Linear error propagation and Monte Carlo simulation for MC-ICP-MS neodymium isotope ratios uncertainty analysis

Abstract

This study presents a comprehensive framework for uncertainty estimation in Nd isotope ratio analysis using both linear error propagation and Monte Carlo simulation. The developed model explicitly incorporates uncertainties from key analytical procedures—including baseline subtraction, isobaric interference correction, and exponential law mass fractionation normalization—providing more accurate theoretical precision limits. For the internally normalized ¹⁴³Nd/¹⁴⁴Nd ratio, predicted cycle-level uncertainties show excellent agreement with measured values, validating the accuracy of both approaches. Evaluation of two interference correction strategies—the natural ¹⁴⁷Sm/¹⁴⁴Sm ratio method and the iterative method—reveals that both yield comparable uncertainties when ¹⁴⁷Sm/¹⁴⁴Nd is below ∼5 × 10⁻³. Uncertainty in Nd isotope ratios exhibits a strong inverse dependence on beam intensity, with Johnson noise dominating below a ¹⁴⁴Nd intensity threshold of ∼0.2 V and counting statistics prevailing at higher intensities. This threshold offers a clear criterion for selecting a 10¹³ Ω amplifier resistor to improve precision in low-signal regimes. Furthermore, baseline correction is shown to introduce Johnson noise derived uncertainty, with a more pronounced effect at lower beam intensities; our results provide specific guidance on baseline cycle number needed to control this contribution under different signal conditions. Monte Carlo simulations demonstrate robust performance when using at least 5 × 10⁴ cycles per simulation, achieving results within 1 % of linear propagation estimates while maintaining computational efficiency (∼1.5 s/simulation). External reproducibility is primarily governed by Johnson noise and counting statistics, with secondary factors such as mass bias variations in the mass spectrometer contributing ∼10 % to the total measured external uncertainty. Finally, we demonstrate that diluting sample solution increases analytical uncertainty, especially at lower sample amounts, despite longer measurement times, whereas concentrating sample solution improves precision provided sample consumption during signal stabilization is accounted for. These findings provide a practical foundation for optimizing precision in Nd isotope analysis via uncertainty model based experimental design.