Chemistry Reference
In-Depth Information
Table 8.3
Genus calculation in Diamond D5 substructures
Hollow structure
v
e
g
=
1
+
u(g
u
−
1)
g
u
u
(C
20
)
12
C
28
_ada_158
158
274
3
1.5
4
(C
20
)
18
(C
28
)
2
_dia_syn_226
226
398
5
2;1.5
3
+
2
(C
20
)
18
(C
28
)
2
_dia_anti_226
226
398
5
1.5
8
Fig. 8.2
D
5_
syn_524_1330-top view (
left
), D
5
_syn_524_1330-side view (
right
)
Fig. 8.3
“Exfoliation” of the hypothetical diamond D
5
leading to hyper-graphenes:
C
20
Hex_333_506 (a planar pure hexagonal C
20
hyper-graphene—
left
); (C
20
C
28
)Hex_331_327 (a
sheet of alternating C
20
/C
28
armchair hyper-hexagonal units—
right
)
The quasi-diamond D
5
_
syn
can form a 1-periodic quasicrystal,
e.g
.D
5
syn_52n,
of Amm2 space group; point symbol for net {5
2
.6}6{5
3
} 4{5
4
.6.8}5{5
5
.6}7{5
6
}3;
12-nodal net 3,4-c (Fig.
8.2
).
8.3
D
5
Substructures as Hyper-Graphenes
The small fullerenes C
20
and C
28
, filling the space in the frame of D
5
can provide, by
“exfoliation”, hyper-graphenes (Diudea MV,
2013
), either as single-cages (Fig.
8.3
,
left) or mixed ones (Fig.
8.3
, right).
The corresponding substructures of the hyper-graphenes in Fig.
8.3
are illustrated
in Fig.
8.4
(top row).
Alternating C
20
/C
28
hyper-graphene domains with five-fold symmetry (Fig.
8.5
)
can result by sectioning a quasi-crystal (Fig.
8.5
, right) by an electron beam (Diudea
