Homogeneous nucleation and growth in iron-platinum vapour investigated by molecular dynamics simulation

Homogeneous nucleation and growth from binary metal vapour is investigated by molecular dynamics simulation. It is focused here mainly on the iron-platinum system with a mole fraction of 0.5. The simulations are started in the highly supersaturated vapour phase. Argon is added as carrier gas removing the heat of condensation from the forming clusters. The embedded atom method is employed for modelling of the force field of iron and platinum. The simulation runs are evaluated with respect to the nucleation rate, monomer temperature, monomer amount, and with respect to the size of the largest cluster in the system including possible pure metal clusters. It turns out that depending on the composition of the complete system pure platinum clusters with sizes up to 10 to 15 atoms are formed in addition to binary clusters. Due to the high temperature of these clusters iron atoms less likely condense at the beginning of the particle formation simulation. This leads to temporary difference in the temperatures of the platinum and the iron subsystems, which eventually approach each other when only binary clusters are present. In summary, the results obtained from the cluster statistics show that pure platinum nucleation and growth can take place to some extent within the binary system.     

Molecular dynamics simulation of the vapour → liquid transition of argon and the reaction coordinate of condensation

We have investigated the n-dependences of the rate constants of absorption and emission of monomers that are attached to and detached from the cluster of n monomers, and have determined n*, the number of monomers that form the critical nucleus of the homogeneous condensation of the Lennard-Jones?Ar vapour. The dynamics was clearly separated into two regions at the critical nucleus; n* did not, however, give the unique dividing point. The observed strong dependences of both the nucleus size and the barrier height of the nucleation on the induction time of the condensation suggest that a slowly changing variable instead of the cluster size is necessary as the reaction coordinate of the nucleation. Although the slow variable is not well characterised at the present stage of the investigation, it seems to be related to the local density of the gas atoms around the liquid-like clusters. Both the slow evolution of the radial distribution function of the gas atoms around the liquid-like atoms, and the correlation between n* and the onset of the condensation indicate that Gibbs energy curves represented in n-space change significantly with the activation of the slow variable.     

Homogeneous and heterogeneous clustering in the accretion regime

Condensation of nano-droplets in a supersaturating vapor decomposes in two steps: the formation of a nucleation center, also called critical nuclei or nucleation seed, and the growth sequence, by accretion of further atoms on the nucleation center. These two steps have been investigated separately through the clustering of homogeneous particles Na_n and heterogeneous particles Na_nX in a helium buffer gas (X = (Na₂O)₂ or (NaOH)₂). The growth sequence is analyzed with preformed molecules X injected in a supersaturating sodium vapor and driving production of Na_nX clusters. Cluster distribution mean sizes are controlled by sodium concentration and by the condensation cell effective length. The signal intensities observed for homogeneous and heterogeneous clusters are proportional to the homogeneous and heterogeneous nucleation center numbers respectively. We can measure the efficiency for the homogeneous nucleation center production versus sodium concentration. This process is the onset of the condensation phase transition.     

Quantitative characterization of critical nanoclusters nucleated on large single molecules

First order phase transitions involve nucleation, formation of nanoscale regions of a new phase within a metastable parent phase. Using the heterogeneous nucleation theorem we show how clusters formed by nucleation on single molecules evolve from the gas phase and determine the critical size beyond which condensation starts to form aerosol particles. Our experiments reveal the activation of molecules into droplets to happen via formation of critical clusters substantially larger than the seed molecule. The nanosized critical clusters were found to be well predicted by the Kelvin-Thomson relation pointing directly to the key step in the phase transition.     

The determination of the integrated condensation coefficient of gold on NaCl cleavage faces by Rutherford ion backscattering

The Rutherford backscattering technique has been applied for the absolute determination of the integrated condensation coefficient of gold on rocksalt cleavage faces. By this method the number of deposited atoms down to an average thickness of $\text{1}\text{100}$ monolayer can be measured. The experimental results at different substrate temperatures and times have been compared with sticking coefficients which are calculated from the nucleation and growth theory of thin films. The contact angle of the microscopic clusters of the deposit on the substrate has been determined from the number of deposited atoms, measured by ion backscattering, and the cluster distribution, measured by electronmicroscopy.     

A new theory of the solid-state growth of embryos during nucleation: the fundamental role of interfacial mobility

One of the major challenges in nucleation theory is to explain the kinetic pathway allowing multicomponent precipitates to grow until they reach stability. This problem is particularly challenging when the supersaturation is low, so that the critical size of nucleation is large and requires the condensation of thousands of atoms. A new theory is proposed to explain the growth of embryos before they reach the critical size of nucleation. This theory is not a substitute of the classical nucleation theory, but a complement aiming to understand the kinetic pathway allowing unstable embryos to grow at the expense of their neighbours. The theory stands on the strong interactions between embryos. The latter may exchange atoms via impingement and coarsening, which are possible when there are no concentration gradients between the embryos. This condition is supposed to be met during the unstable growth regime of nucleation considering that the growth is limited by the interface during that period. Assuming that the embryos behave in a collective manner when they are grouped in a cloud, we show that the growth velocity of the most active embryos will be limited only by their interfacial mobility and the available driving force.     

Adaptive clustering of a quantum solvent: the LiH+ cation in bosonic helium from stochastic calculations

Calculations of the quantum structures describing the initial solvation shells of bosonic helium atoms around a polar, ionic system like LiH⁺ are reported, together with the corresponding quantum energies. The calculations were carried out using the Diffusion Monte Carlo (DMC) approach and parametric trial functions. Its final radial and angular distributions for clusters of varying size are analysed and discussed. The solvation of this ionic dopant is shown to occur in a way which is strongly affected by the orientational induction forces between the latter molecule and the solvent atoms, indicating the onset of “snowball" structures at the location of the dopant and the clear distinction between “heliophilic" and “heliophobic" regions of microsolvation.     

The energetics of large Lennard-Jones clusters: transition to the hexagonal close-packed structure

The energetics of large multiply twined particles (MTPs) such as decahedra with fivefold symmetry, face-centred cubic (fcc) and hexagonal close-packed (hcp) clusters in size from 2000 to ~45000 atoms was numerically analysed. Clusters were relaxed freely under the Lennard-Jones pair potential to the energy minimum. The essential extension of size compared to previous studies and the additional shape-optimisation of hcp and fcc clusters as well as truncated decahedra appears to be of high importance in the potential energy analysis. The best-optimised decahedra were confirmed to be the most favourable structure from 2000 to ~10⁵ atoms. Only in the short size interval, above N ∼10000 atoms, the best-optimised fcc clusters and simplest Marks' decahedra could alternate, while above N ∼14000 atoms does the shape-optimised hcp structure be proved to become more favourable for single crystal particles compared to the best-optimised fcc structure. Depending on shapes and sizes, decahedra and hcp clusters can alternate in the wide size interval above N ∼ 14000 atoms and presumably form the mixed abundances of clusters belonging to the both symmetries. Finally, the upper limit for stable MTPs was estimated to be about N ∼10⁵ atoms, while above only the hcp clusters are the most favourable.     

Nucleation on substrates from the vapour phase

Recent developments in the theory of nucleation of vapour deposits on crystalline substrates are reviewed. To facilitate comparison, the theories are formulated in a common dimensionless notation, and an examination of the major underlying assumptions reveals the basic similarity of many of them. The capture and dissociation rates are expressed in terms of the cluster geometry and the pertinent energy parameters, and from these the ‘chemical’ rate equations are set up. The following types of approximate solutions are discussed: (a) long-time asymptotic solutions, from which the conditions for saturation in the cluster concentration may be deduced, (b) a generalization of the type of approximate solution used by Logan (1969), and (c) numerical solutions employing a minimum number of simplifying assumptions. Based on a simple model, agreement between the latter two seems reasonably good. For any given set of fixed parameters (energies, geometrical constants, and arrival rate from the vapour) several temperature ranges may be distinguished. The main division is between ‘initially complete condensation’ at low temperatures and ‘initially incomplete condensation’ at high temperatures. Within each of the latter cases there are further transitions (a) between different values of the ‘critical size’ i*, and (b) from negligible growth to rapid growth of the supercritical clusters. The influence of all of these factors on the final cluster concentration is described.

The distributions of the clusters in size and spacing are discussed briefly and qualitatively, as are the types of effects that can be induced by defects or other ‘special sites’ on the substrate.

Comparisons are made with some recent experimental studies. In many of these, defects in the substrate seem to play a dominant role, and no detailed comparison with theory seems possible. One notable exception is the nucleation of rare gas crystals on graphite substrates (Venables and Ball 1970), and here, for at least two of the three gases studied, excellent quantitative agreement is obtained.     

Non-equilibrium agglomeration of helium-vacancy clusters in irradiated materials

Abstract

Time evolution of non-equilibrium systems, where the probability density is described by a continuum Fokker-Planck (F-P) equation, is a central area of interest in stochastic processes. In this paper, a numerical solution of a two-dimensional (2-D) F-P equation describing the growth of helium-vacancy clusters (HeVCs) in metals under irradiation is given. First, nucleation rates and regions of stability of HeVCs in the appropriate phase space for fission and fusion devices are established. This is accomplished by solving a detailed set of cluster kinetic rate equations. A nodal line analysis is used to map spontaneous and stochastic nucleation regimes in the helium-vacancy (h-v) phase space. Growth trajectories of HeVCs are then used to evaluate the average HeVC size and helium content during the growth phase of HeVCs in typical growth instability regions.

The growth phase of HeVCs is modeled by a continuum 2-D, time-dependent F-P equation. Growth trajectories are used to define a finite solution space in the h-v phase space. A highly efficient dynamic remeshing scheme is developed to solve the F-P equation. As a demonstration, typical HFIR irradiation conditions are chosen. Good agreement between the computed size distributions and those measured experimentally are obtained.     

Study of luminescence and optical resonances in Sb2O3 micro- and nanotriangles

Bimetallic clusters display new characteristics that could not be obtained by varying either the size of pure metallic systems or the composition of bulk bimetals alone. Coating of pre-deposited clusters by vapour deposition is a typical synthesis process of bimetallic clusters. Here, we have demonstrated that hierarchical, gold cluster-decorated copper clusters as well as both heterogeneous and homogeneous Cu?CAu bimetallic clusters (4.6 to 10.7?nm) can be prepared by coating pre-deposited, size-selected Cu₅₀₀₀ (4.6?±?0.2?nm) with Au evaporation at various temperatures. These bimetallic clusters were analyzed by aberration-corrected scanning transmission electron microscopy and associated electron energy loss spectroscopy. The results indicate that the growth of bimetallic clusters is controlled by a competition between nucleation and diffusion of the coating Au atoms.     

Kinetics and energy states of nanoclusters in the initial stage of homogeneous condensation at high supersaturation degrees

The condensation of metal vapor in an inert gas is studied by the molecular dynamics method. Two condensation regimes are investigated: with maintenance of partial pressure of the metal vapor and with a fixed number of metal atoms in the system. The main focus is the study of the cluster energy distribution over the degrees of freedom and mechanisms of the establishment of thermal equilibrium. It is shown that the internal temperature of a cluster considerably exceeds the buffer gas temperature and the thermal balance is established for a time considerably exceeding the nucleation time. It is found that, when the metal vapor concentration exceeds 0.1 of the argon concentration, the growth of clusters with the highest possible internal energy occurs, the condensation rate being determined only by the rate of heat removal from clusters.     

The structure of 55-atom Cu–Au bimetallic clusters: Monte Carlo study

We have investigated segregation phenomena in Cu–Au bimetallic clusters with decahedral structures at 100 K and 300 K, based on the second-moment approximation of the tight-binding (TB-SMA) potentials by using Monte Carlo method. The simulation results indicate that there are three regions (split, three-shell onion-like and core-shell region) at 100 K and two regions (split and core-shell) at 300 K with the structure of decahedral clusters, as the chemical potential difference Δμ changes. It is found that the structure of decahedral clusters undergoes a division into smaller clusters in the split region. In the core-shell structure, Au atoms are enriched in surface and Cu atoms occupy the core of the clusters because of the different surface energy of Cu and Au. The Au atoms are enriched in the surface shell, and the Cu atoms are in the middle shell, while a single Au atom is located in the center to form the three-shell onion-like structure. The structure and binding energy of smaller clusters after splitting are also discussed. The Au atoms generally lie on the surface of the smaller clusters after splitting.     

Growth of Au clusters on amorphous Al2O3: evidence of cluster mobility above a critical size

We study the 3D growth of clusters during the deposition of Au atoms on amorphous Al2O3. By comparing transmission electron microscopy images of the growth with Monte Carlo simulations, we show that nucleation takes place on substrate defects, but that further stages of growth imply that clusters leave the defects after they have reached a given critical size, and diffuse. An interesting consequence of this property is that, in contrast to intuition, and in a certain range of size, larger clusters are more mobile than smaller ones in this system.     

Silicon monoxide clusters: the favorable precursors for forming silicon nanostructures

Using density-functional calculations, we show that the energetically favorable configurations of silicon monoxide clusters (SiO)n for n> or =5 facilitate the nucleation and growth of silicon nanostructures as the clusters contain sp3 silicon cores surrounded by silicon oxide sheaths. The frontier orbitals of (SiO)n clusters are localized to a significant degree on the silicon atoms on the surface, providing high reactivity for further stacking with other clusters. The oxygen atoms in the formed larger clusters prefer to migrate from the centers to the exterior surfaces, leading to the growth of sp3 silicon cores.     

Primary nucleation processes in binary oxide growth: The case of MgO

The smallest forms of stoichiometric and non-stoichiometric MgO clusters appearing on the MgO(0 0 1) surface during the growth under atomic and/or molecular deposition are investigated from first-principles and empiric potentials. The basic entities (MgO molecule and (MgO)₂ cluster) result from a very exoenergetic and spontaneous redox reaction that involves directly the deposited species (Mg and O atoms, O₂ molecule). The stoichiometric clusters, resulting from the agglomeration of MgO molecules, are very stable under non-polar forms. Their formation energy is modelized, down to very small sizes, within an independent defect model. We point out the specificity of such clusters in the framework of the classical nucleation theory. The high-energy polar isomers are associated to destabilizing macroscopic electric fields and dipoles. These forms may nevertheless be strongly stabilized by incorporating extra Mg adatoms that give part of their valence shell to the cluster and decrease the total dipole in this way, illustrating the delicate coupling between chemistry and electrostatics in growth processes of oxides. Based on these considerations, we propose a scenario describing MgO growth both in the step-flow and in the nucleation regime.     

Size controlled deposition of Cu and Si nano-clusters by an ultra-high vacuum sputtering gas aggregation technique

In this paper we have reported the syntheses of copper and silicon nano-clusters by a sputtering-gas-aggregation type growth technique. The process involves typical magnetron sputtering vaporization of target materials followed by an inert gas condensation to form clusters of varying sizes. The size-distributions of the clusters typically follow a normal-distribution and the peak cluster sizes of the distributions depends on several factors, which include gas-flow rate, length of the growth region, deposition pressure etc. We have observed a variation in the peak cluster size with the variation of the gas (argon) flow rates. The experimental values are compared with the existing models and the results are found to be in good agreement. The results are significant since it demonstrates that proper optimization of operation conditions can lead to desired cluster sizes as well as desired cluster-size distributions. PACS 81.07.-b; 61.46.Bc; 39.10.+j; 81.20.-n; 36.40.-c     

Tuning the microstructure of pulsed laser deposited polymer–metal nanocomposites

Pulsed laser deposition was used to grow complex polymer–metal nanocomposites consisting of Ag, Cu and Nb clusters embedded in a poly(methyl-methacrylate) (PMMA) matrix. During deposition at room temperature, the size and amount of the metal clusters can be tuned in different ways. First, it is controlled by the number of laser pulses hitting the respective targets. In the case of Ag, a bimodal size distribution of the clusters is observed, induced by total coalescence and secondary nucleation processes. For Cu and Nb, much smaller clusters and higher cluster densities are obtained due to a stronger reactivity with the polymer and thus a lower diffusivity in the PMMA. Additionally, the microstructure of the Ag clusters is affected by the degree of cross linking of the polymer and can be influenced by pre-deposition of nucleation seeds in the form of small Cu clusters. PACS 68.55.-a; 81.15.Fg; 82.35.Np     

The kinetics of homogeneous nucleation of silver nanoparticles stabilized by polymers

The formation of Ag nanoparticles synthesized by homogeneous nucleation, stabilized by polymers (PVA and PVP) was monitored by UV–Vis spectrophotometry and transmission electron microscopy. Our aim was to differentiate between the two main phases of particle formation, i.e. nucleation and growth and to characterize their rates with the help of appropriate kinetic equations. Time resolved spectrophotometric measurements revealed that particle formation is an autocatalytic process: a slow, continuous nucleation phase (3–5 min) is followed by a rapid, autocatalytic growth phase where the maximal particle size is 5–7 nm. By freezing the reaction mixture, the process of particle growth can be followed from 5 to 40 min on TEM pictures. The first order rate constants were calculated and they are strongly depend on the polymer concentration. If the growing particles are attached by PEI to the surface of a solid support, the formation of silver nanoparticles can also be followed by atomic force microscopy (AFM) and we can control the particle growth on mica surface. The cross section analysis of the pictures show, that the particle growing process can be also monitored at solid–liquid interface.     

Helium implanted CuHf as studied by TDPAC and positron lifetime measurements

¹⁸¹Ta time differential perturbed angular correlation (TDPAC) and positron lifetime measurements were carried out on homogeneously α-implanted CuHf samples. TDPAC measurements indicate the trapping of vacancy clusters and helium associated defect complexes by Hf atoms. The presence of helium-vacancy complexes and helium stabilised voids has been identified by positron lifetime measurements. Further the nucleation and growth stages of helium bubbles have been identified. TDPAC and positron lifetime measurements indicate that Hf atoms act as heterogeneous nucleating centers for helium bubbles. Hf atoms are found to suppress the bubble growth in CuHf as indicated by the results of positron lifetime measurements.