LobatoParametrization#
- class abtem.parametrizations.LobatoParametrization(parameters='lobato.json', sigmas=None)[source]#
Bases:
Parametrization
Potential parametrization by Ivan Lobato and Dirk Van Dyck.
- 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 theabtem/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
Ivan Lobato and Dirk Van Dyck. Acta Crystallographica Section A, 70:636–649, 2014.
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
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:
- 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