Two-dimensional microclusters of vortices: Shell structure and melting

The melting of two-dimensional microclusters of “particles” which repel one another according to a logarithmic law and are confined by an external quadratic potential is investigated. The model describes Abrikosov vortices in a superconducting island of vortices in a rotating superfluid liquid and electrons in a semiconductor nanostructure surrounded by a low-permittivity medium. The structure of clusters and its dependence on temperature and melting are investigated. The melting of microclusters of vortices proceeds in two stages: 1. A transition from a frozen phase into a state corresponding to rotational reorientation of crystal shells relative to one another. 2. At a higher temperature, the radial order vanishes. This is connected with the fact that the barrier for rotation of the shells is much lower than the barrier for radial breakup of the shells. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 3, 268–273 (10 February 1997)     

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.     

The structure and thermodynamics of binary microclusters: A Monte Carlo simulation

The Monte Carlo computer simulation technique of classical statistical mechanics is employed to determine the structure and thermodynamics of binary microclusters of Lennard-Jones atoms as a function of cluster size, composition and temperature. Further, amorphous microclusters are prepared by a Monte Carlo quench, and their structural properties are examined. The properties of interest include the internal energy, instantaneous “snapshot” pictures of the microcluster's atomic configuration, and the single-particle and pair distribution functions. The Lennard-Jones potential parameters are chosen to model Ar₁₃, Ar₇Kr₆, Ar₃₆Kr₁₉ and Ar₁₉Kr₃₆, as well as to crudely model the bimetallic clusters of Cu₁₉Ni₃₆, Cu₁₉Ru₃₆ and Cu₁₉Os₃₆. A large variety of interesting features associated with these systems are described.     

Two-dimensional melting of dislocation vector systems

Dislocation vector systems with various dislocation core energies are simulated, and the nature and the mechanism of the melting phase transition there is determined by means of the energy, specific heat, dislocation density, renormalized coupling constant, shear modulus and orientational stiffness constant as well as microscopic configurations of dislocation vectors. For a system with a large core energy the melting transition is found to be continuous, caused by the dislocation unbinding mechanism predicted by Kosterlitz-Thouless and Halperin-Nelson-Young. For a system with a small core energy, grain boundary loops are nucleated in the process of melting and the phase transition turns out to be first order. The latter agrees with most of the computer experiments on atomistic systems.     

Two-dimensional melting of physisorbed submonolayers of argon and nitrogen

We have studied two-dimensional argon and nitrogen physisorbed on grafoil by conducting positron lifetime and Doppler broadening measurements as functions of adsorbate coverage and temperature. Positron lifetime and Doppler broadening parameters show turnarounds near one-half monolayer coverages at 77 K. The s parameter of the Doppler broadening spectra measured for one-half monolayer coverages of argon and nitrogen increases with temperature across the melting phase transition. We discuss the observed coverage and temperature effects following models based on Kosterlitz-Thouless-Nelson-Halperin-Young theory of two dimensional melting and positron localization in surface defects.     

Two-dimensional melting transition observed in a block copolymer

We report the observation of two-dimensional melting in a monolayer film of a sphere-forming diblock copolymer. By annealing in a well-controlled temperature gradient we obtain a complete record of the transition from a low-temperature hexatic phase to a high-temperature liquid in a single experiment. We investigate the temperature dependence of the orientational and translational correlation lengths, as well as of the topological defect density. All evidence suggests that the melting transition is first-order, but correlations in the liquid phase indicate the existence of an underlying second-order transition preempted by the first-order freezing.     

Two-dimensional melting far from equilibrium in a granular monolayer

We report an experimental investigation of the transition from a hexagonally ordered solid phase to a disordered liquid in a monolayer of vibrated spheres. The transition occurs as the intensity of the vibration amplitude is increased. Measurements of the density of dislocations and the positional and orientational correlation functions show evidence for a dislocation-mediated continuous transition from a solid phase with long-range order to a liquid with only short-range order. The results show a strong similarity to simulations of melting of hard disks in equilibrium, despite the fact that the granular monolayer is far from equilibrium due to the effects of interparticle dissipation and the vibrational forcing.     

Shell structure in nuclei

A review of shell structure for spherical and a variety of deformed nuclei is presented. The microscopic-macroscopic method of Strutinsky is used to calculate potential energy surfaces with the pure harmonic oscillator and the modified harmonic oscillator. New sets of “magic numbers” for a variety of different prolate, oblate and axially asymmetric shapes are generated. Experimental evidence for the special stability caused by these shell effects is presented with special emphasis on the lightest and heaviest nuclei where the effects are most pronounced. The radial diffuseness parameter is treated as a Strutinsky variable and its significance in extrapolating into the superheavy region considered. The calculation of shell effects for high spin states is also reviewed.     

Morphology and statistical statics of simple microclusters

In this paper we discuss the statics of small assemblies of soft, rare-gas type atoms (N=4 to 13) interacting under simple two-body central forces such as the Lennard-Jones and Morse type. Our main concern is to characterize the problem of isomer multiplicity in small packed structures and to devise practical algorithms for the discovery of a representative majority, if not all, stable soft-packing structures for clusters of atoms in the above size-range.

We illustrate one such possible ‘Aufbau algorithm’ by demonstrating the existence of no less than 988 distinct, stable minimum configurations for 13 Lennard-Jones atoms and of correspondingly smaller numbers in the range N=7 to 12. The minimal structures obtained may be classified broadly into ‘crystallographic’ and ‘non-crystallographic’ types, the latter predominating among those of greatest binding energy.

A surprising result is that, when the softer (α=3) Morse potential is used, the great majority of the Lennard-Jones minima are not supported and only a much smaller class of distinct structures survive. Moreover, broadly speaking, crystallographic configurations are favoured by the softer potential, in confirmation of the intuitive view that relatively hard potentials dispose to amorphous structure.

These results, representing the probable structures of free condensation nuclei near 0 K, provide an interesting statistical morphology for small nuclei, as well as being a necessary first step in the construction of a statistical thermodynamics valid at finite temperatures.     

Shell structure and shapes of superheavy nuclei

Shell structure and shapes of superheavy nuclei are discussed. Both deformed and spherical nuclei are considered. Theoretical results obtained for even-even nuclei with the proton numberZ=82–120 and neutron numberN=126–190 are examined.     

Magnetic monopole interactions: Shell structure of meson and baryon states

It is suggested that a low-mass magnetic monopole of Dirac chargeg=(137/2)e may be interacting with ac-quark's magnetic dipole moment to produce Zeeman splitting of meson states. The massM ₀=2397 MeV of the monopole is in contrast to the 10¹⁶-GeV monopoles of grand unification theories (GUT). It is shown that shell structure of energyE _n =M ₀+1/4nM ₀+ exists for meson states. The presence of symmetric meson states leads to the identification of the shell structure. The possible existence of the 2397-MeV magnetic monopole is shown to quantize quark masses in agreement with calculations of quantum chromodynamics (QCD). From the shell structure of meson states, the existence of two new mesons is predicted:(1814±50 MeV) withI ^G(J ^PC =0⁺(0^–+) and _c (3907±100 MeV) withJ ^PC =0^–+. The presence of shell structure for baryon states is shown.     

Two-dimensional electronic structure in InAs-GaSb superlattices

We have achieved by molecular-beam-epitaxy the new type of superlattice of InAs and GaSb whose energy gaps do not overlap. The observed Shubnikov-de Haas oscillations manifest the two-dimensional electronic subband structure, corroborating theoretical calculations. The deduced electron mass is enhanced primarily as a result of the strong nonparabolicity in the conduction-band of InAs.     

Shell structure fingerprints of tensor interaction

We address the consequences of strong tensor terms in the local energy density functional, resulting from fits to the f _5/2 -f _7/2 splittings in ⁴⁰Ca , ⁴⁸Ca , and ⁵⁶Ni . In this study, we focus on the tensor contribution to the nuclear binding energy. In particular, we show that it exhibits an interesting topological feature closely resembling that of the shell correction. We demonstrate that in the extreme single-particle scenario at spherical shape, the tensor contribution shows tensorial magic numbers equal to N(Z) = 14 , 32, 56, and 90, and that this structure is smeared out due to configuration mixing caused by pairing correlations and migration of proton/neutron sub-shells with neutron/proton shell filling. Based on a specific Skyrme-type functional SLy4_T, we show that the proton tensorial magic numbers shift with increasing neutron excess to Z = 14 , 28, and 50.     

Shell structure for deformed nuclear shapes

Eigenvalues for the harmonic oscillator without l·s or l² terms suggest a deformed shell structure for nuclei with axes ratios 2 : 1 and deformation ? = 0.6 with corresponding nucleon “magic numbers” 2, 4, 10, 16, 28, 40, 60, 80 110 and 140, subject to small modifications due to spin-orbit and other correction terms. Experimental evidence of reasonably stable highly deformed structures corresponding to nucleon numbers 16, 20, 28, 40 and 60 (64) is presented. Attempts to calculate the corresponding potential energy surfaces using the Strutinsky shell correction method are described.