Formation Energies Of Clusters Research Articles

Formation and Redispersion of Silver Clusters in Ag-MFI Zeolite as Investigated by Time-Resolved QXAFS and UV−Vis

Dynamic structural changes of Ag in Ag-MFI upon H2 reduction and subsequent reoxidation treatments were investigated by various characterization methods. Results of in situ time-resolved spectroscopies, UV−vis and quick XAFS, at 573 K show that Ag+ ions at a cation-exchange site of preoxidized Ag-MFI are reduced by H2 to a Ag4δ+ cluster. Protons on the zeolite (Bronsted acid sites) are also produced by the H2 reduction of Ag-MFI as evidenced by IR measurements after D2 adsorption. At higher reduction temperatures, the aggregation of Ag4δ+ clusters results in the formation of larger Agn (n > 8) clusters, and Ag metal particles appear on the external surface of the zeolite. Upon reoxidation at 573 K, the silver clusters are redispersed to Ag+ ions. The rate constant of cluster redispersion at 573 K depends on the oxidants used and increases in the order of NO(0.1%) + O2(10%) > O2(10%) > NO(0.1%). The activation energy for cluster formation in H2 was lower than that for cluster redispersion during reoxidatio...

Simulation of Vacancy Cluster Formation and Binding Energies in Single Crystal Germanium

AbstractResults are presented of the simulation of the properties of vacancy clusters in single crystal germanium. Classical molecular dynamics calculations based on a Stillinger and Weber potential were used in a theoretical investigation of different growth patterns of vacancy clusters Vi. The formation and binding energies of vacancy clusters have been studied in the range 1 ≤ i ≤ 35. The energetically favourable growth mode and an estimate of the effective surface energy was determined for a vacancy clusters containing up to 35 vacancies

Dissolution kinetics of nanodispersed γ-alumina in aqueous solution at different pH: Unusual kinetic size effect and formation of a new phase

The dissolution of a technical, nanodispersed γ-alumina in water was studied at 25 °C in the pH range 3.0 ⩽ pH ⩽ 11.0 . The obtained kinetic dissolution curves showed a distinct pH dependency, whereas only for pH ⩾ 4.5 the typical behavior of nanodispersed materials could be observed. X-ray powder diffraction analysis and nitrogen adsorption, as well as IR and UV-Raman spectroscopy, were used to characterize the solid material collected during and at the end of each dissolution experiment. As a result the formation of a new aluminum phase—bayerite—could be proven. The analysis of the equilibrium concentration enabled us to determine the solubility constant of the corresponding phase assuming a pH-dependent species distribution. The rate constants of the dissolution process were evaluated using the model of Gibbs free energy of cluster formation, which considers the size effect, among other things. As a result, we could show that the observed maxima in the concentration profiles are due to a size effect of the starting material having a primary particle radius of 10.1 nm.

Theoretical Study of the Electronic Structure and Stability of Titanium Dioxide Clusters (TiO2)n with n = 1−9

The electronic structure and the stability of both neutral and singly charged (TiO2)n clusters with n = 1-9 have been investigated using the density functional B3LYP/LANL2DZ method. The lowest-lying singlet clusters tend to form some compact structures with one or two terminal Ti-O bonds, which are about 1.4-2.5 eV more stable than the corresponding triplet structures. For the lowest-lying structures, strong infrared absorption lines at 988-1020 cm(-1) due to terminal Ti-O bonds and below 930 cm(-1) due to Ti-O-Ti bridging bonds may be observed, with some characteristic lines at 530-760 cm(-1) due to 3-fold coordinated O-atoms that are comparable with the spectra of rutile and anatase bulk. The holes and excited electrons within triplet structures tend to be localized on the least coordinated O- and Ti-atoms, respectively, with some exceptions possibly due to the electron-hole interaction. The extra electrons within (TiO2)n- clusters and the holes within (TiO2)n+ clusters show a clearer preference of location on the least coordinated Ti- and O-atoms, respectively. For the lowest-lying (TiO2)n clusters, the cluster formation energy per TiO2 unit and the electron affinity tend to increase whereas the ionization potential tends to decrease with the cluster size n. On the other hand, the singlet-triplet and HOMO-LUMO gaps represent the lower and upper limits of the TiO2 bulk band gaps, respectively. The theoretical results agree well with the available experimental data and may be helpful for understanding the chemistry of small (TiO2)n clusters.

Calculation of helium defect clustering properties in iron using a multi-scale approach

Electronic structure calculations were used to study the relaxation, formation and binding energies of small helium clusters in iron. We considered three He defect configurations: two He atoms in an interstitial position and two and three He atoms located in one vacancy. To study He–vacancy clusters containing more He atoms, we used a multi-scale approach and constructed an empirical potential fitted to both formation and relaxation energies of a single He defect and small He clusters obtained from the first principles calculations. The potential consists of a repulsive pair-interaction part and a many-body attractive term describing the cohesion. The potential was used to study stability of He–vacancy clusters at zero temperature. The binding energy of a He atom to a He-cluster varies from 1.3 eV to 1.9 eV depending on the cluster size. When more than six He atoms are placed into a vacancy an Fe self-interstitial atom (SIA) is produced. The SIA binding energy to a He–di-vacancy cluster decreases from 5.0 eV to 0.7 eV as the number of He atoms increases. The results obtained are consistent with experimental observations of helium desorption reported in the literature.

A relation between the vacancy concentration and hydrogen concentration in the Ni–H, Co–H and Pd–H systems

The formation of superabundant vacancies (Vac-H clusters) has been observed in many M–H alloys, but the factors that determine the equilibrium concentration of vacancies have not been identified yet. To identify these factors, the equilibrium concentration of vacancies was estimated from lattice contraction measurements on Ni, Co and Pd having a fcc structure, at high temperatures (930–1350 K) and high hydrogen pressures (2.4–7.4 GPa). The results show that the vacancy concentration is not so much dependent on temperature and hydrogen pressure as the hydrogen concentration. In Ni and Co, the vacancy concentration ( x cl ) increases linearly with the hydrogen concentration ( x H ) for the whole concentration range, reaching x cl ∼ 0.3 at x H ∼ 1.0 . In Pd, the vacancy concentration is very small up to x H ∼ 0.6 and increases linearly thereafter with nearly the same slope as in Ni and Co. The maximum vacancy concentration reached in Pd is x cl ∼ 0.12 . It is noted that the observed difference in the x H – x cl relation correlates with the magnitude of the formation energy of Vac-H clusters, which is very small in Ni and Co and relatively large in Pd.

Hydrogen-Promoted Grain Boundary Embrittlement and Vacancy Activity in Metals: Insights from <I>Ab Initio</I> Total Energy Calculatons

The rapid diffusion of H in metals permits an easy segregation to the grain boundary and an easy trapping to the vacancy. H-induced intergranular embrittlement in metals such as Fe and Ni is generally a result of coalition of segregated H and other embrittling impurities at the grain boundary. Ah initio total energy calculations based on the density functional theory have shown that H alone can also weaken the cohesion across the grain boundary. The stronger binding of H with a free surface than with a grain boundary, which results in grain boundary embrittlement according to the Rice--Wang theory, can be ascribed to its monovalency. New tensile experiments point to a H-enhanced vacancy contribution to the increased susceptibility of steel to H embrittlement. Ah initio density functional calculations on the energetics of interstitial H, vacancy, and H-monovacancy complexes (VacHn) in bcc Fe have shown that the predominant complex under ambient condition of H pressure is vacH 2 , not vacH 6 , as previously'suggested by effective-medium theory calculations. The linear structure of VacH 2 clusters, a consequence of repulsion between negatively charged H atoms, facilitates the formation of linear and tabular vacancy clusters and such anisotropic clusters may lead to void or crack nucleation on the cleavage planes. On the other hand, the H-induced increase of vacancy cluster formation energy is a support of the experimentally observed enhancement of dislocation mobility in the presence of H, which, through the mechanism of H-enhanced localized plasticity, makes fracture easier.

Scaling of the Nucleation Rate and a Monte Carlo Discrete Sum Approach to Water Cluster Free Energies of Formation

The intent of this work is to examine small cluster discrete size effects and their effect on the free energy of cluster formation. There is evidence that such terms can cancel in part the temperature dependence of the monomer flux factor of the classical nucleation rate and result in a scaled form for the nucleation rate. In this work, Monte Carlo configurational free energy differences between neighboring sized n molecule TIP4P water clusters are calculated and used in a Monte Carlo discrete summation (MCDS) technique to generate steady-state nucleation rates. The free energy differences, when plotted versus n-1/3, show evidence of a bulklike effective surface tension for n ≥ 10, and for the range of T examined the free energy differences appear to scale in temperature like (Tc/T − 1). This scaling can provide estimates of nucleation rates for arbitrary temperatures within the range of T simulated. Nucleation rates generated from the model TIP4P free energy differences are compared with the experimental water nucleation rate data of Wölk and Strey (J. Chem. Phys. 2001, 105, 11683) and with the data of Miller et al. (J. Chem. Phys. 1983, 78, 3204). The TIP4P MCDS results provide some evidence of the cancellation effect and generate the scaling of the nucleation rate data at higher temperatures. The magnitudes of the nucleation rates are, however, too large by a factor of 104. Other discrete sum models are also presented and give similar results.

Dissolution Kinetics of Synthetic Amorphous Silica in Biological-Like Media and Its Theoretical Description

Different types of synthetic amorphous silica have been dissolved under biological-like conditions in a buffer system. The buffer solution named TRIS buffer provides a system with comparable pH value, buffer capacity, and osmotic pressure as it can be found in extracellular fluid. Additionally, the phospholipid l-α-dipalmitoylphosphatidylcholine (DPPC) has been used in several dissolution experiments to simulate conditions which are found in extracellular lung fluid. The molybdic acid method (used as standard procedure) and partly ICP−OES have been applied to determine the total amount of silica dissolved. The dissolution of nanodisperse silica shows a strong size effect, which leads to a significant higher silica concentration when compared with the bulk phase. At longer dissolution time a slight decrease of solubility can be observed. The Gibbs free energy of cluster formation is calculated numerically for the dissolution process to predict the temporal development of silica concentration. Theoretical curves are adapted by nonlinear regression of a free parameter. This parameter can be understood as the rate constant of the dissolution process.

Ab initiostructural and electronic properties of hydrogenated silicon nanoclusters in the ground and excited state

Electronic and structural properties of small hydrogenated silicon nanoclusters as a function of dimension are calculated from ab initio technique. The effects induced by the creation of an electron-hole pair are discussed in detail, showing the strong interplay between the structural and optical properties of the system. The distortion induced on the structure after an electronic excitation of the cluster is analyzed together with the role of the symmetry constraint during the relaxation. We point out how the overall effect is that of significantly changing the electronic spectrum if no symmetry constraint is imposed to the system. Such distortion can account for the Stokes shift and provides a possible structural model to be linked to the four-level scheme invoked in the literature to explain recent results for the optical gain in silicon nanoclusters. Finally, formation energies for clusters with increasing dimension are calculated and their relative stability discussed.

Thermal stability of helium–vacancy clusters in iron

Molecular dynamics calculations were performed to evaluate the thermal stability of helium–vacancy clusters (He n V m ) in Fe using the Ackland Finnis–Sinclair potential, the Wilson–Johnson potential and the Ziegler–Biersack–Littmark–Beck potential for describing the interactions of Fe–Fe, Fe–He and He–He, respectively. Both the calculated numbers of helium atoms, n, and vacancies, m, in clusters ranged from 0 to 20. The binding energies of an interstitial helium atom, an isolated vacancy and a self-interstitial iron atom to a helium–vacancy cluster were obtained from the calculated formation energies of clusters. All the binding energies do not depend much on cluster size, but they primarily depend on the helium-to-vacancy ratio ( n/ m) of clusters. The binding energy of a vacancy to a helium–vacancy cluster increases with the ratio, showing that helium increases cluster lifetime by dramatically reducing thermal vacancy emission. On the other hand, both the binding energies of a helium atom and an iron atom to a helium–vacancy cluster decrease with increasing the ratio, indicating that thermal emission of self-interstitial atoms (SIAs) (i.e. Frenkel-pair production), as well as thermal helium emission, may take place from the cluster of higher helium-to-vacancy ratios. The thermal stability of clusters is decided by the competitive processes among thermal emission of vacancies, SIAs and helium, depending on the helium-to-vacancy ratio of clusters. The calculated thermal stability of clusters is consistent with the experimental observations of thermal helium desorption from α-Fe during post-He-implantation annealing.

High-spin electronic interaction of small lithium and sodium cluster formation in the excited states

We have carried out the MRCI ab initio calculations for small lithium and sodium clusters, and elucidate the interaction between atoms in various high-spin electronic states, in terms of the quantum mechanical energy densities based on the regional density functional theory [Tachibana, J. Chem. Phys. 115, 3497 (2001)]. When the separated two electronic drop regions, where the electronic kinetic-energy density is positive, connect to each other, it is observed that ratios of occupation on configurations change rapidly in the Li2 molecule. These results are considered as one of the evidences that valence electrons can move around both two Li atoms freely in the meaning of classical mechanics. The shape of electronic drop region depends strongly on the electronic state and represents the characteristics of interaction clearly, and the electronic tension density also gives new images of microscopic electronic stresses. Furthermore, we have clarified the most stable structures of Li3 and Li4 for the high-spin electronic state, which are respectively different from the most stable structures for the low-spin electronic state. The stabilization energy due to taking in a Li atom is raised gradually as the number of atoms in Lin cluster increases in the initial stage of cluster propagation. The formation energies of Na2, Na3, and Na4 clusters are much smaller than that of the corresponding lithium clusters.

Calculation of the Gibbs Energy of the Reaction OH-·(H2O)n-1 + H2O = OH-·(H2O)n by the Monte-Carlo Method

The energy, the Gibbs energy of the reaction OH-·(H2O) n- 1 + H2O = OH-·(H2O) n are calculated by the Monte-Carlo method with a large canonical ensemble for n = 1, ..., 20. The ion-waternonpair interaction potential was obtained by numerical fitting of calculated Gibbs energy and entropy of (H2O)n clusters (n = 1, ..., 5) to experimental ones. A good fit to experiment both of the internal energy and the Gibbs energy can be obtained in terms of a model allowing for nonpair interaction. It is shown that constructing an ion-water interaction potential without allowance for the entropy factor can lead to considerable errors in the Gibbs energy of cluster formation and in the nucleation rate.

Vapor Phase Homogeneous Nucleation of Higher Alkanes: Dodecane, Hexadecane, and Octadecane. 2. Corresponding States and Scaling Law Analysis

The results from corresponding states and scaled nucleation models indicate that the nucleation behavior of the normal alkanes follows a predictable trend. Systematic deviations from ideal fluid behavior can be correlated to physical properties, such as the increase in the entropy of vaporization and the increase in the excess surface entropy of the nucleating clusters. Hale's scaled nucleation model allows for the accurate prediction of nucleation threshold behavior for the alkanes. Experimental agreement with the model is maintained throughout the temperature range studied. The scaled model for the nucleation rate provides a better description of the experimental rates than the classical nucleation theory. The addition of extra terms to the classical expression of the free energy of cluster formation and the inclusion of the Fisher's droplet model term significantly compensate for the strong temperature dependence present in the flux prefactor of the classical rate equation. For accurate predictions of ...

A New Kinetic Model for The Nucleation and Growth of Self-Interstitial Clusters in Silicon

ABSTRACTA model for nucleation and growth of {311} defects is proposed on the basis of thermodynamic and kinetic considerations. Simulated results are discussed and compared to experimental results found in the literature. According to our model it is found that formation energies of self-interstitial clusters depends on the local interstitial supersaturation. Physical parameters extracted from experimental results by inverse modeling are in good agreement with recent values published in the literature.

Molecular Mechanism of Vapor-Liquid Nucleation

Molecular dynamics simulations were executed to investigate the mechanism of nucleation in Lennard-Jones binary vapor. It is found that nucleation around an ion-like, or “seed” particle takes place at the supersaturation ratio which is too low to cause homogeneous nucleation. At lower supersaturation ratio, no clusters larger than a certain size (15 ∼ 20) appear around the seed. We also executed Monte Carlo simulations to estimate the free energy of cluster formation under the same conditions. The free energy curves estimated from Monte Carlo simulations are consistent with the results of the molecular dynamics simulations.

Dynamical nucleation theory: Calculation of condensation rate constants for small water clusters

In previous work we began the description of a molecular theory of homogeneous vapor-to-liquid nucleation based on the kinetics of cluster formation and decomposition. In this work we focused on a new theoretical approach to calculating rate constants for evaporation of molecules from clusters. In the present work, we present a molecular theory for calculating condensation rate constants that are consistent with the evaporation rate constants. The new method, which uses variational transition state theory (VTST), provides an expression for the evaporation rate constant that is proportional to the derivative of the Helmholtz free energy for cluster formation with respect to the radius of the spherical volume constraining the cluster. Furthermore, the theory provides a physically justified procedure for selecting a unique value of the radius of the spherical volume for each i-molecule cluster. Since VTST obeys detailed balance, condensation rate constants can be obtained from the evaporation rate constants and the corresponding equilibrium constants. In the present work, we provide a theoretical approach to obtain the equilibrium constants that are consistent with the evaporation rate constants. Monte Carlo methods are presented for calculating the dependence of the Helmholtz free energy of cluster formation on the radius of the constraining volume, which are needed for the evaporation rate constants. In addition, Monte Carlo methods are presented for calculating the relative differences in Helmholtz free energies for clusters of different sizes, which are needed for the equilibrium constants and condensation rate constants. The volume dependent Helmholtz free energies for the water dimer up to the decamer are calculated at 243 K.

Energetics of Self-Interstitial Clusters in Si

The transient supersaturation in a system undergoing Ostwald ripening is related to the cluster formation energy ${E}_{\mathrm{fc}}$ as a function of cluster size $n$. We use this relation to study the energetics of self-interstitial clusters in Si. Measurements of transient enhanced diffusion of B in Si-implanted Si are used to determine $S(t)$, and inverse modeling is used to derive ${E}_{\mathrm{fc}}(n)$. For clusters with $n>15$, ${E}_{\mathrm{fc}}\ensuremath{\approx}0.8\mathrm{eV}$, close to the fault energy of ${113}$ defects. For clusters with $n<10$, ${E}_{\mathrm{fc}}$ is typically 0.5 eV higher, but stabler clusters exist at $n\ensuremath{\approx}4$ ( ${E}_{\mathrm{fc}}\ensuremath{\approx}1.0\mathrm{eV}$) and $n\ensuremath{\approx}8$ ( ${E}_{\mathrm{fc}}\ensuremath{\approx}0.6\mathrm{eV}$).

Study of the geometry of KCl clusters nucleating from vapour and in aqueous solutions

The molecular interaction model of cluster formation was used to compute the formation energy of KCl clusters having ions from 4 to ca 10000, taking into consideration repulsion forces between ions. Four types of cluster geometries were analysed: spherical, cube-shaped (perfect cubes or cuboids with steps on one of their {1 0 0} faces) and octahedral with {1 1 1} and {1 1 1} 2 faces. It was found that cube-shaped clusters forming from the vapour phase are always preferential (more abundant) due to Coulomb interactions. In aqueous solutions, the subcritical clusters, both spherical and cube-shaped, can be preferential. Larger KCl clusters should have the cubic geometry due to the small values of the average adsorption energy of water molecules on their surface. Spherical and octahedral {1 1 1} 2 clusters adsorb water molecules more strongly, which leads to their significantly lower growth.

Variational transition state theory of vapor phase nucleation

An expression for the rate of vapor phase nucleation is developed that is based on variational transition state theory. The method depends on a definition of a dividing surface in phase space that separates reactants from products. For this surface we choose a spherical shell in coordinate space that is centered about the center of mass of a cluster of i molecules having an interior volume v. In a manner that is consistent with variational transition state theory, we vary v to minimize the reactive flux through our chosen dividing surface. The resulting expression for the rate constant involves a definition of a physical cluster that is consistent with previous developments in nucleation theory. In formulating the rate in this manner we obtain a new expression for the evaporation rate constant that is proportional to the derivative with respect to v of the Helmholtz free energy for cluster formation. In addition, we have a fundamentally justified procedure for selecting a unique volume v for each i cluster. Application of the method to the nucleation of water clusters will be presented.