A common technique to quantitatively estimate P speciation in soil samples is to apply linear combination fitting (LCF) to normalized P K-edge X-ray absorption near-edge structure (XANES) spectra. Despite the rapid growth of such applications, the uncertainties of the fitted weights are still poorly known. Further, there are few reports to what extent the LCF standards represent unique end-members. Here, the co-variance between 34 standards was determined and their significance for LCF was discussed. We present a probabilistic approach for refining the calculation of LCF weights based on Latin hypercube sampling of normalized XANES spectra, where the contributions of energy calibration and normalization to fit uncertainty were considered. Many of the LCF standards, particularly within the same standard groups, were strongly correlated. This supports an approach in which the LCF standards are grouped. Moreover, adsorbed phytates and monetite were well described by other standards, which puts into question their use as end-members in LCF. Use of the probabilistic method resulted in uncertainties ranging from 2 to 11 percentage units. Uncertainties in the calibrated energy were important for the LCF weights, particularly for organic P, which changed with up to 2.7 percentage units per 0.01 eV error in energy. These results highlight the necessity of careful energy calibration and the use of frequent calibration checks. The probabilistic approach, in which at least 100 spectral variants are analyzed, improves our ability to identify the most likely P compounds present in a soil sample, and a procedure for this is suggested in the paper.

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Several studies have shown that the distribution of cation adsorption sites (CASs) is patchy at a millimetre to centimetre scale. Often, larger concentrations of CASs in biopores or aggregate coatings have been reported in the literature. This heterogeneity has implications on the accessibility of CASs and may influence the performance of soil system models that assume a spatially homogeneous distribution of CASs. In this study, we present a new method to quantify the abundance and 3-D distribution of CASs in undisturbed soil that allows for investigating CAS densities with distance to the soil macropores. We used X-ray imaging with Ba 2+ as a contrast agent. Ba 2+ has a high adsorption affinity to CASs and is widely used as an index cation to measure the cation exchange capacity (CEC). Eight soil cores (approx. 10 cm 3 ) were sampled from three locations with contrasting texture and organic matter contents. The CASs of our samples were saturated with Ba 2+ in the laboratory using BaCl 2 (0.3 mol L −1 ). Afterwards, KCl (0.1 mol L −1 ) was used to rinse out Ba 2+ ions that were not bound to CASs. Before and after this process the samples were scanned using an industrial X-ray scanner. Ba 2+ bound to CASs was then visualized in 3-D by the difference image technique. The resulting difference images were interpreted as depicting the Ba 2+ bound to CASs only. The X-ray image-derived CEC correlated significantly with results of the commonly used ammonium acetate method to determine CEC in well-mixed samples. The CEC of organic-matter-rich samples seemed to be systematically overestimated and in the case of the clay-rich samples with less organic matter the CEC seemed to be systematically underestimated. The results showed that the distribution of the CASs varied spatially within most of our samples down to a millimetre scale. There was no systematic relation between the location of CASs and the soil macropore structure. We are convinced that the approach proposed here will strongly aid the development of more realistic soil system models.

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