Atomistic Nucleation Theory Research Articles

Critical Nucleus Size and Activation Energy of Ag Nucleation by Electrochemical Observation of Isolated Nucleation Events.

The induction times for electrodeposition of individual Ag nanoparticles on Pt nanodisk electrodes in acetonitrile were used to determine the critical nucleus size and activation energy barrier associated with the formation of Ag nuclei. Induction times for the nucleation and growth of a single Ag nanoparticle were determined following the application of a potential step to reduce Ag+ at overpotentials, η, ranging from -130 to -70 mV. Sufficiently small Pt electrodes (5.1 × 10-10-2.6 × 10-11 cm2) were used to ensure that the detection of a single Ag nucleation event occurred during the experimental observation time (150 ms-1000 s). Multiple measurements of Ag nucleation induction times were recorded to determine nucleation rates as a function of η using cumulative probability theory. Both classical nucleation theory (CNT) and the atomistic theory of electrochemical nucleation were employed to analyze experimental nucleation rates, without a requisite knowledge of the nucleus geometry or surface free energy. Using the CNT, the number of atoms comprising the critical size nucleus, Nc, was estimated to be 1-9 atoms for η ranging from -130 to -70 mV, in good agreement with 1-5 atoms obtained using atomistic theory. The experimental nucleation rates were also used to determine the activation energy barriers for nucleation from the CNT, which varied from 3.31 ± 0.05 to 13 ± 1 kT over the same range of η.

An atomistic theory of nucleation: Self-organization via non-equilibrium work and fluctuations

Insights from non-equilibrium statistical mechanics, highlighting the role of work and fluctuations at the microscale, are applied toward the development of a fundamental, rigorous and purely atomistic theory of nucleation. Nanoscale fluctuations in order, density and heat influence the local nucleation rate by orders of magnitude, necessitating their inclusion through a modern approach. Coarse-graining over the underlying Hamiltonian dynamics allows derivation of a microscale expression for the nucleation rate in terms of a classical path integral over far from equilibrium trajectories and their associated work. Second law violating states at the microscale, as found from the dynamics of small critical nucleation clusters, contribute exponentially to the observable macroscale nucleation rate.

Preferred growth of molybdenum thin films during magnetron sputtering

Molybdenum films deposited on a fused silica substrate by magnetron sputtering were investigated. Two types of film textures were identified: nucleation textures and growth textures. The experimental results showed that the nucleation texture of molybdenum films is characterized by the <110> axis, perpendicular to the substrate surface. Theoretical studies based on the atomistic theory of nucleation showed that the work of nucleation with the (110) orientation is the smallest in comparison with the work of nucleation of all other orientations. It was found that during film growth under the characteristic deposition conditions of the structural zone T, a transformation of the (110) nucleation texture into the (211) growth texture is observed, which is probably due to minimization of the overall energy of the growing film. It was found that increasing the working gas pressure within the range of 0.39 ​Pa–0.74 ​Pa reduces the thickness of the molybdenum film at which the texture (110) changes to the texture (211) by 30–40%.

Nucleation and growth mechanism of tin electrodeposition on graphene oxide: A kinetic, thermodynamic and microscopic study

Nucleation and growth mechanism of Sn deposition over graphene oxide (GO) was investigated by cyclic voltammetry, chronoamperometry and transmission electron microscopy (TEM) using an aqueous electrolyte containing 10 mM SnSO4 at pH 2.0. Chronoamperometry studies revealed adsorption phenomena of Sn atoms over GO electrode before the nucleation. Simultaneous reactions that happened over the GO electrode were hydrogen ion reduction along with 3D diffusion-controlled nucleation and growth of Sn. The reaction rates of nucleation and hydrogen reduction increased with increase in the applied potential towards more negative values. Application of atomistic theory of nucleation revealed the fact that a supercritical nucleus can be formed even with one Sn atom over GO sheet which implied that every single atom of deposited Sn can act as a stable nucleus which can grow with further addition of Sn atoms. Further application of classical nucleation theory suggested that the thermodynamic activation energy barrier for nucleation under the applied potential ranges is comparable to that of room temperature thermal energy, kT (2.476 kJ/mol) implying that the deposition was heavily governed by formation of initial adsorption layer of Sn adatoms. Characterization of surface morphology, size and distribution of Sn nanoparticles over GO was performed using TEM and a quantitative comparison of number density of nucleation sites has been presented.

Temperature-dependent nucleation kinetics of Guinier-Preston zones in Al–Cu alloys: An atomistic kinetic Monte Carlo and classical nucleation theory approach

Guinier-Preston (GP) zones, which form in Al–Cu alloys, exhibit characteristic patterns of Cu-rich, disk-shaped atomic clusters along the {100} planes. GP zones have received much attention not only for their precipitation-hardening effect on the Al matrix, but also from fundamental interest in the physics and chemistry of the nanoscale organization of solute atoms. In this study, we established an atomistic kinetic Monte Carlo (kMC) modeling technique for exploring the nucleation and formation processes of GP zones in Al–Cu alloys by constructing an effective on-lattice multibody potential for a dilute Al–Cu-vacancy system by density functional theory calculations. Our model can describe the clustering of Cu atoms via successive exchanges with vacancies and reproduce the characteristic planar nanoprecipitates along the {100} planes in a manner consistent with the crystallographic nature of the GP zones in the early-stage aging of Al–Cu alloys. The time evolution and critical nucleus size of Cu clusters were characterized at various temperatures based on the kMC results. Consequently, we predicted the existence of an optimum temperature (i.e., nose temperature) for the formation of Cu clusters at which the cluster growth was maximized, which was attributable to the interplay between the critical nucleation barrier and the diffusion rate. In addition, the critical nucleus size and temperature for cluster formation were examined based on classical nucleation theory along with the developed multibody potential. These provided an insight into the competition between the enthalpic and entropic effects on the formation of GP zones in the Al–Cu system.

The formation of astrophysical Mg-rich silicate dust

We present new results for ground-state candidate energies of Mg-rich olivine (MRO) clusters and use the binding energies of these clusters to determine their nucleation rates in stellar outflows, with particular interest in the environments of core-collapse supernovae (CCSNe). Low-lying structures of clusters (Mg2SiO4)n 2 ≤ n ≤ 13 are determined from a modified minima hopping algorithm using an empirical silicate potential in the Buckingham form. These configurations are further refined and optimized using the density functional theory code Quantum Espresso. Utilizing atomistic nucleation theory, we determine the critical size and nucleation rates of these clusters. We find that configurations and binding energies in this regime are very dissimilar from those of the bulk lattice. Clusters grow with SiO4–MgO layering and exhibit only global, rather than local, symmetries. When compared to classical nucleation theory we find suppressed nucleation rates at most temperatures and pressures, with enhanced nucleation rates at very large pressures. This implies a slower progression of silicate dust formation in stellar environments than previously assumed.

A method for evaluating glass-forming ability based on atomistic theory of crystal nucleation

A method for evaluating glass-forming ability based on atomistic theory of crystal nucleation

Nucleation and Growth of Lithium Peroxide in the Li/O2 Cell

The aprotic Li–O2 battery offers a vast improvement in theoretical energy density up to ten times that of current Li-ion batteries, but still suffers from shortcomings in cell and material design. Some of these shortcomings stem from the large gap in understanding between fundamental studies and cell cycling experiments. In particular, it is known from computational studies that the solid Li2O2 discharge product is an electronic insulator, but SEM images of discharged cathodes show particles of Li2O2 much larger than what electron conduction and tunneling would allow. In addition, the shape of the discharge curves does not match the expected exponential resistance rise of a cell limited by electron tunneling. In order to bridge Li2O2 properties with experimental observations, we developed a model in which Li2O2 forms as discrete particles on the cathode surface by using a combination of Kolmogorov’s statistical phase transformation theory and the atomistic nucleation theory. Nucleation rate was modeled according to a two-step process involving formation of a LiO2 intermediate. Despite its relative simplicity, the proposed model provides a near-quantitative description of empirically observed discharge curves (Figure 1). We find that the sudden potential drop at the end of discharge is caused by the reduction in active surface area as Li2O2 covers the cathode surface. Thus, the extra overpotential gained during discharge is the kinetic overpotential of the ORR rather than an ohmic overpotential through the Li2O2 bulk. This model can be used as a guide for cathode and electrolyte design, by maximizing the amount of Li2O2 that can be collected for a given amount of electrochemically active surface area. One strategy is to promote the growth of larger Li2O2 particles. For cathodes, this means reducing the rate of nucleation by having a higher nucleation energy barrier or a lower concentration of active sites. For electrolytes, this means solvating the LiO2 intermediate to promote the superoxide disproportionation pathway. In principle, the general form of this model is applicable to any electrochemical cell that produces a solid passivation layer. Figure 1: (a) Empirically observed discharge curves (symbols), compared with fit of the nucleation and growth model (lines). (b) Analysis of model parameters shows that they are independent of operating conditions. Figure 1

Coalescence-controlled and coalescence-free growth regimes during deposition of pulsed metal vapor fluxes on insulating surfaces

The morphology and physical properties of thin films deposited by vapor condensation on solid surfaces are predominantly set by the processes of island nucleation, growth, and coalescence. When deposition is performed using pulsed vapor fluxes, three distinct nucleation regimes are known to exist depending on the temporal profile of the flux. These regimes can be accessed by tuning deposition conditions; however, their effect on film microstructure becomes marginal when coalescence sets in and erases morphological features obtained during nucleation. By preventing coalescence from being completed, these nucleation regimes can be used to control microstructure evolution and thus access a larger palette of film morphological features. Recently, we derived the quantitative criterion to stop coalescence during continuous metal vapor flux deposition on insulating surfaces—which typically yields 3-dimensional growth—by describing analytically the competition between island growth by atomic incorporation and the coalescence rate of islands [Lü et al., Appl. Phys. Lett. 105, 163107 (2014)]. Here, we develop the analytical framework for entering a coalescence-free growth regime for metal vapor deposition on insulating substrates using pulsed vapor fluxes, showing that there exist three distinct criteria for suppressing coalescence that correspond to the three nucleation regimes of pulsed vapor flux deposition. The theoretical framework developed herein is substantiated by kinetic Monte Carlo growth simulations. Our findings highlight the possibility of using atomistic nucleation theory for pulsed vapor deposition to control morphology of thin films beyond the point of island density saturation.

Homogeneous two-dimensional nucleation of guest-free silicon clathrates

The difficulty in synthesizing guest-free semiconductor clathrates complicates the process of determining how these cage-like structures form. This work studies the microscopic mechanism of the nucleation of guest-free Si136 clathrate using molecular dynamics simulations with the Stillinger–Weber potential. The homogeneous nucleation of Si136, which is realized in a narrow negative pressure range before liquid cavitation, exhibits the characteristic feature of the two-dimensional (2D) mode. The critical nucleus is composed of one to two five-membered rings, and the nucleation barrier is close to 1 kBT. According to a thermodynamic model based on atomistic nucleation theory, the effective binding energy associated with the formation of 2D critical nuclei is significantly low, which is responsible for the low nucleation barrier of Si136 clathrate. In the post-nucleation period, the critical nucleus preferentially grows into a dodecahedron, and the latter continuously grows with sharing face along 〈1 1 0〉.

Dynamic competition between island growth and coalescence in metal-on-insulator deposition

The morphology of thin metal films and nanostructures synthesized from the vapor phase on insulating substrates is strongly influenced by the coalescence of islands. Here, we derive analytically the quantitative criterion for coalescence suppression by combining atomistic nucleation theory and a classical model of coalescence. Growth simulations show that using this criterion, a coalescence-free growth regime can be reached in which morphological evolution is solely determined by island nucleation, growth, and impingement. Experimental validation for the ability to control the rate of coalescence using this criterion and navigate between different growth regimes is provided by in situ monitoring of Ag deposition on SiO2. Our findings pave the way for creating thin films and nanostructures that exhibit a wide range of morphologies and physical attributes in a knowledge-based manner.

Morphological Evolution of Nanocluster Aggregates and Single Crystals in Alkaline Zinc Electrodeposition

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 (0002) 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 f...

On the induction period for crystallization in solute−solvent systems by polythermal method

The data of induction period tin derived from the data of maximum undercooling ΔTmax at different cooling rates R for some solute−solvent systems at different saturation temperature T0 are discussed using classical and atomistic theories of three‐dimensional nucleation. In the case of potassium nitrate aqueous solutions the tin data are analyzed in terms of the maximum supersaturation ratio Smax calculated from temperature dependence of solubility and the maximum undercooling ΔTmax and the values of solid−solution interfacial energy γ and number i* of molecules in the stable critically‐sized nuclei predited from tin(lnSmax) and tin(ΔTmax) data are compared. These results revealed that: (1) the values of supersaturation calculated as lnS from solubility data are lower than the real values expected from the chemical potential difference Δμ and that the description of Δμ in terms of undercooling ΔTmax is realistic, and (2) analysis of induction period data for solute−solvent systems should be carried out using applied undercooling ΔT or maximum undercooling ΔTmax instead of the usually used lnS or lnSmax. Examination of tin(ΔTmax) data for different systems showed that: (1) the value of γ lies between 1.7 and 13.2 mJ/m2 while that of i* between 2 and 50, and (2) in several cases atomistic nucleation theory describes the tin(ΔTmax) data adequately.

Rate-limiting processes in the fast SET operation of a gapless-type Cu-Ta2O5 atomic switch

The speed of the SET operation of a Cu/Ta2O5/Pt atomic switch from a high-resistance state to a low-resistance state was measured by transient current measurements under the application of a short voltage pulse. The SET time decreased exponentially with increasing pulse amplitude, reaching as low as 1 ns using moderate pulse voltages. This observation shows that oxide-based atomic switches hold potential for fast-switching memory applications. From a comparison with atomistic nucleation theory, Cu nucleation on the Pt electrode was found to be the likely rate-limiting process determining the SET time.

Nucleation and growth phenomena in nanosized electrochemical systems for resistive switching memories

The impact of the electrochemical nucleation on the switching kinetics in many nanoscaled redox-based resistive switching memories is critically discussed. In the case of the atomic switch, the system is site invariant and the nucleation process is strictly localized below the STM tip. Using RbAg4I5 solid electrolyte, nucleation was found to be rate limiting. The electrochemical metallization memory cells (gapless type atomic switch) operate at conditions closer to the conventional nucleation. They introduce additional difficulties for interpretation of the experimental results due to formation of hillocks, of surface oxide barrier films, induction of strain, and the influence of the high electric field. In valence change memories, the nucleation seems to be less important because of the higher applied voltages. The results are discussed in the context of the atomistic theory of electrochemical nucleation. We believe that re-analysis of the experimental data for many systems will reveal that the nucleation is limiting the switching time.

Magic Cluster Sizes in Nucleation of Crystals

In an ensemble of nanoscale crystalline clusters, those of magic sizes are evidenced by their greater number. The respective cluster size distribution is multipeaked and cannot be described by the classical nucleation theory. Employing the atomistic nucleation theory, we present expressions for the cluster size distribution in stationary nucleation of two- or three-dimensional crystals. We show that this distribution is multipeaked at magic cluster sizes and compare these sizes with those obtained from computer simulations of cluster evolution on square Kossel–Stranski or Ising lattice and from experiments on formation of Si islands on Si(111).

Size Distribution of Amyloid Nanofibrils

We consider the size distribution of amyloid nanofibrils (protofilaments) in nucleating protein solutions when the nucleation process occurs by the mechanism of direct polymerization of β-strands (extended peptides or protein segments) into β-sheets. Employing the atomistic nucleation theory, we derive a general expression for the stationary size distribution of amyloid nanofibrils constituted of successively layered β-sheets. The application of this expression to amyloid β1-40 (Aβ40) fibrils allows us to determine the nanofibril size distribution as a function of the protein concentration and temperature. The distribution is most remarkable with its exhibiting a series of peaks positioned at “magic” nanofibril sizes (or lengths), which are due to deep local minima in the work for fibril formation. This finding of magic sizes or lengths is consistent with experimental results for the size distribution of aggregates in solutions of Aβ40 proteins. Also, our approach makes it possible to gain insight into the effect of point mutations on the nanofibril size distribution, an effect that may play a role in experimentally observed substantial differences in the fibrillation lag-time of wild-type and point-mutated amyloid-β proteins.

Amyloid Fibrillation Kinetics: Insight from Atomistic Nucleation Theory

We consider the nucleation of nanosized amyloid fibrils composed of successively layered β-sheets at the molecular level when this process takes place by direct polymerization of protein segments (β-strands) into β-sheets. Application of the atomistic nucleation theory (ANT) to amyloid nucleation of β2-microglobulin and amyloid β40 allows us to predict the fibril nucleus size and the fibril nucleation rate as functions of the supersaturation of the protein solution. The ANT predictions are compared to recent time-resolved optical experiments where they measure the effect of the protein concentration and mutations on the initial lag time before amyloid fibrils form in the protein solution. The presented analysis reveals the general principles underlying the nucleation kinetics of nanosized amyloid fibrils and indicates that it can be treated in the framework of existing general theories of the nucleation of new phases.

Atomistic theory of amyloid fibril nucleation

We consider the nucleation of amyloid fibrils at the molecular level when the process takes place by a direct polymerization of peptides or protein segments into β-sheets. Employing the atomistic nucleation theory (ANT), we derive a general expression for the work to form a nanosized amyloid fibril (protofilament) composed of successively layered β-sheets. The application of this expression to a recently studied peptide system allows us to determine the size of the fibril nucleus, the fibril nucleation work, and the fibril nucleation rate as functions of the supersaturation of the protein solution. Our analysis illustrates the unique feature of ANT that the size of the fibril nucleus is a constant integer in a given supersaturation range. We obtain the ANT nucleation rate and compare it with the rates determined previously in the scope of the classical nucleation theory (CNT) and the corrected classical nucleation theory (CCNT). We find that while the CNT nucleation rate is orders of magnitude greater than the ANT one, the CCNT and ANT nucleation rates are in very good quantitative agreement. The results obtained are applicable to homogeneous nucleation, which occurs when the protein solution is sufficiently pure and/or strongly supersaturated.

Effect of sulfate ion adsorption on the rate of copper electrocrystallization on Ag(111) face

The process of copper electrocrystallization on the Ag(111) face was studied in acidic perchlorate-sulfate electrolytes. Enhanced rate of charge transfer in the course of nucleation and growth of epitaxial copper crystallites was observed in the solutions with additives of sulfate ion as a result of local electrostatic effects under specific adsorption of anions. Copper nucleation parameters were estimated in the framework of the diffusion models and atomistic theory of electrochemical nucleation.