PengParametrization#

class abtem.parametrizations.PengParametrization(parameters='peng_high.json', sigmas=None)[source]#

Bases: Parametrization

Potential parametrization by Lian-Mao Peng.

Parameters:
  • parameters (str or dict) – A given string must be either the full path to a valid .json file or the name of a valid .json file in the abtem/parametrizations/data/ folder. A given dictionary must be a mapping from chemical symbols to anything that can converted to a NumPy array of shape (2, 5).

  • sigmas (dict or float) – The standard deviation of isotropic displacements for each element as a mapping from chemical symbols to a number. If given as a float the standard deviation of the displacements is assumed to be identical for all atoms.

References

  1. Peng. Micron, 30(6):625–648, 1999.

__init__(parameters='peng_high.json', sigmas=None)[source]#

Methods

__init__([parameters, sigmas])

charge(symbol[, charge])

Radial charge distribution for given chemical symbol and charge.

finite_projected_potential(symbol[, charge])

X-ray scattering factor for given chemical symbol and charge.

finite_projected_scattering_factor(symbol[, ...])

Analytical infinite projection of radial scattering factor for given chemical symbol and charge.

from_json(file)

get_function(name, symbol[, charge])

Returns the line profiles for a parameterized function for one or more element.

line_profiles(symbol, cutoff[, sampling, name])

Returns the line profiles for a parameterized function for one or more element.

potential(symbol[, charge])

Radial electrostatic potential for given chemical symbol and charge.

projected_potential(symbol[, charge])

Analytical infinite projection of radial electrostatic potential for given chemical symbol and charge.

projected_scattering_factor(symbol[, charge])

Analytical infinite projection of radial scattering factor for given chemical symbol and charge.

scaled_parameters(symbol, name)

The parameters of the parametrization scaled to the abTEM units for a given function.

scattering_factor(symbol[, charge])

Radial scattering factor for given chemical symbol and charge.

to_json(file)

x_ray_scattering_factor(symbol[, charge])

X-ray scattering factor for given chemical symbol and charge.

Attributes

parameters

sigmas

The standard deviation of isotropic displacements.

charge(symbol, charge=0.0)#

Radial charge distribution for given chemical symbol and charge.

Parameters:
  • symbol (str) – Chemical symbol of element.

  • charge (float) – Charge of element. Given as elementary charges.

Returns:

charge – Function describing charge parameterized by the radial distance to the core [Å].

Return type:

callable

finite_projected_potential(symbol, charge=0.0)#

X-ray scattering factor for given chemical symbol and charge.

Parameters:
  • symbol (str) – Chemical symbol of element.

  • charge (float) – Charge of element. Given as elementary charges.

Returns:

x_ray_scattering_factor

Return type:

callable

finite_projected_scattering_factor(symbol, charge=0.0)#

Analytical infinite projection of radial scattering factor for given chemical symbol and charge.

Parameters:
  • symbol (str) – Chemical symbol of element.

  • charge (float) – Charge of element. Given as elementary charges.

Returns:

projected_scattering_factor – Function describing projected scattering parameterized by the squared reciprocal radial distance to the core [1/Å^2].

Return type:

callable

get_function(name, symbol, charge=0.0)#

Returns the line profiles for a parameterized function for one or more element.

Parameters:
  • name (str) – Name of the function to return.

  • symbol (str) – Chemical symbol of element.

  • charge (float) – Charge of element. Given as elementary charges.

Return type:

callable

line_profiles(symbol, cutoff, sampling=0.001, name='potential')#

Returns the line profiles for a parameterized function for one or more element.

Parameters:
  • symbol (str or list of str) – Chemical symbol(s) of atom(s).

  • cutoff (float) – The outer radial cutoff distance of the line profiles in units of Ångstrom for potentials and units of reciprocal Ångstrom for scattering factors.

  • sampling (float, optional) – The radial sampling of the line profiles in units of Ångstrom for potentials and units of reciprocal Ångstrom for scattering factors. Default is 0.001.

  • name (str) – Name of the line profile to return.

Return type:

RealSpaceLineProfiles | ReciprocalSpaceLineProfiles

potential(symbol, charge=0.0)#

Radial electrostatic potential for given chemical symbol and charge.

Parameters:
  • symbol (str) – Chemical symbol of element.

  • charge (float) – Charge of element. Given as elementary charges.

Returns:

electrostatic_potential – Function describing electrostatic potential parameterized by the radial distance to the core [Å].

Return type:

callable

projected_potential(symbol, charge=0.0)#

Analytical infinite projection of radial electrostatic potential for given chemical symbol and charge.

Parameters:
  • symbol (str) – Chemical symbol of element.

  • charge (float) – Charge of element. Given as elementary charges.

Returns:

projected_potential – Function describing projected electrostatic potential parameterized by the radial distance to the core [Å].

Return type:

callable

projected_scattering_factor(symbol, charge=0.0)#

Analytical infinite projection of radial scattering factor for given chemical symbol and charge.

Parameters:
  • symbol (str) – Chemical symbol of element.

  • charge (float) – Charge of element. Given as elementary charges.

Returns:

projected_scattering_factor – Function describing projected scattering parameterized by the squared reciprocal radial distance to the core [1/Å^2].

Return type:

callable

scaled_parameters(symbol, name)[source]#

The parameters of the parametrization scaled to the abTEM units for a given function.

Parameters:
  • symbol (str) – Chemical symbol to get the scaled parameters for.

  • name (str) – Name of the function to get the scaled parameters for.

Returns:

scaled_parameters

Return type:

np.ndarray

scattering_factor(symbol, charge=0.0)#

Radial scattering factor for given chemical symbol and charge.

Parameters:
  • symbol (str) – Chemical symbol of element.

  • charge (float) – Charge of element. Given as elementary charges.

Returns:

scattering_factor – Function describing scattering parameterized by the squared reciprocal radial distance to the core [1/Å^2].

Return type:

callable

property sigmas#

The standard deviation of isotropic displacements.

x_ray_scattering_factor(symbol, charge=0.0)#

X-ray scattering factor for given chemical symbol and charge.

Parameters:
  • symbol (str) – Chemical symbol of element.

  • charge (float) – Charge of element. Given as elementary charges.

Returns:

x_ray_scattering_factor

Return type:

callable