SWNTMixin

class sknano.core.structures.SWNTMixin

Bases: object

Mixin class for nanotube classes.

Attributes

Ch	SWNT circumference $|\mathbf{C}_h|$ in Å
Ch_vec	SWNT chiral vector.
Lz	SWNT length $L_z = L_{\mathrm{tube}}$ in Angstroms.
M	$M = np - nq$
N	Number of graphene hexagons in nanotube unit cell.
Natoms	Number of atoms in nanotube.
Natoms_per_tube	Number of atoms in nanotube $N_{\mathrm{atoms/tube}}$.
Natoms_per_unit_cell	Number of atoms in nanotube unit cell.
R	Symmetry vector $\mathbf{R} = (p, q)$.
T	Length of nanotube unit cell $|\mathbf{T}|$ in Å.
Tvec	SWNT translation vector.
chiral_angle	Chiral angle $\theta_c$ in degrees.
chiral_type	SWNT chiral type.
d	$d=\gcd{(n, m)}$
dR	$d_R=\gcd{(2n + m, 2m + n)}$
dt	Nanotube diameter $d_t = \frac{|\mathbf{C}_h|}{\pi}$ in Å.
electronic_type	SWNT electronic type.
fix_Lz	bool indicating whether SWNTMixin.Lz is fixed or calculated.
linear_mass_density	Linear mass density of nanotube in g/Å.
m	Chiral index $m$.
mass	SWNT mass in grams.
n	Chiral index $n$.
nz	Number of nanotube unit cells along the $z$-axis.
rt	Nanotube radius $r_t = \frac{|\mathbf{C}_h|}{2\pi}$ in Å.
t1	$t_{1} = \frac{2m + n}{d_{R}}$
t2	$t_2 = -\frac{2n + m}{d_R}$
tube_length	Alias for SWNT.Lz
tube_mass	An alias for mass.
unit_cell_mass	Unit cell mass in atomic mass units.
unit_cell_symmetry_params	Tuple of SWNT unit cell symmetry parameters.

Attributes Summary

Ch	SWNT circumference $|\mathbf{C}_h|$ in Å
Ch_vec	SWNT chiral vector.
Lz	SWNT length $L_z = L_{\mathrm{tube}}$ in Angstroms.
M	$M = np - nq$
N	Number of graphene hexagons in nanotube unit cell.
Natoms	Number of atoms in nanotube.
Natoms_per_tube	Number of atoms in nanotube $N_{\mathrm{atoms/tube}}$.
Natoms_per_unit_cell	Number of atoms in nanotube unit cell.
R	Symmetry vector $\mathbf{R} = (p, q)$.
T	Length of nanotube unit cell $|\mathbf{T}|$ in Å.
Tvec	SWNT translation vector.
chiral_angle	Chiral angle $\theta_c$ in degrees.
chiral_type	SWNT chiral type.
d	$d=\gcd{(n, m)}$
dR	$d_R=\gcd{(2n + m, 2m + n)}$
dt	Nanotube diameter $d_t = \frac{|\mathbf{C}_h|}{\pi}$ in Å.
electronic_type	SWNT electronic type.
fix_Lz	bool indicating whether SWNTMixin.Lz is fixed or calculated.
linear_mass_density	Linear mass density of nanotube in g/Å.
m	Chiral index $m$.
mass	SWNT mass in grams.
n	Chiral index $n$.
nz	Number of nanotube unit cells along the $z$-axis.
rt	Nanotube radius $r_t = \frac{|\mathbf{C}_h|}{2\pi}$ in Å.
t1	$t_{1} = \frac{2m + n}{d_{R}}$
t2	$t_2 = -\frac{2n + m}{d_R}$
tube_length	Alias for SWNT.Lz
tube_mass	An alias for mass.
unit_cell_mass	Unit cell mass in atomic mass units.
unit_cell_symmetry_params	Tuple of SWNT unit cell symmetry parameters.

Attributes Documentation

Ch

SWNT circumference $|\mathbf{C}_h|$ in Å

Ch_vec

SWNT chiral vector.

Lz

SWNT length $L_z = L_{\mathrm{tube}}$ in Angstroms.

M

$M = np - nq$

$M$ is the number of multiples of the translation vector $\mathbf{T}$ in the vector $N\mathbf{R}$.

N

Number of graphene hexagons in nanotube unit cell.

$$N = \frac{4(n^2 + m^2 + nm)}{d_R}$$

Natoms

Number of atoms in nanotube.

Changed in version 0.3.0: Returns total number of atoms per nanotube. Use Natoms_per_unit_cell to get the number of atoms per unit cell.

$$N_{\mathrm{atoms}} = 2N\times n_z = \frac{4(n^2 + m^2 + nm)}{d_R}\times n_z$$

where $N$ is the number of graphene hexagons mapped to the nanotube unit cell and $n_z$ is the number of unit cells.

Natoms_per_tube

Number of atoms in nanotube $N_{\mathrm{atoms/tube}}$.

Natoms_per_unit_cell

Number of atoms in nanotube unit cell.

$$N_{\mathrm{atoms}} = 2N = \frac{4(n^2 + m^2 + nm)}{d_R}$$

where $N$ is the number of graphene hexagons mapped to the nanotube unit cell.

R

Symmetry vector $\mathbf{R} = (p, q)$.

$$\mathbf{R} = p\mathbf{a}_1 + q\mathbf{a}_2$$

T

Length of nanotube unit cell $|\mathbf{T}|$ in Å.

$$|\mathbf{T}| = \frac{\sqrt{3} |\mathbf{C}_{h}|}{d_{R}}$$

Tvec

SWNT translation vector.

chiral_angle

Chiral angle $\theta_c$ in degrees.

$$\theta_c = \tan^{-1}\left(\frac{\sqrt{3} m}{2n + m}\right)$$

chiral_type

SWNT chiral type.

d

$d=\gcd{(n, m)}$

$d$ is the Greatest Common Divisor of $n$ and $m$.

dR

$d_R=\gcd{(2n + m, 2m + n)}$

$d_R$ is the Greatest Common Divisor of $2n + m$ and $2m + n$.

dt

Nanotube diameter $d_t = \frac{|\mathbf{C}_h|}{\pi}$ in Å.

electronic_type

SWNT electronic type.

New in version 0.2.7.

The electronic type is determined as follows:

if $(2n + m)\,\mathrm{mod}\,3=0$, the nanotube is metallic.

if $(2n + m)\,\mathrm{mod}\,3=1$, the nanotube is semiconducting, type 1.

if $(2n + m)\,\mathrm{mod}\,3=2$, the nanotube is semiconducting, type 2.

The $x\,\mathrm{mod}\,y$ notation is mathematical shorthand for the modulo operation, which computes the remainder of the division of $x$ by $y$. So, for example, all armchair nanotubes must be metallic since the chiral indices satisfy: $2n + m = 2n + n = 3n$ and therefore $3n\,\mathrm{mod}\,3$ i.e. the remainder of the division of $3n/3=n$ is always zero.

Note

Mathematically, $(2n + m)\,\mathrm{mod}\,3$ is equivalent to $(n - m)\,\mathrm{mod}\,3$ when distinguishing between metallic and semiconducting. However, when distinguishing between semiconducting types, one must be careful to observe the following convention:

• Semiconducting, type 1 means:
  • $(2n + m)\,\mathrm{mod}\,3=1$
  • $(n - m)\,\mathrm{mod}\,3=2$
• Semiconducting, type 2 means:
  • $(2n + m)\,\mathrm{mod}\,3=2$
  • $(n - m)\,\mathrm{mod}\,3=1$

fix_Lz

bool indicating whether SWNTMixin.Lz is fixed or calculated.

linear_mass_density

Linear mass density of nanotube in g/Å.

m

Chiral index $m$.

The component of the chiral vector $\mathbf{C}_h$ along $\mathbf{a}_2$:

$$\mathbf{C}_h = n\mathbf{a}_1 + m\mathbf{a}_2 = (n, m)$$

mass

SWNT mass in grams.

n

Chiral index $n$.

The component of the chiral vector $\mathbf{C}_h$ along $\mathbf{a}_1$:

$$\mathbf{C}_h = n\mathbf{a}_1 + m\mathbf{a}_2 = (n, m)$$

nz

Number of nanotube unit cells along the $z$-axis.

rt

Nanotube radius $r_t = \frac{|\mathbf{C}_h|}{2\pi}$ in Å.

t1

$t_{1} = \frac{2m + n}{d_{R}}$

where $d_R = \gcd{(2n + m, 2m + n)}$.

The component of the translation vector $\mathbf{T}$ along $\mathbf{a}_1$:

$$\mathbf{T} = t_1\mathbf{a}_{1} + t_2\mathbf{a}_2$$

t2

$t_2 = -\frac{2n + m}{d_R}$

where $d_R = \gcd{(2n + m, 2m + n)}$.

The component of the translation vector $\mathbf{T}$ along $\mathbf{a}_2$:

$$\mathbf{T} = t_1\mathbf{a}_1 + t_2\mathbf{a}_2$$

tube_length

Alias for SWNT.Lz

tube_mass

An alias for mass.

unit_cell_mass

Unit cell mass in atomic mass units.

unit_cell_symmetry_params

Tuple of SWNT unit cell symmetry parameters.