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Atomic Quantification

The analysis.quantification module converts peak intensities into atomic concentrations using Relative Sensitivity Factors (RSF).

Theory

Quantification is based on the fundamental XPS intensity equation:

\[ I_i = n_i \cdot \sigma_i \cdot \Phi \cdot T(E_i) \cdot \lambda(E_i) \cdot A \]

where \(I_i\) is the peak area for element \(i\), \(\sigma_i\) is the photoionization cross-section (RSF), \(\Phi\) is the X-ray flux, \(T\) is the analyzer transmission function, \(\lambda\) is the inelastic mean free path, and \(A\) is the analysis area. The atomic concentration is:

\[ X_i = \frac{I_i / \text{RSF}_i}{\sum_j I_j / \text{RSF}_j} \times 100\% \]

RSF Databases

Database Source Coverage
Scofield Scofield, 1976 All elements, Al K\(\alpha\)
Wagner Wagner, 1983 Empirical, common XPS lines 
from xps_analyzer.analysis import load_sensitivity_factors

rsf = load_sensitivity_factors(database="scofield")
# rsf is a dict: {element_symbol: sensitivity_factor}

API Reference

calculate_atomic_concentration

from xps_analyzer.analysis import calculate_atomic_concentration

concentrations = calculate_atomic_concentration(
    dataset=dataset,
    rsf_database=rsf,
    corrections=["transmission", "imfp"]
)

Parameters:

Parameter Type Description
dataset XPSDataset Calibrated dataset with fitted peaks
rsf_database dict Element RSF values
corrections list[str] Optional corrections: transmission, imfp

Returns: dict[str, float] — atomic percentages keyed by element.

normalize_to_100

from xps_analyzer.analysis import normalize_to_100

normalized = normalize_to_100(concentrations)

Normalizes concentrations to sum to 100%. Detected elements below detection threshold (configurable, default 0.1 at.%) are excluded.

quantify_dataset

Runs the full quantification pipeline on an entire dataset:

from xps_analyzer.analysis import quantify_dataset

summary = quantify_dataset(dataset, rsf_database="scofield")
# summary is a DataFrame with elements, peak areas, RSF, and at.%

Correction Factors

Transmission Function Correction

The analyzer transmission function \(T(E)\) depends on the pass energy and lens mode. Correction factors are loaded from config/instrument_profiles.toml:

[instrument.profiles.thermo_k_alpha]
transmission_function = "E^-0.7"
pass_energy = 50.0

IMFP Correction

The inelastic mean free path \(\lambda(E)\) is energy-dependent. The correction uses the TPP-2M formula (Tanuma, Powell, Penn):

\[ \lambda(E) = \frac{E}{E_p^2 [\beta \ln(\gamma E) - (C/E) + (D/E^2)]} \]

where \(E_p\) is the free-electron plasmon energy and \(\beta, \gamma, C, D\) are material-dependent parameters.