Quantifying isotopic heterogeneity of candidate reference materials at the picogram sampling scale

We propose a method for quantifying the in situ heterogeneity of solid materials at the picogram test portion scale, illustrating its use by investigating the oxygen isotope ratio (18O-/16O-) of four quartz samples. Using Secondary Ion Mass Spectrometry we could estimate the intrinsic heterogeneity using a large number (~100) of closely-spaced duplicated measurements. An analysis of variance was then applied to these large data sets to extract the measurement repeatability (typically 0.10 - 0.15‰, 1s) from the total variability, thereby revealing a variability ranging from 0.18 ‰ to 2.3 ‰ which can be attributed to the genuine isotope ratio heterogeneities. A small proportion of outlying values were either rejected manually after inspection, or were accommodated using robust statistics. We also evaluated two distinct approaches for estimating and correcting instrumental drift; the use of a sub-area of the test material (if shown to have sufficiently low heterogeneity) is judged to be preferable to using a piece of unrelated silicate glass which we believe to be homogeneous. We also compared three approaches for estimating measurement repeatability, from which we show that the ‘duplicate method’ applied to the reference material is preferable to using other methods based either on the drift monitoring material or on assessing residuals of the drift monitoring material after drift correction. Finally, here we propose a strategy for predicting the number of measurements on individual fragments of a material that would be required to achieve a specified target uncertainty.