode, rather than the frequently assumed polarization resistance of the electric charge transfer migration process.

The unique architecture of ordered mesoporous oxides makes them a promising class of materials for various electrochemical applications, such as gas sensing or energy storage and conversion. The high accessibility of the internal surface allows tailoring of their electrochemical properties, e.g., by adjusting the pore size or surface functionalization, resulting in superior device performance compared to nanoparticles or disordered mesoporous counterparts. However, optimization of the mesoporous architecture requires reliable electrochemical characterization of the system. Unfortunately, the interplay between nanocrystalline grains, grain boundaries, and the open pore framework hinders a simple estimation of material-specific transport quantities by using impedance spectroscopy. Here, we use a 3D electric network model to elucidate the impact of the pore structure on the electrical transport properties of mesoporous thin films. It is demonstrated that the impedance response is dominated only by the geometric current constriction effect arising from the regular pore network. Estimating the effective conductivity from the total resistance and the electrode geometry, thus, differs by more than 1 order of magnitude from the material-specific conductivity of the solid mesoporous framework. A detailed analysis of computed impedances for varying pore size allows for the correlation of the effective conductivity with the material-specific conductivity. We derive an empirical expression that accounts for the porous structure of the thin films and allows a reliable determination of the material-specific conductivity with an error of less than 8%.

Disorder effects in alloys are usually modeled by averaging various supercell calculations considering different positions of the alloy atoms. This approach, however, is only possible as long as the portion of the individual components of the alloy are sufficiently large. Herein we present an ab initio study considering the lithium insertion material Li1−x[Ni0.33Co0.33Mn0.33]O2 as model system to demonstrate the power of the coherent potential approximation within the Korringa-Kohn-Rostoker Green's function method. This approach enables the description of disorder effects within alloy systems of any composition. It is applied in this study to describe the (de-)intercalation of arbitrary amounts of lithium from the cathode active material. Moreover, we highlight that using either fully optimized structures or experimental lattice parameters and atomic positions both lead to comparable results. Our findings suggest that this approach is also suitable for modeling the electronic structure of state-of-the-art materials such as high-nickel alloys.