Films grown through the anodic oxidation of metal substrates are promising for applications ranging from solar cells to medical devices, but the underlying mechanisms of anodic growth are not fully understood. To provide a better understanding of these mechanisms, we present a new 1D model for the anodization of aluminum. In this model, a thin space charge region at the oxide/electrolyte interface couples the bulk ionic transport and the interfacial reactions. Charge builds up in this region, which alters the surface overpotential until the reaction and bulk fluxes are equal. The model reactions at the oxide/electrolyte interface are derived from the Valand−Heusler model, with modifications to allow for deviations from stoichiometry at the interface and the saturation of adsorption sites. The rate equations and equilibrium concentrations of adsorbed species at the oxide/electrolyte interface are obtained from the reactions using Butler−Volmer kinetics, whereas transport-limited reaction kinetics are utilized at the metal/oxide interface. The ionic transport through the bulk oxide is modeled using a newly proposed cooperative transport process, the counter-site defect mechanism. The model equations are evolved numerically. The model is parametrized and validated using experimental data in the literature for the rate of ejection of aluminum species into the electrolyte, embedded charge at the oxide/electrolyte interface, and the barrier thickness and growth rate of porous films. The parametrized model predicts that the embedded charge at the oxide/electrolyte interface decreases monotonically for increasing electrolyte pH at constant current density. The parametrized model also predicts that the embedded charge during potentiostatic anodization is at its steady-state value; the embedded charge at any given time is equal to the embedded charge during galvanostatic anodization at the same current. In addition to simulations of anodized barrier films, this model can be extended to multiple dimensions to simulate anodic nanostructure growth.

A new phase-field modeling framework with an emphasis on performance, flexibility, and ease of use is presented. Foremost among the strategies employed to fulfill these objectives are the use of a matrix-free finite element method and a modular, application-centric code structure. This approach is implemented in the new open-source PRISMS-PF framework. Its performance is enabled by the combination of a matrix-free variant of the finite element method with adaptive mesh refinement, explicit time integration, and multilevel parallelism. Benchmark testing with a particle growth problem shows PRISMS-PF with adaptive mesh refinement and higher-order elements to be up to 12 times faster than a finite difference code employing a second-order-accurate spatial discretization and first-order-accurate explicit time integration. Furthermore, for a two-dimensional solidification benchmark problem, the performance of PRISMS-PF meets or exceeds that of phase-field frameworks that focus on implicit/semi-implicit time stepping, even though the benchmark problem's small computational size reduces the scalability advantage of explicit timeintegration schemes. PRISMS-PF supports an arbitrary number of coupled governing equations. The code structure simplifies the modification of these governing equations by separating their definition from the implementation of the numerical methods used to solve them. As part of its modular design, the framework includes functionality for nucleation and polycrystalline systems available in any application to further broaden the phenomena that can be used to study. The versatility of this approach is demonstrated with examples from several common types of phase-field simulations, including coarsening subsequent to spinodal decomposition, solidification, precipitation, grain growth, and corrosion.

The development of a practical magnesium-anode battery requires electrolytes that allow for highly efficient magnesium exchange while also being compatible with cathode materials. Here, a one-dimensional continuum-scale model is developed to simulate cyclic plating/stripping voltammetry of a model magnesium-based electrolyte system employing magnesium borohydride/dimethoxyethane [Mg(BH 4 ) 2 /DME] solutions on a gold substrate. The model is developed from non-electroneutral dilute-solution theory, using Nernst-Planck equations for the mass flux and Poisson's equation for the electrostatic potential. The electrochemical reaction is modeled with multistep Butler-Volmer kinetics, with a modified current/overpotential relationship that separately accounts for the portions of the current responsible for nucleating new deposits and propagating or dissolving existing ones. The diffusivities of the electrolyte species, standard heterogeneous rate constant, charge-transfer coefficient, formal potential, and nucleation overpotential are determined computationally by reproducing experimental voltammograms. The model is computationally inexpensive and therefore allows for broad parametric studies of electrolyte behavior that would otherwise be impractical. A rechargeable magnesium battery was first demonstrated 25 years ago when Gregory et al. 1 showed that magnesium could be reversibly deposited onto and dissolved from a magnesium-metal surface, as well as intercalated into and deintercalated from various host cathodes. Further interest in secondary magnesium batteries arose following the work of Aurbach et al., 2 which demonstrated a highly efficient organohaloaluminate electrolyte using a magnesium anode and a Mo 6 S 8 Chevrel-phase cathode. As a battery anode, magnesium metal offers important advantages over both intercalation compounds and lithium metal, including a higher theoretical volumetric energy capacity (3833 mAh/cm 3 vs. 2046 mAh/cm 3 for lithium metal and 760 mAh/cm 3 for graphite-based lithium-ion anodes), as well as a higher abundance in the earth's crust.3 Additionally, magnesium is less prone to dendrite formation than lithium when electrodeposited and therefore offers potential for improved battery cycle life and safety. 4 In addition to high-capacity electrode materials, a practical magnesium battery will also require an efficient electrolyte that is compatible with (i.e., chemically stable in contact with) these electrodes. Compared to lithium electrolytes, magnesium electrolytes remain in a relatively early developmental stage.1-29 Electrolytes formulated from Grignard reagents have been widely studied both in the battery and general electrochemistry communities. 1,6,28,[30][31][32][33][34][35] The speciation of these electrolytes is complex because, in addition to ionic dissociation, the reagents also undergo the Schlenk equilibrium process (a type of ligand exchange) and form multimeric species in many solvents. Both organohaloaluminates and the so-called magnesium aluminum chloride complex (MACC) a...

A new model of electrodeposition and electrodissolution is developed and applied to the evolution of Mg deposits during anode cycling. The model captures Butler-Volmer kinetics, facet evolution, the spatially varying potential in the electrolyte, and the time-dependent electrolyte concentration. The model utilizes a diffuse interface approach, employing the phase field and smoothed boundary methods. Scanning electron microscope (SEM) images of magnesium deposited on a gold substrate show the formation of faceted deposits, often in the form of hexagonal prisms. Orientation-dependent reaction rate coefficients were parameterized using the experimental SEM images. Three-dimensional simulations of the growth of magnesium deposits yield deposit morphologies consistent with the experimental results. The simulations predict that the deposits become narrower and taller as the current density increases due to the depletion of the electrolyte concentration near the sides of the deposits. Increasing the distance between the deposits leads to increased depletion of the electrolyte surrounding the deposit. Two models relating the orientation-dependence of the deposition and dissolution reactions are presented. The morphology of the Mg deposit after one deposition-dissolution cycle is significantly different between the two orientation-dependence models, providing testable predictions that suggest the underlying physical mechanisms governing morphology evolution during deposition and dissolution. Magnesium batteries have garnered substantial attention as a successor to Li-ion batteries due to their potential for high energy density and safe operation.1-3 Metallic Mg anodes provide a substantially higher specific volumetric capacity (3833 mA h/cm 3 ) than either Ligraphite anodes (760 mA h/cm 3 ) or metallic Li anodes (2046 mA h/cm 3 ). 2 Furthermore, unlike metallic Li anodes, 5 metallic Mg anodes can be cycled without the formation of dendrites. 4 Dendrite growth poses a hazard because dendrites can grow across the separator to the cathode and short the battery, leading to thermal runaway. 5,6 Instead of forming dendrites, metallic Mg anodes form compact, faceted films, practically eliminating this risk. 4 Understanding the evolution of this Mg film during cycling is a critical factor in the development of high-performance magnesium batteries. 7Although the development of electrolytes for the efficient and reversible deposition and dissolution of Mg has been pursued extensively (see Refs. 1 and 2 for comprehensive reviews on this topic), much less attention has been given to the morphological evolution of the Mg deposits during cycling. SEM and AFM images of the Mg film typically show a highly faceted film with grains on the order of 1 μm in width. [8][9][10][11] However, other morphologies with either larger 10 or smaller 12,13 features have also been observed. The most comprehensive examination of the morphology of electrodeposited Mg was conducted by Matsui, 4 who examined the morphology of 1 C/cm 2 of Mg deposited at 0.5...