Biomedical Engineering Reference
In-Depth Information
7.4
Parameterization
In general, Eq. (7.12) is a very simple model that requires a small
number of input parameters;
0
0
D
H
D
H
) which are the
standard heats of formation for carbon and the gas species
(
C
)
and
(
X
f
f
X
,
2
3
respectively, and
) which
must be determined individually. Using the same computational
method described above, this has may be done in a systematic
fashion, at the
E
(sp
),
E
(sp
),
E
,
E
(Θ,
R
,
X
) and
E
(Θ,
X
DB
ad
s
ab inito
level [26, 29].
3
-bonded diamond
nanowires reported in Ref. [26] (that employ the same method
and convergence criteria), the values of
To begin with, using the energies from the sp
E
(sp
3
) = −7.54 eV and
E
= 1.32 eV have been obtained from the intercept and coefficient
(respectively) of a linear fit to the total energy per C atom versus
the number of dangling bonds per atom. This is shown in Fig. 7.9.
Similarly, by plotting the total energy per C atom for zigzag and
armchair CNT (in the range
DB
= 4 to 12) versus the inverse square
of the radius of curvature the values of
m
2
E
(sp
) = −7.82 eV and
E
(Θ = 0) = 2.04 eV Å/atom have been obtained from the intercept
and coefficient, respectively (see Fig. 7.10). Note that the value of
E
S
(Θ = 0) is in good agreement with the value of 2.14 eV Å/atom
obtained by Gülseren
S
et al
. (where
ρ
is unity) [43].
N
DB
/
N
C
Figure 7.9
Energy per carbon atom calculated for a set of one-dimensional
(infinite) diamond nanowires. The slope provides the dangling
bond energy
(sp
3
) cohesive energy.
Reproduced with permission from Ref. [29]. Cpoyright
American Institute of Physics, 2004.
E
, and intercepts the
E
DB
