hyperspy.misc.eds.utils module

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.
Returns:
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_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’)).
Returns:
Return type:

List of xray-lines sorted by energy difference to given energy.
hyperspy.misc.eds.utils.quantification_cliff_lorimer(intensities, kfactors, 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’]
  • mask (array of bool) – 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)

Quantification using EDX cross sections Calculate the atomic compostion and the number of atoms per pixel from the raw X-ray intensity :param intensity: The integrated intensity for each X-ray line, where the first axis

is the element axis.
Parameters:
  • 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.
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)

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).
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)

Calculate the take-off-angle (TOA).

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

Parameters:
  • tilt_stage (float) – The 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 tilt axis.
  • elevation_angle (float) – The elevation of the detector in degrees.
Returns:

take_off_angle – In degrees.
Return type:

float.

Examples

>>> hs.eds.take_off_angle(tilt_stage=10.,
>>>                          azimuth_angle=45., elevation_angle=22.)
28.865971201155283

Notes

Defined by M. Schaffer et al., Ultramicroscopy 107(8), pp 587-597 (2007)

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 = utils_eds.simulate_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.
Returns:
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