pyEELSMODEL.misc package

Submodules

pyEELSMODEL.misc.data_simulator module

pyEELSMODEL.misc.data_simulator.make_circular_mask(xco, yco, Rin, Rout, shape)
pyEELSMODEL.misc.data_simulator.make_rectangular_mask(xco, yco, width, height, shape)
pyEELSMODEL.misc.data_simulator.simulate_data()

Small function which simulates a typical STEM-EELS map.

pyEELSMODEL.misc.hs_gdos module

pyEELSMODEL.misc.hs_gdos.dsigma_dE_HS(energy_axis, Z, ek, E0, beta, alpha, filename, q_steps=100)

Calculates the cross section from the Hartree-Slater cross sections from Rez. They are not used since they are not open-access.

pyEELSMODEL.misc.hs_gdos.dsigma_dE_from_GOSarray(energy_axis, rel_energy_axis, ek, E0, beta, alpha, q_axis, GOSmatrix, q_steps=100, swap_axes=False)

Calculates the cross section from the GOS array. The integral over q-axis is done on a logarithmic scale. Note the speed of the calculation is not super-fast and could be improved by a better implementation of the interpolation and integration.

Parameters:

  • energy_axis (1d numpy array) – The energy axis on which the cross section is calculated. [eV]

  • rel_energy_axis (1d numpy array) – The energy axis on which the GOS table is calculated. [eV]

  • ek (float) – The onset energy of the calculated edge [eV]

  • E0 (float) – The acceleration voltage of the incoming electrons [V]

  • alpha (float) – The convergence angle of the incoming probe [rad]

  • beta – The collection angle of the outgoing electrons [rad]

  • q_axis (1d numpy array) – The momentum on which the GOS table are calculated. [kg m /s]?

  • GOSmatrix (2d numpy array) – The GOS

  • q_steps (uint) – The number of q points used to numerically calculate the integral over the q direction. (default: 100)

  • swap_axes (boolean) – The two GOS tables from Segger and Zhang have different axes. So for one, the energy axis is the first one and for the other it is the q-axis. Hence by swapping the axes we can use the same function for both. (default: False)

Returns:

dsigma_dE – The calculated cross section in m^2

Return type:

1d numpy array

pyEELSMODEL.misc.hs_gdos.dsigma_dE_from_GOSarray_approx(energy_axis, rel_energy_axis, E0, beta, GOSmatrix, swap_axes=False)

Calculates the cross section by using the approximation shown in https://doi.org/10.1016/0304-3991(89)90197-6, see Eq. 3

pyEELSMODEL.misc.hs_gdos.dsigma_dE_from_GOSarray_bound(energy_axis, free_energies, ek, E0, beta, alpha, q_axis, GOSmatrix, q_steps=100)

Calculates the cross section from the GOS array. The integral over q-axis is done on a logarithmic scale. This is a new method which is able to take the bounded states into account. Provided by Zezhong Zhang.

Parameters:

  • energy_axis (1d numpy array) – The energy axis on which the cross section is calculated. [eV]

  • free_energies (1d numpy array) – The energy axis on which the GOS table is calculated without the onset energy [eV]

  • ek (float) – The onset energy of the calculated edge [eV]

  • E0 (float) – The acceleration voltage of the incoming electrons [V]

  • alpha (float) – The convergence angle of the incoming probe [rad]

  • beta – The collection angle of the outgoing electrons [rad]

  • q_axis (1d numpy array) – The momentum on which the GOS table are calculated. [kg m /s]?

  • GOSmatrix (2d numpy array) – The GOS

  • q_steps (uint) – The number of q points used to numerically calculate the integral over the q direction. (default: 100)

  • swap_axes (boolean) – The two GOS tables from Segger and Zhang have different axes. So for one, the energy axis is the first one and for the other it is the q-axis. Hence by swapping the axes we can use the same function for both. (default: False)

Returns:

dsigma_dE – The calculated cross section in m^2

Return type:

1d numpy array

pyEELSMODEL.misc.hs_gdos.gaussian(E, integral, x0, sigma)
pyEELSMODEL.misc.hs_gdos.get_powerLaw_extrapolation(rel_energy_axis, q_axis, GOSmatrix, E0, beta, alpha, q_steps=100, swap_axes=False)

If the energy axis for the cross section extends the range of calculated GOS then the last two point are used to extrapolate a power-law from.

Parameters:

  • rel_energy_axis (float) – The energy from which the GOS should be interpolated

  • q (float) – The q from the GOS should be interpolated

  • E_axis (numpy array) – The energy axis on which the GOS is calculated

  • q_axis (numpy array) – The q axis on which the GOS is calculated

  • swap_axes (boolean) – Indicates if the axes for q and E should be swapped. There is a difference between the GOS from Segger and Zhang.

Returns:

  • A (float) – The amplitude of the power-law

  • r (float) – The power of the power-law

pyEELSMODEL.misc.hs_gdos.getgosenergy(info2_1, info2_2, n)
pyEELSMODEL.misc.hs_gdos.getgosq(info1_1, info1_2, n)
pyEELSMODEL.misc.hs_gdos.getinterpolatedgos(E, q, E_axis, q_axis, GOSmatrix, swap_axes=False)

Gets the interpolated value of the GOS from the E and q value.

Parameters:

  • E (float) – The energy from which the GOS should be interpolated

  • q (float) – The q from the GOS should be interpolated

  • E_axis (numpy array) – The energy axis on which the GOS is calculated

  • q_axis (numpy array) – The q axis on which the GOS is calculated

  • swap_axes (boolean) – Indicates if the axes for q and E should be swapped. There is a difference between the GOS from Segger and Zhang.

Return type:

interpolated GOS matrix

pyEELSMODEL.misc.hs_gdos.getinterpolatedq(q, GOSarray, q_axis)

Gets the interpolated value of the GOS array as a function of q. Usefull for the bounded states

Parameters:

  • q (float) – The q from the GOS should be interpolated

  • GOSarray – dddd

  • q_axis (numpy array) – The q axis on which the GOS is calculated

Return type:

interpolated GOS matrix

pyEELSMODEL.misc.hs_gdos.linear_interpolation(x, y, x1)
pyEELSMODEL.misc.hs_gdos.powerlaw(x, A, r)

pyEELSMODEL.misc.hydrogen_gdos module

pyEELSMODEL.misc.hydrogen_gdos.convergence_correction_factor(alpha, beta, theta_sampling)

geometric correction factor for convergent beam in STEM #BY ZEZHONG Reference:

Kohl, H. “A simple procedure for evaluating effective scattering cross-sections in STEM.” Ultramicroscopy 16.2 (1985): 265-268.

Parameters:

  • alpha (float) – incident beam convergence angle in rad

  • beta (float) – collection angle in rad

  • theta_sampling (np.array) – scattering angle in rad

Returns:

correction factor for each scattering angle

Return type:

np.array

pyEELSMODEL.misc.hydrogen_gdos.correction_factor_kohl(alpha, beta, theta, min_alpha=1e-06)

STILL NEEDS TO BE VALIDATED Calculates the correction factor when using a convergent probe. For probes having is convergence angle smaller than min_alpha no correction is applied. Ultramicroscopy 16 (1985) 265-268: https://doi.org/10.1016/0304-3991(85)90081-6

alphafloat

Convergence angle in radians

betafloat

Collection angle in radians

thetafloat

The angle for which the correction factor should be calculated

min_alphafloat

Minimum convergence angle for which the correction is applied

corr_factorfloat

correction factor used in the integration

pyEELSMODEL.misc.hydrogen_gdos.dsigma_dE_hydrogenic(energy_axis, Z, ek, E0, beta, alpha, shell='K', q_steps=100)

Calculates the differential cross section for a given energy axis. It uses the approximation of a convergent beam (alpha).

energy_axisnumpy array

The energy in eV

Zint

Atomic number

ek: float

The energy of the edge onset

E0: float

Energy of the incoming electron in eV

beta: float

Collection angle in radians

alpha: float

Convergence angle in radians (NOT YET IMPLEMENTED)

shell: string

Should be “K” or “L” to indicate which edge to calculate

q_steps: int

The number of calculations for every energy which is used to integrate over in q-space

dsigma_dE: numpy_array

The differential energy cross section

pyEELSMODEL.misc.hydrogen_gdos.gdos_k(E, qa0sq, Z)

Calculates the hydrogenic GDOS for the k edge of an atom with atomic number Z.

Parameters:

  • E (float) – The energy in eV.

  • qa0sq (float) – The q*a0**2 value (derived from momentum)

  • Z (int) – Atomic number

Return type:

GDOS

pyEELSMODEL.misc.hydrogen_gdos.gdos_l(E, qa0sq, Z)

Calculates the hydrogenic GDOS for the l edge of an atom with atomic number Z.

Parameters:

  • E (float) – The energy in eV.

  • qa0sq (float) – The q*a0**2 value (derived from momentum)

  • Z (int) – Atomic number

Return type:

GDOS

pyEELSMODEL.misc.hydrogen_gdos.get_EK()
pyEELSMODEL.misc.hydrogen_gdos.get_IE1()
pyEELSMODEL.misc.hydrogen_gdos.get_IE3()
pyEELSMODEL.misc.hydrogen_gdos.get_XU()
pyEELSMODEL.misc.hydrogen_gdos.get_qmin_max(E, E0, beta, alpha=1e-09, return_q=False)

Returns the minimum and maximum q vector over which to integrate to get the cross section.

pyEELSMODEL.misc.make_element_hdf5 module

pyEELSMODEL.misc.pdf_maker module

class pyEELSMODEL.misc.pdf_maker.PDF(orientation='P', unit='mm', format='A4')

Bases: FPDF

Class which makes a pdf, this is useful when wanting to have some information used on a procedure you applied to the data. For instance, the FastAlignZeroLoss class can generate a file with the relevant information which can be checked if everything went fine.

add_figure(fig)
get_figname()
get_savename()
get_time_name()
intitialize(path)

pyEELSMODEL.misc.physical_constants module

Definition of the physical constants used with its units.

pyEELSMODEL.misc.physical_constants.R()

Rydberg constant in eV

pyEELSMODEL.misc.physical_constants.T(E0, m=9.11e-31)

The effective incident energy in eV

:param E0:energy in eV? :param m:mass in kg :return:

pyEELSMODEL.misc.physical_constants.Zs_k(Z)

Corrects for the screening of the electrons for the k shell. :param Z: The number of protons :return: Corrected Z value

pyEELSMODEL.misc.physical_constants.a0()

Bohr radius in m

pyEELSMODEL.misc.physical_constants.c()

Speed of light in m/s

pyEELSMODEL.misc.physical_constants.characteristic_angle(E, E0, use_rel=True)
pyEELSMODEL.misc.physical_constants.e()

Electron charge in C

pyEELSMODEL.misc.physical_constants.gamma(E0, m=9.11e-31)

The formula works for energies of the electron which are not to close to the speed of light?

Parameters:

E0 – Energy incoming electron (eV) m: mass of the particle (kg) electron mass as default

Returns:

gamma: float

pyEELSMODEL.misc.physical_constants.h(unit='J')
pyEELSMODEL.misc.physical_constants.hbar(unit='J')
pyEELSMODEL.misc.physical_constants.joule_to_eV(J)
pyEELSMODEL.misc.physical_constants.m0()

Rest mass in kg

pyEELSMODEL.misc.physical_constants.speed_electron(E0)

Relativistic speed of electron

Module contents