Fig. 1

The principle of isotope dilution. a Simplified cartoon (adapted from Alonso and González [33]) illustrating the principle of absolute quantification by dilution. The addition of a known amount of an internal standard (black marbles) to a sample containing an unknown (N) number of an analyte (yellow marbles) changes the concentration of the analyte. By determining the ratio of internal standard to unknown analyte in the resulting mixture, it is possible to back-calculate the amount of the analyte present in the sample. b A more complex situation arises in isotope dilution analysis when the sample, of natural isotopic composition, is mixed with an isotopically enriched spike. The image illustrates an example for an element containing two different isotopes (1 and 2). The resulting isotopic composition of the mixture to be measured is the combination of the sample’s and spike’s individual isotopic compositions and their molar ratios because the moles of the element in the mixture is the sum of the moles coming from the sample and the spike. If the number of moles added with the spike (N_sp), as well as the isotopic composition of sample and spike (abundances of the isotopes 1 and 2 in the sample and spike: A ¹ _s , A ² _s and A ¹ _sp , A ² _sp , respectively) are known, it is hence possible to determine the number of moles of the element in the sample (N_s) from the measurement of a single isotope ratio in the mixture (R_m)