autoemxsp.core.XSp_quantifier module

X-ray Spectrum Quantification Module

Created on Thu Jun 27 14:23:22 2024

@author: Andrea Giunto

This module provides classes and functions for matrix correction and quantitative analysis of X-ray spectra, implementing the peak-to-background (P/B) method and related ZAF corrections for scanning electron microscopy (SEM) energy-dispersive X-ray spectroscopy (EDS).

Class Structure and Interactions

The main classes are: - XSp_Quantifier

Performs quantification of X-ray spectra using matrix corrections. Interfaces with spectral fitting routines from XSp_Fitter to extract peak/background intensities and applies the full suite of correction factors from Quant_Corrections to obtain quantitative elemental concentrations. Additionally provides functions to plot and print the results.

• Quant_Corrections Provides methods for calculating matrix correction factors (Z, A, R) for the P/B method. This class is instanced by XSp_Quantifier to calculate the matrix correction factors.

Typical Usage

1. Initialize the quantifier object:

   quantifier = XSp_Quantifier(…) # See class docs for initialization

2. Quantify a spectrum:

   quant_result = quantifier.quantify_spectrum()

   quant_result contains quantified atomic and weight fractions, analytical error, and spectral fitting metrics (reduced chi-square, and R-squared).

3. Print quantification results:

   quantifier.print_quant_result(quant_result)

3. Plot spectrum:

   quantifier.plot_quantified_spectrum()

Customization & Calibration

Detector calibration, physical constants, and mass absorption coefficients are handled via the calibs module and supporting utility functions. Users should calibrate the values in the calibs module corresponding to their microscope and EDS settings prior usage.

Dependencies

numpy, scipy, sympy, pandas lmfit, pymatgen.core.Element (from supporting libraries) XSp_Fitter (required for spectral fitting; see separate module) calibs, lib modules

How the classes interact

XSp_Quantifier is the main user-facing class for quantification. It uses Quant_Corrections to compute all correction factors and matrix effects, and relies on the XSp_Fitter module to extract peak/background intensities from measured spectra. Quant_Corrections provides the core physical models for all matrix corrections, and is initialized with the relevant sample and measurement parameters. The XSp_Fitter module must be installed and available for spectral fitting and deconvolution.

class autoemxsp.core.XSp_quantifier.XSp_Quantifier(spectrum_vals, spectrum_lims, microscope_ID, meas_type, meas_mode, det_ch_offset, det_ch_width, beam_e, emergence_angle, energy_vals=None, background_vals=None, els_sample=None, els_substrate=None, els_w_fr=None, is_particle=False, sp_collection_time=None, max_undetectable_w_fr=0.1, fit_tol=0.0001, standards_dict=None, verbose=False, fitting_verbose=False)

Bases: object

Class for quantitative analysis of EDS spectra.

spectrum_vals

The measured EDS spectrum (counts per channel).

Type:

numpy.ndarray

energy_vals

Energy scale corresponding to spectrum_vals.

Type:

numpy.ndarray

spectrum_lims

Start and end indices for the spectrum region to analyze.

Type:

tuple of int

fit_background

Whether to fit a background model. True, if background_vals are not provided.

Type:

bool

background_vals

Fitted or provided background spectrum counts.

Type:

numpy.ndarray

els_sample

All elements present in the sample, including undetectable elements.

Type:

list of str

els_to_quantify

Elements to be quantified (excluding undetectable).

Type:

list of str

els_substrate

Elements present in the substrate or sample holder appearing in spectra (excluding undetectable).

Type:

list of str

els_w_fr

Dictionary of fixed elemental mass fractions, by element symbol, e.g. {‘Si’:0.33, ‘O’:0.67}.

Type:

dict or None, optional

max_undetectable_w_fr

Maximum allowed total mass fraction for undetectable elements during fitting.

Type:

float

force_total_w_fr

Whether total mass fraction is normalized 1 during fitting. False, if undetectable elements are present in the sample. True otherwise.

Type:

bool

is_particle

Whether the sample is a particle (affects fitting and quantification corrections).

Type:

bool

sp_collection_time

Live time of spectrum acquisition (in seconds).

Type:

float or None

fit_tol

Tolerance for spectrum fitting convergence.

Type:

float

bad_quant_flag

Flag indicating quantification issues, or None if successful.

Type:

int or None

microscope_ID

Microscope identifier for calibration.

Type:

str

meas_type

Measurement type (e.g., ‘EDS’).

Type:

str

meas_mode

Measurement mode, defining detector calibrations and (optionally) beam current (e.g., ‘point’).

Type:

str

det_ch_offset

Detector channel energy offset (keV).

Type:

float

det_ch_width

Detector channel width (keV).

Type:

float

beam_energy

Electron beam energy (keV).

Type:

float

emergence_angle

Detector emergence (take-off) angle (degrees).

Type:

float

verbose

Print information during quantification.

Type:

bool

fitting_verbose

If True, print detailed information during each fitting step.

Type:

bool

Class attributes

----------------

xray_quant_ref_lines

List of X-ray lines used as reference

Type:

list(str)

xray_quant_ref_lines = ['Ka1', 'La1', 'Ma1', 'Mz1']

initialize_and_fit_spectrum(params: Parameters | None = None, print_results: bool | None = False) → None

Perform a complete fit of the spectrum provided to the instance of XSp_Quantifier. This method is intended for single-iteration fits where sample composition is known and constrained (e.g., EDS standards).

The fit results and all relevant fitted parameters are stored as instance attributes.

Parameters:

• params (Optional[lmfit.Parameters], optional) – Parameters object to pass to the spectrum fitter. If None, default parameters are used.

• print_result (bool, optional) – If True, prints the fitting results.

Returns:

• None

• Nested Calls

• ————

• Calls the following methods to further store values extracted from the fit –

  • self._initialize_spectrum_fitter(): initializes the spectrum fitter

  • self._fit_spectrum(): fits the spectrum and stores the fit results

get_starting_K_val() → float | None

Estimate the initial background scaling factor K by fitting the high-energy portion of the spectrum.

This method fits only the region of the spectrum above a threshold energy to avoid regions heavily affected by absorption. It is intended to provide an optimal starting value for K, especially for particle spectra, to prevent the algorithm from compensating for background intensity via particle geometry parameters, which are only intended for background shape fitting.

Returns:

K_val – Estimated initial value for the background scaling factor K, or None if a suitable value could not be determined.

Return type:

Optional[float]

Notes

• Uses XSp_Fitter with particle geometry disabled for this quick fit.

• Prints diagnostic information if self.verbose is True.

quantify_spectrum(force_single_iteration=False, interrupt_fits_bad_spectra=True, print_result=True)

Quantifies a spectrum, using iterative fitting to refine elemental fractions. At each iteration, elemental fractions are quantified and enforced in the next iteration. Algorithm converges when quantified elemental fractions all change by less than 0.01%.

Instead, if elemental fractions are provided (i.e., fitting of experimental standards), background values are provided, or if force_single_iteration = True, only a single iteration is performed.

Parameters:

• force_single_iteration (bool, optional) – If True, only a single fit iteration is performed, even if some elemental fractions are undefined.

• interrupt_fits_bad_spectra (bool, optional) – If True, fitting is interrupted early if the spectrum is deemed unreliable.

• print_result (bool, optional) – If True, prints the quantification results.

Returns:

• quant_result (dict or None) – Dictionary with quantification results, or None if fit failed.

• min_bckgrnd_ref_lines (float) – Minimum background counts across reference peaks, or 0 if fit failed.

• bad_quant_flag (int or None) – Flag indicating quantification issues, or None if successful.

print_quant_result(quant_result: dict, Z_sample: dict = None) → None

Print the quantification results, including fit quality metrics and elemental composition.

Parameters:

• quant_result (dict) –

  Dictionary containing quantification results with keys:

  • cnst.REDCHI_SQ_KEY: Reduced Chi-square of the fit.

  • cnst.R_SQ_KEY: R-squared of the fit.

  • cnst.COMP_W_FR_KEY: Weight fractions (as decimals).

  • cnst.COMP_AT_FR_KEY: Atomic fractions (as decimals).

  • cnst.AN_ER_KEY: Analytical error (as decimal).

• Z_sample (dict, optional) –

  Dictionary containing mean atomic numbers (optional), e.g.:

  • ’Statham2016’: Mean atomic number (Z̅) calculated according to Statham (2016).

  • ’mass-averaged’: Mean atomic number (Z̅) weighted by composition.

Return type:

None

References

Statham P, Penman C, Duncumb P. IOP Conf Ser Mater Sci Eng. 2016;109(1):0–10.

plot_quantified_spectrum(annotate_peaks: str = 'all', plot_bckgrnd_cnts_ref_peaks: bool = True, plot_initial_guess: bool = False, plot_title: str | None = None, peaks_to_zoom: str | List[str] | None = None) → None

Plot the quantified spectrum. The background counts under reference peaks are highlighted for spectra used for quantification.

Parameters:

• annotate_peaks (str, optional) – Which peaks to annotate. Options: ‘all’, ‘most’, ‘main’, ‘none’. Default is ‘all’.

• plot_bckgrnd_cnts_ref_peaks (bool, optional) – If True, plot vertical lines that illustrate value of background counts used for quantification. This is shown underneath the corresponding reference characteristic peaks for each element.

• plot_initial_guess (bool, optional) – If True, plot the initial guess as well. Default is False.

• plot_title (str, optional) – Title printed at the top of the plot. Default is None.

• peaks_to_zoom (str or list of str, optional) – Peak label (e.g. ‘Si_Ka1’) or list of labels to zoom in on. If provided, creates a new figure for each.

Return type:

None.

plot_zoomed_peak(zoom_peak: str, plot_title: str | None = None) → None

Create a new figure zoomed in on a specific peak.

Parameters:

• zoom_peak (str) – The el_line string of the peak to zoom on (e.g. ‘Si_Ka1’).

• plot_title (str, optional) – Title for the zoomed plot.

Return type:

None.

class autoemxsp.core.XSp_quantifier.Quant_Corrections(elements: Sequence[str], beam_energy: float, emergence_angle: float, meas_mode: str, energies: Sequence[float] | ndarray | None = None, verbose: bool = False)

Bases: object

Implements matrix correction factors for quantitative X-ray microanalysis using the peak-to-background (P/B) method.

This class provides methods for calculating Z (atomic number), A (absorption), and R (backscattering) correction factors, as well as mass absorption coefficients for a given set of elements and measurement conditions. It is designed for both standard-based and standardless quantification workflows in electron probe microanalysis (EPMA) or energy-dispersive X-ray spectroscopy (EDS).

References

7. Love, V.D. Scott, “Evaluation of a new correction procedure for quantitative electron probe microanalysis”,

   10. Phys. D. Appl. Phys. 11 (1978) 1369–1376. https://doi.org/10.1088/0022-3727/11/10/002

P.J. Statham, “A ZAF PROCEDURE FOR MICROPROBE ANALYSIS BASED ON MEASUREMENT OF PEAK-TO-BACKGROUND RATIOS”,

in: D.E. Newbury (Ed.), Fourteenth Annu. Conf. Microbeam Anal. Soc., San Francisco Press, 1979: pp. 247–253.

13. Essani, E. Brackx, E. Excoffier, “A method for the correction of size effects in microparticles using a peak-to-background approach

    in electron-probe microanalysis”, Spectrochim. Acta B 169 (2020) 105880. https://doi.org/10.1016/j.sab.2020.105880

elements

List of element symbols included in the quantification (excluding undetectable elements).

Type:

list of str

energies

X-ray energies (keV) for each element/line.

Type:

np.ndarray

emergence_angle

Detector emergence angle (degrees).

Type:

float

beam_energy

Incident electron beam energy (keV).

Type:

float

meas_mode

Detector mode (for calibration parameters).

Type:

str

Z_els

Atomic numbers for each element.

Type:

np.ndarray

W_els

Atomic weights for each element.

Type:

np.ndarray

els_nu

Backscattering coefficients for each element.

Type:

np.ndarray

mass_abs_coeffs_lines

Mass absorption coefficients for each element at each characteristic energy.

Type:

list of list of float

verbose

If True, enables verbose output for debugging.

Type:

bool

get_ZAF_mult_f_pb(weight_fractions: ndarray, el_lines_energies_d: Dict[str, float] | None = None) → Tuple[ndarray, Dict[str, float]]

Calculate the ZAF multiplicative correction factors for the measured sample P/B ratio.

This method accounts for:

1. Differences in average Z between the sample and the employed standard, which affect continuum intensity.

2. Second-order corrections for backscattering and absorption due to differential mean generation path between characteristic and continuum X-rays.

Fluorescence and particle-size corrections are ignored.

Parameters:

• weight_fractions (np.ndarray) – Estimated weight fractions of the elements to quantify.

• el_lines_energies_d (dict[str, float], optional) – Dictionary mapping peak labels (e.g., ‘Fe_Ka’) to energies (keV). If None, uses all elements and energies in the class.

Returns:

• ZAF_pb_corrections (np.ndarray) – ZAF correction factors to multiply with the measured sample P/B ratio.

• Z_sample (dict) – Dictionary with various sample mean atomic numbers.

References

[1] Statham P, Penman C, Duncumb P. Improved spectrum simulation for validating SEM-EDS analysis.

IOP Conf. Ser. Mater. Sci. Eng. 109, 0 (2016).

[2] Markowicz AA, Van Grieken RE. Composition dependence of bremsstrahlung background in electron-probe

x-ray microanalysis. Anal. Chem. 56, 2049 (1984).

Potential improvements

Include fluorescence corrections for large particles Include particle size corrections, from:

[1] J. L. Lábár and S. Török, A peak‐to‐background method for electron‐probe x‐ray microanalysis

applied to individual small particles, X-Ray Spectrom. 21, 183 (1992).

[2] M. Essani, E. Brackx, and E. Excoffier, A method for the correction of size effects in microparticles

using a peak-to-background approach in electron-probe microanalysis, Spectrochim. Acta - Part B At. Spectrosc. 169, 105880 (2020).