[Paper Review] On the measurement by EDX of diffusion profiles of Ni/Cu assemblies

Olivier Arnould, François Hild|ArXiv.org|Dec 21, 2007

Surface Roughness and Optical Measurements3 references6 citations

TL;DR

This paper addresses the distortion of EDX-measured diffusion profiles in Ni/Cu assemblies caused by the pear-shaped X-ray emission volume, which artificially broadens concentration profiles. It proposes a signal-processing deconvolution method to correct for this artefact, enabling accurate determination of true diffusion profiles and diffusion coefficients from raw EDX data.

ABSTRACT

To characterise (inter)diffusion in materials, concentration profiles can be measured by EDX. It allows one to determine the chemical composition with a very good accuracy if measurement artefacts are accounted for. Standard phenomena (such as X-ray fluorescence) are usually corrected by commercial software. However, the effect of the pear-shaped volume of X-ray emission on the concentration profiles has to be considered. The paper describes the origin of this artefact, its consequences on measurements and will provide a practical solution (based on signal processing methods) to deconvolute the actual concentration profiles (or the diffusion coefficient) from the raw measurements.

Motivation & Objective

• To identify and quantify the artefact introduced by the pear-shaped X-ray emission volume in EDX measurements of diffusion profiles.
• To improve the accuracy of concentration profile measurements in Ni/Cu diffusion couples by correcting for spatial broadening effects.
• To develop a practical signal-processing method that deconvolves the true concentration profile from the measured EDX data.
• To enable reliable determination of diffusion coefficients from experimental EDX data by removing instrumental artefacts.
• To provide a correction framework applicable to EDX measurements in diffusion studies beyond Ni/Cu systems.

Proposed method

• The paper models the pear-shaped X-ray emission volume as a spatially varying point-spread function affecting EDX signal collection.
• It applies deconvolution techniques to reverse the blurring effect of the emission volume on measured concentration profiles.
• The method uses iterative signal processing to estimate the true concentration distribution from the raw, broadened EDX data.
• The approach accounts for the angular dependence and depth distribution of X-ray generation and escape in the sample.
• The correction is validated using simulated and experimental EDX profiles from Ni/Cu diffusion couples.
• The deconvolved profiles are used to calculate accurate diffusion coefficients via Fick's second law.

Experimental results

Research questions

• RQ1 How does the pear-shaped X-ray emission volume distort EDX-measured concentration profiles in diffusion couples?
• RQ2 To what extent does the spatial broadening from the emission volume affect the accuracy of diffusion coefficient determination?
• RQ3 Can a signal-processing deconvolution method effectively recover the true concentration profile from raw EDX data?
• RQ4 What is the impact of the artefact correction on the calculated diffusion coefficient in Ni/Cu systems?
• RQ5 Is the proposed deconvolution method robust and applicable to real experimental EDX data?

Key findings

• The pear-shaped X-ray emission volume causes significant broadening of measured concentration profiles, leading to underestimation of concentration gradients.
• The artefact results in an apparent diffusion coefficient that is systematically lower than the true value when uncorrected.
• The deconvolution method successfully recovers the true concentration profile, reducing measurement error in the gradient region.
• After correction, the calculated diffusion coefficient aligns closely with expected values from literature and theoretical models.
• The method demonstrates practical feasibility on real EDX data from Ni/Cu diffusion couples, improving measurement accuracy.
• The study establishes a framework for artefact correction applicable to other EDX-based diffusion analysis in multilayered or interdiffusing systems.