Cavansite is a visually stunning blue vanadosilicate mineral with limited occurrences worldwide, whereas Pentagonite is a closely related dimorph with similar physical and chemical properties, yet is extremely rare compared to Cavansite. The reasons behind Pentagonite’s exceptional rarity remain largely unknown. In this study, (a) density functional theory (DFT) is utilized to investigate the electronic structures of Cavansite and Pentagonite at ground state and finite pressures; (b) a two-state Boltzmann probability model is then employed to construct a comprehensive phase diagram that reveals the abundance of each species across a wide range of pressure and temperature conditions; and (c) dehydration characteristics of these two minerals are explored. The present analysis reveals the key factors that contribute to the relative scarcity of Pentagonite, including differences in structural arrangement and electronic configurations between the two minerals. Specifically, it shows that (a) because of the peculiar arrangements of SiO₄ polyhedra, Cavansite forms a compact structure (about 2.7% less in volume) resulting in lower energy; (b) at a temperature of about 650K only about 1% Pentagonite can form; (c) vanadium induces a highly localized state in both of these otherwise large-band-gap insulators resulting in an extremely weak magnetic phase that is unlikely to be observed at any reasonable finite temperature; and (d) water molecules are loosely bound inside the microporous crystals of Cavansite and Pentagonite, suggesting potential applications of these minerals in various technological fields.

中文翻译：

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关于钙锰矿和五方矿的相对丰度

钙钒石是一种视觉上令人惊叹的蓝色钒硅酸盐矿物，在世界范围内的产量有限，而五方石是一种密切相关的二晶型，具有相似的物理和化学性质，但与钙锰矿相比极为罕见。五角星石异常稀有的原因在很大程度上仍不得而知。在这项研究中，（a）利用密度泛函理论（DFT）研究了Cavansite和Pentagonite在基态和有限压力下的电子结构； (b) 然后采用二态玻尔兹曼概率模型构建综合相图，揭示各种压力和温度条件下每种物质的丰度； (c) 探索这两种矿物的脱水特性。目前的分析揭示了导致五方矿相对稀缺的关键因素，包括两种矿物之间结构排列和电子构型的差异。具体来说，它表明(a)由于SiO ₄多面体的特殊排列，Cavansite形成致密结构(体积减少约2.7%)，从而导致较低的能量； (b)在约650K的温度下，仅能形成约1%的五方石； (c) 钒在这两个大带隙绝缘体中诱发高度局域化状态，导致极弱的磁相，在任何合理的有限温度下都不太可能观察到； (d) 水分子松散地结合在钙钒石和五方石的微孔晶体内，表明这些矿物在各种技术领域的潜在应用。