https://doi.org/10.1007/s10053-000-8808-y
Mesoscopic and macroscopic dipole clusters: Structure and phase transitions
Laboratory of Nanophysics, Institute of Spectroscopy, Russian Academy of
Sciences, Troitsk, 142092,
Moscow region, Russia
Received:
22
April
1999
Revised:
13
July
1999
Published online: 13 August 2013
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 
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.
PACS: 61.46.+w – Clusters, nanoparticles, and nanocrystalline materials / 68.65.+g – Low-dimensional structures (superlattices, quantum well structures, multilayers): structure, and nonelectronic properties / 36.40.Ei – Phase transitions in clusters
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
