Mesoscopic and macroscopic dipole clusters: Structure and phase transitions

A two dimensional (2D) classical system of dipole particles confined by a quadratic potential is studied. This system can be used as a model for rare electrons in semiconductor structures near a metal electrode, indirect excitons in coupled quantum dots etc. For clusters of N ≤ 80 particles ground state configurations and appropriate eigenfrequencies and eigenvectors for the normal modes are found. Monte-Carlo and molecular dynamic methods are used to study the order-disorder transition (the “melting” of clusters). In mesoscopic clusters (N < 37) there is a hierarchy of transitions: at lower temperatures an intershell orientational disordering of pairs of shells takes place; at higher temperatures the intershell diffusion sets in and the shell structure disappears. In “macroscopic” clusters (N > 37) an orientational “melting” of only the outer shell is possible. The most stable clusters (having both maximal lowest nonzero eigenfrequencies and maximal temperatures of total melting) are those of completed crystal shells which are concentric groups of nodes of 2D hexagonal lattice with a number of nodes placed in the center of them. The picture of disordering in clusters is compared with that in an infinite 2D dipole system. The study of the radial diffusion constant, the structure factor, the local minima distribution and other quantities shows that the melting temperature is a nonmonotonic function of the number of particles in the system. The dynamical equilibrium between “solid-like” and “orientationally disordered” forms of clusters is considered.     

Structure, melting, and potential barriers in mesoscopic clusters of repulsive particles

This paper discusses two-dimensional mesoscopic clusters of particles that repel according to dipole, Coulomb, and logarithmic laws and are confined by an external parabolic potential. These models describe a number of physical systems, in particular, electrons in semiconductor structures or on a liquid-helium surface allowing for image forces, indirect excitons in coupled semi-conductor dots, and a small number of vortices in an island of a second-order superconductor or in superfluid helium. Two competing forms of ordering are detected in the particles in the mesoscopic clusters-the formation of a triangular lattice or of a shell structure. The temperature dependences of the potential energy, the mean-square radial and angular deviations, the radial and angular distributions of the particles, and the distribution of the particles over the local minima are studied. Melting in mesoscopic clusters occurs in two stages: at lower temperatures, there is orientation melting, from the frozen phase into a phase with rotational reorientation of “crystalline” shells with respect to each other; subsequently, a transition occurs in which the radial order disappears. Melting in dipole macroclusters occurs in a single stage. However, in Coulomb and logarithmic macroclusters, orientation melting occurs only for the outer pairs of shells. Orientation melting is also detected in three-dimensional Coulomb clusters. A connection is established between the character of the melting and the ratio of the energy barriers that describe the breakdown of the orientational and radial structure of a cluster. Zh. éksp. Teor. Fiz. 116, 2012–2037 (December 1999)     

Quantum melting of mesoscopic clusters

The phase diagram of a two-dimensional mesoscopic system of charges or dipoles, whose realizations could be electrons in a semiconductor quantum dot or indirect excitons in a system of two vertically coupled quantum dots, is investigated. Quantum calculations using ab initio Monte Carlo integration along trajectories determine the properties of such objects in the temperature-quantum de-Boer-parameter plane. At zero (sufficiently low) temperature, as the quantum fluctuations of the particles increase, two types of quantum disordering phenomena occur with increasing quantum de Boer parameter q: first, for q∼10⁻⁵ the systems transform into a radially ordered but orientationally disordered state wherein various shells of the “atom” rotate relative to one another. For much larger q∼0.1, a transition occurs to a disordered state (a superfluid in the case of a system of bosons). Fiz. Tverd. Tela (St. Petersburg) 41, 1856–1862 (October 1999)     

Static electric dipole polarizabilities of Na clusters

The static electric dipole polarizability of Na _N clusters with even N has been calculated in a collective, axially averaged and a three-dimensional, finite-field approach for , including the ionic structure of the clusters. The validity of a collective model for the static response of small systems is demonstrated. Our density functional calculations verify the trends and fine structure seen in a recent experiment. A pseudopotential that reproduces the experimental bulk bond length and atomic energy levels leads to a substantial increase in the calculated polarizabilities, in better agreement with experiment. We relate remaining differences in the magnitude of the theoretical and experimental polarizabilities to the finite temperature present in the experiments. Received 8 November 1999     

Coulomb clusters: melting and potential barriers

The melting of two-dimensional and three-dimensional Coulomb micro- and macroclusters is studied. Temperature dependences of radial and angular square deviations of particles are investigated. The melting of microclusters has two stages: at lower temperature there is a transition from a frozen phase to a state with a rotatory reorientation of “crystalline” shells relative to each other, different pairs of shells melting at different temperatures. In the case of large N and high triangular symmetry inside the cluster, orientational melting takes place only for external pairs of shells. In this case external shells lose their order. At higher temperature a transition with a loss of radial shell order occurs. The origin of two-stage melting is in the smallness of the barrier energy relative to the rotation of shells in comparison with the barrier corresponding to the radial disordering of shells. It is shown also that the temperatures of orientational and total melting are at 5–15 times lower than the temperatures of disappearance of corresponding potential barriers. The influence of confinement anisotropy on the character of cluster melting is considered. It is found that at some degree of anisotropy the melting becomes one stage. The last is connected with an increase of the ratios of barriers of intershell rotation to barriers of jumps of a particle between the shells.     

Superfluidity and quantum melting of p-H2 clusters

Structural and superfluid properties of p-H2 clusters of size up to N=40 molecules, are studied at low temperature (0.5 K相似文献   

Surface and bulk melting of small metal clusters

We present an analytical solution to the two-parabola Landau model, applied to melting of metal particles with sizes in the nanoscale range. The results provide an analytical understanding of the recently observed pseudo-crystalline phase of nanoscale Sn particles. Liquid skin formation as a precursor of melting is found to occur only for particles with radii greater than an explicitly given critical radius. The size dependences of the melting temperature, and of the latent heat, have been calculated, and a quantitative agreement is found with the experiment on tin particles.     

Solid clusters above the bulk melting point

The fact that the melting points of nanoparticles are always lower than those of the corresponding bulk material is a paradigm supported by extensive experimental data for a large number of systems and by numerous calculations. Here we demonstrate that tin cluster ions with 10-30 atoms remain solid at approximately 50 K above the melting point of bulk tin. This behavior is possibly related to the fact that the structure of the clusters is completely different from that of the bulk element.     

Structure and melting of Morse solids

Isothermal-isobaric ensemble Monte Carlo simulations are used to study the melting of Morse solids. At a given pressure, the temperature at which the solid ceases to be metastable and also the fractional changes in density and potential energy increase with decreasing range of the Morse pair potential. The structural properties of the liquid and solid phases vary significantly with the range. The longer range, softer potentials are associated with increased densities and cohesive energies in both the solid and liquid phases. The extent of local disorder associated with lattice sites in the solid phase, as measured by the Lindemann and bond orientational order parameters, increases with increasing range of the pair potential.     

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. Received 1st November 2002 Published online 24 April 2003 RID="a" ID="a"e-mail: ar@phys.jyu.fi     

Ternary alloying effect on the melting of metal clusters

Canonical ensemble Monte Carlo simulations are applied to investigate the melting of the icosahedral 55-atom Ag-Cu-Au clusters. The clusters are modeled by the second-moment approximation of the tight-binding (TB-SMA) many-body potentials. Results show that the introduction of the only Cu atom of the third alloying metal in the bimetallic Ag₄₃Au₁₂ cluster, forming the Ag₄₂Cu₁Au₁₂ cluster, can greatly increase the melting point of the cluster by about 100 K. It is also found that the substitution of the only Cu atom of the third alloying metal in the Ag₁Au₅₄ clusters, forming the Ag₁Cu₁Au₅₃ cluster, can result in an increase of 40 K in the melting point. It can be concluded that the melting points of the bimetallic clusters can be tuned by the third metal impurities doping. In addition, the surface segregation of Ag atoms in the Ag-Cu-Au trimetallic clusters occurs even after melting.     

Splitting of the giant dipole resonance in deformed metal clusters

The photoabsorption in small deformed metal clusters is considered. The valence electron spill-out is disregarded. It is shown that in the deformed clusters the giant dipole resonance splits into two separate resonances. This splitting is due to the difference of the oscillator frequencies for the electron motion in the effective field of the deformed clusters. The ratio of the cross-sections in the resonance maxima is obtained. The theoretical results are compared with the experimental data.     

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.     

Influence of electronic and geometric properties on melting of sodium clusters

Systematics of the melting transition for sodium clusters with 40-355 atoms has been studied with both ab initio and semiclassical molecular dynamics simulations. The melting temperatures obtained with an ab initio method for Na₅₅ ⁺ and Na₉₃ ⁺ correlate well with the experimental results. The semiclassically determined melting temperatures show similarities with the experimentally determined ones in the size region from 55 to 93 and near size 142, and the latent heat in the size region from 55 to 139, but not elsewhere in the size region studied. This indicates that the nonmonotonical melting behavior observed experimentally cannot be fully explained by geometrical effects. The semiclassically determined melting temperature and the latent heat correlate quite well, indicating that they respond similarly to changes in cluster geometry and size. Similarly, the binding energy per atom seems to correlate with the melting temperature and the latent heat of fusion.Received: 30 October 2003, Published online: 20 January 2004PACS: 36.40.Ei Phase transitions in clusters