Characterizing Homogeneous Raw Material via Non-Invasive X-ray Flourescence Spectroscopy


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\label{tab:transitions}Atomic transitions relevant to XRF in the present work.
initial state final state transition
2p\({{}_{1/2}}\) 1p\({{}_{1/2}}\) K\({}_{\alpha~{}2}\)
2p\({{}_{3/2}}\) 1p\({{}_{1/2}}\) K\({}_{\alpha~{}1}\)
3p\({{}_{3/2}}\) 1p\({{}_{1/2}}\) K\({}_{\beta~{}1}\)
4p\({{}_{1/2}}\) 1p\({{}_{1/2}}\) K\({}_{\beta~{}2}\)


\label{subsec:energy_calibration}Energy Calibration

In the bottom panel of Figure \ref{fig:energy_calibration} all the calibration spectra (Ba, Cu, Rb, Tb) are stacked for display purposes. The blue, downward pointing triangular markers indicate the emission peaks that were fit 11These corresponding to the \(K_{\alpha 1}\), \(K_{\alpha 2}\), \(K_{\beta 1}\), and \(K_{\beta 2}\). Other features exist in these spectra but were ignored for the purpose of the calibration analysis. for the calibration analysis. All partner pairs (e.g. K\(\alpha_{1}\) and K\(\alpha_{2}\)) were fitted as blended, double gaussians over a linear background (an 8 parameter \(X^{2}\) minimization). In the middle panel, all peak centroids from the bottom panel are represented with the currently reported energies from the literature. 22NIST X-ray Transitions Energy Database The horizontal error bars are scaled to the FWHM of the fitted gaussians for each corresponding emission peak. The uncertainties reported for each transition energy are too small to be represented meaningfully here. A linear regression gives the reported calibration curve. The results and statistics for this regression are provided in the figure. In the top panel, the standard residuals to the linear regression (middle panel) are provided.

\label{fig:energy_calibration}Energy calibration.