We have studied the phase transitions in atomic clusters by molecular dynamics
simulation, assuming Lennard-Jones interatomic pair potential. Calculations are
performed by DAP parallel computer. The results are analyzed by simulating their
orientational distribution plots (dot-plot), and neutron diffraction patterns. It is shown
that all the main features of the bulk phase transitions are essentially exhibited by such
a small sample. It is seen that by cooling the sample below the melting temperature,
the atoms establish an icosahedral quasi-crystal structure with five fold symmetry.
The Mackay predicted magic numbers are confirmed by our simulation. Finally, we
conclude that in cooling the sample blow the melting point, nucleation initiates from
the central region and then propagates toward the surface