  A few experiments have already detected the presence of icosahedral
superclusters in undercooled liquids, confirming a possible homogeneous
nucleation of such entities as suggested by Franck. These superclusters survive
in melts above the crystal melting temperature Tm because all their surface
atoms have the same fusion heat as their core atoms and are melted by
homogeneous nucleation of liquid in their core, depending on overheating time
and temperature. In complete contrast to current ideas, a long time is
necessary to melt them and to attain the thermodynamic equilibrium above Tm.
They act as heterogeneous growth nuclei of crystallized phase at a temperature
Tc of the undercooled melt when they are not melted. They contribute to the
reduction of the critical barrier, which becomes smaller than that of crystals
containing the same atom number n. The undercooling rate is always limited,
even in a liquid at thermodynamic equilibrium, because the homogeneous
nucleation of 13-atom superclusters reduces the energy barrier, and increases
Tc above the homogeneous nucleation temperature equal to Tm/3 in liquid
elements. After weak superheating, the most stable superclusters containing n =
13, 55, 147, 309 and 561 atoms survive or melt and determine Tc during
undercooling, which depends on n and on the sample volume. The experimental
nucleation temperatures Tc of 32 liquid elements and the melting temperatures
of superclusters are predicted without any adjustable parameter using a sample
volume varying by nearly 18 orders of magnitude. The classical Gibbs free
energy change is used, adding an enthalpy saving related to the Laplace
pressure change associated with supercluster formation, which is quantified and
strongly weakened for n = 13 and 55.
