[Paper Review] Improved self-absorption correction for fluorescence measurements of extended x-ray absorption fine-structure

Corwin H. Booth, F. Bridges|arXiv (Cornell University)|Jun 10, 2003

X-ray Spectroscopy and Fluorescence Analysis4 citations

TL;DR

This paper presents a nearly exact, model-independent self-absorption correction for fluorescence-mode EXAFS that accounts for sample thickness and concentration by retaining EXAFS oscillations in the correction term. The method uses a k-space correction formula derived from radiative transfer, validated on a 4.6 µm copper foil where corrected fluorescence data closely match transmission data, demonstrating large corrections even in moderately thick samples.

ABSTRACT

Extended x-ray absorption fine-structure (EXAFS) data collected in the fluorescence mode are susceptible to an apparent amplitude reduction due to the self-absorption of the fluorescing photon by the sample before it reaches a detector. Previous treatments have made the simplifying assumption that the effect of the EXAFS on the correction term is negligible, and that the samples are in the thick limit. We present a nearly exact treatment that can be applied for any sample thickness or concentration, and retains the EXAFS oscillations in the correction term.

Motivation & Objective

• To address the long-standing problem of self-absorption-induced amplitude reduction in fluorescence EXAFS measurements.
• To develop a correction method valid for any sample thickness or concentration, overcoming the limitations of the thick-limit approximation.
• To retain the full EXAFS oscillation structure in the correction term, rather than approximating it as negligible.
• To provide a model-independent, direct correction in k-space applicable to thin films, single crystals, and concentrated materials.
• To validate the method experimentally on a 4.6 µm copper foil, demonstrating its accuracy and necessity.

Proposed method

• Derives the fluorescence intensity from a point source in a sample using radiative transfer, integrating over depth and escape path using geometry-dependent absorption coefficients.
• Introduces a correction factor that explicitly includes the energy-dependent EXAFS oscillation in the absorption coefficient, avoiding the assumption that its modulation is negligible.
• Uses the relation between measured chi_exp and true chi via a derived equation involving the total and fluorescent absorption coefficients, and the sample thickness d.
• Applies a small-angle approximation (χμ̄_a d / sinφ << 1) to reduce the correction to a solvable quadratic equation in chi.
• Derives a closed-form correction formula (Eq. 4) that reduces to the thick-limit and thin-limit cases correctly, ensuring consistency across regimes.
• Validates the method by comparing corrected fluorescence EXAFS data to transmission data on a 4.6 µm copper foil at the Cu K-edge.

Experimental results

Research questions

• RQ1 How can self-absorption effects in fluorescence EXAFS be corrected accurately for samples that are not in the thick limit?
• RQ2 To what extent does the inclusion of EXAFS oscillations in the absorption coefficient affect the self-absorption correction?
• RQ3 Can a model-independent, k-space correction be derived that remains valid across a wide range of sample thicknesses and concentrations?
• RQ4 How large are the amplitude corrections in intermediate-thickness samples, and do they significantly alter EXAFS analysis outcomes?
• RQ5 Does the corrected fluorescence EXAFS data agree quantitatively with transmission-mode EXAFS for a well-characterized sample?

Key findings

• The correction factor χ/χ_exp for a 4.6 µm copper foil reaches up to ~3 times the value in the thick limit, indicating a substantial amplitude reduction due to self-absorption.
• The approximation in Eq. (3) exceeds 1% error only below ~1 Å⁻¹, but remains accurate for typical EXAFS analysis windows.
• The corrected fluorescence EXAFS data in k-space are nearly indistinguishable from transmission-mode data, confirming the method’s accuracy.
• The method reduces to χ = χ_exp in the thin limit and matches the thick-limit result of Tröger et al. (1992) when d → ∞, ensuring consistency.
• The correction is effective for a wide range of materials, including oxides, intermetallics, single crystals, and thin films below 20 µm.
• The study demonstrates that self-absorption corrections can be large even in moderately thick samples, and that neglecting the EXAFS modulation in the correction leads to significant errors.