Morphological Evolution of Nanocluster Aggregates and Single

Article pubs.acs.org/JPCC

Morphological Evolution of Nanocluster Aggregates and Single Crystals in Alkaline Zinc Electrodeposition Divyaraj Desai,† Damon E. Turney,† Balasubramanian Anantharaman,† Daniel A. Steingart,*,‡ and Sanjoy Banerjee*,† †

Department of Chemical Engineering, City College of New York, New York, New York 10031, United States Department of Mechanical Engineering, Princeton University, Princeton, New Jersey 08544, United States

‡

S Supporting Information *

ABSTRACT: The morphology of Zn electrodeposits is studied on carbon-coated transmission electron microscopy grids. At low overpotentials (η = −50 mV), the morphology develops by aggregation at two distinct length scales: ∼5 nm diameter monocrystalline nanoclusters form ∼50 nm diameter polycrystalline aggregates, and the aggregates form a branched network. Epitaxial (000̅2) growth above an overpotential of |ηc| > 125 mV leads to the formation of hexagonal single crystals up to 2 μm in diameter. Potentiostatic current transients were used to calculate the nucleation rate from Scharifker et al.’s model. The exp(η) dependence of the nucleation rates indicates that atomistic nucleation theory explains the nucleation process better than Volmer− Weber theory. A kinetic model is provided using the rate equations of vapor solidification to simulate the evolution of the different morphologies. On solving these equations, we show that aggregation is attributed to cluster impingement and cluster diffusion while single-crystal formation is attributed to direct attachment.

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models14 both hypothesize that metal electrodeposition occurs by the formation of a critical cluster which has the maximum Gibbs free energy with respect to size and equal attachment or detachment probabilities. However, the predicted critical size varies widely between these theories. Growth is assumed to occur by the direct attachment of metal ions, while aggregation as a result of nanocluster interactions has been typically ignored. Recent work15,16 has suggested electrochemical aggregation to be one of the key mechanisms in metal electrodeposition. For example, Ustarroz et al.17 reported the formation of aggregates with twinning and stacking faults in Ag electrodeposits. Borisenko et al.18 deposited Si on single-crystal gold using in situ scanning tunneling micrsoscopy (STM) and observed nanocluster aggregation. Although there is comprehensive experimental evidence for electrochemical aggregation, the factors driving it have not yet been completely clarified. It is desired to have a mathematical model of the nucleation and growth processes that accounts for the contributions of both electrochemical aggregation and direct attachment. Electrochemical nucleation models are based on the analysis of potentiostatic current transients. The nature of the controlling mechanism can be identified from the asymptotic behavior of the current transient.19 The current decays to an

INTRODUCTION Zinc deposition from alkaline electrolytes is of special interest to the battery industry. Despite offering low cost, high energy density, and low toxicity, such electrodes are difficult to recharge, their cycle life being limited by shape change and dendrite formation during charging. If the nanoscale phenomena controlling the electrodeposition process were better understood, methods of dealing with electrode degradation1 could perhaps be developed. Some progress has been made in this direction on the basis of previous work,2 but a fundamental understanding is needed to develop a potentially scalable and low-cost solution to grid-scale energy storage devices3 based on rechargeable Zn batteries. The study of electrodeposited metal nanostructures has applications in energy storage, semiconductors, optics, and metal coatings.4,5 Electrodeposited Zn forms a variety of overpotential-dependent morphologies. “Compact” Zn has low corrosion rates and high density, excellent characteristics for battery anodes and protective coatings. “Mossy” Zn6 has poor adhesion and high porosity, undesirable in batteries, but potentially useful for catalytic purposes.7 A significant issue is that, despite an abundance of published research, the morphological evolution of electrodeposited nanostructures is uncertain and the driving mechanisms for the conditions under which mossy and compact structures form are not clear.8,9 Despite considerable published research,10−12 there is insufficient understanding of electrodeposited nanostructure evolution. Volmer−Weber theory13 and atomistic nucleation © 2014 American Chemical Society

Received: November 11, 2013 Revised: March 14, 2014 Published: March 25, 2014 8656

dx.doi.org/10.1021/jp411104a | J. Phys. Chem. C 2014, 118, 8656−8666

The Journal of Physical Chemistry C

Article

Research Versastat 4. After each experiment, the excess electrolyte was immediately rinsed by repeated immersion in deionized water and ethanol and dried in a vacuum desiccator. Low-resolution TEM images were obtained on a Zeiss EM 902 (80 kV). High-resolution TEM and electron diffraction images were obtained on a JEOL 2100 (200 kV) with a LaB6 source. Potentiostatic current transients on the TEM grids were noisy due to small changes in the active area available for deposition. For this reason, chronoamperometry experiments were performed using highly polished (50 nm alumina) glassy carbon disk electrodes to investigate the overpotential dependence of the nucleation rate. The nucleation densities of hexagonal zinc crystals on glassy carbon and the TEM grid are both O(108) cm−2 (where O is the symbol for order of magnitude), making the former a suitable choice of substrate.

asymptotic nonzero value for kinetically controlled nucleation and decays as 1/t1/2 for bulk diffusion-controlled nucleation. Scharifker et al.20 postulated that metal growth in a stagnant electrolyte is limited by the hemispherical diffusion of ions to the substrate. Electrodeposition begins with the formation of a hemispherical nucleation exclusion zone around a growing particle. The exclusion zones grow with time and overlap during the latter stages of nucleation, leading to a maximum in the current density (jm) at time tm. The current drops off after tm as the ion-depleted zone around the growing nucleus covers the entire substrate. Nucleation ceases at deposition times much larger than tm and eventually follows the Cottrell equation21 for diffusion-limited growth. Two limiting regimes were proposed, identified from potentiostatic current transients. In the first type, progressive nucleation, nuclei are formed on the substrate at a fixed nucleation rate (AN0), and in the second type, instantaneous nucleation, all the nuclei are formed at t = 0. The nucleation rate obtained by fitting experimental current transients to the Scharifker model can be interpreted using either the Volmer−Weber or the atomistic nucleation theory.22,23 The Volmer−Weber theory assumes growth to occur by direct attachment, while the atomistic theory postulates that growth is driven by the attachment and detachment of atomic clusters. The distinction between the two theories is the dependence of the nucleation rate on the overpotential. Volmer−Weber theory predicts the nucleation rate to be proportional to exp(−1/η2), while the atomistic theory postulates an exp(η) relation. Although the atomistic theory is in good agreement with potentiostatic current transient data,24,25 its assumptions have not yet been validated by direct nanoscale microscopic observations. Holzle et al.26 and Torrent-Burgues27 compared the steady-state nucleation rates to the atomistic and Volmer−Weber models. Although the number of atoms in the critical cluster was determined, the role of cluster interactions in morphological growth was not addressed. We investigated Zn nucleation on carbon-coated transmission electron microscopy (TEM) grids in alkaline electrolyte. The nucleation and early-stage growth of mossy and compact morphologies were studied with high-resolution transmission electron microscopy (HRTEM), scanning electron microscopy (SEM), and chronoamperometry. The results were compared with both the Scharifker model and the atomistic theory of nucleation. We modified the kinetic rate equations of vapor solidification and applied them to the electrodeposition problem to investigate the overpotential dependence of the morphological transitions. This approach provides insight into the driving forces for nucleation at different overpotentials and helps predict the electrodeposited morphology under a given set of experimental conditions.

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RESULTS AND DISCUSSION Evolution of Nanocluster Aggregates and Single Crystals. Potentiostatic deposition was performed at η = −50 mV to determine the typical morphology of Zn aggregates (Figure 1 a−c). It is useful to understand the morphological evolution of the aggregate structure by comparing phenomena at different deposition times in relation to the time for the maximum nucleation current (tm). The time of maximum current (tm) varied from 1 to 2.5 s across multiple experiments. At early times (t ≪ tm), nanoclusters of size ∼5 nm are deposited on the substrate and form aggregates about 50 nm in diameter. The typical density of aggregates and nanoclusters is O(1010) cm−2. At t ≈ tm, some of the aggregates grow in size while others impinge to form a networked structure. At later times (t ≫ tm), a highly branched three-dimensional network covers the entire substrate. Isolated aggregates are observed, which may attach to the growing network due to cluster diffusion and impingement. The typical size and morphology of the aggregates are comparable in magnitude to those of Borisenko,18 who reported nanocluster aggregation to occur in silicon deposits on gold. The similarity in the morphologies indicates that the aggregation process is not unique to Zn deposition only. At an overpotential of η = −150 mV, initially deposited nuclei grew to form symmetric hexagonal crystals. The current transients showed a maximum in the nucleation current between 0.03 and 0.3 s in all of our η = −150 mV cases. Deposition initiates by the formation of isolated crystals on the substrate (Figure 1d), the typical density of which is O(108) cm−2. Although the crystals are initially circular, anisotropic growth leads to the formation of facets for crystals larger than 50 nm in diameter. The crystals strongly diffract the electron beam, indicating long-range ordering. A second layer grows from the centers of the existing crystal, indicating a layer plus island (Stranski− Krastanov) growth (Figure 1f). A ∼10 nm peripheral layer is observed surrounding the crystals at the crystal−electrolyte interface, later deduced to be ZnO. The crystals grow to a maximum diameter of 2 μm before they begin to merge into each other, forming grain boundaries. Dendritic structures are formed at significantly higher overpotentials.28 This represents the early stages of the formation of compact Zn deposits. Morphology and Crystal Structure. The morphology of nanocluster aggregates and single crystals is determined by the spatial distribution and surface diffusivity of Zn nanoclusters. The morphology is discussed in terms of the particle size, spatial distribution, and crystal structure. The experimentally

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EXPERIMENTAL METHODS The electrolyte used was 0.1 M ZnO + 5 M KOH, prepared using materials from Sigma-Aldrich. The reference and counter electrodes were 3 mm diameter Zn (99.99%) rods (Alfa-Aesar) in a three-electrode configuration. Carbon-coated Cu TEM grids (300 mesh) from Ted Pella and 5 mm glassy carbon disk electrodes were used as working electrodes for the deposition and chronoamperometry experiments, respectively. The TEM grid was held in a vertical stage and immersed until it rested on the surface of the electrolyte. Potentiostatic deposition experiments were performed using a Princeton Applied 8657



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rc =

2γVm zF |η|

(1)

where γ = 0.99 J/m is the surface energy, Vm is the specific molar volume, z is the valency, F = 96485 C/mol, and η is the overpotential. The value of surface energy was experimentally determined by Vitos29 and used to calculate rc from eq 1 as 1.88 nm. This is in good agreement with the smallest experimentally observed nanoclusters in Figure 2a (2.1 nm). However, this agreement should be taken cautiously because clusters smaller than 1 nm are not discernible in our image analysis. Furthermore, the surface tension varies with the cluster size for clusters of a few atoms, whose stability is better described by the atomistic theory. Although a few aggregates (r ≈ 25 nm) are observed, their density is significantly lower than that of the nanoclusters. In the limit of t ≪ tm, it is fair to assume that the nanoclusters are instantaneously nucleated and grow to approximately the same size. The size distribution of deposits in Figure 2b,c is shown in Figure 2e. The mean particle size (rx) is calculated to be 12 nm for η = −50 mV and 27.5 nm for η = −150 mV. Assuming that the particles are nucleated at the same time, the particle size can be approximated (see the Supporting Information) by a fourthorder Weibull distribution given as 2

p(r ) = 4(r 3/λ 4) exp[−(r /λ)4 ]

(2)

where λ is a constant. The average particle size can be calculated using rx = λΓ(5/4). The particles deposited at both −50 and −150 mV obey Weibull statistics at early times (t < tm), and instantaneously nucleated particles can be expected to follow the distribution at t ≫ tm as well. The particle size distribution is expected to deviate from Weibull statistics for the case of progressive nucleated Zn. Although an analytical expression cannot be determined, a bimodal distribution is expected,16 with modes corresponding to the sizes of the nanoclusters and aggregates. This behavior probably arises due to two stages of the nucleation process, wherein nanoclusters are continuously nucleated and also diffuse to form larger aggregates. Thus, two populations can be expected to dominate, one of nanoclusters and the other of aggregates. At longer times (t ≫ tm), all nanoclusters would aggregate and impinge to form a network whose statistical analysis is rather intractable. Spatial Distribution. The spatial distribution of particles provides information about the nucleation process and is ultimately related to the size distribution. The nearest-neighbor distributions of particles from Figure 2b,c are shown in Figure 2f. Scharifker et al. predict a Rayleigh probability distribution p(s) for the distance between nearest neighbors (s), with the form

Figure 1. (a−c) Typical TEM images of morphologies formed at η = −50 mV. Nanoclusters attach to aggregates due to cluster diffusion, and aggregates impinge to form a network. (d−f) TEM images of hexagonal zinc deposits formed at η = −150 mV. (g) Chronoamperograms of deposition on TEM grids at η = −50 and −150 mV.

p(s) = 2πN0s exp( −πN0s 2)

observed nanoclusters are compared with the critical nanocluster size predicted by the Gibbs−Thomson equation. The experimental size and spatial distributions of aggregates and crystals were compared with theoretical expressions to elucidate the nucleation process. The data for the size and spatial distribution were obtained from Figure 2a−c. HRTEM and electron diffraction were used to probe the crystal structure of aggregates and crystals to extract phase information and also investigate crystal defects. Size Distribution. Image analysis of the deposit in Figure 2a indicates a mean radius of 2.9 nm for individual nanoclusters. The radius of the surface energetically stable nanocluster (rc) is calculated using the Gibbs−Thomson equation:

(3)

where N0 is the surface density of nucleation sites. The dimensionless spatial distribution has a maximum [sm = (2πN0)−1/2],30 and the mean distance between nearest neighbors is given by s ̅ = (4N0)−1/2. The nearest-neighbor distribution of the particles in Figure 2b,c was is in good agreement with the theoretical Rayleigh fit, indicating that Zn nucleation follows the predicted statistics at both potentials. The fitting parameters of 62 and 266 nm were computed using observed values of the particle density. The experimentally observed mean separation distances of 84 nm (η = −50 mV) and 370 nm (η = −150 mV) are in agreement with calculated values of 78 and 335 nm, respectively. The 8658



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Figure 2. Images used for the analysis of size and spatial distributions of the (a) nanoclusters, (b) aggregates, and (c) single crystals. (d) Size distribution of nanoclusters. (e) The dimensionless size distribution of aggregates and crystals is compared with the Weibull distribution. (f) The dimensionless spatial distribution of aggregates and crystals is compared with the Rayleigh distribution.

short times (t ≪ tm). Lattice fringes are 2.31 Å apart, corresponding to the lattice spacing for (000̅2) Zn (Figure 3a). Longer deposition times led to the aggregated growth of individual nanoclusters as shown to the right in Figure 3a. SAD of the center of ∼50 nm aggregate shows a speckled ring pattern, which indicates polycrystallinity, likely due to crystal twinning. The electron diffraction pattern in Figure 3a was processed to obtain the plot of intensity versus the d spacing (Figure 3b). The most prominent reflections of Zn are (101̅1), (000̅2), and (112̅0), while those of ZnO are (000̅2) and (101̅3). The HRTEM images do not reveal ZnO lattice fringes in aggregates, leading us to conclude that ZnO exists as a

probability of nearest-neighbor separation greater than ∼4sm is nearly zero, which puts a limit of 124 and 532 nm on the radius of the largest individual aggregate and crystal, respectively. Previously reported nearest-neighbor distributions were determined using microelectrodes and typically have mean separation distances of O(10) μm,31 which is a gross overestimation. The number of active sites at which deposition occurs is typically 108−1012 cm−2, in which case rm should realistically be in the 10 nm to 1 μm range.15,32 HRTEM Analysis of Aggregates. HRTEM and selected area diffraction (SAD) were used to obtain crystallographic information. Individual nanoclusters are observed only at very 8659



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Figure 4. Zinc nanoclusters formed at η = −50 mV (a) before aggregation and (b, c) after aggregation. The monocrystalline domains are limited to 10 nm even after aggregation. (d) Some of the aggregates form hollow Zn microcages, possibly due to the nanoscale Kirkendall effect.

Figure 3. (a) Monocrystalline nanoclusters deposited at η = −50 mV aggregate due to cluster diffusion. (b) Image analysis of the diffraction pattern from the aggregate in (a) (right) shows it is a polycrystalline mix of Zn and ZnO.

misoriented layer that fills the void space between aggregated Zn nanoclusters. Figure 4 suggests the process by which nanoclusters form aggregates. Although the nanoclusters are clearly monocrystalline, the aggregate itself is not. The network (Figure 4d) is comprised of repeating polycrystalline nearly circular aggregates ∼50 nm in diameter, some of which either are hollow or are surrounded by a denser shell with a thickness of 7.8 ± 1.7 nm. The formation of the hollow nanostructures could be due to the formation of a Zn−ZnO core−shell through the process of nanoscale Kirkendall diffusion. Although Kirkendall diffusion has been used to explain the formation of ZnO microcages by the dry oxidation of Zn polyhedra,33−35 electrodeposition has not been explored as the means to fabricate hollow nanostructures via the Kirkendall effect. The structural voids may be due to the outward diffusion of Zn into the electrolyte by corrosion. The formation of Kirkendall voids within the nanocluster possibly causes the degradation of its mechanical and electrical properties, undesirable in electrochemical applications. However, the formation of hollow ZnO nanostructures through direct electrodeposition has interest for fabrication of photonics components and catalysts.36 HR-TEM Analysis of Crystals. A layer about 10−20 nm thick is observed around the edge of a hexagonal crystal deposited at η = −150 mV (Figure 5). The SAD of the crystal bulk matches (000̅2) Zn. Weak reflections of (000̅2) ZnO are also observed on the diffraction pattern. Lattice fringes from the center are

Figure 5. (a) TEM image of the ZnO layer around the hexagonal Zn crystal. (b) The electron diffraction pattern of the bulk crystal is matched to (000̅2) Zn and weak reflections of (000̅2) ZnO. (c) The HRTEM image of the center of the crystal has lattice fringes of (000̅2) Zn. (d) The phase boundary between Zn and ZnO is resolved by FFTfiltering to reveal an interphase layer (Zn + ZnO).

2.31 Å apart, indicating a defect-free, symmetric (000̅2) Zn crystal. Lattice fringes from the edge of the crystal are 2.80 Å apart and correspond to the lattice spacing for (0002̅ ) ZnO. The phase boundary is quite well-resolved by FFT-filtering the fringes for Zn and ZnO. Additionally, a 1.5 nm layer is detected in which the lattice fringes vary between Zn and ZnO, 8660



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from the diagnostic equations provided by Scharifker et al., given by

attributed to an adsorbate or Zn|ZnO interphase. It should be noted that the presence of an oxide layer has been hypothesized to be part of the Zn reaction pathway.37 The thickness of the oxide layer agrees with the value predicted by Cachet.38 The presence of a (0002̅ ) ZnO layer growing epitaxially on Zn has been previously reported in acidic solutions,39 and here we report an analogous result in alkaline electrolytes as well. The presence an oxide layer supports the reaction pathway hypothesized by Dirkse et al., in which the zincate ion loses its hydroxide ions as it approaches the interface and precipitates as a Zn(OH)2 layer, detected as ZnO after dehydration. The electron charge-transfer reactions occurring at the Zn|ZnOH and ZnOH|Zn(OH)2 interfaces are a more feasible mechanism than that previously reported,40 where the charge-transfer reaction occurred in the Helmholtz plane.41 This is represented in the following reaction scheme: Zn(OH)4 2 − (aq) ⇌ Zn(OH)2 (s) + 2(OH)− (aq)

(4a)

Zn(OH)2 (s) + e− ⇌ Zn(OH)(s) + (OH)− (aq)

(4b)

Zn(OH)(s) + e− ⇌ Zn(s) + (OH)− (aq)

(4c)

progressive nucleation ⎧ ⎫2 ⎡ ⎛ j ⎞2 1.2254 ⎪ ⎛ t ⎞ 2 ⎤⎪ ⎜⎜ ⎟⎟ = ⎨1 − exp⎢ − 2.3367⎜ ⎟ ⎥⎬ ⎢⎣ t /tm ⎪ ⎝ tm ⎠ ⎥⎦⎪ ⎝ jm ⎠ ⎩ ⎭

instantaneous nucleation ⎫2 ⎧ ⎛ j ⎞2 ⎡ ⎛ t ⎞ ⎤⎪ 1.9542 ⎪ ⎜⎜ ⎟⎟ = ⎢ − 1.2564⎜ ⎟⎥⎬ ⎨ 1 exp − ⎢⎣ t /tm ⎪ ⎝ tm ⎠⎥⎦⎪ ⎝ jm ⎠ ⎭ ⎩

Figure 6. Dimensionless plots of (j/jm)2 versus t/tm for η = −30, −80, and −130 mV are compared with the diagnostic curves for progressive and instantaneous nucleation.

from eqs 7 and 8. At η = −30 mV, the experimental current transient closely follows the curve for progressive nucleation, which changes at η = −80 mV to an intermediate nucleation mode. Finally, at potentials in excess of η = −125 mV all the nucleation sites are instantaneously activated. The diagnostic plots suggest that the morphological change from aggregates to single crystals is correlated to a transition from progressive nucleation at η = −30 mV to mixed at η = −80 mV and finally to instantaneous nucleation at η = −130 mV. The current transients in Figure 7a were analyzed to determine values of the nucleation rate AN0 (s−1) and active site density N0 (cm−2). These values are calculated using a nonlinear least-squares algorithm (Levenberg−Marquardt) to fit the current transient. The fitting parameters of D = 6.78 × 10−6 ± 2.85 × 10−7 cm2 s−1 and N0 = 9 × 107 cm−2 are in good agreement with previously reported values of diffusivity (D = (6.11−6.4) × 10−6 cm2 s−1)44 and saturation density (N0 = 107 cm−2).45 The nucleation rate increases exponentially with the overpotential and levels off after ηc = −125 mV. It is clear that the nucleation rate is independent of the applied overpotential in the regime where single crystals are formed. An important difference between aggregates and single crystals is the number of adatoms required to form the critical cluster (nc) given by

⎛ D ⎞1/2 j(t ) = zFC ⎜ ⎟ [1 − exp{N0πk′D(1 − e−At − At )/A}] ⎝ πt ⎠ (5)

where C is the bulk zincate concentration, D is the ionic diffusivity, k′ = (8πCMVm)1/2, and AN0 is the nucleation rate. The fractional coverage of the exclusion zones increases in accordance with the Avrami theorem. The exclusion zones grow with time till the entire surface is covered and no nucleation may occur. The magnitude of the current transient goes through a maximum jm at t = tm. The nucleation is characterized as progressive if A → 0 and instantaneous for A → ∞. In progressive nucleation, active sites are continually occupied until they are completely covered by the growing diffusion zones. The nucleus density at saturation (Ns) is given by ⎛ AN0 ⎞1/2 ⎜ ⎟ ⎝ 2k′D ⎠

(8)

The current transients at η = −30, −80, and −130 mV are compared (Figure 6) with the dimensionless diagnostic plots

Mechanism and Theory. We use existing electrochemical theories of nucleation to explain the formation of nanoclusters, aggregates, and single crystals. Our proposed model combines the kinetic rate equations of vapor solidification42 with the atomistic theory of electrochemical nucleation. The potentiostatic current transients were fit to Scharifker’s et al.’s model to obtain the nucleation rate. The contributions of adsorption, nucleation, and surface diffusion were determined according to the atomistic nucleation theory, and these parameters are taken as inputs for the proposed kinetic model. Analysis of Chronoamperometry Data. At sufficiently high overpotentials (|η| > 10 mV), Zn deposition in a stagnant electrolyte is controlled by Zn nucleation and the hemispherical diffusion43 of zincate ions. The initial portion of the current transient is nucleation-controlled, and the transient asymptotically decays as 1/t1/2, implying diffusional control. The general form of the nucleation current j(t) is given by the Scharifker model as

Ns =

(7)

(6)

nc =

In instantaneous nucleation, all the active sites on the substrate are occupied at t = 0. The nucleation regime can be determined 8661

kT ⎛ d ln AN0 ⎞ ⎜ ⎟−β ze0 ⎝ dη ⎠

(9)



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the kinetic rate expressions proposed by Zinsmeister46 and others47−49 to investigate the role of cluster−cluster interactions. We can then predict, at least in an average sense, the evolution of cluster size and density. According to atomistic theory, the nucleation rate (AN0) calculated from Scharifker et al.’s model is assumed to be given by50−52 ⎛ (nc + 1)Ea + En − Ed ⎞ ⎛ R ⎞nc c ⎟⎟ AN0 = N0Ra 2⎜ ⎟ exp⎜⎜ ν N kT ⎝ 0⎠ ⎝ ⎠

(10)

where R is the adatom arrival rate and a is the lattice spacing. In a liquid, the arrival rate depends on the local concentration of electrodepositing ions and an adsorption energy barrier, which is a deviation from the gas-phase model of Venables. As a first approximation, we assume a constant arrival rate. A detailed model considering a time-dependent arrival rate will be presented in upcoming work. The frequency of lattice vibration is calculated from the Debye temperature relation v = kTD/h and is typically 1012− 1013 Hz, where h is Planck’s constant. We assume the energy for the formation of the energy barrier for adatom surface diffusion (Ed) to be constant. The adatom binding energy (Ea) is a function of the overpotential, given by eq Ea = zFη

(11)

The binding energy of the critical cluster (Enc) is assumed to be

Enc = −βEa

(12)

The values of the parameters derived from our fits to the current transients are presented in Table 1. The adatom Figure 7. Potentiostatic current transients at different overpotentials and Scharifker et al.’s model fit (inset). (b) Nucleation rate (AN0) and saturation density (Ns) computed from fitting the current transients.

Table 1. Nucleation Parameters Calculated from the Current Transient Data

where β is a fitting parameter used to account for the cluster− substrate interaction, e0 is the electronic charge, and k is the Boltzmann constant. The number of atoms in the critical nucleus is determined by the slope of ln AN0 (Figure 7b). The number of atoms constituting a critical nucleus undergoes a transition at ηc = −125 mV. While nanoclusters require the formation of a single adatom on the surface (nc = 1; β = 0.5), single crystals can spontaneously grow at active centers without such a requirement (nc = 0; β = 1). For nc = 0, a single atom behaves as a supercritical nucleus and can grow irreversibly. The stability of critical nuclei comprising only a few atoms might seem to be in contradiction with the nanocluster size predicted by eq 1, i.e., 1.88 nm. However, eq 1 is valid at the continuum scale and may not be used to investigate the stability of atomistic clusters. While it is plausible that such stable clusters might be present in our system, their size is too small to be detectable. Analysis of the Nucleation Rate Using Atomistic Theory. The nucleation rate computed from the current transients comprises the contributions of adsorption, desorption, and adatom surface diffusion into a single parameter (AN0). An insightful analysis cannot be performed unless the contribution of each of these processes is evaluated. We use the formulation provided by the atomistic theory to interpret the nucleation rate in terms of the adatom binding energy (Ea), critical cluster binding energy (Enc), and energy barrier for surface diffusion (Ed). Once these energies are determined, it is possible to use

parameter

value

parameter

value

R (cm−2 s−1) v (THz)

1.93 × 1014 5

Ds (cm2 s−1) Dx (cm2 s−1)

6.52 × 10−7 3.26 × 10−9

binding energy is related to the adatom desorption time scale (τa), given by τa =

⎛ E ⎞ N0 exp⎜ − a ⎟ ⎝ kT ⎠ R

(13)

At η = −50 mV, the adatom desorption time scale is smaller than the duration of the experiment (τa = 24 μs). Adatoms nucleating on an active site might desorb back into the electrolyte or diffuse over the substrate until they are captured by a growing nanocluster. The loss of adatoms by desorption decreases with increasing overpotential. At potentials in excess of ηc (τa = 67 ms), a negligibly small fraction of Zn adatoms undergo desorption from the substrate. Kinetic Rate Equations for Electrochemical Nucleation. Scharifker et al.’s model and the atomistic theory are silent about the kinetics of phenomena occurring on the substrate itself. The kinetic rate expressions proposed by Venables50 for heterogeneous nucleation from vapor are used to model the time evolution of the adatom density (n1), density of meansized clusters (nx), and fractional coverage (Z). The parameters calculated from the atomistic theory have the same meaning in Venables’s framework as well and can be applied to Venables’s equations. Adatoms are deposited on the substrate at a rate R, desorbed at a rate n1/τa, and captured by growing clusters at a 8662



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rate σxDsn1nx, where Ds is the surface diffusivity of adatoms. The density of supercritical clusters grows at a rate Unc, and the loss of clusters occurs due to cluster impingement (UCI) or cluster diffusion (UCD). The final balanced equations are for adatoms dn1 n = R(1 − Z) − 1 − σxDsn1nx dt τa

diffusivity, which is a small fraction (δm) of the surface diffusivity given by ⎛ E ⎞ Dx = δmDs = δm D0 exp⎜ − d ⎟ ⎝ kT ⎠

where D0 = a2v/4 is the prefactor for the surface diffusivity. In theory, Dx should scale as rx−n depending on the cluster size.53,54 However, the precise dependence is currently ambiguous, so we use a constant value of Dx. Our computed value Dx = 3.26 × 10−9 cm2/s is within the range of diffusivities of other metals on carbon.55 The cluster diffusivity can be used to interpret the recrystallization process reported to occur in metals.16,17 Assuming recrystallization to be controlled by rearrangements at rates comparable to Dx, the characteristic length scale is (4Dxτa)1/2, which is calculated to be 5 nm (η = −50 mV) and 300 nm (η = −150 mV). This could explain the formation of monocrystalline nanoclusters (Figure 3a) and also the absence of recrystallization in Zn aggregates (Figure 4b). The dimensionless capture numbers σnc, σx, and σxx account for nucleation, adatom diffusion, and cluster diffusion, respectively, and are calculated using the “uniform depletion” and “lattice approximation” given by

(14)

for mean-sized clusters dnx = Unc(1 − Z) − UCI − UCD dt

(15)

for fractional coverage (2-D) dZ = Ω2/3{(nc + 1)Unc(1 − Z) + σxDsn1nx + RZ} dt

(16)

where Ω is the atomic volume, Unc is the growth rate of the stable cluster, and UCI and UCD are the rates of loss of clusters due to impingement and cluster diffusion, respectively. The nucleation regimes are characterized depending on the value of the dimensionless quantity σxDsτanx, the ratio of the desorption time scale to that of adatom surface diffusion. If σxDsτanx ≪ Z, growth occurs by cluster impingement, and if σxDsτanx ≫ 1, growth occurs by direct attachment. In the intermediate regime of Z < σxDsτanx < 1, growth occurs by adatom diffusion (Figure 8).

The growth rates used as inputs are calculated using the equations provided. The growth rate (Unc) of a stable cluster is determined using the Walton relationship51 given as

(17)

The rate of loss to cluster impingement (UCI) is given by

dZ dt The rate of loss to cluster diffusion (UCD) is given by UCI = 2nx

(18)

UCD = σxxDx nx 2

(19)

⎛ 2πa σnc = ⎜⎜ ⎝ Dsτa

⎞ ⎛ a2 ⎞ ⎛ a2 ⎞ ⎟⎟K1⎜ ⎟ / K 0⎜ ⎟ ⎝ Dsτa ⎠ ⎠ ⎝ Dsτa ⎠

(21)

σx = σxx = −

8π (1 − Z) 2 ln Z + (3 − Z)(1 − Z)

(22)

where K0 and K1 are modified Bessel functions of the second kind. Although eq 21 is strictly valid at high overpotentials (direct attachment), it is more amenable to a numerical solution. The ODE45 algorithm in MATLAB was used to simultaneously solve eqs 14−16 using the parameters determined from the current transients. Assuming circular clusters, the mean radius can be computed at any time (rx = (Z/πnx)1/2). The parameters used in the simulations were chosen from Table 1. The simulated curves are compared with experimental data obtained from TEM image analysis of individual particles at different deposition times. Simulation of Aggregate Growth (η = −50 mV). The simulated cluster density initially increases linearly with coverage (nx ∝ Z). The clusters do not grow in size or aggregate until saturation, and after this time adatom diffusion becomes important (Z < σxDsτanx < 1). The particle density (1.14 × 1010 cm−2) and size (rx = 1.86 nm) at saturation are in agreement with experimentally observed values (Figure 9a). The saturation densities are comparable to those of Ustarroz,16 who also reported similarly elevated values in Pt nanoclusters. The experimental value of saturation density is 10 000 times larger than the value calculated by eq 6. This discrepancy is a result of Scharifker’s model assuming growth solely by direct attachment and not considering aggregation as a growth mechanism. This results in an underestimation of the cluster density and overestimation of the size. The process of nanocluster saturation is analogous to a cluster self-limiting mechanism described in the above work. The cluster density increases until it is limited by diffusive capture (UCD), forming nanocluster aggregates, which leads to a decrease in the cluster density.

Figure 8. Dimensionless parameter σxDsτanx versus coverage (Z) at η = −50 and −150 mV.

⎛ En ⎞ Unc = σncN01 − nc exp⎜ c ⎟Dsn1nc + 1 ⎝ kT ⎠

(20)

where Dx is the diffusivity of an x-sized cluster. We used the rather simplistic assumption that all clusters have the same 8663



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recrystallization, described for silver electrodeposition.17 A recrystallization step would have a characteristic length of 300 nm and is responsible for the formation of large monocrystal7 −2 is in line crystals. The saturation density nmax x = 9.78 × 10 cm agreement with values predicted by chronoamperometry and experimentally observed values. Since growth is primarily by direct attachment, the Scharifker model can accurately predict the cluster density. The terms in the governing equations are compared to obtain insight into the nucleation regime. The nucleation term (Unc = 5.28 × 109 cm−2 s−1) in the governing equations is 2 orders of magnitude smaller than that at η = −50 mV and is responsible for the lower values of saturation density. The second term in eq 16 is dominant until intermediate coverage, implying that growth occurs by direct attachment. The impingement term (UCI) dominates for cluster radii larger than 1.2 μm (t = 4 s), and the merging of clusters is responsible for the rapid increase in cluster size. The density rapidly decreases after saturation due to cluster impingement, typically when crystals have grown to O(1 μm) in radius. Summarily, the early stages of compact zinc deposition are attributable to direct attachment forming single crystals which later impinge to form compact Zn films. Although the kinetic rate equations are quite generic, certain factors might be considered prior to applying them to predict nucleation phenomena for other materials. The governing equations can be applied to 2-D growth, and the model can be extensible to 3-D by simply changing eq 16.50 Experiments might be needed to theoretically capture the size dependence of cluster diffusivity. We assume hemispherical diffusion to drive the diffusion process and that the nucleation processes on the substrate are always at the steady state. In reality, the adatom arrival rate used in Venables’s equations should be timedependent, and our simplifying assumption needs to be validated by matching the equations at the substrate and electrolyte phases. Though it is possible to predict the evolution of average particle radius, the precise morphology is dependent on local conditions and could be obtained from heuristic kinetic Monte Carlo simulations. However, the above treatment is able to account for cluster interactions and predict the evolution of size and density to first-order accuracy.

Figure 9. (a) Simulated plot of nx and rx versus time at η = −50 and −150 mV. The error bars are minimum and maximum experimental values. (b) Simulated plot of nx and rx versus surface coverage at η = −50 and −150 mV.

A transition in the nucleation regime occurs at Zc = 0.3, after which the nanoclusters rapidly grow in size as they impinge and aggregate. The value of Zc is the upper limit on the radius of the individual aggregates (80 nm). This is in agreement with the largest experimentally observed aggregate (78 nm). This impingement of clusters is pronounced at higher surface coverage, and the morphology corresponds to the random branching of aggregates reported in Figure 1b,c. It is essential to compare the magnitude of terms in eqs 15 and 16 to understand the growth mechanism. The large magnitude of the nucleation term (Unc = 2 × 1012 cm−2 s−1) is responsible for the saturation of the substrate by stable clusters at extremely low coverage O(10−4) which diffuse to form aggregates. The cluster mobility term (Um) then dominates, forming aggregates, leading to a decrease in the density of average-sized clusters. Due to the low desorption time (τa), recrystallization in aggregates might be limited to 5 nm domains, leading to polycrystallinity. The impingement term then dominates (t > 6 s) and leads to the rapid increase in cluster size associated with the branched network. Simulation of Crystal Growth (η = −150 mV). The cluster density is observed to have an initial power law dependence on surface coverage (nx ∝ Z1/2). Growth occurs by surface-diffusive capture at extremely low surface coverage to form nanoclusters which grow to form crystals primarily by direct attachment (σxDsτanx ≫ 1). This is similar to the growth by full

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CONCLUSIONS The overpotential-dependent Zn morphologies were investigated using TEM and chronoamperometry. Instantaneously nucleated hexagonal (000̅2) Zn single crystals grow by the direct attachment of ions and eventually form compact Zn thin films. Progressively nucleated nanoclusters grow by adatom surface diffusion to form polycrystalline aggregates, which form a network of mossy Zn by cluster impingement. Using the atomistic nucleation theory, we are able to conclude that the nucleation regime changes with increasing overpotential from surface diffusion to direct attachment. We use the cluster diffusivity as a free parameter to fit the density and size evolution of both nanoclusters and crystals, which could be used to effectively simulate morphology at any given condition. Alternatively, if the adatom and cluster diffusivities are known through in operando experiments, the rate equations can be easily solved to obtain an ab initio estimate of the evolution of a given morphology under all conditions. 8664



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ASSOCIATED CONTENT

S Supporting Information *

Support for the use of carbon-coated TEM grids in our experiments, comparison of the effect of overpotential on the nucleation rate with both Volmer−Weber theory and the atomistic theory of nucleation, and analysis of HR-TEM and selected-area diffraction data. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The support of the Department of Energy (ARPA-E Grant DEAR0000150) and the National Science Foundation (NSF Grant 1031820) is gratefully acknowledged. We acknowledge the use of TEM facilities at the City College Electron Microscopy Facility, IBM T. J. Watson Research Center, and Department of Chemistry, Hunter College.

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Morphological Evolution of Nanocluster Aggregates and Single

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