Abstract
The thermodynamic properties of a cluster of point Coulomb charges on a sphere have been analyzed using the Monte Carlo method for the number of charges 20 ≤ N ≤ 90. The ground state of the system of charges is described in the model of a closed quasi-two-dimensional triangular lattice with topological defects. We have determined the dependence of the Lindeman parameter δL of this system on N and on the dimensionless parameter \( \tilde T \), which is proportional to the temperature T and to the radius R of the cluster: \( \tilde T = {{k_B T\varepsilon R} \mathord{\left/ {\vphantom {{k_B T\varepsilon R} {e^2 }}} \right. \kern-\nulldelimiterspace} {e^2 }} \), where ∈ is the dielectric constant of the medium and e is the charge of a particle. The “magic numbers,” i.e., the N values, for which the melting point of the closed triangular lattice of charges is much higher than those for neighboring N values, have been found. The evolution of the lattice-melting mechanisms with an increase in the number of charges N in a mesoscopic cluster has been analyzed. For N ≤ 32, the melting of the lattice does not involve dislocations (nontopological melting); this behavior of the mesoscopic system of charges on the sphere differs from the behavior of the extended planar two-dimensional system. At N ≳ 50, melting is accompanied by the formation of dislocations. The mechanism of dislocation-free non-topological melting of a closed lattice, which occurs at small N values and is associated with the cooperative rotational motion of “rings” of particles, has been analyzed. The model has various implementations in the mesoscopic region; in particular, it describes the system of electrons over the liquid-helium cluster, the liquid-helium cluster with incorporated charged particles, a multielectron bubble in liquid helium, a charged quantum dot, etc.
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Original Russian Text © A.M. Livshits, Yu.E. Lozovik, 2010, published in Zhurnal Éksperimental’noı i Teoreticheskoı Fiziki, 2010, Vol. 138, No. 5, pp. 955–969.
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Livshits, A.M., Lozovik, Y.E. “Magic numbers” in the melting of a cluster of point charges on a sphere. J. Exp. Theor. Phys. 111, 844–856 (2010). https://doi.org/10.1134/S1063776110110154
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DOI: https://doi.org/10.1134/S1063776110110154