Computational Examination of Orientation-Dependent Morphological Evolution during the Electrodeposition and Electrodissolution of Magnesium

Abstract

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...

Size Dependence of Transport Non-Uniformities on Localized Plating in Lithium-Ion Batteries

“…We model a constant applied current by using an iterative bisection scheme to solve at each time step for the cell potential φ applied such that the total current in the cell is within an error tolerance factor of 2.5 × 10 −3 of the target current. 39 Estimates for the cell potential φ applied for the next step are made using linear extrapolation based on the cell potential from the previous and current time steps, and the window of estimated potential input into the bisection algorithm is ±0.0005V . Total current I in the cell is calculated by integrating the normal component of the current density over the area of the cell in a cross-section in the separator just above the anode via I = − κ ef f ∂φ 2 ∂z d A.…”

Application of phase-field method in rechargeable batteries

“…Liang and Chen 70,84 presented a nonlinear phase-field model, which takes the Butler-Volmer reaction kinetics into account, which can simulate and predict the Li deposit growth during charging processes without considering the SEI layer effect. Enrique et al 85 generalized DeWitt's model to study the morphological evolution of Limetal electrode during electrodeposition 86 . In 2015, Chen et al 87 established a consistent thermodynamic phase-field model to investigate the dendritic patterns, as shown in Fig.…”

Computational Model of Magnesium Deposition and Dissolution for Property Determination via Cyclic Voltammetry

“…As in the analytical models, simplifying approximations have commonly been used to improve numerical efficiency, such as electroneutrality of the electrolyte, which may be expressed as ρ = 0, 25,46,50,54,55 or that the current density, i, is solenoidal, ∇ · i = 0. 25,50 Cohen and Cooley 56 presented one of the earliest attempts to solve the PNP equations numerically by assuming electroneutrality and adding a displacement current proportional to the time derivative of the electric field to the expression describing local current density. They then solved the resulting system of equations using an explicit finite difference method (FDM) with a predictor-corrector scheme.…”

“…Magnesium deposited from organohaloaluminate electrolytes has been observed to nucleate in a hexagonal plate morphology. 4,25 Unfortunately, the available micrographs for Mg(BH 4 ) 2 in tetraglyme only show the deposit morphology well after the initial nucleation process has completed. 24 Thus we assume that magnesium deposits from Mg(BH 4 ) 2 /DME also nucleate as hexagonal plates with a constant ratio between the height and the deposit spacing; as these plates grow, they increasingly cover the WE surface and eventually merge.…”

“…Additional phase-field models have also been derived in two or three dimensions to examine deposition of copper, 42 lithium, [43][44][45] zinc, 46 and, most recently, magnesium. 25 All of these models have increased scientific understanding of the rich set of phenomena observed during electrodeposition and electrodissolution. Nevertheless, they are commonly limited by high computational cost, which can hinder parameterization efforts as well as the rapid determination of physical properties of materials based on the model results.…”