exspy.utils.eds

cross_section_to_zeta(cross_sections, elements)	Convert a list of cross_sections in barns (b) to zeta-factors (kg/m^2).
electron_range(element, beam_energy[, ...])	Returns the maximum electron range for a pure bulk material according to the Kanaya-Okayama parameterziation.
get_xray_lines(elements[, weight_threshold, ...])	Get all X-ray lines for the given elements.
get_xray_lines_near_energy(energy[, width, ...])	Find X-ray lines near a specific energy, more specifically all X-ray lines that satisfy only_lines and are within the given energy window width around the passed energy.
print_lines(elements[, weight_threshold, ...])	Display a table of X-ray lines for given elements.
print_lines_near_energy(energy[, width, ...])	Display a table of X-ray lines close to a given energy.
take_off_angle(tilt_stage, azimuth_angle, ...)	Calculate the take-off-angle (TOA).
xray_range(xray_line, beam_energy[, density])	Return the maximum range of X-ray generation according to the Anderson-Hasler parameterization.
zeta_to_cross_section(zfactors, elements)	Convert a list of zeta-factors (kg/m^2) to cross_sections in barns (b).

Utility functions for EDS analysis.

exspy.utils.eds.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 – The zeta factors with units kg/m^2.

Return type:

list of float

See also

zeta_to_cross_section

exspy.utils.eds.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 or str ('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:

electron_range – Electron range in micrometers.

Return type:

float

See also

exspy.utils.eds.xray_range

Examples

>>> # Electron range in pure Copper at 30 kV in micron
>>> exspy.utils.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.

exspy.utils.eds.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:

FWHM – FWHM of the peak in keV

Return type:

float

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.

exspy.utils.eds.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.

exspy.utils.eds.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.

exspy.utils.eds.get_xray_lines(elements, weight_threshold=0.1, energy_range=None, only_lines=None)

Get all X-ray lines for the given elements.

Parameters:

• elements (tuple or list) – The list of elements.

• weight_threshold (float) – Define the threshold of the weight below which the lines are ignored. Must be between 0 and 1. Default is 0.1.

• energy_range (list or tuple of length 2) – Define the start and the end of the X-ray energy range to consider. X-ray energies outside the range will be ignored. If None, all X-ray energies are considered. Default is None.

• only_lines (list of str, optional) – Define the lines to be considered (eg. (‘a’,’Kb’)). If None, all lines are included. Default is None.

Return type:

hyperspy.misc.utils.DictionaryTreeBrowser

Examples

Get the X-ray lines of a single element:

>>> from exspy.utils.eds import get_xray_lines
>>> get_xray_lines(["O"])
└── O
    └── Ka
        ├── energy (keV) = 0.5249
        └── weight = 1.0

Get the X-ray lines of multiple elements:

>>> get_xray_lines(["O", "Fe"])
├── Fe
│   ├── Ka
│   │   ├── energy (keV) = 6.4039
│   │   └── weight = 1.0
│   ├── Kb
│   │   ├── energy (keV) = 7.058
│   │   └── weight = 0.1272
│   ├── La
│   │   ├── energy (keV) = 0.7045
│   │   └── weight = 1.0
│   ├── Ll
│   │   ├── energy (keV) = 0.6152
│   │   └── weight = 0.3086
│   └── Ln
│       ├── energy (keV) = 0.6282
│       └── weight = 0.12525
└── O
    └── Ka
        ├── energy (keV) = 0.5249
        └── weight = 1.0

Restrict to a specific energy range:

>>> exspy.utils.eds.get_xray_lines(["O", "Fe"], energy_range=[0.5, 1.0])
├── Fe
│   ├── La
│   │   ├── energy (keV) = 0.7045
│   │   └── weight = 1.0
│   ├── Ll
│   │   ├── energy (keV) = 0.6152
│   │   └── weight = 0.3086
│   └── Ln
│       ├── energy (keV) = 0.6282
│       └── weight = 0.12525
└── O
    └── Ka
        ├── energy (keV) = 0.5249
        └── weight = 1.0

Restrict to specific lines:

>>> exspy.utils.eds.get_xray_lines(["O", "Fe"], energy_range=[0.5, 1.0], only_lines=["a"])
├── Fe
│   └── La
│       ├── energy (keV) = 0.7045
│       └── weight = 1.0
└── O
    └── Ka
        ├── energy (keV) = 0.5249
        └── weight = 1.0

Specify a threshold to only return high intensity X-ray lines

>>> exspy.utils.eds.get_xray_lines(["O", "Fe"], weight_threshold=0.5)
├── Fe
│   ├── Ka
│   │   ├── energy (keV) = 6.4039
│   │   └── weight = 1.0
│   └── La
│       ├── energy (keV) = 0.7045
│       └── weight = 1.0
└── O
    └── Ka
        ├── energy (keV) = 0.5249
        └── weight = 1.0

See also

get_xray_lines_near_energy, print_lines, print_lines_near_energy

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

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

Parameters:

• energy (float) – Energy in keV around which to search.

• width (float) – Window width in keV around energy in which to find nearby energies, i.e. a value of 0.1 keV (the default) means to search +/- 0.05 keV.

• only_lines (list of str, optional) – Define the lines to be considered (eg. (‘a’,’Kb’)). If None, all lines are included. Default is None.

Returns:

xray_lines – List of X-ray-lines sorted by energy difference to the given energy.

Return type:

list

See also

get_xray_lines, print_lines, print_lines_near_energy

exspy.utils.eds.print_lines(elements, weight_threshold=0.1, energy_range=None, only_lines=None, sorting='elements', float_format='.2')

Display a table of X-ray lines for given elements.

Parameters:

• elements (list, tuple or None) – The list of elements.

• weight_threshold (float) – Define the threshold of the weight below which the lines are ignored. Must be between 0 and 1. Default is 0.1.

• energy_range (list or tuple of length 2) – Define the start and the end of the X-ray energy range to consider. X-ray energies outside the range will be ignored. If None, all X-ray energies are considered. Default is None.

• only_lines (list of str, optional) – Define the lines to be considered (eg. (‘a’,’Kb’)). If None, all lines are included. Default is None.

• sorting (str) – Define the sorting of the table, either "elements" or "energy". Default is "elements".

• float_format (str) – The formatting of the float in the table passed to prettytable.PrettyTable. Default is “.2”.

Examples

>>> import exspy
>>> exspy.utils.eds.print_lines(elements=["Fe", "Pt"])
+---------+------+--------------+--------+------------+
| Element | Line | Energy (keV) | Weight | Intensity  |
+---------+------+--------------+--------+------------+
|    Fe   |  Ka  |     6.40     |  1.00  | ########## |
|         |  Kb  |     7.06     |  0.13  | #          |
|         |  La  |     0.70     |  1.00  | ########## |
|         |  Ll  |     0.62     |  0.31  | ###        |
|         |  Ln  |     0.63     |  0.13  | #          |
+---------+------+--------------+--------+------------+
|    Pt   |  Ka  |    66.83     |  1.00  | ########## |
|         |  Kb  |    75.75     |  0.15  | #          |
|         |  La  |     9.44     |  1.00  | ########## |
|         | Lb1  |    11.07     |  0.41  | ####       |
|         | Lb2  |    11.25     |  0.22  | ##         |
|         |  Ma  |     2.05     |  1.00  | ########## |
|         |  Mb  |     2.13     |  0.59  | #####      |
+---------+------+--------------+--------+------------+

See also

get_xray_lines, get_xray_lines_near_energy, print_lines_near_energy

exspy.utils.eds.print_lines_near_energy(energy, width=0.1, weight_threshold=0.1, only_lines=None, sorting='energy', float_format='.2')

Display a table of X-ray lines close to a given energy.

Parameters:

• energy (float) – The energy to search around, in keV.

• width (float) – Window width in keV around energy in which to find nearby energies, i.e. a value of 0.1 keV (the default) means to search +/- 0.05 keV.

• weight_threshold (float) – Define the threshold of the weight below which the lines are ignored. Must be between 0 and 1. Default is 0.1.

• only_lines (list of str, optional) – Define the lines to be considered (eg. (‘a’,’Kb’)). If None, all lines are included. Default is None.

• sorting (str) – Define the sorting of the table, either "elements" or "energy". Default is "elements".

• float_format (str) – The formatting of the float in the table passed to prettytable.PrettyTable. Default is “.2”.

Examples

>>> import exspy
>>> exspy.utils.eds.print_lines_near_energy(energy=6.4)
+---------+------+--------------+--------+------------+
| Element | Line | Energy (keV) | Weight | Intensity  |
+---------+------+--------------+--------+------------+
|    Sm   | Lb3  |     6.32     |  0.13  | #          |
|    Pm   | Lb2  |     6.34     |  0.20  | #          |
|    Fe   |  Ka  |     6.40     |  1.00  | ########## |
|    Eu   | Lb1  |     6.46     |  0.44  | ####       |
|    Mn   |  Kb  |     6.49     |  0.13  | #          |
|    Dy   |  La  |     6.50     |  1.00  | ########## |
+---------+------+--------------+--------+------------+

See also

get_xray_lines, get_xray_lines_near_energy, print_lines

exspy.utils.eds.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.

exspy.utils.eds.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.

exspy.utils.eds.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.

exspy.utils.eds.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:

• tilt_stage (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 – The take off angle in degrees.

Return type:

float

Examples

>>> exspy.utils.eds.take_off_angle(tilt_stage=10., beta_tilt=0.
>>>                          azimuth_angle=45., elevation_angle=22.)
28.865971201155283

exspy.utils.eds.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()

exspy.utils.eds.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:

xray_range – The X-ray range in micrometer.

Return type:

float

See also

exspy.utils.eds.electron_range

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

exspy.utils.eds.zeta_to_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 – The cross sections with units in barns.

Return type:

list of float

See also

cross_section_to_zeta