Melting Of Clusters Research Articles

Structure and melting of two-species charged clusters in a parabolic trap

We consider a system of charged particles interacting with an unscreened Coulomb repulsion in a two-dimensional parabolic confining trap. The static charge on a portion of the particles is twice as large as the charge on the remaining particles. The particles separate into a shell structure with those of greater charge situated farther from the center of the trap. As we vary the ratio of the number of particles of the two species, we find that for certain configurations, the symmetry of the arrangement of the inner cluster of singly charged particles matches the symmetry of the outer ring of doubly charged particles. These matching configurations have a higher melting temperature and a higher thermal threshold for intershell rotation between the species than the nonmatching configurations.

Hot and solid gallium clusters: too small to melt.

A novel multicollision induced dissociation scheme is employed to determine the energy content for mass-selected gallium cluster ions as a function of their temperature. Measurements were performed for Ga(+)(n) (n=17 39, and 40) over a 90-720 K temperature range. For Ga+39 and Ga+40 a broad maximum in the heat capacity-a signature of a melting transition for a small cluster-occurs at around 550 K. Thus small gallium clusters melt at substantially above the 302.9 K melting point of bulk gallium, in conflict with expectations that they will remain liquid to below 150 K. No melting transition is observed for Ga+17.

Adsorbate Effects on Structure and Shape of Supported Nanoclusters: A Molecular Dynamics Study

Classical molecular dynamics simulations are used to examine the effects of adsorption of inert-gas atoms (Ar, Xe, and He) at various pressures and temperatures on the shape, structure, and diffusion of a 256-atom platinum nanocluster supported on a graphite substrate. The many-body Sutton Chen potential is used to model the Pt−Pt interactions, and the Lennard-Jones potential is employed for the rest of the pair interactions. Gas adsorption on the metal cluster is monitored as a function of pressure at constant temperature, and the evolution of the structure is analyzed as the pressure is increased and then as the gas phase is gradually removed. It is found that the gas phase substantially alters the vacuum cluster structure, and the changes are mostly irreversible in the time frame of the simulations (2 ns), especially at temperatures well below the cluster melting point, where the low energy structures determined under high pressures are very stable. The dynamic properties are also modified by the gas phase; the cluster diffusion depends on the inert gas pressure, being lower at high gas pressures. Although the contact area cluster−substrate is significantly smaller compared to the vacuum case, the size mismatch is reduced because of the presence of the gas-adsorbed layer that forces the rearrangement of the metal atoms leading to distorted structures which favor the Pt−C interactions.

Finite Temperature Properties of (CO2)nClusters

The parallel-tempering Monte Carlo procedure is used to characterize the (CO2)n, n = 6, 8, 13, and 19, clusters. The heat capacity curves of the n = 13 and 19 clusters are found to have pronounced peaks that can be associated with cluster melting. In addition, there is evidence of a low temperature “solid ↔ solid” transition in the case of (CO2)19. The low-energy minima and rearrangement pathways are determined and used to examine the complexity of the potential energy surfaces of the clusters.

Effect of melting on ionization potential of sodium clusters

The effect of melting transition on the ionization potential has been studied for sodium clusters with 40, 55, 142, and 147 atoms, using ab initio and classical molecular dynamics. Classical and ab initio simulations were performed to determine the ionization potential of Na142 and Na147 for solid, partly melted, and liquid structures. The results reveal no correlation between the vertical ionization potential and the degree of surface disorder, melting, or the total energy of the cluster obtained with the ab initio method. However, in the case of 40 and 55 atom clusters, the ionization potential seems to decrease when the cluster melts.

Melting of 55-atom Morse clusters

Canonical ensemble Monte Carlo simulations of 55-atom Morse clusters are used to study the effect of the range of the pair interaction on the cluster melting transition. Several different structural indicators are employed to monitor the solid–liquid transition and to locate the melting and freezing temperatures. The behavior of Landau free energy curves in the solid–liquid phase coexistence regime is correlated with the distribution of inherent minima sampled by the system. The melting transition temperatures, the width of the phase coexistence regime, and the internal energy change on melting are shown to increase with decreasing range of the pair interaction, which parallels the behavior seen in bulk Morse systems. Unlike in the case of bulk melting, cluster melting falls into three distinct categories based on the range of the pair interaction: (i) a rigidity transition in long-range systems with a low density of metastable states, (ii) the cluster analogue of bulk melting where the system transits from the basin of an ordered global minima into a set of metastable, amorphous packing minima, and (iii) transition from a set of defected solid-like minima into a set of amorphous packing minima.

Melting of palladium clusters – density of states determination by Monte Carlo simulation

Abstract The density of states (DOS) has been calculated for the metal clusters Pd 13 , Pd 55 and Pd 147 using the recently proposed reference system equilibration (RSE) method. The interaction within the clusters was described by a many-body alloy potential. Using this DOS, the caloric curve of Pd 13 has been calculated and excellent agreement with canonical Monte Carlo simulations is obtained. For Pd 55 and Pd 147 , the solid and one molten isomers have been isolated in order to calculate the DOS for the isomers separately. The melting of the clusters occurs when the DOS for the solid and the molten isomers are equal. Comparison with previous microcanonical Monte Carlo simulations shows that the number of statistically equivalent molten isomers are 1.1×10 18 for Pd 55 and 4.1×10 41 for Pd 147 .

The effect of ions on solid–liquid phase transition in small water clusters. A molecular dynamics simulation study

Small water clusters, containing ions, have been studied using molecular dynamics simulations at temperatures ranging from 0 to 250 K. The simulations are carried out systematically by varying the ion size, shape, and charge as well as the cluster size and the initial configuration. Transitions between solid and liquid phases are followed to study the effects of the ions on the cluster melting temperature, compared to pure water clusters of the same size. The effect of the ion on the ice-cluster melting appears to be a complicated process which depends simultaneously on a variety of factors, such as the initial cluster configuration and the ion position inside the cluster as well as the ion mass, size and its charge. In the case of monovalent cations the most important characteristics for the cluster evolution is the ion mass, while for divalent cations the ion charge is the most dominant factor. In the case of negatively charged ions the main factor of the system evolution is the ion size. Two principally different types of cluster structures can be observed from the simulations: The peripheral structure where the ion takes up a position, preferably on the cluster surface and the interior structure where the ion prefers the center of the system. The peripheral structure is typical for clusters containing the small monovalent Li+ cation but also for those containing the large Cl− anion, while divalent cations, large monovalent Na+ cation and small F− anions gave rise to the interior type of structure. Generally, an increase of the ion size changes the cluster structure making the peripheral variant more preferable.

Influence of energy and entropy on the melting of sodium clusters.

Energetic and entropic influences on the melting temperatures of size selected sodium clusters are experimentally separated. It is shown that the energetic difference between solid and liquid is the leading influence for the still puzzling features in the size dependence of sodium melting points. Additionally, this energy difference decreases towards smaller cluster sizes and causes steplike melting phase transitions to vanish. The entropy difference between solid and liquid has been found to be strongly correlated with the energy and causes a pronounced damping of the energetic influences.

Topological defects and nonhomogeneous melting of large two-dimensional Coulomb clusters.

The configurational and melting properties of large two-dimensional (2D) clusters of charged classical particles interacting with each other via the Coulomb potential are investigated through the Monte Carlo simulation technique. The particles are confined by a harmonic potential. For a large number of particles in the cluster (N>150), the configuration is determined by two competing effects, namely, the fact that in the center a hexagonal lattice is formed, which is the groundstate for an infinite 2D system, and the confinement that imposes its circular symmetry on the outer edge. As a result, a hexagonal Wigner lattice is formed in the central area while at the border of the cluster the particles are arranged in rings. In the transition region defects appear as dislocations and disclinations at the six corners of the hexagonal-shaped inner domain. Many different arrangements and types of defects are possible as metastable configurations with a slightly higher energy. The particle motion is found to be strongly related to the topological structure. Our results clearly show that the melting of the clusters starts near the geometry induced defects, and that three different melting temperatures can be defined corresponding to the melting of different regions in the cluster.

Tight-binding molecular-dynamics study of melting behaviour of small silicon clu sters

The Tight_binding molecular_dynamics(TBMD) has been used to study the melting behaviour of small silicon clusters Sin（n=5—10）. We report the calcu lated res ults of the latent heat of fusion Δμls and the melting temperature Tm as a function of cluster size. Δμls and Tm exhibit a s trong dependen ce on cluster size. The melting mechanisms of silicon clusters are distinguished from metal clusters. The melting of metal clusters can be described as a tran sition from a low_energy solid_like structure at low temperatures to a higher_en ergy liquid_like structure at high temperatures. At the transition temperature, metal clusters undergo a dynamics coexistence of the two states, while the silic on clusters undergo an intermediate state which is neither liquid_like structure nor solid_like structure. The melting points obtained by using different calcul ation methods and definitions also have been compared in this work.

Melting of palladium clusters—Canonical and microcanonical Monte Carlo simulation

We present Monte Carlo simulations of single palladium clusters of 13, 34, 54, 55, 147 and 309 atoms. The clusters are modeled by a many-body potential and they have been simulated at constant temperature or constant total energy. The caloric curves of the clusters, with the exception of Pd34, exhibit an S-bend at melting which is typical for a finite system. We have also observed the typical coexistence region of solid and molten clusters both in the canonical and the microcanonical ensembles. Pd34, in contrast, melts without an accompanying peak in heat capacity and at melting the atoms become mobile without any significant change in geometric structure. For the larger clusters a free energy barrier inhibits phase switching. In some cases of phase change from molten to solid structure the barrier is of purely entropic character. By a conversion of the results in the microcanonical simulations into temperature-dependent data, the simulations at fixed temperature and fixed total energy have been compared. The agreement is in most cases good. The results are furthermore compared to earlier molecular dynamics simulations with the Nose–Hoover thermostat. These results are in good agreement with the Monte Carlo simulations as well.

Melting of Bimetallic Cu−Ni Nanoclusters

The thermal evolution of bimetallic Cu−Ni 343- and 1000-atom nanoclusters of compositions (Cu0.25Ni0.75) and (Cu0.5Ni0.5) is examined with molecular dynamics simulations using the Sutton-Chen many-body potential function. A heating curve is constructed starting from 0 K up to 1400 K, and the melting characteristics are determined on the basis of the variations of the potential energy and heat capacity with temperature. The shape evolution of the nanoclusters is analyzed in terms of deformation parameters. It is found that the bimetallic clusters melt in two stages. The first transition, corresponding to surface melting of the external Cu layers whereas the Ni core remains solid, is located at 400−500 K depending on the overall composition and cluster size. The second transition corresponds to homogeneous melting and takes place in the range of 700 to 900 K depending on the nanocluster size and composition. Thus, the melting temperature is much lower than those of bulk Cu and Ni, and the heat capacity shows a broader peak. At temperatures just before the melting transition, the heat capacity curves exhibit either a shoulder or an extra peak attached to the main melting transition peak; this is associated with isomerization structural transitions due to the diffusion of Cu atoms toward the cluster interior.

Solid–liquid phase diagram of the water octamer

By implementing the parallel-tempering algorithm to the isothermal–isobaric ensemble, the thermodynamic properties of (H 2O) 8 were determined. The constant pressure heat capacity, C p, as a function of temperature at various pressures was computed in order to identify the cluster melting temperature. The temperature at which C p reaches a maximum in the transition region was associated to the melting temperature of the cluster and used for the construction of the pressure–temperature phase diagram. The water octamer showed the usual solid–liquid transition with the melting temperature increasing as the pressure decreases, hence a negative slope in the solid–liquid line was obtained.

Submonolayer molecular hydrogen on graphite: A path-integral Monte Carlo study

We have used path-integral Monte Carlo (PIMC) to simulate molecular hydrogen on graphite at submonolayer coverage. First we use a flat substrate and we study the first layer for various values of the coverage up to layer completion. We found that the first layer has a solid-gas coexistence phase at low densities and a triangular solid phase at and above the equilibrium density ${\ensuremath{\rho}}_{0}=0.0705 {\AA{}}^{\ensuremath{-}2}.$ We also determine that the first layer promotion coverage is at $0.094 {\AA{}}^{\ensuremath{-}2}$ in agreement with experiment. Second we introduce the full ${\mathrm{H}}_{2}$-graphite interaction, i.e., we include the effects of substrate corrugations. In this case we carry our PIMC simulations on a variety of systems at and below the 1/3 coverage. We calculate the energy as a function of coverage, contour plots of the molecule probability distribution, the pair distribution function, the static structure function and the specific heat. When the substrate corrugation part of the interaction is included we find that at 1/3 coverage the system is in a $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ commensurate solid phase. At coverages below that and at low enough temperature the system exists in solid clusters surrounded by vapor. At coverages below a critical density, defining a tricrical point, as the system is heated up these clusters melt into a uniform fluid phase. We find that below the commensurate density and above the tricritical point, as the clusters are heated up, first they undergo a transition into a phase where the vapor phase disappears and a commensurate phase with vacancies arises. This commensurate solid melts at higher temperature into a uniform fluid phase.

Two-dimensional mesoscopic vortex clusters in a superconducting ring: Shell structure and melting

The structure and phase transitions in the mesoscopic system of vortices in a quasi-two-dimensional superconducting ring are investigated. The shell structure of the mesoscopic system of vortices is studied, and its variation with the number of vortices and the parameters of the superconducting ring is analyzed. Two mechanisms of formation of new shells in vortex clusters with an increasing number of vortices in an increasing magnetic field are discovered: the generation of a new shell in a cluster and the splitting of the internal shell into two shells. The melting of vortex clusters and their thermodynamic parameters are analyzed using the Monte Carlo method. It is found that the melting of shell-type clusters occurs in two stages, orientation melting taking place at the lower temperature (during which nearly crystalline adjacent shells start rotating relative to each other) and blurring of the vortex structure occurring at the higher temperature. The shells obtained by splitting upon an increase in the number of vortices do not participate in orientational melting. The two-stage form of melting is associated with the smaller height of potential barriers being surmounted during the rotation of shells relative to one another as compared to the barrier for vortices jumping from one shell to another.

Modeling chondrule melting using a resizing box_tree code

Current theories hold that chondrule formation results from the melting of clusters of relict grains in the protoplanetary nebula. Although it is possible to simulate the coagulation of dust particles in the protoplanetary nebula, the accuracy of such a simulation is dependent on the number of particles used. A larger number of particles yields a more accurate simulation, but comes at the expense of considerably longer CPU times. On the other hand, once the number of particles used by the simulation drops below a certain threshold, the model begins to lose relevance. box_tree is a program that divides the protoplanetary disk into self-similar patches or boxes. Boundary conditions on a box are imposed using twenty-six “ghost” boxes. box_tree utilizes tree code to deal with gravitational and electrostatic forces between particles within the ring. This paper introduces a scheme whereby the box_tree model can significantly enlarge its simulation parameters allowing for more realistic data generation.

Theoryof zeolite supralattices: Se in zeolite Linde type A

We study theoretically properties of Se clusters in zeolites, andchoose zeolite Linde type A (LTA) as a prototype system. Thegeometries of free-space Se clusters are first determined, and wereport the energetics and electronic and vibrational properties ofthese clusters. The work on clusters includes an investigation ofthe energetics of C3-C1 defect formation in Se rings andchains. The electronic properties of two Se crystalline polymorphs,trigonal Se and α-monoclinic Se, are also determined.Electronic and vibrational properties of the zeolite LTA areinvestigated. Next we investigate the electronic and opticalproperties of ring-like Se clusters inside the large α-cagesof LTA. We find that Se clusters inside cages of silaceous LTA havevery little interaction with the zeolite, and that the HOMO-LUMOgaps (HOMO standing for highest occupied molecular orbital and LUMOfor lowest unoccupied molecular orbital) are nearly those of theisolated cluster. The HOMO-LUMO gaps of Se6, Se8, andSe12 are found to be similar, which makes it difficult toidentify them experimentally by absorption spectroscopy. We findthat the zeolite/Se8 nanocomposite is lower in energy than thetwo separated systems. We also investigate two types of infinitechain encapsulated in LTA. Finally, we carry out finite-temperaturemolecular dynamics simulations for an encapsulated Se12cluster, which shows cluster melting and formation of nanoscale Sedroplets in the α-cages of LTA.

Thermal behavior of Cu–Co bimetallic clusters

Based on a Gupta-like many-body potential, we have investigated the thermal behavior of Co–Cu bimetallic clusters with n=18, 19, 20 by using Monte Carlo techniques. A relation between cluster melting temperature and Cu concentration is obtained. We find the melting behavior of a bimetallic cluster strongly depends on the component materials, stoichiometries, size and structure of the cluster. The structural transition between isomers or degenerated states happens in the 18-atom clusters. Local melting occurs in the Co 13Cu 5 cluster because of the segregation of Cu and a novel layered structure.

Melting of sodium clusters in the extended Thomas-Fermi approximation

We study the melting of small sodium clusters ${\mathrm{Na}}_{N}$ $(N=8,20,40)$ and ${\mathrm{Na}}_{N}^{+}$ $(N=53\ensuremath{-}57,93,139,147)$ using an ab initio treatment of valence electrons within the extended Thomas-Fermi approximation. The ionic entropy and specific heats are extracted using a multiple-histogram analysis. The smaller clusters show multi-process melting, while the larger clusters favor predominantly single-process melting. We find a pronounced maximum in the melting point around $N=55.$