“…The list of twenty most structurally complex minerals known so far given in Table 3 reveals the following most important complexity-generating mechanisms in minerals: - the presence of large (sometimes nanometre-scale) clusters such as polyoxometalates or related finite-cluster structures (Krivovichev, 2020b) isolated from each other; such multinuclear atomic units possess a large number of atoms with different topological functions; the examples are ewingite, morrisonite, vanarsite, bouazzerite and postite; as a rule, natural polyoxometalate minerals are also highly hydrated, with the exception of arsmirandite and lehmannite, which are anhydrous polyoxocuprates formed in volcanic fumaroles (Britvin et al , 2020);
- the presence of large clusters linked together to form three-dimensional frameworks; the examples are ilmajokite and paddlewheelite (both minerals are also highly hydrated, which contributes greatly to their structural complexities);
- the formation of complex three-dimensional modular frameworks formed by cages of different sizes and topologies; this complexity type corresponds to paulingite-group minerals, fantappièite and sacrofanite (members of the sodalite–cancrinite ABC series (Bonaccorsi and Nazzareni, 2015; Chukanov et al , 2021), tschörtnerite, mendeleevite-(Ce) and rowleyite;
- the formation of complex layers with different combinations of modules (chains or rings); this type is characteristic for layered uranyl minerals (such as vandendriesscheite and gauthierite) and layered silicates (parsettensite);
- a high hydration state in salts with complex heteropolyhedral units (alfredstelznerite and voltaite-group minerals);
- the formation of ordered superstructures of relatively simple structure types; the examples are meerschautite (which is the only sulfide species in the list and was described by Biagioni et al (2016) as an expanded derivative of owyheeite) and manitobaite (that has a fivefold superstructure relative to alluaudite (Tait et al , 2011)); for further discussion on the relations between superstructures and complexity see Krivovichev et al (2019a, 2021), Kornyakov et al (2021) and Kornyakov and Krivovichev (2021).
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