Instrument response functions, mass bias and matrix effects in isotope ratio measurements and semi-quantitative analysis by single and multi-collector ICP-MS

This paper proposes a new approach to the estimation and correction of mass bias based on modelling the underlying instrument response function. Conventional definitions of mass bias are shown to be flawed and it is proposed that this quantity be recognised as merely the consequence of the instrument response function whose constants have a more fundamental importance. More accurate prediction of the bias in isotope ratio determinations is necessary and possible because of the improved precision afforded by multi-collector ICP-MS instrumentation. Isotope ratio measurements of Cd and Sn were used to study the variation of the mass bias with time, absolute mass and mass difference. No statistically significant variations were seen over a 20 min period, after which the data deviated significantly from the original measurement. After inclusion of the uncertainties in the natural abundances used to calculate the mass bias, no significant variation with increasing average isotope mass was observed. The reproducibility of the pattern of the points about the mean value suggested spectral interference and/or inaccurate values for the true isotope ratios. This was illustrative of the danger of using locally determined parameters to predict the mass bias. The variation of bias with mass difference showed a linear relationship, the implications of this for modelling are discussed. The common mass bias correction models are shown to be directly derivable from assumptions about the nature of the instrument response function. When the true instrument response function was investigated using a multi-element solution, a second order polynomial was found to provide the best fit to the data. The mass bias correction expression derived from such a model was used to calculate corrected Cd isotope ratios that were closer to the natural values than those obtained from the commonly used correction expressions. Increasing the concentration of a matrix element (bismuth or calcium) was found to significantly affect the value of Cd and Mg isotope ratios measured by multi-collector ICP-MS. The direction and magnitude of the effect was dependent on the position on the multi-collector array in which the isotopes were collected, with the heavier isotopes suffering higher levels of suppression. Measurements using an instrument with different multi-collector hardware did not show the same behaviour. A method of semi-quantitative analysis was developed that used the bias of 16 isotope ratios across the mass range to define the parameters in a quadratic instrument response function. This function was then applied to calculate the concentration of 24 analyte elements based on knowledge of ionisation efficiencies and the concentration of a single internal standard. This approach gave errors in the calculated concentrations that were comparable to the results obtained by using 6 internal standards, and did not require separate measurement of a standard solution to predetermine the instrument response.