ABSTRACT X‐ray fluorescence (XRF) analysis combines spectral inverse modeling, elemental support selection and spatial interpretation. We develop quadratic unconstrained binary optimization (QUBO) and Ising formulations for these tasks. A detector‐response dictionary of broadened candidate emission‐line profiles induces a spectral overlap graph that determines the coupling topology: strongly overlapping lines produce strongly coupled binary variables, providing a diagnostic of ambiguity before optimization. We formulate elemental identification using exact binary selection with physical line‐consistency penalties, derive a fixed‐point non‐negative encoding for quantized deconvolution, and express elemental‐map segmentation and trace detection as spatially regularized binary energies extending established Markov‐random‐field and detection‐limit approaches. Synchrotron low‐energy XRF combines weak fluorescence, overlapping soft X‐ray lines and large hyperspectral datacubes. The formulations are exercised on a published soft X‐ray map of THP‐1‐derived macrophages exposed to erionite fibers, acquired at the TwinMic beamline of Elettra Sincrotrone Trieste, using its detector calibration, fitted peak areas and uncertainties. The browser‐based XRFQubo demonstrator implements overlap analysis, spatial trace detection and reduced 39‐variable support selection with classical simulated annealing. Fit‐derived tests identify practical requirements for per‐line amplitude scaling, amplitude‐block moves with classical warm starts, and statistical weighting. Selection frequency broadly follows fitted peak‐area significance, while spatial regularization consolidates contiguous trace detections and suppresses isolated labels. A separate four‐qubit experiment executes restricted conditional support‐selection objectives from two measured spectra on IBM and IQM processors. No quantum advantage is claimed. Extending our companion computed tomography study, this work provides quantum‐compatible formulations and a classical demonstrator for controlled benchmarking against established XRF methods.
Crystalline quartz, the most common crystalline silica polymorph, is widely found in industrial products. It is of high regulatory relevance, because its fine fraction, a form of respirable crystalline silica, is classified as an occupational carcinogen, with product-content thresholds (e.g., 0.1% (w/w) in the European Union) and stringent occupational exposure limits. Since larger size fractions can be reduced to the fine one during work processes and use, a silica-free approach should be pursued, driving the need for accurate and sensitive quantification of crystalline quartz, even in complex matrices. X-ray diffraction (XRD) is a reference technique for selective quartz determination; however, paraffin-rich abrasive and polishing pastes pose a major analytical challenge due to their dense, viscous rheology, which prevents homogeneous incorporation of crystalline internal standards or spikes required by validated quantitative XRD approaches (e.g., EN 13925, EN 17289). Here, we develop and optimize a low-viscosity sample pretreatment, termed low-viscosity doping (LVD), to overcome matrix-driven inhomogeneity. LVD mitigates rheological constraints, enables uniform internal-standard distribution, and improves the reliability of quantitative XRD. Using LVD, crystalline quartz mass fractions were determined with good accuracy and repeatability at levels well below the 0.1% product threshold. The proposed workflow is standardized, time-efficient, and compatible with modern benchtop diffractometers, potentially paving the way for a standard aimed at enhancing safety compliance and risk mitigation in the abrasive and polishing products industry.
The Ruland streak method is widely used in small-angle x-ray scattering (SAXS) to quantify the length and orientation of scatterers, but lacks systematic error quantification under varying microstructural conditions, limiting its quantitative reliability. In this work, we present a benchmarking and computational verification framework for the Ruland streak method, utilizing simulated SAXS patterns of dilute cylindrical scatterers parameterized by distribution full width at half maximum (FWHM), aspect ratio, and size distribution. This framework is applied to assess the accuracy, limitations, and scope of applicability of the Ruland streak method in microstructural characterization. Furthermore, contour maps of relative errors are presented to quantitatively evaluate the fitting errors of the results, allowing the extracted parameters to more closely approximate the true physical values. In addition, preliminary validation is carried out using oriented gold nanorod samples. Although the Ruland streak method demonstrates certain computational deviations, the core principles the Ruland streak method embodies remain fundamentally valid. Additionally, by modifying the scattering intensity function, the proposed framework can be extended and applied to error validation for other SAXS-based methods.
Snack foods are widely consumed among children and adults. However, they may act as a source of toxic element exposure through raw material contamination, processing additives, and packaging practices. This study quantified Cu, Ni, Zn, Mn, and Fe in 30 snack samples (corn, n = 21; potato, n = 9) using EDXRF spectroscopy. Health risks were evaluated for adults and children through estimated daily intake (EDI), target hazard quotient (THQ), hazard index (HI), and lifetime cancer risk (LCR). Fe and Zn were the dominant elements in both snack types. Mn was detected in only 12 of 30 samples across corn and potato snacks. Ni was detected in just 2 corn samples (n = 2) and was not found in any potato sample. Fe and Mn exceeded permissible regulatory limits in multiple samples. THQ values for Cu, Ni, Zn, and Mn remained within safe limits for both age groups. Fe exceeded the threshold, and cumulative HI values surpassed the threshold for adults and children alike, with children showing greater modeled vulnerability. For Ni, LCR values of 1.6E-4 and 2.5E-4 were calculated for adults in the two samples where it was detected, both at or above the accepted risk benchmark, with higher corresponding values for children. These findings support the need for continued toxic element monitoring in snack products.
In this study, a non-invasive, multi-analytical approach combining hypercolorimetric multispectral imaging (HMI), stereomicroscopy, X-ray fluorescence (XRF) spectroscopy, principal component analysis (PCA) and X-ray radiography (RX) is used to investigate three reused musical parchment fragments dating from the late 14th or early 15th century and preserved in the Archivio di Stato di Siena. The aim is to characterise and differentiate the inks used for musical texts and notations, as well as marginal annotations, with the broader objective of identifying distinct writing interventions. Imaging analyses revealed differences in the preservation state of the writing within the script, while also enhancing the visibility of faded and partially lost traces. The black inks generally exhibited spectral behaviour consistent with iron-gall formulations, whereas selected annotations were compatible with carbon-based writing materials. XRF analysis identified iron (Fe) and copper (Cu) as the principal elemental markers. PCA was used as an exploratory tool to identify the main compositional differences and to guide the subsequent interpretation of the spectroscopic dataset. The Fe/Cu ratio enabled the chemical discrimination and spatial mapping of multiple ink formulations across all three fragments, revealing the coexistence of primary writing materials and localised secondary interventions. The integrated investigation of the miniature on one of the fragments identified the pictorial palette and provided evidence of the gilding technique. The results demonstrate the effectiveness of the workflow for the multi-analytical investigation of reused parchment fragments, improving the characterisation of heterogeneous materials and supporting the identification of historical hands involved in producing and subsequently reusing the fragments.
