autoemx.core.quantifier.corrections module

Quantification correction models for EDS peak-to-background analysis.

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

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

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

  • M. 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

Variables:

  • elements (list of str) – List of element symbols included in the quantification (excluding undetectable elements).

  • energies (np.ndarray) – X-ray energies (keV) for each element/line.

  • emergence_angle (float) – Detector emergence angle (degrees).

  • beam_energy (float) – Incident electron beam energy (keV).

  • meas_mode (str) – Detector mode (for calibration parameters).

  • Z_els (np.ndarray) – Atomic numbers for each element.

  • W_els (np.ndarray) – Atomic weights for each element.

  • els_nu (np.ndarray) – Backscattering coefficients for each element.

  • mass_abs_coeffs_lines (list of list of float) – Mass absorption coefficients for each element at each characteristic energy.

  • verbose (bool) – If True, enables verbose output for debugging.

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

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:

  • 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).

  • 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).