High precision Lu and Hf isotope analyses of both spiked and unspiked samples: A new approach

<jats:p>The functional form of instrumentally produced mass fractionation associated with MC‐ICP‐MS analysis is not accurately known and therefore cannot be fully corrected by traditional approaches of internal normalization using power, linear, or exponential mass‐bias laws. We present a method for robust correction of instrumentally produced mass‐fractionation of both spiked and unspiked samples that can be applied to mass analysis of Hf as well as Nd, Sr, Os, etc. Correction of <jats:sup>176</jats:sup>Hf/<jats:sup>177</jats:sup>Hf for unspiked samples follows a traditional approach of internal normalization using an exponential law, followed by normalization to a standard of known composition, such as JMC‐475. For spiked samples, standards are used to characterize a linear instrumental mass‐bias coefficient; the mass‐bias coefficient is defined by the slope of a tie‐line between measured and true values of a standard. This approximation results in identical precision and accuracy of measurements for spiked and unspiked samples (±0.005% 2σ, external reproducibility). The effects of the spike on the <jats:sup>176</jats:sup>Hf/<jats:sup>177</jats:sup>Hf ratio and calculation of the molar spike‐sample ratio is determined by a closed‐form solution modified from the double‐spike approach used for Fe isotope analysis by TIMS [<jats:italic>Johnson and Beard</jats:italic>, 1999]. The measured <jats:sup>176</jats:sup>Lu/<jats:sup>175</jats:sup>Lu ratios are corrected by doping the sample with Er and using the <jats:sup>167</jats:sup>Er/<jats:sup>166</jats:sup>Er ratio to externally normalize the <jats:sup>176</jats:sup>Lu/<jats:sup>175</jats:sup>Lu ratio using an exponential law. Finally, spike‐sample equilibration is confirmed for our sample dissolution protocol through analysis of varying physical mixtures of 1 Ga garnet and hornblende, where all the data lie on a mixing‐line, within error, on a <jats:sup>176</jats:sup>Lu/<jats:sup>177</jats:sup>Hf‐<jats:sup>176</jats:sup>Hf/<jats:sup>177</jats:sup>Hf diagram. Precision of <jats:sup>176</jats:sup>Lu/<jats:sup>177</jats:sup>Hf ratios is determined to be ±0.2% (2σ) for standards and for physical mixtures of garnet and hornblende.</jats:p>