ZAFG Method for Quantitative Characterization of Spherical Particles: Deriving a Universal Equation for Geometrical...

Area of Science:

• Materials Science
• Analytical Chemistry
• Physics

Background:

• Accurate quantification of small particles in electron probe microanalysis (EPMA) is challenging.
• The conventional ZAF method requires corrections for atomic number, absorption, and fluorescence effects.
• A geometrical correction factor (G) is needed for accurate analysis of spherical particles.

Purpose of the Study:

• To develop a universal equation for the geometrical correction factor (G) in X-ray microanalysis.
• To validate the proposed G factor model using NIST-K411 glass microspheres.
• To investigate the dependence of the G factor on particle size and X-ray emission range.

Main Methods:

• Development of a theoretical model for the geometrical correction factor (G).
• Experimental quantification of NIST-K411 glass microspheres on a carbon substrate.
• Comparison of model predictions with experimental data.

Main Results:

• The geometrical correction factor (G) is best modeled as a function of particle diameter (D) and X-ray range (Xe).
• Excellent agreement was observed between the predicted G factor and experimental results.
• The G factor decays exponentially when Xe > D, independent of beam energy and composition.
• When D*Xe > 1, the particle behaves as a bulk sample with G = 1.

Conclusions:

• The proposed universal equation for the geometrical correction factor (G) provides accurate quantification for spherical particles.
• The G factor is primarily dependent on the product of particle diameter and X-ray range (D*Xe).
• This model simplifies the analysis of small particles in EPMA, reducing reliance on composition and beam energy.