SWNTMixin¶

class sknano.core.structures.SWNTMixin[source] [edit on github][source]

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

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.