, where cpssamj and cpsrmj are net count rates of analyte element j of the sample and reference material for calibration, Crmj is concentration of element j in the reference material, N is the number of elements that can be determined by LA-ICP-MS. When multiple reference materials were used for calibration, l value can be calculated with regression statistics according to the used reference materials.
Applying an AYCF and using the USGS reference glasses BCR-2G, BHVO-2G and BIR-1G as reference materials for external calibration, analyses of MPI-DING reference glasses generally agree with recommended values within 5 % for major elements (relative standard deviation (RSD) = 0.3–3.9 % except for P2O5, n = 11), and 5–10 % for trace elements. Analyses of anhydrous silicate minerals (clinopyroxene, orthopyroxene, olivine, plagioclase and garnet) and spinel generally agree with the results of electron microprobe analysis within 0.2–7 % for SiO2, Fe2O3, MgO and CaO. RSD are generally < 5 % for elements with concentrations > 0.1 wt. % . The results indicate that, by applying an AYCF and using USGS reference glasses as multiple reference materials for calibration, elements of these anhydrous minerals can be precisely analyzed in situ by LA-ICP-MS without applying internal standardization. The different element fractionations between the NIST glasses and those glasses with natural compositions indicate that NIST SRM 610 is a less than ideal reference material for external calibration of analyses of natural silicates.