EE599 Innovation and Nanotechnology
Homework Assignment #2
Prof. Steve Cronin
Due Sept 27, 2011
Carbon Nanotubes:
In the following problems, write a MatLab
*
program that includes a function for
each of the quantities requested below.
When you turn in this problem set, submit the
MatLab file as well as the solutions to the following problems.
We will use this MatLab
program in subsequent homework assignments, so be thorough in your execution.
The unit cell of a (4,2) carbon nanotube is shown below on a graphene lattice.
The unit vectors are given by:
a
a
a
a
−
=
=
2
1
,
2
3
2
1
,
2
3
2
1
where
a
=0.249nm.
1.)
Derive expressions for the circumference C
h
, diameter
d
t
, chiral angle
θ
, and
length of the unit cell
T
for an
(n,m)
nanotube.
Write functions in MatLab for
these quantities as function of
n
,
m
and
a
.
2.)
Derive an expression for the number of hexagons in the unit cell of an
(n,m)
nanotube. Write functions in MatLab for the number of hexagons in the unit cell
and for the number of carbon atoms in the unit cell as a function of
n
and
m.
3.)
Calculate the circumference C
h
, diameter
d
t
, chiral angle
θ
, length of the unit cell
T
and the number of atoms in the unit cell of the following nanotubes:
(9,0), (10,0), (9,9), (10,10), (13,7), (10,1)