KirklandParametrization

KirklandParametrization#

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

Bases: Parametrization

Potential parametrization by Earl J Kirkland.

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 (4, 3).
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

E.J. Kirkland. Advanced computing in electron microscopy. Springer, 2. edition, 2010.

__init__(parameters='kirkland.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.
`fit`(Z, k, f[, guess])
`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

KirklandParametrization

Contents

KirklandParametrization#