A QUANTITATIVE GOLDSCHMIDT TERNARY CLASSIFICATION USING CORRELATIONS OF MINERAL-FORMING ELEMENTS

The mineralogy of terrestrial planets is governed not only by size, bulk composition, and geochemical processes, but also by how its constituent elements parse themselves into mineral species. To quantify mineral-forming behavior in Earth’s naturally occurring elements, we used a mineral database (rruff.info/ima) to analyze the number of mineral species containing elements X and Y for every possible X-Y pair (and X, Y and Z for every possible X-Y-Z triplet) for all 72 mineral-forming elements occurring in 5477 known mineral species. The frequency of each element pair (or triplet) was compared with the expected frequency if elements were distributed among mineral species randomly. The resulting element correlations and anti-correlations had p-values ranging from ~1 to 10^-308 (in a chi-squared test for element pairs, and a Cochran-Mantel-Haenszel test [1] for element triplets). Moderate to strong correlations of most natural elements with either O or S conform exceptionally well to Goldschmidt’s qualitative classification as either lithophile or chalcophile [2]. The correlation of an element with zero-valent iron was used as a proxy for siderophile behavior, since association with the more abundant higher oxidation states of iron is more indicative of chalcophile or lithophile behavior. Together, the correlations of mineral-forming elements with O, S, and Fe⁰ can be used to build a quantitative, ternary Goldschmidt classification that helps us better understand geochemical trends on Earth and other planetary bodies.

[1] Mantel, M. (1963) J. Am. Stat. Assoc. 58, 690-700.

[2] Goldschmidt, V. (1937) J. Chem. Soc. 655-673.