After many years of study, the polymorphism of group IV elements still remains unresolved. This is due to the existence of metastable phases. On depressurisation of the group IV elements silicon and germanium from their first high pressure metallic phase, they do not return to the initial diamond phase, but form complex 4-fold coordinated high density structures.

This chapter presents complete *ab initio* total energy calculations
on the behaviour of diamond and dense metastable 4-fold coordinated
phases (known as BC8 and ST12) carbon, silicon and germanium. The
effects of pressure on structure and bonding is also discussed. The
calculations incorporate direct relaxation of the atomic positions under
the Hellmann-Feynman forces and a search through unit cell parameters
for the BC8 structure
and, in the case of ST12, a full relaxation of the *c*/*a* ratio of the
tetragonal unit cell is performed at each volume in order to obtain the
complete pressure dependance of the unit cell.

Experiment suggests that similar structures in III-V semiconductors do
not exist. For this reason *ab initio* calculations have been
performed to try to explain why these phases are not found.

This chapter is organised as follows. A summary of the total energy
calculations discussed in Chapter 2 including the conditions for
convergence are given in the next section. A discussion of the BC8 and
ST12 structures will be given next followed by the full pressure
dependance of these structures. It is possible to extract phonon
frequencies from an *ab initio* molecular dynamics simulation at
finite temperature from the ensemble average of the velocity
autocorrelation function. This method will be given in Section
4.6 and the method is applied to silicon in the diamond, BC8
and ST12 structures. This can be compared to the phonon calculations in
Chapter 4 found using an empirical potential and the harmonic
approximation. The electronic structure of carbon, silicon and
germanium in these three structures will be discussed in the form of
band structures in Section 4.7. It is found that there is a
fundamental difference in the nature of the bonding between carbon and
silicon or germanium which is presented in Section 4.8.
Finally, an investigation into why these metastable structures are not
found in III-V semiconductors will be presented in Section
4.10 in terms of a total energy calculations, molecular
dynamics and a fully *ab initio* calculation of ionicities.

Thu Oct 31 19:32:00 GMT 1996