Journal Publications

The impedance of a charged flat-plate electric double-layer capacitor

A. L. Usler, D. Fertig, M. Janssen, arXiv preprint , (2026).

We calculate the impedance of a flat-plate electric double-layer (EDL) capacitor by means of Finite Element Method simulations of modified Poisson--Nernst--Planck equations. In Nyquist representation, the impedance spectra show a slanted line at intermediate frequencies if the capacitor is biased by a voltage, or if the cation and anion diffusion coefficients differ. By inspecting the concentration perturbations in the relevant frequency range, we confirm that the slanted line is in both cases related to ambipolar salt diffusion. On the basis of our impedance data, we disprove two previously made claims: 1) that the width of the slanted-line region represents an EDL resistance; and 2) that the slope of the slanted line is a measure of the ratio of the diffusion and charging time scales. For the quantitative analysis of flat-electrode EDL capacitor impedance, we propose instead two equivalent circuits, for the cases of unequal diffusivities and nonzero bias. These two cases give rise to antisymmetric and symmetric salt perturbations, which are best described by a Warburg short and Warburg open element, respectively. From our circuit analysis, we obtain quantitative relations that link the Warburg prefactors to the ambipolar diffusion coefficient, the chemical capacitance of the bulk electrolyte, and the differential charge efficiency of the EDLs. We thus provide a theoretical framework that explains why the width of the slanted line saturates at large biases, why it vanishes for large ion packing fractions, and how the system's overall capacitance is limited by the finite amount of ions in a closed system.

Grain-Boundary Corrosion in UO_2+δ from a Defect Chemical Perspective&colon; A Case Study of the Σ5(310)[001] Grain Boundary

M. J. Wolf, A. L. Usler, R. A. De Souza, ACS Appl. Mater. Interfaces 17, 7906-7915 (2025).

We combine atomistic and continuum simulation methods to study the defect chemistry of a model grain boundary in UO_2+δ. Using atomistic methods, we calculate the formation energies of oxygen interstitials, uranium vacancies, and hole polarons (U⁵⁺ ions) across the Σ5(310)[001] symmetric tilt grain boundary. This information is then used as input in a continuum model of point-defect concentrations at the grain boundary and in its vicinity, taking into account electrostatic (space-charge) effects. Two scenarios are modeled: one in which oxygen interstitials are the majority ionic defect and one in which uranium vacancies are the majority ionic defect, with bulk charge neutrality being maintained by hole polarons in both cases. Our results indicate that, irrespective of the majority ionic defect, the Σ5(310)[001] grain boundary in UO_2+δ is negatively charged, with positively charged adjacent space-charge zones in which the hole-polaron concentration is enhanced. We propose that the enhanced U⁵⁺ concentration at the grain boundary and within the space-charge zones renders grain-boundary regions more susceptible to oxidative corrosion, an effect that could be counteracted by acceptor doping.

Point-Defect Segregation and Space-Charge Potentials at the Σ5(310)[001] Grain Boundary in Ceria

A. L. Usler, H. J. Heelweg, R. A. De Souza, A. R. Genreith-Schriever, Solids 5, 404-421 (2024).

The atomistic structure and point-defect thermodynamics of the model Σ5(310)[001] grain boundary in CeO₂ were explored with atomistic simulations. An interface with a double-diamond-shaped structural repeat unit was found to have the lowest energy. Segregation energies were calculated for oxygen vacancies, electron polarons, gadolinium and scandium acceptor cations, and tantalum donor cations. These energies deviate strongly from their bulk values over the same length scale, thus indicating a structural grain-boundary width of approximately 1.5 nm. However, an analysis revealed no unambiguous correlation between segregation energies and local structural descriptors, such as interatomic distance or coordination number. From the segregation energies, the grain-boundary space-charge potential in Gouy–Chapman and restricted-equilibrium regimes was calculated as a function of temperature for dilute solutions of (i) oxygen vacancies and acceptor cations and (ii) electron polarons and donor cations. For the latter, the space-charge potential is predicted to change from negative to positive in the restricted-equilibrium regime. For the former, the calculation of the space-charge potential from atomistic segregation energies is shown to require the inclusion of the segregation energies for acceptor cations. Nevertheless, the space-charge potential in the restricted-equilibrium regime can be described well with an empirical model employing a single effective oxygen-vacancy segregation energy.

How space-charge behaviour at grain boundaries in electroceramic oxides is modified by two restricted equilibria

A. L. Usler, F. Ketter, R. A. De Souza, Phys. Chem. Chem. Phys. 26, 8287-8298 (2024).

Determining the space-charge potential at grain boundaries in oxides by various experimental methods bears the promise of providing a comprehensive, quantitative description of interfacial defect chemistry. In this study, we draw attention to the problem of unifying data measured in different temperature ranges. We focus on unifying data from elevated-temperature electrical methods, such as impedance spectroscopy and current–voltage measurements, with data from room-temperature imaging techniques, such as Scanning Probe Microscopy (SPM), Transmission Electron Microscopy (TEM), and Atom Probe Tomography (APT). By means of continuum simulations, we calculate the space-charge potential Φ₀ at grain boundaries in the model electroceramic oxide acceptor-doped SrTiO₃, taking into account, first, a restricted equilibrium that leads to frozen-in acceptor-dopant profiles, and subsequently, a restricted equilibrium that leads to frozen-in bulk oxygen-vacancy concentrations. Our results indicate non-trivial differences between experimental values of Φ₀ obtained from electrical and from imaging methods, differences that arise from the different measurement temperatures and that are aggravated by the restricted equilibria. We also show that grain-boundary widths determined from elemental acceptor-cation profiles will not, on principle, agree with the electrical width extracted from impedance spectroscopy data.

A general expression for the statistical error in a diffusion coefficient obtained from a solid‐state molecular‐dynamics simulation

A. L. Usler, D. Kemp, A. Bonkowski, R. A. De Souza, J. Comput. Chem. 44, 1347-1359 (2023).

Analysis of the mean squared displacement of species k, ⟨r_k²⟩, as a function of simulation time t constitutes a powerful method for extracting, from a Molecular-Dynamics (MD) simulation, the tracer diffusion coefficient, D_k*. The statistical error in D_k* is seldom considered, and when it is done, the error is generally underestimated. In this study, we examined the statistics of ⟨r_k²⟩(t) curves generated by solid-state diffusion by means of kinetic Monte Carlo sampling. Our results indicate that the statistical error in D_k* depends, in a strongly interrelated way, on the simulation time, the cell size, and the number of relevant point defects in the simulation cell. Reducing our results to one key quantity—the number of k particles that have jumped at least once—we derive a closed-form expression for the relative uncertainty in D_k*. We confirm the accuracy of our expression through comparisons with self-generated MD diffusion data. With the expression, we formulate a set of simple rules that encourage the efficient use of computational resources for MD simulations.

A Critical Examination of the Mott–Schottky Model of Grain-Boundary Space-Charge Layers in Oxide-Ion Conductors

A. L. Usler, R. A. De Souza, J. Electrochem. Soc. 168, 23876 (2021).

The electrical properties of grain boundaries in ionic conductors are studied most frequently and most easily by Electrochemical Impedance Spectroscopy (EIS). The resistance data obtained in this manner are typically analyzed with the Mott–Schottky space-charge model to extract a space-charge potential. In this study, taking CeO₂ containing acceptor-dopant cations and oxygen vacancies as our model system, we calculate impedance spectra by solving the drift–diffusion equation for oxygen vacancies for a bicrystal geometry with space-charge layers at the grain boundary. Three different cases are considered for the behavior of the acceptor-dopant cations: a uniform distribution (Mott–Schottky), an equilibrium distribution (Gouy–Chapman), and a distribution frozen-in from a much higher temperature (restricted equilibrium). Analyzing our impedance data for the restricted-equilibrium case with the Mott–Schottky model, we find that the obtained space-charge potentials are substantially underestimated. In view of such a discrepancy not normally being apparent (the true values being unknown), we propose a specific set of EIS experiments that allow the Mott–Schottky model to be discounted.