Internal structure of dense electrodeposits

Nanoscale evolution of interface morphology during electrodeposition

Control of interfacial morphology in electrochemical processes is essential for applications ranging from nanomanufacturing to batteries. Here, we quantify the evolution of an electrochemical growth front, using liquid cell electron microscopy to access unexplored length and time scales. During galvanostatic deposition of copper from an acidic electrolyte, we find that the growth front initially evolves consistent with kinetic roughening theory. Subsequently, it roughens more rapidly, consistent with diffusion-limited growth physics. However, the onset of roughening is strongly delayed compared to expectations, suggesting the importance of lateral diffusion of ions. Based on these growth regimes, we discuss morphological control and demonstrate the effects of two strategies, pulse plating and the use of electrolyte additives.

Understanding structure evolution during electrochemical growth is crucial in materials processing and design of devices such as batteries. Here, the authors image copper during electrodeposition to provide strategies for controlling interface morphology.

Stabilizing effect of tip splitting on the interface motion

Pattern-forming processes, such as electrodeposition, dielectric breakdown, or viscous fingering, are often driven by instabilities. Accordingly, the resulting growth patterns are usually highly branched fractal structures. However, in some of the unstable growth processes the envelope of the structure grows in a highly regular manner, with the perturbations smoothed out over the course of time. In this paper we show that the regularity of the envelope growth can be connected to small-scale instabilities leading to the tip splitting of the fingers at the advancing front of the structure. Whenever the growth velocity becomes too large, the finger splits into two branches. In this way it can absorb an increased flux and thus damp the instability. Hence, somewhat counterintuitively, the instability at a small scale results in a stability at a larger scale. The quantitative analysis of these effects is provided by means of the Loewner equation, which one can use to reduce the problem of the interface motion to that of the evolution of the conformal mapping onto the complex plane. This allows an effective analysis of the multifingered growth in a variety of different geometries. We show how the geometry impacts the shape of the envelope of the growing pattern and compare the results with those observed in natural systems.

Morphological instability during steady electrodeposition at overlimiting currents

We present a linear stability analysis of a planar metal electrode during steady electrodeposition. We extend the previous work of Sundstrom and Bark by accounting for the extended space-charge density, which develops at the cathode once the applied voltage exceeds a few thermal voltages. In accordance with Chazalviel's conjecture, the extended space-charge region is found to greatly affect the morphological stability of the electrode. To supplement the numerical solution of the stability problem, we have derived analytical expressions valid in the limit of low and high voltage, respectively.

Sharp-interface model of electrodeposition and ramified growth

We present a sharp-interface model of two-dimensional ramified growth during quasisteady electrodeposition. Our model differs from previous modeling methods in that it includes the important effects of extended space-charge regions and nonlinear electrode reactions. The electrokinetics is described by a continuum model, but the discrete nature of the ions is taken into account by adding a random noise term to the electrode current. The model is validated by comparing its behavior in the initial stage with the predictions of a linear stability analysis. The main limitations of the model are the restriction to two dimensions and the assumption of quasisteady transport.

Quantifying the dependence of dead lithium losses on the cycling period in lithium metal batteries

We have developed a novel method to compute the irreversible loss of anode material in rechargeable lithium metal batteries.

Potential-induced copper periodic micro-/nanostructures by electrodeposition on silicon substrate

We demonstrate the fabrication of large scale nano- and micropatterned copper periodic structures on a silicon substrate without imposed templates. In the electrodeposition process, we employ a periodic variation voltage in an ultrathin layer of concentrated CuSO(4) electrolyte. The pattern can be controlled by varying the frequency of the applied potential. We suggest that the observed periodic micro-/nanostructures are caused by the lag of the migrating ion concentration profile versus the applied voltage profile near the tip of the growth.

Unified moving-boundary model with fluctuations for unstable diffusive growth

We study a moving-boundary model of nonconserved interface growth that implements the interplay between diffusive matter transport and aggregation kinetics at the interface. Conspicuous examples are found in thin-film production by chemical vapor deposition and electrochemical deposition. The model also incorporates noise terms that account for fluctuations in the diffusive and attachment processes. A small-slope approximation allows us to derive effective interface evolution equations (IEEs) in which parameters are related to those of the full moving-boundary problem. In particular, the form of the linear dispersion relation of the IEE changes drastically for slow or for instantaneous attachment kinetics. In the former case the IEE takes the form of the well-known (noisy) Kuramoto-Sivashinsky equation, showing a morphological instability at short times that evolves into kinetic roughening of the Kardar-Parisi-Zhang (KPZ) class. In the instantaneous kinetics limit, the IEE combines the Mullins-Sekerka linear dispersion relation with a KPZ nonlinearity, and we provide a numerical study of the ensuing dynamics. In all cases, the long preasymptotic transients can account for the experimental difficulties in observing KPZ scaling. We also compare our results with relevant data from experiments and discrete models.

Morphological evolution in the electrodeposition of the Pb-Sn binary system

Morphological evolution in the electrodeposition of Pb-Sn binary system is studied. As the second component increases, the morphology of the codeposit changes from dendrite to ramification, to dense branch, and finally to fractal structure, respectively. The evolution arises from the influence of crystallographic texture, which leads to a splitting of dendritic tips and the formation of ramified morphology. This work provides direct evidence to explore the crystallographic influence on the morphological evolution in electrodeposition.

Mean-field kinetic lattice gas model of electrochemical cells

We develop electrochemical mean-field kinetic equations to simulate electrochemical cells. We start from a microscopic lattice-gas model with charged particles, and build mean-field kinetic equations following the lines of earlier work for neutral particles. We include the Poisson equation to account for the influence of the electric field on ion migration, and oxido-reduction processes on the electrode surfaces to allow for growth and dissolution. We confirm the viability of our approach by simulating (i) the electrochemical equilibrium at flat electrodes, which displays the correct charged double layer, (ii) the growth kinetics of one-dimensional electrochemical cells during growth and dissolution, and (iii) electrochemical dendrites in two dimensions.