Four factors contribute to the roles played by chance and necessity in determining mineral distribution and diversity at or near the surfaces of terrestrial planets: (1) crystal chemical characteristics; (2) mineral stability ranges; (3) the probability of occurrence for rare minerals; and (4) stellar and planetary stoichiometries in extrasolar systems.The most abundant elements generally have the largest numbers of mineral species, as modeled by relationships for Earth's upper continental crust (E) and the Moon (M), respectively: LogðN E Þ ¼ 0:22 LogðC E Þ þ 1:70 ðR 2 ¼ 0:34Þð4861 minerals; 72 elementsÞ LogðN M Þ ¼ 0:19 LogðC M Þ þ 0:23 ðR 2 ¼ 0mineral species await discovery or could have occurred at some point in Earth's history, only to be subsequently lost by burial, erosion, or subduction-i.e., much of Earth's mineral diversity associated with rare species results from stochastic processes.Measurements of stellar stoichiometry reveal that stars can differ significantly from the Sun in relative abundances of rock-forming elements, which implies that bulk compositions of some extrasolar Earth-like planets likely differ significantly from those of Earth, particularly if the fractionation processes in evolving stellar nebulas and planetary differentiation are factored in. Comparison of Earth's upper continental crust and the Moon shows that differences in element ratios are reflected in ratios of mineral species containing these elements.In summary, although deterministic factors control the distribution of the most common rock-forming minerals in Earth's upper continental crust and on the Moon, stochastic processes play a significant role in the diversity of less common minerals. Were Earth's history to be replayed, and thousands of mineral species discovered and characterized anew, it is probable that many of those minerals would differ from species known today.

A fundamental goal of mineralogy and petrology is the deep understanding of mineral phase relationships and the consequent spatial and temporal patterns of mineral coexistence in rocks, ore bodies, sediments, meteorites, and other natural polycrystalline materials. The multi-dimensional chemical complexity of such mineral assemblages has traditionally led to experimental and theoretical consideration of 2-, 3-, or n-component systems that represent simplified approximations of natural systems. Network analysis provides a dynamic, quantitative, and predictive visualization framework for employing "big data" to explore complex and otherwise hidden higher-dimensional patterns of diversity and distribution in such mineral systems. We introduce and explore applications of mineral network analysis, in which mineral species are represented by nodes, while coexistence of minerals is indicated by lines between nodes. This approach provides a dynamic visualization platform for higher-dimensional analysis of phase relationships, because topologies of equilibrium phase assemblages and pathways of mineral reaction series are embedded within the networks. Mineral networks also facilitate quantitative comparison of lithologies from different planets and moons, the analysis of coexistence patterns simultaneously among hundreds of mineral species and their localities, the exploration of varied paragenetic modes of mineral groups, and investigation of changing patterns of mineral occurrence through deep time. Mineral network analysis, furthermore, represents an effective visual approach to teaching and learning in mineralogy and petrology.

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Analyses of the temporal and geographic distribution of earliest recorded appearances of the 88 IMA-approved mercury minerals plus two potentially valid species exemplify principles of mineral evolution. Metacinnabar (HgS) and native Hg are the only two species reported from meteorites, specifically, the primitive H3 Tieschitz chondrite with an age of 4550 Ma. Since the first terrestrial appearance of cinnabar more than 3 billion years ago, mercury minerals have been present continuously at or near Earth's surface.Mercury mineral evolution is characterized by episodic deposition and diversification, perhaps associated with the supercontinent cycle. We observe statistically significant increases in the number of reported Hg mineral localities and new Hg species at ~2.8-2.6, ~1.9-1.8, and ~0.43-0.25 Gaintervals that correlate with episodes of presumed supercontinent assembly and associated orogenies of Kenorland (Superia), Columbia (Nuna), and Pangea, respectively. In constrast, few Hg deposits or new species of mercury minerals are reported from the intervals of supercontinent stability and breakup at ~2.5-1.9, ~1.8-1.2, and 1.1-0.8 Ga. The interval of Pangean supercontinent stability and breakup (~250-65 Ma) is also marked by a significant decline in reported mercury mineralization; however, rocks of the last 65 million years, during which Pangea has continued to diverge, is characterized by numerous ephemeral near-surface Hg deposits.The period ~1.2-1.0 Ga, during the assembly of the Rodinian supercontinent, is an exception because of the absence of new Hg minerals or deposits from this period. Episodes of Hg mineralization reflect metamorphism of Hg-enriched marine black shales at zones of continental convergence. We suggest that Hg was effectively sequestered as insoluble nanoparticles of cinnabar (HgS) or tiemannite (HgSe) during the period of the sulfidic "intermediate ocean" (~1.85-0.85 Ga); consequently, few Hg deposits formed during the aggregation of Rodinia, whereas several deposits date from 800-600 Ma, a period that overlaps with the rifting and breakup of Rodinia.Nearly all Hg mineral species (87 of 90 known), as well as all major economic Hg deposits, are known to occur in formations ≤400 million years old. This relatively recent diversification arises, in part, from the ephemeral nature of many Hg minerals. In addition, mercury mineralization is strongly enhanced by interactions with organic matter, so the relatively recent pulse of new Hg minerals may reflect the rise of a terrestrial biosphere at ~400 Ma.

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