To ensure that the SC16 structures are mechanically stable a finite
temperature molecular dynamics simulation was performed. For a structure
to be mechanically stable, positive restoring forces must oppose any
small displacement of an atom about its equilibrium position. An
equivalent statement is that the square of all phonon frequencies must
be greater than zero (except for the 
point acoustic modes).
Ideally, all possible vibrational modes should be investigated in order to fully explore mechanical stability, but due the extremely long run time required to run a molecular dynamics simulation on a large unit cell only the zone centre modes are investigated here.
A similar calculation to that described in Section 4.6 is
performed on a single GaAs SC16 unit cell. The initial configuration is
that of the fully relaxed structure described above. The average
temperature was maintained at 300K by use of a Nosé thermostat. The
simulation was run for a time of 2.0ps in steps of 0.5fs. The velocity
autocorrelation function was found and Fourier transformed to obtain
the zone centre spectral density given in Figure 4.31.
Again, the first 0.3ps of the simulation was not included in the phonon
calculation to allow for equilibration of the system. The
position autocorrelation function (and hence the velocity
autocorrelation function) was found to oscillate about zero indicating
that the point modes are stable. Note that Figure
4.31 shows the phonon spectral density at a temperature
of 300K. To make a comparison to a full density of states calculation,
ie. in the high temperature limit, the density must first be corrected
by multiplication by the Boltzmann factor, which, in this case,
increased the height of the density of the high frequency phonons.
Figure 4.31: Spectral density of the
point modes of GaAs in the SC16 structure as computed by first
principles molecular dynamics.
The effect of disorder on the vibrational spectrum is expected to be
similar to its effect on the electronic spectrum. That is, disorder
introduces a broadening relative to the crystalline density of states. In
the calculation of the point density of states it is found that
the positions of the prominent features at 2THz and 8THz correspond to
the positions of the TA and TO phonon branches of the zincblende phase.
These features are also seen in the amorphous form of GaAs at similar
frequencies.
The vibrational density of states obtained for SC16 GaAs in this way appears similar to that of BC8 silicon. Thus, the non-existence of SC16 cannot be attributed to entropic effects.