Chemistry Reference
In-Depth Information
using forces on each atom retaining the minimal residual stress. The stress
on the graphene and BN-monolayer is shown in the Fig. 2(a). It is clear
that the graphene possess slightly higher stress than that of BN at all values
of applied strain.
Fig. 2. (Color online) (a) Stress on graphene and BN-monolayer as a function of uniaxial
compressive strain. (b) Phonon dispersion of graphene and BN-monolayer.
3.2.
Phonons
Phonon dispersion of graphene and BN-monolayer over the symmetry point
on the Brillouin zone is shown in the Fig. 2(b). It is evident from the
phonon dispersion that flexural acoustic modes are significantly softer in BN
(310 cm
−
1
at K point) than those in graphene (527 cm
−
1
at K point). The
Brillouin zone along with symmetry points of graphene and BN-monolayer
with 4 atoms in the unit cell, with strain along
-direction is shown in the
Fig. 3. Comparison of flexural modes of graphene and BN-monolayer when
the compressive strain is applied along
Z
-direction is shown in Fig. 4. It is
clearly seen that the negative frequencies shown by both BN-monolayer and
graphene indicate the structures are unstable with the applied compressive
strain. The instability of BN-monolayer is stronger than that of graphene.
The dependence of frequency on wave vector gives an indication of the
elastic nature of the graphene or BN-monolayer. The best fit to omega (
Z
ω
)
vs q needs the following terms at the lowest order.
ω
flex
=
α ∗ q
2
+
β ∗ q
4
does not change much for small strains, but drops to
negative value for large enough compressive strain (see Fig. 5(a)). In the
The value of
α
