Parametrization

class abtem.parametrizations.Parametrization(parameters, sigmas=None)

Bases: EqualityMixin

Base class for potential parametrizations.

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 with the correct shape for the given parametrization.

• 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.

__init__(parameters, sigmas=None)

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

abstract scaled_parameters(symbol, name)

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