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.