Validity evaluation of SQX analysis results
Yasujiro Yamada
Winter 2025 Volume 41, No. 1 , 08-11
Highlights
- A Compton fit coefficient provides a practical way to validate standardless FP (SQX) XRF results by comparing theoretical and measured Compton scattering intensities.
- Coefficients close to 1.0 indicate a well-defined sample model, while values significantly above or below 1.0 quickly reveal errors such as missing light elements, incorrect sample dimensions, or improper balance components.
- Validation using the Compton fit coefficient improves confidence in standardless XRF analysis across powders, polymers, liquids, and samples containing non-measured elements such as lithium.
Summary
Standardless fundamental parameter (FP) X-ray fluorescence analysis is widely used when calibration standards are unavailable, making it valuable for research, development, and non-routine sample analysis. However, because it relies on theoretical models rather than calibration curves, there has traditionally been no straightforward way to determine whether the calculated elemental concentrations are trustworthy.
A practical validation approach is to compare the theoretical Compton scattering intensity calculated from the analytical results with the measured Compton scattering intensity. Their ratio, referred to as the Compton fit coefficient, serves as an indicator of how well the analytical model matches the actual sample. Values between approximately 0.9 and 1.1 indicate good agreement, while lower values often suggest missing light elements or incorrect sample parameters, and higher values typically indicate that light elements have been overestimated in the sample model.
The method is demonstrated using several representative examples. Quartz glass illustrates how omitting oxygen from the model produces an unrealistically low coefficient and incorrect composition. Polymer analysis shows that inaccurate sample dimensions can significantly distort heavy-element concentrations. Lithium phosphate demonstrates how including non-measured elements such as lithium substantially improves analytical reliability, while liquid zinc standards show that selecting the correct solvent model is essential for obtaining accurate concentrations.
Because Compton scattering is highly sensitive to the amount of light elements present, the coefficient provides an effective diagnostic tool for identifying incorrect sample models, improper balance components, missing elemental information, and inadequate correction parameters before analytical results are accepted. This makes standardless XRF analysis more robust and reliable, particularly for challenging materials where conventional calibration standards are unavailable.
Frequently asked questions
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The Compton fit coefficient is the ratio of the theoretical Compton scattering intensity calculated from a standardless FP analysis to the measured Compton scattering intensity collected during the XRF measurement. It provides a simple numerical indicator of how well the assumed sample model represents the actual sample. Values close to 1 indicate strong agreement between the model and the measurement, increasing confidence in the reported elemental concentrations.
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A coefficient between approximately 0.9 and 1.1 generally indicates that the analytical model accurately represents the sample. Values below 0.9 typically suggest that light elements or other important sample information are missing, causing theoretical scattering to be underestimated. Values above 1.1 often indicate that the model contains too many light elements or otherwise overestimates scattering, leading to inaccurate elemental concentrations.
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Compton scattering intensity is strongly influenced by the concentration of light elements within a sample. If elements such as oxygen, lithium, hydrogen, or carbon are omitted or incorrectly modeled, the calculated scattering intensity no longer matches the measured value. Comparing theoretical and measured scattering therefore provides an effective way to detect missing or incorrectly defined light-element contributions that may not be obvious from elemental results alone.
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Yes. Standardless FP calculations depend on accurate information about sample geometry, including weight, thickness, and dimensions. Incorrect sample size information changes the calculated X-ray absorption and scattering behavior, which causes the Compton fit coefficient to deviate from unity. This makes it possible to identify errors in sample preparation or input parameters before accepting the analytical results.
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Some elements, particularly very light elements such as lithium, cannot be measured directly under many XRF conditions. Including these elements as known or fixed components within the sample model increases the accuracy of the calculated scattering intensity. An improvement in the Compton fit coefficient indicates that the revised model better represents the actual sample and produces more reliable concentrations for the measurable elements.
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The balance component represents the portion of the sample that is not directly measured. In liquids, for example, defining the correct solvent is essential because different solvents contain different amounts of light elements that significantly affect Compton scattering. Using an incorrect balance component can produce large errors in calculated elemental concentrations even when the measured peaks themselves appear normal.
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The approach is particularly valuable for powders, polymers, liquids, research materials, and unknown samples analyzed without calibration standards. It is especially useful whenever sample composition, light-element content, geometry, or balance components are uncertain, providing an additional quality check that helps identify modeling errors before analytical results are reported.
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