Statistical evaluation of analytical methods for the determination of rare-earth elements in geological materials and implications for detection limits

We briefly describe the analytical methods commonly employed for determining rare-earth elements (REE) in geological materials. A compilation of analytical data for 24 International Geochemical Reference Materials (IGRM) from the United States and Japan is used to evaluate statistically the inter-laboratory performance of various methods. The most frequently employed method groups for measuring REE include mass spectrometry (MS), nuclear methods (NM), and emission spectrometry (ES), although separation methods (SM) such as high-performance liquid chromatography (HPLC), ion chromatography (IC), or capillary electrophoresis (CE) have shown great potential as cheap, rapid, precise, and accurate methods. X-ray fluorescence (XRF), atomic absorption (AA), and classical colorimetric (CL) methods are not generally recommended for the determination of REE in geological materials, unless suitable pre-concentration procedures are used. The initial inter-laboratory REE data are generally positively skewed due to the presence of mostly high analyte concentration outliers. After an appropriate statistical rejection of outlying observations, the remaining data sets for individual groups of methods show that MS provides the most precise REE data. Inter-laboratory detection limits obtained by weighted regression of a linear precision model are generally in the sub-ppm range (0.07-1.5 ppm for MS methods; 0.05-3.1 ppm for NM; 0.1-4.2 ppm for ES). No overall significant bias was found among the MS, NM, and ES groups of methods for the analysis of the REE, but the Student's t-test revealed significant differences (even at a strict significance level of 1%, equivalent to a confidence level of 99%) for some REE in a few IGRM (for MS-NM methods, La in granite JG-1, Ce in diabase W-1, Tb in basalt BHVO-1, Dy in andesite AGV-1, Tm in basalt BCR-1, and Lu in basalt BIR-1; for MS-ES methods, La in rhyolite JR-1). For these cases, the analytical data must be treated separately to define mean concentration values for methods and to assign one of the method means (probably from the most precise method MS, NM, or ES) as the mean value of that element in the IGRM. The average concentration data from well-established methods can be successfully used to evaluate the performance of other analytical methods such as SM and XRF, not in general use for determination of REE. Finally, the method detection limits obtained for inter-laboratory data, as well as for individual laboratories are shown, for the first time, to depict a zigzag pattern, obeying the well-known odd-even effect of nuclear stability that governs element concentrations in the solar system and the abundance of individual isotopes. We show that the REE detection limits for all analytical methods mimic completely the zigzag patterns for actual REE concentration data in all kinds of geological and cosmological materials, and we hypothesize, on this basis, that the analytical detection and quantification process is also governed by the same nuclear odd-even effect.