Melting transitions in isotropically confined three-dimensional small Coulomb clusters

Experimental determination of phase transitions by means of configurational entropies in finite Yukawa balls

The phase transition of finite Yukawa balls (ordered systems of microspheres in a gaseous plasma environment) with less than 100 particles is studied experimentally by means of configurational entropies. We have developed cylindrical two- and three-particle-correlation functions to measure these entropies for multiple cluster sizes over a wide temperature range. The cluster temperature is finely tuned using a stochastic laser heating setup. It is shown that the correlation functions give a detailed insight into the structural properties of the cluster. The derived configurational entropies give a clear indication of the transition temperature from a solid-like to a fluid-like state. Comparing the transition temperatures of different sized clusters it is found that the transition temperature increases with cluster size in general agreement with theoretical predictions.

Resolving structural transitions in spherical dust clusters

Finite systems in confining potentials are known to undergo structural transitions similar to phase transitions. However, these systems are inhomogeneous, and their "melting" point may depend on the position in the trap and vary with the particle number. Focusing on three-dimensional Coulomb systems in a harmonic trap a rich physics is revealed: in addition to radial melting we demonstrate the existence of intrashell disordering and intershell angular melting. Our analysis takes advantage of a novel melting criterion that is based on the spatial two- and three-particle distribution functions and the associated reduced entropy which can be directly measured in complex plasma experiments.

Effect of confinement on the mode dynamics of dipole clusters

Dynamical properties of colloidal clusters composed of paramagnetic beads are presented. The clusters were trapped either in a parabolic trough or in a hard-wall confinement. In order to access the dynamics of the ensembles, the instantaneous normal mode (INM) approach is utilized, which uses cluster configurations as an input. The peaks in the mode spectra weaken when the system size is increased and when the coupling strength is lowered. The short-time diffusive properties of the clusters are deduced using the INM technique. It is found that angular diffusion is always larger than radial diffusion regardless of the shape of the external trap. Further, short-time diffusion seems to be almost independent of the coupling strength in the solid regime, but decreases with increasing packing fraction and size of the ensembles. In general, it is found that diffusion is larger for parabolically confined than for hard-wall trapped clusters.

Structural orderings of anisotropically confined colloids interacting via a quasi-square-well potential

We implement Brownian dynamics to investigate the static properties of colloidal particles confined anisotropically and interacting via a potential which can be tailored in a repulsive-attractive-respulsive fashion as the interparticle distance increases. A diverse number of structural phases are self-assembled, which were classified according to two aspects, that is, their macroscopic and microscopic patterns. Concerning the microscopic phases we found the quasicrystalline, triangular, square, and mixed orderings, where this latter is a combination of square and triangular cells in a 3×2 proportion, i.e., the so-called (3(3),4(2)) Archimedian lattice. On the macroscopic level the system could self-organize in a compact or perforated single cluster surrounded or not by fringes. All the structural phases are summarized in detailed phases diagrams, which clearly show that the different phases are extended as the confinement potential becomes more anisotropic.

Angular melting scenarios in binary dusty-plasma Coulomb balls: magic versus normal clusters

Molecular-dynamic simulations were performed in order to investigate the melting processes of isotropically confined binary systems. We considered two species of particles, which differ by their amount of electric charge. A Lindemann type of criterion was used to determine the angular melting temperature. We demonstrate that the magic-to-normal cluster transition can evolve in two distinct ways, that is, through a structural phase transition of the first order or via a smooth transition where an increase of the shells' width leads to a continuous decreasing mechanical stability of the system. Moreover, for large systems, we demonstrate that the internal cluster exerts a minor effect on the mechanical stability of the external shell. Furthermore, we show that highly symmetric configurations, such as those found for multiple ring structures, have large mechanical stability, i.e., high angular melting temperature.

Structural properties of anisotropically confined binary Coulomb balls

We investigate the structural properties of a small binary system of dusty plasma subjected to an anisotropic external confinement. We have found that the ground state can form various symmetrical configurations, which generally correspond to variations of a multiple-ring structure. The presence of such structures is given through a detailed phase diagram constructed for the systems with N=18 and 24 particles. Furthermore, we show that the configurations of multiple rings can present a persistent behavior for the case in which the number of less-charged particles is equal to a multiple of the number of particles per ring. Finally, we discuss the main characteristics of the transitions of first and second orders since these are related to the main configurational changes of the ground states.

Asymptotic equivalence of the shell-model and local-density descriptions of Coulombic systems confined by radially symmetric potentials in two and three dimensions

Asymptotic equivalence of the shell-model and local-density (LDA) descriptions of Coulombic systems confined by radially symmetric potentials in two and three dimensions is demonstrated. Tight upper bounds to the numerical constants that enter the LDA expressions for the Madelung energy are derived and found to differ by less than 0.5% from the previously known approximate values. Thanks to the variational nature of the shell-model approximate energies, asymptotic expressions for other properties, such as mean radial positions of the particles and number densities, are also obtained. A conjecture that generalizes the present results to confining potentials with arbitrary symmetries is formulated.

Melting scenarios for three-dimensional dusty plasma clusters

The melting transition of finite three-dimensional dust clouds (Yukawa balls) from a solid-like to a liquid-like state is systematically studied with high spatial and temporal resolution of the individual grains by means of stereoscopy. Two different melting scenarios are reported: Melting is induced first by an increase of plasma power, and second by laser-induced heating. The experiments confirm that melting starts with a loss of orientational correlation, followed by a loss of the radial order upon further heating. While the plasma-power melting is driven via the ion wakefield, laser heating provides a more equilibrium scenario. The internal loss of correlations is well captured by the triple correlation function (TCF) which is insensitive to particle exchanges and the rotation of the cluster as a whole. The critical Coulomb coupling parameter for N=35 is determined as Γ(crit)≈570. The experimental findings are in good agreement with thermodynamic Monte Carlo simulations.

Binary dusty plasma Coulomb balls

We investigated the mixing and segregation of a system consisting of two different species of particles, having different charges, interacting through a pure Coulomb potential, and confined in a three-dimensional parabolic trap. The structure of the cluster and its normal mode spectrum are analyzed as a function of the relative charge and the relative number of different types of particles. We found that (a) the system can be in a mixed or segregated state depending on the relative charge ratio parameter and (b) the segregation process is mediated by a first or second order structural phase transition which strongly influences the magic cluster properties of the system.

Probability of metastable configurations in spherical three-dimensional Yukawa crystals

Recently the occurrence probabilities of ground and metastable states of three-dimensional Yukawa clusters with 27 and 31 particles have been analyzed in dusty plasma experiments [D. Block, Phys. Plasmas 15, 040701 (2008)]. There it was found that, in many cases, the ground state appeared substantially less frequently than excited states. Here we analyze this question theoretically by means of molecular dynamics (MD) and Monte Carlo simulations and an analytical method based on the canonical partition function. We confirm that metastable states can occur with a significantly higher probability than the ground state. The results strongly depend on the screening parameter of the Yukawa interaction and the damping coefficient used in the MD simulations. The analytical method allows one to gain insight into the mechanisms being responsible for the occurrence probabilities of metastable states in strongly correlated finite systems.