hyperspy.misc.eds.utils module

hyperspy.misc.eds.utils._get_element_and_line(xray_line)

Returns the element name and line character for a particular X-ray line as a tuple.

By example, if xray_line = ‘Mn_Ka’ this function returns (‘Mn’, ‘Ka’)

hyperspy.misc.eds.utils._get_energy_xray_line(xray_line)

Returns the energy (in keV) associated with a given X-ray line.

By example, if xray_line = ‘Mn_Ka’ this function returns 5.8987

hyperspy.misc.eds.utils._get_xray_lines_family(xray_line)

Returns the family to which a particular X-ray line belongs.

By example, if xray_line = ‘Mn_Ka’ this function returns ‘Mn_K’

hyperspy.misc.eds.utils._quantification_cliff_lorimer(intensities, kfactors, absorption_correction, ref_index=0, ref_index2=1)

Quantification using Cliff-Lorimer

Parameters:

  • intensities (numpy.array) – the intensities for each X-ray lines. The first axis should be the elements axis.

  • absorption_correction (numpy.ndarray) – value between 0 and 1 in order to correct the intensities based on estimated absorption.

  • kfactors (list of float) – The list of kfactor in same order as intensities eg. kfactors = [1, 1.47, 1.72] for [‘Al_Ka’,’Cr_Ka’, ‘Ni_Ka’]

  • ref_index (int) – index of the elements that will be in the denominator. Should be non zeros if possible.

  • ref_index2 (int) – index of the elements that will be in the denominator. Should be non zeros if possible.

Returns:

  • numpy.array containing the weight fraction with the same

  • shape as intensities.

hyperspy.misc.eds.utils.edx_cross_section_to_zeta(cross_sections, elements)

Convert a list of cross_sections in barns (b) to zeta-factors (kg/m^2).

Parameters:

  • cross_section (list of float) – A list of cross sections in barns.

  • elements (list of str) – A list of element chemical symbols in the same order as the cross sections e.g. [‘Al’,’Zn’]

Returns:

zeta_factors – zeta_factors with units kg/m^2.

Return type:

list of float

hyperspy.misc.eds.utils.electron_range(element, beam_energy, density='auto', tilt=0)

Returns the maximum electron range for a pure bulk material according to the Kanaya-Okayama parameterziation.

Parameters:

  • element (str) – The element symbol, e.g. ‘Al’.

  • beam_energy (float) – The energy of the beam in keV.

  • density ({float, 'auto'}) – The density of the material in g/cm3. If ‘auto’, the density of the pure element is used.

  • tilt (float.) – The tilt of the sample in degrees.

Return type:

Electron range in micrometers.

Examples

>>> # Electron range in pure Copper at 30 kV in micron
>>> hs.eds.electron_range('Cu', 30.)
2.8766744984001607

Notes

From Kanaya, K. and S. Okayama (1972). J. Phys. D. Appl. Phys. 5, p43

See also the textbook of Goldstein et al., Plenum publisher, third edition p 72.

hyperspy.misc.eds.utils.get_FWHM_at_Energy(energy_resolution_MnKa, E)

Calculates an approximate FWHM, accounting for peak broadening due to the detector, for a peak at energy E given a known width at a reference energy.

The factor 2.5 is a constant derived by Fiori & Newbury as references below.

Parameters:

  • energy_resolution_MnKa (float) – Energy resolution of Mn Ka in eV

  • E (float) – Energy of the peak in keV

Returns:

float

Return type:

FWHM of the peak in keV

Notes

This method implements the equation derived by Fiori and Newbury as is documented in the following:

Fiori, C. E., and Newbury, D. E. (1978). In SEM/1978/I, SEM, Inc., AMF O’Hare, Illinois, p. 401.

Goldstein et al. (2003). “Scanning Electron Microscopy & X-ray Microanalysis”, Plenum, third edition, p 315.

hyperspy.misc.eds.utils.get_abs_corr_cross_section(composition, number_of_atoms, take_off_angle, probe_area)

Calculate absorption correction terms.

Parameters:

  • number_of_atoms (list of signal) – Stack of maps with number of atoms per pixel.

  • take_off_angle (float) – X-ray take-off angle in degrees.

hyperspy.misc.eds.utils.get_abs_corr_zeta(weight_percent, mass_thickness, take_off_angle)

Calculate absorption correction terms.

Parameters:

  • weight_percent (list of signal) – Composition in weight percent.

  • mass_thickness (signal) – Density-thickness map in kg/m^2

  • take_off_angle (float) – X-ray take-off angle in degrees.

hyperspy.misc.eds.utils.get_xray_lines_near_energy(energy, width=0.2, only_lines=None)

Find xray lines near a specific energy, more specifically all xray lines that satisfy only_lines and are within the given energy window width around the passed energy.

Parameters:

  • energy (float) – Energy to search near in keV

  • width (float) – Window width in keV around energy in which to find nearby energies, i.e. a value of 0.2 keV (the default) means to search +/- 0.1 keV.

  • only_lines – If not None, only the given lines will be added (eg. (‘a’,’Kb’)).

Return type:

List of xray-lines sorted by energy difference to given energy.

hyperspy.misc.eds.utils.quantification_cliff_lorimer(intensities, kfactors, absorption_correction=None, mask=None)

Quantification using Cliff-Lorimer

Parameters:

  • intensities (numpy.array) – the intensities for each X-ray lines. The first axis should be the elements axis.

  • kfactors (list of float) – The list of kfactor in same order as intensities eg. kfactors = [1, 1.47, 1.72] for [‘Al_Ka’,’Cr_Ka’, ‘Ni_Ka’]

  • absorption_correction (numpy.ndarray or None) – If None (default), absorption correction is ignored, otherwise, the array must contain values between 0 and 1 to correct the intensities based on estimated absorption.

  • mask (array of bool, signal of bool or None) – The mask with the dimension of intensities[0]. If a pixel is True, the composition is set to zero.

Returns:

  • numpy.array containing the weight fraction with the same

  • shape as intensities.

hyperspy.misc.eds.utils.quantification_cross_section(intensities, cross_sections, dose, absorption_correction=None)

Quantification using EDX cross sections Calculate the atomic compostion and the number of atoms per pixel from the raw X-ray intensity

Parameters:

  • intensity (numpy.ndarray) – The integrated intensity for each X-ray line, where the first axis is the element axis.

  • cross_sections (list of floats) – List of X-ray scattering cross-sections in the same order as the intensities.

  • dose (float) – the dose per unit area given by i*t*N/A, i the current, t the acquisition time, and N the number of electron by unit electric charge.

  • absorption_correction (numpy.ndarray or None) – If None (default), absorption correction is ignored, otherwise, the array must contain values between 0 and 1 to correct the intensities based on estimated absorption.

Returns:

  • numpy.array containing the atomic fraction of each element, with

  • the same shape as the intensity input.

  • numpy.array of the number of atoms counts for each element, with the same

  • shape as the intensity input.

hyperspy.misc.eds.utils.quantification_zeta_factor(intensities, zfactors, dose, absorption_correction=None)

Quantification using the zeta-factor method

Parameters:

  • intensities (numpy.array) – The intensities for each X-ray line. The first axis should be the elements axis.

  • zfactors (list of float) – The list of zeta-factors in the same order as intensities e.g. zfactors = [628.10, 539.89] for [‘As_Ka’, ‘Ga_Ka’].

  • dose (float) – The total electron dose given by i*t*N, i the current, t the acquisition time and N the number of electrons per unit electric charge (1/e).

  • absorption_correction (numpy.ndarray or None) – If None (default), absorption correction is ignored, otherwise, the array must contain values between 0 and 1 to correct the intensities based on estimated absorption.

Returns:

  • A numpy.array containing the weight fraction with the same

  • shape as intensities and mass thickness in kg/m^2.

hyperspy.misc.eds.utils.take_off_angle(tilt_stage, azimuth_angle, elevation_angle, beta_tilt=0.0)

Calculate the take-off-angle (TOA).

TOA is the angle with which the X-rays leave the surface towards the detector.

Parameters:

  • alpha_tilt (float) – The alpha-tilt of the stage in degrees. The sample is facing the detector when positively tilted.

  • azimuth_angle (float) – The azimuth of the detector in degrees. 0 is perpendicular to the alpha tilt axis.

  • elevation_angle (float) – The elevation of the detector in degrees.

  • beta_tilt (float) – The beta-tilt of the stage in degrees. The sample is facing positive 90 in the azimuthal direction when positively tilted.

Returns:

take_off_angle – In degrees.

Return type:

float.

Examples

>>> hs.eds.take_off_angle(alpha_tilt=10., beta_tilt=0.
>>>                          azimuth_angle=45., elevation_angle=22.)
28.865971201155283
hyperspy.misc.eds.utils.xray_lines_model(elements, beam_energy=200, weight_percents=None, energy_resolution_MnKa=130, energy_axis=None)

Generate a model of X-ray lines using a Gaussian distribution for each peak.

The area under a main peak (alpha) is equal to 1 and weighted by the composition.

Parameters:

  • elements (list of strings) – A list of chemical element symbols.

  • beam_energy (float) – The energy of the beam in keV.

  • weight_percents (list of float) – The composition in weight percent.

  • energy_resolution_MnKa (float) – The energy resolution of the detector in eV

  • energy_axis (dic) – The dictionary for the energy axis. It must contains ‘size’ and the units must be ‘eV’ of ‘keV’.

Example

>>> s = xray_lines_model(['Cu', 'Fe'], beam_energy=30)
>>> s.plot()
hyperspy.misc.eds.utils.xray_range(xray_line, beam_energy, density='auto')

Return the maximum range of X-ray generation according to the Anderson-Hasler parameterization.

Parameters:

  • xray_line (str) – The X-ray line, e.g. ‘Al_Ka’

  • beam_energy (float) – The energy of the beam in kV.

  • density ({float, 'auto'}) – The density of the material in g/cm3. If ‘auto’, the density of the pure element is used.

Return type:

X-ray range in micrometer.

Examples

>>> # X-ray range of Cu Ka in pure Copper at 30 kV in micron
>>> hs.eds.xray_range('Cu_Ka', 30.)
1.9361716759499248

>>> # X-ray range of Cu Ka in pure Carbon at 30kV in micron
>>> hs.eds.xray_range('Cu_Ka', 30., hs.material.elements.C.
>>>                      Physical_properties.density_gcm3)
7.6418811280855454

Notes

From Anderson, C.A. and M.F. Hasler (1966). In proceedings of the 4th international conference on X-ray optics and microanalysis.

See also the textbook of Goldstein et al., Plenum publisher, third edition p 286

hyperspy.misc.eds.utils.zeta_to_edx_cross_section(zfactors, elements)

Convert a list of zeta-factors (kg/m^2) to cross_sections in barns (b).

Parameters:

  • zfactors (list of float) – A list of zeta-factors.

  • elements (list of str) – A list of element chemical symbols in the same order as the cross sections e.g. [‘Al’,’Zn’]

Returns:

cross_sections – cross_sections with units in barns.

Return type:

list of float