Classification of microheterogeneity in solid samples using µXRF

Abstract

Micro X-ray fluorescence (microXRF) has been used nondestructively to investigate elemental heterogeneity by constructing two-dimensional maps of elemental concentrations in reference materials. microXRF probes sample sizes well below the 100 mg mass usually recommended for reference materials by NIST. Multivariate methods of analysis, such as principal-component analysis (PCA), show promise in identifying whether "nugget" effects exist within a material, where an element is enriched in small, isolated areas of the sample. The PCA model is built based on data taken in one location and compared with each elemental map. This methodology is shown for several reference materials including SRM 2702 and SRM 2703 to show how PCA treatment can be used to identify which elements exhibit nugget effects within the sub-mg mass range. A method of calculating the minimum recommended mass for solid samples is suggested using PCA iteratively on X-ray maps from which adjacent data points have been averaged. This is repeated until the mass sampled in a map is indistinguishable from data taken at a single location, suggesting no nugget effects can be detected. For SRM 1577c, a mass as low as 370 microg can be used without measurable nugget effects.

Assessing microscale heterogeneity in batches of reference materials using microbeam XRF

“…bottles, ingots, or vials) as well as within units. For evaluations of single samples, a method using PCA has already been demonstrated that compares the behaviors of constituent elements and enables the analyst to calculate the estimated minimum mass for each element 6. This approach for estimating heterogeneity within a sample can be extended to cover a set of samples plotting all samples together in principal component space as shown in Fig.…”

“…Other authors have shown principal component analysis (PCA) to be a useful tool for processing the large amount of data arising from analyses by µXRF 5. Using descriptive statistics of µXRF data instead of the raw data in combination with PCA has yielded a method6 which can predict the minimum amount of sample that can be used with confidence that nugget effects are not contributing significantly to the overall uncertainty. This method was demonstrated for several reference materials, and a minimum recommended sample mass was calculated for Standard Reference Material (SRM) 1577c (Bovine Liver) and compared to another study3 which used Monte Carlo techniques to predict minimum sample size.…”

“…Using PCA has yielded a relatively simple method for classifying the heterogeneity of a sample, a foundation for the work discussed in this paper. However, all of the prior work using this method6 only considered a small part of one sample which has been analyzed to represent the heterogeneity of an entire material. A related procedure for applying this method to larger sets of samples will be presented with emphasis on sampling type and discussion of how much data must be taken before an accurate representation of the material is obtained.…”

Spatial Geochemistry: A Characterisation of Heterogeneity in Reference Materials

“…, ). There have been a few studies on RM mapping (Eggins and Shelley , Molloy and Sieber ). One interesting contribution was provided by Molloy and Sieber (), who mapped RMs and fed their results into principal component analysis to determine the presence of nuggets.…”

“…More recently, beam diameters have been varied with position relative to the sample recorded (at the centre versus the border of the RM sample) before computing the average and standard deviation (Wilson et al 2002, Jochum et al 2005, 2011. There have been a few studies on RM mapping (Eggins andShelley 2002, Molloy andSieber 2008). One interesting contribution was provided by Molloy and Sieber (2008), who mapped RMs and fed their results into principal component analysis to determine the presence of nuggets.…”