Supplementary material to: Critical evaluation of internal and external calibration methods for accurate strontium isotope ratio determination

Table 1. Details on the sampling sites of soil and water obtained in the area of the former Avar settlements in Leobersdorf, Austria. The sampling sites were chosen based on existing archaeological knowledge and likelihood of being food production areas as well as drinking water sources for humans and animals living at the investigated Avar-age settlement. Sampling was performed during dry weather in December 2023, to take care that the geochemical fingerprints were stable (no input by rain or fertilizers). Lithological information is based on geological maps obtained from the Austrian Geological Survey (now Geosphere Austria; Geologische Karte der Republik Österreich, 1:50.000, number 76). Table 2. Comparison of the determined and expected element content of an in-house quality control standard. Uncertainty of the elemental mass fractions corresponds to 10 % (Urel, k = 2). Table 3. Elution parameters used for the separation of Sr from matrix elements. Table 4. MC ICP-MS faraday cup configuration. Table 5. Comparison of the average I(87Sr)/I(86Sr) signal ratios (only outlier and blank correction performed, but no Rb or IIF correction) of 100 replicate measurements of the SRM 987 at different integration times for an 88Sr signal of approximately 20 V. Table 6. Comparison of n(87Sr)/n(86Sr) isotope ratios in soil (n = 6) and water (n = 4) samples determined by internal and external (SSB, SSB-Zr) calibration. Errors correspond to the expanded uncertainty (U, k=2). Table 7. δ(88Sr/86Sr)SRM987 values in the SRM 987 (n = 36), SRM 1400 (n = 6) and SRM 1486 (n = 4) determined by external calibration (SSB, SSB-Zr). The reference materials were processed in the same way as samples. Errors correspond to the combination of the standard deviation of repeated measurements and the combined measurement uncertainty (uc) to obtain the expanded uncertainty (U, k = 2). The δ(88Sr/86Sr)SRM987 reference value of the SRM 987 was obtained from the CIAAW webpage [1]. It defines the δ(88Sr/86Sr)SRM987 scale, thus does not have an uncertainty. The δ(88Sr/86Sr)SRM987 reference value of the SRM 1400 was from [4]; the uncertainty of this value corresponds to the expanded uncertainty (U, k = 2). The δ(88Sr/86Sr)SRM987 reference value of the SRM 1486 was from [5]; the uncertainty of this value corresponds to the standard uncertainty (2 SD, n = 72). Table 8. To investigate if MIF was present in our MC ICP-MS we conducted an 11 point measurement of the SRM 987 at different RF power settings ranging from 1150 - 1250 W and obtained blank corrected signal ratios of I(88Sr)/I(86Sr) and I(87Sr)/I(86Sr). These values were further logarithmized and plotted agains each other (see supplementary figure 2 below). Table 9. n(87Sr)/n(86Sr) isotope ratios in six tooth enamel samples, which were measured in different MC ICP-MS sessions in the course of approximately one year and determined using external calibration (SSB-Zr) and the revised exponential model following Baxter et al [8]. Errors correspond to the expanded uncertainty (U, k=2). Uncertainty estimation of n(87Sr)/n(86Sr) isotope ratios considered the contributions of the measurement precision, blank correction, Rb-correction and IIF correction following SSB-Zr or the revised exponential model. Table 10. δ(88Sr/86Sr)SRM987 values determined by external calibration using a combination of standard-sample-bracketing and Zr as internal standard (SSB-Zr) in 10 environmental (soil, water) and 125 tooth enamel samples obtained in the area of the archeological excavation site Leobersdorf, Austria. Data are stated in the delta notation relative to the SRM 987 and sorted from highest to lowest values. Errors correspond to the expanded uncertainty (U, k = 2).