  The pressure-induced structural transition in fcc C$_{60}$ fullerene by shock
compression and rapid quenching is investigated by a semi-empirical
tight-binding molecular dynamics simulation, adopting a constant-pressure
scheme and a method of the order N electronic structure calculation. At first,
the process of the amorphization of C$_{60}$ is demonstrated. The simulated
results indicated that, in the material fabricated after the quenching, the
remaining dangling bonds have a large influence on physical properties, such
as, the density and the presence of the band gap at the Fermi level. We have
furthermore studied the formation of the short-range order, observed as
amorphous diamond. In order to form the amorphous diamond phase, the bonding
state of sp$^2$ must be turned into that of sp$^3$. The transition process is
seriously influenced from the the external pressure, the temperature, or the
presence of hydrogen. The comparison to the pressure-induced structural
transition in the graphite is also executed and a brief discussion on the
difference in those carbon crystals is given.
