Role of natural isotopic fractionation in isotope geo- and cosmo-chronology: A theoretical investigation

We introduce a new isotope chronological model in which the natural mass-dependent isotopic fractionation effects of the radioactive (“parent”) and radiogenic (“daughter”) elements are systematically and rigorously considered. Using this model, we show that internally-normalized radiogenic isotopic ratios, commonly determined for daughter elements such as Sr, Nd, Cr, Ni, Hf, W, and Os, are dependent on the extent of natural isotopic fractionation of the daughter and parent elements at the time of system closure. This dependence indicates that (1) in two samples derived from the same isotopically homogeneous source at the same time and with identical radiogenic ingrowth over time, the present-day internally-normalized radiogenic isotope ratios would be different if they were initially fractionated to different degrees, and (2) if different internally-normalized radiogenic isotopic ratios are observed for two co-genetic objects, the difference between them would include contributions from both radiogenic ingrowth and natural isotopic fractionation. Consequently, the isochron dating equations employed in traditional chronological studies will yield inaccurate results when significant natural isotopic fractionation are present among the studied samples. Modified isochron equations that can be used to retrieve correct chronological information from isotopically-fractionated samples are presented. These theoretical considerations are applied to the ⁸⁷Rb–⁸⁷Sr, ¹⁴⁷Sm–¹⁴³Nd, and ¹⁴⁶Sm–¹⁴²Nd isotope systems of calcium–aluminium-rich inclusions (CAIs), a set of samples that have undergone significant natural Sr, Nd, and Sm isotope fractionation during their formation. The large natural Sr isotope fractionation (up to ca. 5.3 ‰ for ⁸⁸Sr/⁸⁶Sr) in fine-grained CAIs can generate analytically well-resolvable biases (>120 ppm) in the internally-normalized ⁸⁷Sr/⁸⁶Sr ratios and lead to significant scatters of their ⁸⁷Rb–⁸⁷Sr isochron (in conjunction with scatters induced by open-system disturbances). The ⁸⁷Rb–⁸⁷Sr systems of coarse-grained CAIs, on the contrary, are essentially not affected by natural Sr isotopic fractionation due to their much subdued fractionation degrees, resulting in a more robust isochron. Similarly, the large natural Nd (up to ca. 4.0 ‰ for ¹⁴⁶Nd/¹⁴⁴Nd) and Sm (up to ca. 7.1 ‰ for ¹⁵²Sm/¹⁴⁸Sm) isotopic fractionation in fine-grained CAIs can induce significant scatters of the ¹⁴⁷Sm–¹⁴³Nd isochron if the natural fractionation followed the kinetic or power law, and ¹⁴⁶Sm–¹⁴²Nd isochron if the natural fractionation followed the equilibrium, Rayleigh, or power law. This implies that when studying radioactive isotope systems in objects whose daughter and parent elements can undergo significant isotope fractionation in nature, accompanying stable isotope analyses are necessary for accurate chronological interpretations.