{'fraction_non_alphanumeric': 0.01744186046511628, 'fraction_numerical': 0.0004472271914132379, 'mean_word_length': 5.657738095238095, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Uncertainty in Measurement of Isotope Ratios by Multi-Collector Mass Spectrometry

Multi-collector mass spectrometry, both inductively coupled plasma source (ICPMS) and thermal ionization source (TIMS), can measure isotope ratios with great precision because the ion beams from different isotopes are measured simultaneously with different detectors. Accurate isotope ratio results require that the measurement system be fully understood. Accounting for all sources of uncertainty in such analyses, according to JCGM Evaluation of measurement data — Guide to the expression of uncertainty in measurement (GUM), requires understanding the characteristics of the ion beam, and the instrument response. Modern multi-collector mass spectrometers record multiple electronic integrations of ion beam signals for a set time period, for example 5 seconds, and ratios of these signals on two detectors are calculated. The standard uncertainty on the mean of these ratios, a measure of the repeatability, is an important part of the combined standard uncertainty, but it is only one component. Often, the instrument software embeds constants and calculations in the data that is recorded, and post data acquisition processing introduces other variables. All of these constants and variables that are corrections to a measurement must be considered in the treatment of uncertainty. A general equation for an isotope ratio measurement by multicollector mass spectrometry is presented which considers the most common of these corrections. Accurate calculation of the combined standard uncertainty using this equation requires that the standard uncertainties for the individual ion beam signals be defined. However, the dispersion of these signals as calculated by standard statistical methods does not necessarily reflect the excellent repeatability of the ratio measurements, which is the hallmark of multi-collector instruments. To capture this repeatability it is necessary to partition the standard uncertainty on the ratio measurement between the signals for the numerator and denominator isotopes. An equation for this partitioning, and the sensitivity coefficients for all of the variables and sub-functions of the general equation are given.