Source code for sknano.structures._swnt

# -*- coding: utf-8 -*-
"""
==============================================================================
SWNT structure class (:mod:`sknano.structures._swnt`)
==============================================================================

.. currentmodule:: sknano.structures._swnt

"""
from __future__ import absolute_import, division, print_function, \
    unicode_literals
__docformat__ = 'restructuredtext en'

from fractions import gcd
import numbers
import numpy as np

from sknano.core.atoms import Atom, BasisAtom, BasisAtoms
from sknano.core.crystallography import Crystal3DLattice, UnitCell
from sknano.core.refdata import aCC, grams_per_Da
from ._base import NanoStructureBase, r_CC_vdw
from ._extras import attr_strfmt, attr_symbols, attr_units, \
    get_chiral_indices, get_chiral_type

__all__ = ['compute_d', 'compute_dR', 'compute_N', 'compute_t1', 'compute_t2',
           'compute_Ch', 'compute_chiral_angle', 'compute_T', 'compute_dt',
           'compute_rt', 'compute_M', 'compute_R', 'compute_R_chiral_angle',
           'compute_symmetry_operation', 'compute_psi', 'compute_tau',
           'compute_Lx', 'compute_Ly', 'compute_Lz',
           'compute_electronic_type', 'compute_Natoms',
           'compute_Natoms_per_tube', 'compute_Natoms_per_unit_cell',
           'compute_unit_cell_mass', 'compute_linear_mass_density',
           'compute_symmetry_chiral_angle', 'compute_tube_diameter',
           'compute_tube_radius', 'compute_tube_length', 'compute_tube_mass',
           'SWNTMixin', 'NanotubeMixin', 'SWNT', 'Nanotube']


[docs]def compute_d(*Ch): """Compute :math:`d=\\gcd{(n, m)}` :math:`d` is the **G**\ reatest **C**\ ommon **D**\ ivisor of :math:`n` and :math:`m`. Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. Returns ------- gcd : :class:`python:int` Greatest Common Divisor of :math:`n` and :math:`m` """ n, m, _ = get_chiral_indices(*Ch) return gcd(n, m)
[docs]def compute_dR(*Ch): """Compute :math:`d_R=\\gcd{(2n + m, 2m + n)}` :math:`d_R` is the **G**\ reatest **C**\ ommon **D**\ ivisor of :math:`2n + m` and :math:`2m + n`. Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. Returns ------- int greatest common divisor of :math:`2n+m` and :math:`2m+n` """ n, m, _ = get_chiral_indices(*Ch) return gcd(2 * m + n, 2 * n + m)
[docs]def compute_N(*Ch): """Compute :math:`N = \\frac{2(n^2+m^2+nm)}{d_R}`. :math:`N` is the number of graphene hexagons mapped to a nanotube *unit cell*. Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. Returns ------- int Number of hexagons per nanotube unit cell: :math:`N = \\frac{2(n^2+m^2+nm)}{d_R}`. """ n, m, _ = get_chiral_indices(*Ch) dR = compute_dR(n, m) try: return int(2 * (n ** 2 + m ** 2 + n * m) / dR) except ZeroDivisionError: return 0
[docs]def compute_t1(*Ch): """Compute :math:`t_1 = \\frac{2m + n}{d_R}` where :math:`d_R = \\gcd{(2n + m, 2m + n)}`. The component of the translation vector :math:`\\mathbf{T}` along :math:`\\mathbf{a}_1`: .. math:: \\mathbf{T} = t_1\\mathbf{a}_{1} + t_2\\mathbf{a}_2 Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. Returns ------- int :math:`t_1` """ n, m, _ = get_chiral_indices(*Ch) dR = compute_dR(n, m) try: return int((2 * m + n) / dR) except ZeroDivisionError: return 0
[docs]def compute_t2(*Ch): """Compute :math:`t_2 = -\\frac{2n + m}{d_R}` where :math:`d_R = \\gcd{(2n + m, 2m + n)}`. The component of the translation vector :math:`\\mathbf{T}` along :math:`\\mathbf{a}_2`: .. math:: \\mathbf{T} = t_1\\mathbf{a}_1 + t_2\\mathbf{a}_2 Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. Returns ------- int :math:`t_2` """ n, m, _ = get_chiral_indices(*Ch) dR = compute_dR(n, m) try: return -int((2 * n + m) / dR) except ZeroDivisionError: return 0
[docs]def compute_Ch(*Ch, bond=None, **kwargs): """Compute nanotube circumference :math:`|\\mathbf{C}_{h}|` in \ **\u212b**. .. math:: |\\mathbf{C}_h| = a\\sqrt{n^2 + m^2 + nm} = \\sqrt{3}a_{\\mathrm{CC}}\\sqrt{n^2 + m^2 + nm} Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. bond : float, optional Distance between nearest neighbor atoms (i.e., bond length). Must be in units of **\u212b**. Default value is the carbon-carbon bond length in graphite, approximately :math:`\\mathrm{a}_{\\mathrm{CC}} = 1.42` \u212b Returns ------- float Nanotube circumference :math:`|\\mathbf{C}_h|` in \u212b. """ n, m, _ = get_chiral_indices(*Ch) if bond is None: bond = aCC return bond * np.sqrt(3 * (n ** 2 + m ** 2 + n * m))
[docs]def compute_chiral_angle(*Ch, degrees=True, **kwargs): """Compute chiral angle :math:`\\theta_c`. .. math:: \\theta_c = \\tan^{-1}\\left(\\frac{\\sqrt{3} m}{2n + m}\\right) Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. degrees : bool, optional If `True`, return angle in degrees. Returns ------- float Chiral angle :math:`\\theta_{c}` in degrees (default) or radians (if `degrees=False`). """ n, m, _ = get_chiral_indices(*Ch) theta = np.arctan(np.sqrt(3) * m / (2 * n + m)) # return np.arccos((2*n + m) / (2 * np.sqrt(n**2 + m**2 + n*m))) if degrees or kwargs.get('rad2deg', False): return np.degrees(theta) else: return theta
[docs]def compute_T(*Ch, bond=None, length=True, **kwargs): """Compute length of nanotube unit cell :math:`|\\mathbf{T}|` in \ \u212b. .. math:: |\\mathbf{T}| = \\frac{\\sqrt{3} |\\mathbf{C}_{h}|}{d_{R}} = \\frac{\\sqrt{3}a\\sqrt{n^2 + m^2 + nm}}{d_{R}} = \\frac{3a_{\\mathrm{CC}}\\sqrt{n^2 + m^2 + nm}}{d_{R}} Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. bond : float, optional Distance between nearest neighbor atoms (i.e., bond length). Must be in units of **\u212b**. Default value is the carbon-carbon bond length in graphite, approximately :math:`\\mathrm{a}_{\\mathrm{CC}} = 1.42` \u212b length : bool, optional Compute the magnitude (i.e., length) of the translation vector. Returns ------- float or 2-tuple of ints If `length` is `True`, then return the length of unit cell in \u212b. If `length` is `False`, return the componets of the translation vector as a 2-tuple of ints (:math:`t_1`, :math:`t_2`). """ n, m, _ = get_chiral_indices(*Ch) if length: if bond is None: bond = aCC Ch = compute_Ch(n, m, bond=bond) dR = compute_dR(n, m) try: return np.sqrt(3) * Ch / dR except (FloatingPointError, ZeroDivisionError): return 0 else: t1 = compute_t1(n, m) t2 = compute_t2(n, m) return (t1, t2)
[docs]def compute_dt(*Ch, bond=None, **kwargs): """Compute nanotube diameter :math:`d_t` in \u212b. .. math:: d_t = \\frac{|\\mathbf{C}_h|}{\\pi} Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. bond : float, optional Distance between nearest neighbor atoms (i.e., bond length). Must be in units of **\u212b**. Default value is the carbon-carbon bond length in graphite, approximately :math:`\\mathrm{a}_{\\mathrm{CC}} = 1.42` \u212b Returns ------- float Nanotube diameter :math:`d_t` in \u212b. """ n, m, _ = get_chiral_indices(*Ch) Ch = compute_Ch(n, m, bond=bond) return Ch / np.pi
[docs]def compute_rt(*Ch, bond=None, **kwargs): """Compute nanotube radius :math:`r_t` in \u212b. .. math:: r_t = \\frac{|\\mathbf{C}_h|}{2\\pi} Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. bond : float, optional Distance between nearest neighbor atoms (i.e., bond length). Must be in units of **\u212b**. Default value is the carbon-carbon bond length in graphite, approximately :math:`\\mathrm{a}_{\\mathrm{CC}} = 1.42` \u212b Returns ------- float Nanotube radius :math:`r_t` in \u212b. """ n, m, _ = get_chiral_indices(*Ch) Ch = compute_Ch(n, m, bond=bond) return Ch / (2 * np.pi)
[docs]def compute_M(*Ch): """Compute :math:`M = mp - nq` :math:`M` is the number of multiples of the translation vector :math:`\\mathbf{T}` in the vector :math:`N\\mathbf{R}`. Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. Returns ------- int :math:`M = mp - nq` """ n, m, _ = get_chiral_indices(*Ch) p, q = compute_R(n, m) return m * p - n * q
[docs]def compute_R(*Ch, bond=None, length=False, **kwargs): """Compute symmetry vector :math:`\\mathbf{R} = (p, q)`. The *symmetry vector* is any lattice vector of the unfolded graphene layer that represents a *symmetry operation* of the nanotube. The symmetry vector :math:`\\mathbf{R}` can be written as: .. math:: \\mathbf{R} = p\\mathbf{a}_1 + q\\mathbf{a}_2 where :math:`p` and :math:`q` are integers. The *symmetry vector* represents a *symmetry operation* of the nanotube which arises as a *screw translation*, which is a combination of a rotation :math:`\\psi` and translation :math:`\\tau`. The symmetry operation of the nanotube can be written as: .. math:: R = (\\psi|\\tau) Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. bond : float, optional Distance between nearest neighbor atoms (i.e., bond length). Must be in units of **\u212b**. Default value is the carbon-carbon bond length in graphite, approximately :math:`\\mathrm{a}_{\\mathrm{CC}} = 1.42` \u212b length : bool, optional If `True`, return :math:`|\\mathbf{R}|`. Returns ------- (p, q) : tuple 2-tuple of ints -- components of :math:`\\mathbf{R}`. float Length of :math:`\\mathbf{R}` (:math:`|\\mathbf{R}|`) if `length` is `True` in units of **\u212b**. """ n, m, _ = get_chiral_indices(*Ch) N = compute_N(n, m) t1 = compute_t1(n, m) t2 = compute_t2(n, m) p = q = 0 for i in range(0, t1 + n + 1): for j in range(t2, m + 1): R = t1 * j - t2 * i if R == 1: M = m * i - n * j if M > 0 and M <= N: p = i q = j if length: if bond is None: bond = aCC return bond * np.sqrt(3 * (p ** 2 + q ** 2 + p * q)) else: return (p, q)
[docs]def compute_R_chiral_angle(*Ch, degrees=True, **kwargs): """Compute "chiral angle" of symmetry vector :math:`\\theta_R`. .. math:: \\theta_R = \\tan^{-1}\\left(\\frac{\\sqrt{3}q}{2p + q}\\right) Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. degrees : bool, optional If `True`, return angle in degrees Returns ------- float Chiral angle of *symmetry vector* :math:`\\theta_R` in degrees (default) or radians (if `degrees=False`). """ n, m, _ = get_chiral_indices(*Ch) p, q = compute_R(n, m) theta = np.arctan((np.sqrt(3) * q) / (2 * p + q)) if degrees or kwargs.get('rad2deg', False): return np.degrees(theta) else: return theta
[docs]def compute_symmetry_operation(*Ch, bond=None): """Compute symmetry operation :math:`(\\psi|\\tau)`. The *symmetry vector* `R` represents a *symmetry operation* of the nanotube which arises as a *screw translation*--a combination of a rotation :math:`\\psi` and translation :math:`\\tau`. The symmetry operation of the nanotube can be written as: .. math:: R = (\\psi|\\tau) Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. bond : float, optional Distance between nearest neighbor atoms (i.e., bond length). Must be in units of **\u212b**. Default value is the carbon-carbon bond length in graphite, approximately :math:`\\mathrm{a}_{\\mathrm{CC}} = 1.42` \u212b Returns ------- (psi, tau) : tuple 2-tuple of floats -- :math:`\\psi` in radians and :math:`\\tau` in \u212b. """ n, m, _ = get_chiral_indices(*Ch) psi = compute_psi(n, m) tau = compute_tau(n, m, bond=bond) return (psi, tau)
[docs]def compute_psi(*Ch): """Compute rotation component of symmetry operation \ :math:`\\psi` in **radians**. .. math:: \\psi = \\frac{2\\pi}{N} Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. Returns ------- float Rotation component of symmetry operation :math:`\\psi` in **radians**. """ n, m, _ = get_chiral_indices(*Ch) N = compute_N(n, m) try: return 2 * np.pi / N except (FloatingPointError, ZeroDivisionError): return 0
[docs]def compute_tau(*Ch, bond=None, **kwargs): """Compute translation component of symmetry operation \ :math:`\\tau` in **\u212b**. .. math:: \\tau = \\frac{M|\\mathbf{T}|}{N} Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. bond : float, optional Distance between nearest neighbor atoms (i.e., bond length). Must be in units of **\u212b**. Default value is the carbon-carbon bond length in graphite, approximately :math:`\\mathrm{a}_{\\mathrm{CC}} = 1.42` \u212b Returns ------- float Translation component of symmetry operation :math:`\\tau` in **\u212b**. """ n, m, _ = get_chiral_indices(*Ch) M = compute_M(n, m) N = compute_N(n, m) T = compute_T(n, m, bond=bond) try: return M * T / N except ZeroDivisionError: return 0
[docs]def compute_electronic_type(*Ch): """Compute nanotube electronic type. .. versionadded:: 0.2.7 The electronic type is determined as follows: if :math:`(2n + m)\\,\\mathrm{mod}\\,3=0`, the nanotube is **metallic**. if :math:`(2n + m)\\,\\mathrm{mod}\\,3=1`, the nanotube is **semiconducting, type 1**. if :math:`(2n + m)\\,\\mathrm{mod}\\,3=2`, the nanotube is **semiconducting, type 2**. The :math:`x\\,\\mathrm{mod}\\,y` notation is mathematical shorthand for the *modulo* operation, which computes the **remainder** of the division of :math:`x` by :math:`y`. So, for example, all *armchair* nanotubes must be metallic since the chiral indices satisfy: :math:`2n + m = 2n + n = 3n` and therefore :math:`3n\\,\\mathrm{mod}\\,3` i.e. the remainder of the division of :math:`3n/3=n` is always zero. .. note:: Mathematically, :math:`(2n + m)\\,\\mathrm{mod}\\,3` is equivalent to :math:`(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: * :math:`(2n + m)\\,\\mathrm{mod}\\,3=1` * :math:`(n - m)\\,\\mathrm{mod}\\,3=2` * Semiconducting, **type 2** means: * :math:`(2n + m)\\,\\mathrm{mod}\\,3=2` * :math:`(n - m)\\,\\mathrm{mod}\\,3=1` Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. Returns ------- str """ n, m, _ = get_chiral_indices(*Ch) if (2 * n + m) % 3 == 1: return 'semiconducting, type 1' elif (2 * n + m) % 3 == 2: return 'semiconducting, type 2' else: return 'metallic'
[docs]def compute_Natoms(*Ch, nz=1): """Compute :math:`N_{\\mathrm{atoms/tube}}` .. math:: N_{\\mathrm{atoms/tube}} = N_{\\mathrm{atoms/cell}} \\times n_{z-\\mathrm{cells}} Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. nz : {int, float} Number of nanotube unit cells Returns ------- int :math:`N_{\\mathrm{atoms/tube}}` """ n, m, _ = get_chiral_indices(*Ch) Natoms_per_unit_cell = compute_Natoms_per_unit_cell(n, m) return int(Natoms_per_unit_cell * nz)
[docs]def compute_Natoms_per_tube(*Ch, nz=1): """Compute :math:`N_{\\mathrm{atoms/tube}}` .. math:: N_{\\mathrm{atoms/tube}} = N_{\\mathrm{atoms/cell}} \\times n_{z-\\mathrm{cells}} Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. nz : {int, float} Number of nanotube unit cells Returns ------- int :math:`N_{\\mathrm{atoms/tube}}` """ return compute_Natoms(*Ch, nz=nz)
[docs]def compute_Natoms_per_unit_cell(*Ch): """Compute :math:`N_{\mathrm{atoms/cell}} = 2N`. .. math:: N_{\\mathrm{atoms}} = 2N = \\frac{4(n^2 + m^2 + nm)}{d_R} where :math:`N` is the number of graphene hexagons mapped to the nanotube unit cell. Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. Returns ------- `2N` : int Number of atoms in nanotube *unit cell*: N_{\\mathrm{atoms}} = 2N = \\frac{4(n^2 + m^2 + nm)}{d_R} """ n, m, _ = get_chiral_indices(*Ch) N = compute_N(n, m) return 2 * N
[docs]def compute_unit_cell_mass(*Ch, element1=None, element2=None, **kwargs): """Compute nanotube unit cell mass in *Daltons*/*atomic mass units* (amu) \ units. Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. element1, element2 : {str, int}, optional Element symbol or atomic number of basis :class:`~sknano.core.atoms.Atom` 1 and 2 Returns ------- float Unit cell mass in **Daltons**. Notes ----- .. todo:: Handle different elements and perform accurate calculation by determining number of atoms of each element. """ n, m, _ = get_chiral_indices(*Ch) N = compute_N(n, m) if element1 is None: element1 = 'C' if element2 is None: element2 = 'C' mass = N * (Atom(element1).mass + Atom(element2).mass) return mass
[docs]def compute_linear_mass_density(*Ch, bond=None, element1=None, element2=None, **kwargs): """Compute nanotube linear mass density (mass per unit length) in \ **grams/nm**. Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. element1, element2 : {str, int}, optional Element symbol or atomic number of basis :class:`~sknano.core.atoms.Atom` 1 and 2 bond : float, optional Distance between nearest neighbor atoms (i.e., bond length). Must be in units of **\u212b**. Default value is the carbon-carbon bond length in graphite, approximately :math:`\\mathrm{a}_{\\mathrm{CC}} = 1.42` \u212b Returns ------- float Linear mass density in units of **g/nm**. """ n, m, _ = get_chiral_indices(*Ch) mass = compute_unit_cell_mass(n, m, element1=element1, element2=element2, **kwargs) T = compute_T(n, m, bond=bond, length=True, **kwargs) try: linear_mass_density = mass / T # there are 1.6605e-24 grams / Da and 10 angstroms / nm linear_mass_density *= 10 * grams_per_Da return linear_mass_density except ZeroDivisionError: return 0
def compute_Lx(*Ch, nx=1, bond=None, gutter=r_CC_vdw): return nx * (compute_dt(*Ch, bond=bond) + 2 * gutter) / 10 def compute_Ly(*Ch, ny=1, bond=None, gutter=r_CC_vdw): return ny * (compute_dt(*Ch, bond=bond) + 2 * gutter) / 10
[docs]def compute_Lz(*Ch, nz=1, bond=None, **kwargs): """Compute :math:`L_z = L_{\\mathrm{tube}}` in **nanometers**. .. math:: L_z = n_z |\\mathbf{T}| Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. nz : {int, float} Number of nanotube unit cells bond : float, optional Distance between nearest neighbor atoms (i.e., bond length). Must be in units of **\u212b**. Default value is the carbon-carbon bond length in graphite, approximately :math:`\\mathrm{a}_{\\mathrm{CC}} = 1.42` \u212b Returns ------- float :math:`L_z = L_{\\mathrm{tube}}` in **nanometers** """ n, m, _ = get_chiral_indices(*Ch) if not (isinstance(nz, numbers.Real) or nz > 0): raise TypeError('Expected a real, positive number') T = compute_T(n, m, bond=bond, **kwargs) return nz * T / 10
def compute_symmetry_chiral_angle(*Ch, degrees=True): """Alias for :func:`compute_R_chiral_angle`.""" return compute_R_chiral_angle(*Ch, degrees=degrees) def compute_tube_diameter(*Ch, bond=None, **kwargs): """Alias for :func:`compute_dt`""" return compute_dt(*Ch, bond=bond, **kwargs) def compute_tube_radius(*Ch, bond=None, **kwargs): """Alias for :func:`compute_rt`""" return compute_rt(*Ch, bond=bond, **kwargs) def compute_tube_length(*Ch, nz=1, bond=None, **kwargs): """Alias for :func:`compute_Lz`""" return compute_Lz(*Ch, nz=nz, bond=bond, **kwargs)
[docs]def compute_tube_mass(*Ch, nz=1, element1=None, element2=None): """Compute nanotube mass in **grams**. Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. nz : {int, float} Number of nanotube unit cells element1, element2 : {str, int}, optional Element symbol or atomic number of basis :class:`~sknano.core.atoms.Atom` 1 and 2 Returns ------- float Nanotube mass in **grams**. Notes ----- .. todo:: Handle different elements and perform accurate calculation by determining number of atoms of each element. """ n, m, _ = get_chiral_indices(*Ch) if not (isinstance(nz, numbers.Real) or nz > 0): raise TypeError('Expected a real, positive number') Natoms = compute_Natoms(n, m, nz=nz) if element1 is None: element1 = 'C' if element2 is None: element2 = 'C' atom1 = Atom(element1) atom2 = Atom(element2) mass = Natoms * (atom1.mass + atom2.mass) / 2 # there are 1.6605e-24 grams / Da mass *= grams_per_Da return mass
[docs]class SWNTMixin: """Mixin class for nanotube classes.""" @property def n(self): """Chiral index :math:`n`. The component of the chiral vector :math:`\\mathbf{C}_h` along :math:`\\mathbf{a}_1`: .. math:: \\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m) """ return self._n @n.setter def n(self, value): """Set chiral index :math:`n`""" if not (isinstance(value, numbers.Real) or value >= 0): raise TypeError('Expected an integer.') self._n = int(value) @n.deleter def n(self): del self._n @property def m(self): """Chiral index :math:`m`. The component of the chiral vector :math:`\\mathbf{C}_h` along :math:`\\mathbf{a}_2`: .. math:: \\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m) """ return self._m @m.setter def m(self, value): """Set chiral index :math:`m`""" if not (isinstance(value, numbers.Real) or value >= 0): raise TypeError('Expected an integer.') self._m = int(value) @m.deleter def m(self): del self._m @property def d(self): """:math:`d=\\gcd{(n, m)}` :math:`d` is the **G**\ reatest **C**\ ommon **D**\ ivisor of :math:`n` and :math:`m`. """ return compute_d(self.n, self.m) @property def dR(self): """:math:`d_R=\\gcd{(2n + m, 2m + n)}` :math:`d_R` is the **G**\ reatest **C**\ ommon **D**\ ivisor of :math:`2n + m` and :math:`2m + n`. """ return compute_dR(self.n, self.m) @property def N(self): """Number of graphene hexagons in nanotube *unit cell*. .. math:: N = \\frac{4(n^2 + m^2 + nm)}{d_R} """ return compute_N(self.n, self.m) @property def t1(self): """:math:`t_{1} = \\frac{2m + n}{d_{R}}` where :math:`d_R = \\gcd{(2n + m, 2m + n)}`. The component of the translation vector :math:`\\mathbf{T}` along :math:`\\mathbf{a}_1`: .. math:: \\mathbf{T} = t_1\\mathbf{a}_{1} + t_2\\mathbf{a}_2 """ return compute_t1(self.n, self.m) @property def t2(self): """:math:`t_2 = -\\frac{2n + m}{d_R}` where :math:`d_R = \\gcd{(2n + m, 2m + n)}`. The component of the translation vector :math:`\\mathbf{T}` along :math:`\\mathbf{a}_2`: .. math:: \\mathbf{T} = t_1\\mathbf{a}_1 + t_2\\mathbf{a}_2 """ return compute_t2(self.n, self.m) @property def Ch_vec(self): """SWNT chiral vector.""" return (self.n, self.m) @property def Ch(self): """SWNT circumference :math:`|\\mathbf{C}_h|` in **\u212b**""" return compute_Ch(self.n, self.m, bond=self.bond) @property def dt(self): """Nanotube diameter :math:`d_t = \\frac{|\\mathbf{C}_h|}{\\pi}` \ in \u212b.""" return compute_dt(self.n, self.m, bond=self.bond) @property def rt(self): """Nanotube radius :math:`r_t = \\frac{|\\mathbf{C}_h|}{2\\pi}` \ in \u212b.""" return compute_rt(self.n, self.m, bond=self.bond) @property def chiral_angle(self): """Chiral angle :math:`\\theta_c` in **degrees**. .. math:: \\theta_c = \\tan^{-1}\\left(\\frac{\\sqrt{3} m}{2n + m}\\right) """ return compute_chiral_angle(self.n, self.m) @property def chiral_type(self): """`SWNT` chiral type.""" return get_chiral_type((self.n, self.m)) @property def Tvec(self): """`SWNT` translation vector.""" return (self.t1, self.t2) @property def T(self): """Length of nanotube unit cell :math:`|\\mathbf{T}|` in \u212b. .. math:: |\\mathbf{T}| = \\frac{\\sqrt{3} |\\mathbf{C}_{h}|}{d_{R}} """ return compute_T(self.n, self.m, bond=self.bond, length=True) @property def M(self): """:math:`M = np - nq` :math:`M` is the number of multiples of the translation vector :math:`\\mathbf{T}` in the vector :math:`N\\mathbf{R}`. """ return compute_M(self.n, self.m) @property def R(self): """Symmetry vector :math:`\\mathbf{R} = (p, q)`. .. math:: \\mathbf{R} = p\\mathbf{a}_1 + q\\mathbf{a}_2 """ return compute_R(self.n, self.m, bond=self.bond, length=False) @property def nz(self): """Number of nanotube unit cells along the :math:`z`-axis.""" return self._nz @nz.setter def nz(self, value): """Set number of nanotube unit cells along the :math:`z`-axis.""" if not (isinstance(value, numbers.Real) or value > 0): raise TypeError('Expected a real, positive number.') self._nz = value if self._integral_nz: self._nz = int(np.ceil(value)) def _update_nz(self): try: self.nz = self.nz except AttributeError: pass @property def electronic_type(self): """SWNT electronic type. .. versionadded:: 0.2.7 The electronic type is determined as follows: if :math:`(2n + m)\\,\\mathrm{mod}\\,3=0`, the nanotube is **metallic**. if :math:`(2n + m)\\,\\mathrm{mod}\\,3=1`, the nanotube is **semiconducting, type 1**. if :math:`(2n + m)\\,\\mathrm{mod}\\,3=2`, the nanotube is **semiconducting, type 2**. The :math:`x\\,\\mathrm{mod}\\,y` notation is mathematical shorthand for the *modulo* operation, which computes the **remainder** of the division of :math:`x` by :math:`y`. So, for example, all *armchair* nanotubes must be metallic since the chiral indices satisfy: :math:`2n + m = 2n + n = 3n` and therefore :math:`3n\\,\\mathrm{mod}\\,3` i.e. the remainder of the division of :math:`3n/3=n` is always zero. .. note:: Mathematically, :math:`(2n + m)\\,\\mathrm{mod}\\,3` is equivalent to :math:`(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: * :math:`(2n + m)\\,\\mathrm{mod}\\,3=1` * :math:`(n - m)\\,\\mathrm{mod}\\,3=2` * Semiconducting, **type 2** means: * :math:`(2n + m)\\,\\mathrm{mod}\\,3=2` * :math:`(n - m)\\,\\mathrm{mod}\\,3=1` """ return compute_electronic_type(self.n, self.m) @property def Lz(self): """SWNT length :math:`L_z = L_{\\mathrm{tube}}` in **nanometers**.""" return self.nz * self.T / 10 @property def fix_Lz(self): return self._fix_Lz @fix_Lz.setter def fix_Lz(self, value): if not isinstance(value, bool): raise TypeError('Expected `True` or `False`') self._fix_Lz = value self._integral_nz = False if self.fix_Lz else True self._update_nz() self._update_fmtstr() def _update_fmtstr(self): if self.fix_Lz: self.fmtstr = self.fmtstr.replace("nz={nz!r}", "Lz={Lz!r}, fix_Lz=True") else: self.fmtstr = self.fmtstr.replace("Lz={Lz!r}, fix_Lz=True", "nz={nz!r}") @property def Natoms(self): """Number of atoms in nanotube. .. versionchanged:: 0.3.0 **Returns total number of atoms per nanotube.** Use :attr:`~SWNT.Natoms_per_unit_cell` to get the number of atoms per unit cell. .. math:: N_{\\mathrm{atoms}} = 2N\\times n_z = \\frac{4(n^2 + m^2 + nm)}{d_R}\\times n_z where :math:`N` is the number of graphene hexagons mapped to the nanotube unit cell and :math:`n_z` is the number of unit cells. """ return compute_Natoms(self.n, self.m, nz=self.nz) @property def Natoms_per_unit_cell(self): """Number of atoms in nanotube unit cell. .. math:: N_{\\mathrm{atoms}} = 2N = \\frac{4(n^2 + m^2 + nm)}{d_R} where :math:`N` is the number of graphene hexagons mapped to the nanotube unit cell. """ return compute_Natoms_per_unit_cell(self.n, self.m) @property def Natoms_per_tube(self): """Number of atoms in nanotube :math:`N_{\\mathrm{atoms/tube}}`.""" return self.Natoms @property def Ntubes(self): """Number of nanotubes.""" return 1 @property def linear_mass_density(self): """Linear mass density of nanotube in g/nm.""" return compute_linear_mass_density(self.n, self.m, bond=self.bond, element1=self.element1, element2=self.element2) @property def tube_length(self): """Alias for :attr:`SWNT.Lz`""" return self.Lz @property def tube_mass(self): """SWNT mass in **grams**.""" return compute_tube_mass(self.n, self.m, nz=self.nz, element1=self.element1, element2=self.element2) @property def unit_cell_mass(self): """Unit cell mass in atomic mass units.""" return compute_unit_cell_mass(self.n, self.m, element1=self.element1, element2=self.element2) @property def unit_cell_symmetry_params(self): """Tuple of `SWNT` unit cell *symmetry parameters*.""" psi, tau = compute_symmetry_operation(self.n, self.m, bond=self.bond) aCh = compute_chiral_angle(self.n, self.m, degrees=False) dpsi = self.bond * np.cos(np.pi / 6 - aCh) / self.rt dtau = self.bond * np.sin(np.pi / 6 - aCh) return psi, tau, dpsi, dtau
NanotubeMixin = SWNTMixin
[docs]class SWNT(SWNTMixin, NanoStructureBase): """SWNT structure class. Parameters ---------- *Ch : {:class:`python:tuple` or :class:`python:int`\ s} Either a 2-tuple of integers (i.e., *Ch = ((n, m)) or 2 integers (i.e., *Ch = (n, m) specifying the chiral indices of the nanotube chiral vector :math:`\\mathbf{C}_h = n\\mathbf{a}_1 + m\\mathbf{a}_2 = (n, m)`. nz : :class:`python:int`, optional Number of repeat unit cells in the :math:`z` direction, along the *length* of the nanotube. basis : {:class:`python:list`}, optional List of :class:`python:str`\ s of element symbols or atomic number of the two atom basis (default: ['C', 'C']) .. versionadded:: 0.3.10 element1, element2 : {str, int}, optional Element symbol or atomic number of basis :class:`~sknano.core.Atom` 1 and 2 .. deprecated:: 0.3.10 Use `basis` instead bond : float, optional :math:`\\mathrm{a}_{\\mathrm{CC}} =` distance between nearest neighbor atoms. Must be in units of **Angstroms**. Lz : float, optional Length of nanotube in units of **nanometers**. Overrides the `nz` value. .. versionadded:: 0.2.5 tube_length : float, optional Length of nanotube in units of **nanometers**. Overrides the `nz` value. .. deprecated:: 0.2.5 Use `Lz` instead fix_Lz : bool, optional Generate the nanotube with length as close to the specified :math:`L_z` as possible. If `True`, then non integer :math:`n_z` cells are permitted. .. versionadded:: 0.2.6 verbose : bool, optional if `True`, show verbose output Examples -------- >>> from sknano.structures import SWNT Create a SWNT with :math:`\\mathbf{C}_{h} = (10, 10)` chirality. >>> swnt = SWNT((10, 10), verbose=True) >>> print(swnt) SWNT((10, 10), nz=1) n: 10 m: 10 t₁: 1 t₂: -1 d: 10 dR: 30 N: 20 R: (1, 0) θc: 30.00° Ch: 42.60 Å T: 2.46 Å dt: 13.56 Å rt: 6.78 Å electronic_type: metallic Change the chirality to :math:`\\mathbf{C}_{h} = (20, 10)`. >>> swnt.n = 20 >>> print(swnt) SWNT((20, 10), nz=1) n: 20 m: 10 t₁: 4 t₂: -5 d: 10 dR: 10 N: 140 R: (1, -1) θc: 19.11° Ch: 65.07 Å T: 11.27 Å dt: 20.71 Å rt: 10.36 Å electronic_type: semiconducting, type 2 Change the chirality to :math:`\\mathbf{C}_{h} = (20, 0)`. >>> swnt.m = 0 >>> print(swnt) SWNT((20, 0), nz=1) n: 20 m: 0 t₁: 1 t₂: -2 d: 20 dR: 20 N: 40 R: (1, -1) θc: 0.00° Ch: 49.19 Å T: 4.26 Å dt: 15.66 Å rt: 7.83 Å electronic_type: semiconducting, type 1 """ # add each attribute in the order I want them to appear in # verbose output mode _structure_attrs = ['n', 'm', 't1', 't2', 'd', 'dR', 'N', 'R', 'chiral_angle', 'Ch', 'T', 'dt', 'rt', 'electronic_type'] def __init__(self, *Ch, nz=None, basis=['C', 'C'], bond=aCC, gutter=None, Lz=None, fix_Lz=False, wrap_coords=False, **kwargs): n, m, kwargs = get_chiral_indices(*Ch, **kwargs) if 'tube_length' in kwargs: Lz = kwargs['tube_length'] del kwargs['tube_length'] super().__init__(basis=basis, bond=bond, **kwargs) if gutter is None: gutter = self.vdw_radius self.gutter = gutter self.wrap_coords = wrap_coords self.L0 = Lz # store initial value of Lz self.n = n self.m = m self.fix_Lz = fix_Lz if Lz is not None: self.nz = 10 * float(Lz) / self.T elif nz is not None: self.nz = nz else: self.nz = 1 self.generate_unit_cell() self.crystal_cell.scaling_matrix = [1, 1, int(np.ceil(self.nz))] fmtstr = "{Ch!r}, " if self.fix_Lz: fmtstr += "Lz={Lz!r}, fix_Lz=True, " else: fmtstr += "nz={nz!r}, " self.fmtstr = fmtstr + "basis={basis!r}, bond={bond!r}" def __str__(self): """Return nice string representation of `SWNT`.""" fmtstr = repr(self) if self.verbose: fmtstr += '\n' for attr in self._structure_attrs: var = attr if attr in attr_symbols: var = attr_symbols[attr] if attr in attr_strfmt: if attr in attr_units: fmtstr += \ "{}: {}{}\n".format( var, attr_strfmt[attr].format( getattr(self, attr)), attr_units[attr]) else: fmtstr += "{}: {}\n".format( var, attr_strfmt[attr].format(getattr(self, attr))) else: if attr in attr_units: fmtstr += "{}: {}{}\n".format( var, getattr(self, attr), attr_units[attr]) else: fmtstr += "{}: {}\n".format( var, getattr(self, attr)) return fmtstr
[docs] def generate_unit_cell(self): """Generate the nanotube unit cell.""" eps = 0.01 e1 = self.element1 e2 = self.element2 N = self.N T = self.T rt = self.rt psi, tau, dpsi, dtau = self.unit_cell_symmetry_params a = compute_dt(self.n, self.m, bond=self.bond) + 2 * self.gutter c = compute_T(self.n, self.m, bond=self.bond, length=True) lattice = Crystal3DLattice.hexagonal(a, c) basis = BasisAtoms() if self.verbose: print('dpsi: {}'.format(dpsi)) print('dtau: {}\n'.format(dtau)) for i in range(N): for j, element in enumerate((e1, e2), start=1): theta = i * psi h = i * tau if j == 2: theta += dpsi h -= dtau x = rt * np.cos(theta) y = rt * np.sin(theta) z = h while z > T - eps: z -= T if z < 0: z += T xs, ys, zs = \ lattice.cartesian_to_fractional([x, y, z]) if self.wrap_coords: xs, ys, zs = \ lattice.wrap_fractional_coordinate([xs, ys, zs]) if self.debug: print('i={}: x, y, z = ({:.6f}, {:.6f}, {:.6f})'.format( i, x, y, z)) print('xs, ys, zs = ({:.6f}, {:.6f}, {:.6f})'.format( xs, ys, zs)) # atom = BasisAtom(element, lattice=lattice, x=x, y=y, z=z) # print('i={}: x, y, z = ({:.6f}, {:.6f}, {:.6f})'.format( # i, x, y, z)) atom = BasisAtom(element, lattice=lattice, xs=xs, ys=ys, zs=zs) atom.rezero() if self.verbose: print('Basis Atom:\n{}'.format(atom)) basis.append(atom) self.unit_cell = UnitCell(lattice=lattice, basis=basis)
[docs] def todict(self): """Return :class:`~python:dict` of `SWNT` attributes.""" return dict(Ch=(self.n, self.m), nz=self.nz, bond=self.bond, basis=self.basis, Lz=self.Lz)
Nanotube = SWNT