COUNTING BORON MINERALS IN EARTH'S CRUST: CAN CONTRADICTORY EVIDENCE BE RECONCILED?

Boron minerals are presently being discovered at an unprecedented rate, implying that there could be no obvious limit to B mineral diversity in Earth’s crust. In contrast, large number of rare event (LNRE) models calculated from the 292 B species discovered through 2015 predict that totals of 478 ± 74 and 548 species reside in Earth's crust, based on a finite Zipf-Mandelbrot (fZM) model and Sichel’s generalized inverse Gauss-Poisson model (GIGP), respectively. As cautioned by Hazen, Hystad and their co-authors, LNRE modeling presumes no changes in how minerals are discovered from the beginning of mineral discoveries in the late 18^th century until 2015. Clearly, this condition has not been met, and changes over time could have been substantial enough to explain the contradictory indications, particularly (1) the advent of the electron microprobe, which replaced “wet” chemistry as the method of choice for chemical analysis of B minerals in 1978; (2) technological advances in single-crystal X-ray diffractrometry and electron microscopy including advent of electron backscattered diffraction; (3) advent of micro-Raman spectroscopy; and (4) changes in mineralogical nomenclature. Increasing sophistication in analytical instrumentation is expected to reduce the size of the mineral grains accessible to study and to increase thereby the number of species that can be properly characterized. Should diversity be independent of scale (fractal), examination of increasingly smaller grains will turn up an even greater diversity. To assess the impact of these changes, we applied LNRE modeling to the 146 B minerals discovered up through 1978, the year the electron microprobe became the analytical method of choice for B minerals. This modeling gave 419 (fZM) and 693 (GIGP) for total species, that is, three of the four estimates from the 2015 and 1978 LNRE models range from 400 to 550 species. We conclude that the impact of the above listed changes on the predicted total species is less than the uncertainty in the modeling. Our comparison of the 1978 and 2015 LNRE models implies that LNRE models are sufficiently robust for boron minerals to justify our conclusion that the B mineral endowment of Earth’s crust is finite.