Theoretical bond-length calculations from ideal bond valences for each ion and coordination allow for the prediction of ion site preference and partitioning in tourmaline structures at low-pressure conditions. A comparison of calculated data with published bond-length values enables the determination of the range of structurally stable bond lengths with a minimal induced distortion—the “Goldilocks zone.” The calculations provided the following conclusions: the B-site occupancy is strictly limited to B3+; the T site can freely accommodate not only Si4+ but also B3+ and Al3+, although these substituents require shrinkage and expansion of the TO4 tetrahedron, respectively; and the Be2+ substitution results in a significant difference in charge. Satisfactory bond lengths for octahedral sites were calculated for Al3+ (Z-site preference), Ti4+, Mn3+, Ga3+, V3+, Fe3+ (mixed preference), Mg2+, Fe2+, Li+, Mn2+, Ni2+, Zn2+, Cu2+, Sc3+, and Zr4+ (Y-site preference). Another group of cations, which includes U4+, Th4+, Y3+, and lanthanoids from Tb to Lu and Ce4+, have significantly longer bonds than typical Y-O and very short bonds for the X site; therefore, it is likely they would prefer an octahedron. The empirical bond length for the X site is met with Na+, Ca2+, Sr2+, Pb2+, and lanthanoids from La to Gd, while K, Rb, and Cs are too large in the low-pressure conditions. However, the final tourmaline composition results from the interaction of the structure with the genetic environment in terms of P-T-X and geochemical conditions. This results in structural and environmental constraints that limit the incorporation of elements into the structure. Consequently, major elements, such as Si, Al, B, Mg, Fe, Na, and Ca usually occur in abundance, whereas other elements (V, Cr, Mn, Ti, Pb) could form end-member compositions, but rarely do because of their low abundance in the environment. The elements with contents limited to trace amounts have either structural (Be, C, REE, Rb, Cs, U, Th) or geochemical (Zr4+, Sc3+, and Sr2+) limits. However, environmental properties, such as high pressure or specific local structural arrangements, can overcome structural constraints and enable the incorporation of elements (K).

中文翻译：

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基于电气石超群矿物中键长约束的结晶位点之间的阳离子分配

根据每个离子和配位的理想键价计算理论键长，可以预测低压条件下电气石结构中的离子位点偏好和分配。将计算数据与公开的键长值进行比较，可以确定结构稳定的键长范围，并具有最小的诱导畸变——“金发姑娘区”。计算得出以下结论：B站占用率严格限制在B3+；T位不仅可以自由容纳Si4+，还可以容纳B3+和Al3+，尽管这些取代基分别需要TO4四面体的收缩和膨胀；Be2+ 取代导致电荷显着差异。对于 Al3+（Z 位优先）、Ti4+、Mn3+、Ga3+、V3+、Fe3+（混合优先）、Mg2+、Fe2+、Li+、Mn2+、Ni2+、Zn2+、Cu2+、Sc3+ 和 Zr4+（Y 位优先）。另一组阳离子，包括 U4+、Th4+、Y3+ 和从 Tb 到 Lu 和 Ce4+ 的镧系元素，它们的键比典型的 YO 键长得多，而 X 位点的键很短；因此，他们很可能更喜欢八面体。X 位点的经验键长满足 Na+、Ca2+、Sr2+、Pb2+ 和从 La 到 Gd 的镧系元素，而 K、Rb 和 Cs 在低压条件下太大。然而，最终的电气石成分来自结构与遗传环境在 PTX 和地球化学条件方面的相互作用。这会导致结构和环境约束，限制元素融入结构。因此，主要元素，如 Si、Al、B、Mg、Fe、Na 和 Ca 通常大量存在，而其他元素（V、Cr、Mn、Ti、Pb）可以形成端元成分，但很少这样做，因为它们在环境中的丰度较低。含量限制为痕量的元素具有结构（Be、C、REE、Rb、Cs、U、Th）或地球化学（Zr4+、Sc3+ 和 Sr2+）限制。然而，环境特性，例如高压或特定的局部结构布置，可以克服结构限制并能够结合元素 (K)。