Constraints on the Mineral Evolution of Terrestrial Planets Using Statistical Correlations Among the Mineral-Forming Elements

Abstract:

The mineralogy of terrestrial planets is governed not only by size, bulk chemical composition, planetary differentiation processes, and secondary geochemical processes, but also by the fundamental way in which a planet’s constituent elements parse themselves into mineral species. To gain insight into which elements tend to associate with each other to form minerals, we have used the IMA mineralogical database (rruff.info/ima) to conduct a statistical analysis of the number of known mineral species containing each of the 72 mineral-forming elements, as well as how many species contain both X and Y for every possible X-Y pair of elements. The frequency with which elements X and Y occur together in the nominal chemical formulae of minerals was compared with the expected rate of co-occurrence (assuming that elements are distributed among mineral species randomly).

 The results reveal that among the most strongly correlated element pairs are H-O, Na-Si, Al-Si, S-Ag, O-Si, Si-Ca, and O-Ca. Examples of strongly anti-correlated pairs are O-S, O-Ag, Si-S, O-Sb, O-Se, H-Ag, and Si-As. The strength of these correlations and anti-correlations varied by many orders of magnitude (as measured by their p-value in a chi-squared test for variable dependence), ranging from near 1 to an astounding 10^-304. Out of 2520 unique element pairs, 1688 were statistically significant (p-value <0.05). These pair correlations can be attributed to an array of geochemical factors, including but not limited to 1) the mutual exclusivity of sulfide vs. silicate anionic groups, 2) crystal chemical considerations of size and charge similarities among cations, especially within silicate structures, 3) group relationships on the periodic table, and 4) soft vs. hard ion relationships. These principles, along with the specific correlations they produce, can serve as a valuable guide in explaining the mineral evolution of Earth’s crust, and predicting the mineralogy of terrestrial planets even when the bulk composition is significantly different than that of Earth.