Implementation of guide to the expression of uncertainty in measurement (GUM) to internal normalization methodologies for TIMS - application to strontium isotopic ratios

Since ⁸⁷Sr/⁸⁶Sr ratio mainly varies according to the radioactive β-decay of ⁸⁷Rb to ⁸⁷Sr, a reaction with a half-life of nearly 50 billion years, ⁸⁷Sr/⁸⁶Sr ratio changes with a function of the geological age and the original Rb/Sr ratio; thus the ratio is a fingerprint of its geological source. Strontium isotopes suffer from mass dependent isotopic fractionation as well as isobaric interference of Rb at ⁸⁷Sr during mass spectrometric analysis. So in order to obtain the accurate isotopic ratio one has to correct for observed fractionation by employing any of the internal normalization correction methodologies, such as Rayleigh, exponential, power etc, if we carry out the analysis by thermal ionization mass spectrometry. By employing these mathematical expressions it is possible to obtain accurate ratio provided the associated uncertainties to the final observed ion intensities includes inputs from various sources such as baseline, cup calibration factors etc. The results of isotope ratio measurements obtained by TIMS are often indicated with only measurement precision statements on single-sample instead of expanded measurement uncertainties as recommended by the authoritative Guide to the Expression of Uncertainty in Measurement (GUM). The GUM guide recommends a standardized approach to expressing uncertainty across the whole spectrum of measurements. Expanded uncertainties can be quantified by means of a Kragten spread sheet approach, uncertainties obtained from the partial derivatives approach and Monte Carlo propagation of distributions. In the present study we performed our internal normalization correction algorithms for ⁸⁷Sr/⁸⁶Sr isotopic ratio following the partial derivatives approach neglecting the higher order terms of Taylor series expansion for expanded uncertainty