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Alpha Clustering with a Hollow Structure --- Geometrical Structure of Alpha Clusters from Platonic Solids to Fullerene Shape
We study -cluster structure based on the geometric configurations
with a microscopic framework, which takes full account of the Pauli principle,
and which also employs an effective inter-nucleon force including finite-range
three-body terms suitable for microscopic alpha-cluster models. Here, special
attention is focused upon the clustering with a hollow structure; all
the clusters are put on the surface of a sphere. All the Platonic
solids (five regular polyhedra) and the fullerene-shaped polyhedron coming from
icosahedral structure are considered. Furthermore, two configurations with dual
polyhedra, hexahedron-octahedron and dodecahedron-icosahedron, are also
scrutinized. As a consequence, we insist on the possible existence of stable
-clustering with a hollow structure for all the configurations.
Especially, two configurations, that is, dual polyhedra of
dodecahedron-icosahedron and fullerene, have a prominent hollow structure
compared with other six configurations
The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry
The phase diagram of model anisotropic particles with four attractive patches
in a tetrahedral arrangement has been computed at two different values for the
range of the potential, with the aim of investigating the conditions under
which a diamond crystal can be formed. We find that the diamond phase is never
stable for our longer-ranged potential. At low temperatures and pressures, the
fluid freezes into a body-centred-cubic solid that can be viewed as two
interpenetrating diamond lattices with a weak interaction between the two
sublattices. Upon compression, an orientationally ordered face-centred-cubic
crystal becomes more stable than the body-centred-cubic crystal, and at higher
temperatures a plastic face-centered-cubic phase is stabilized by the increased
entropy due to orientational disorder. A similar phase diagram is found for the
shorter-ranged potential, but at low temperatures and pressures, we also find a
region over which the diamond phase is thermodynamically favored over the
body-centred-cubic phase. The higher vibrational entropy of the diamond
structure with respect to the body-centred-cubic solid explains why it is
stable even though the enthalpy of the latter phase is lower. Some preliminary
studies on the growth of the diamond structure starting from a crystal seed
were performed. Even though the diamond phase is never thermodynamically stable
for the longer-ranged model, direct coexistence simulations of the interface
between the fluid and the body-centred-cubic crystal and between the fluid and
the diamond crystal show that, at sufficiently low pressures, it is quite
probable that in both cases the solid grows into a diamond crystal, albeit
involving some defects. These results highlight the importance of kinetic
effects in the formation of diamond crystals in systems of patchy particles.Comment: 15 pages, 13 figure
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