A theoretical study of the use of internal standards for precise isotopic analysis by the surface ionization technique Part II: Error relationships

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Abstract
Using an idealized model it is shown that, to minimize errors in double-spiked isotopic analyses, spike mass numbers should alternate with normal. The comprehensive error analysis which follows assumes that the individual ion currents are the independent varietes for statistical purposes: errors in these are obtained by combining (i) a coefficient of variation eP due to fluctuations in ion emission with (ii) a resistor noise index eR and (iii) a shot noise index eS: the noise indices are the ratios [error due to noise]/[error (i) due to emission fluctuation] for the largest ion beam in the spectrum. Methods of computing error multipliers (operating on eP) from eR, eS and the isotopic abundances, are developed. For a particular element each error multiplier can be regarded as a function of two variables, the ratio of the two spikes selected and the spike/normal ratio, which can then be optimized by numerical methods. Optimum values of spike composition and spike/normal ratio are given for observations of isotopic fractionation of lead, molybdenum and iron using various pairs of spike mass numbers. If both noise indices are taken to be zero the minimum error multipliers are not very much increased by deviations from the ideal model. When eR is given values corresponding to experience with a typical electrometer, it is shown that satisfactory results would be obtained on Pb and Mo with quite low ion currents, but that for iron, because of its difficult isotopic composition, the maximum ion current should be as large as possible. Some possible deviations from first-order fractionation theory are considered. A general algebraic analysis for the determination of radiogenic isotopes is given, and different approaches to fractionation computations are discussed.