Conflicting results exist regarding the mechanisms, direction, and magnitude of Zr isotope fractionation in igneous systems. To better understand the origin of the fractionations observed in magmatic Zr-bearing minerals and bulk rocks, we theoretically investigated the main potential driving processes: thermodynamic equilibrium effects driven by either (i) vibrational energy or (ii) nuclear volume, and (iii) diffusion-driven kinetic effects. Vibrational equilibrium fractionation properties were estimated for zircon (^(VIII)ZrSiO₄), baddeleyite (^(VII)ZrO₂), gittinsite (^(VI)ZrCaSi₂O₇), sabinaite (Na₄^(VIII)Zr₂TiC₄O₁₆), and vlasovite (Na₂^(VI)ZrSi₄O₁₁). These properties show dependency on Zr coordination, as well as the presence of strong covalent bonds (C O, Si O by order of decreasing effect) in the material. More importantly, despite the large variety of structures investigated, the predicted mass-dependent equilibrium fractionations (Δ⁹⁴/⁹⁰Zr ∼±0.05‰ relative to zircon at 800 °C) are systematically one order of magnitude smaller than required to explain the natural variability observed to date in natural settings (δ⁹⁴/⁹⁰Zr from ∼+1 to −5‰). Likewise, careful evaluation of expected nuclear field shift (NFS) effects predict a magnitude of fractionation of ∼0.08‰ (at 800 °C), further supporting the conclusion that equilibrium effects cannot be invoked to explain extreme δ⁹⁴/⁹⁰Zr zircon values. Furthermore, the mass-dependency of all Zr isotope ratios reported in zircon crystals precludes a contribution of NFS effects larger than ∼0.01‰ on δ⁹⁴/⁹⁰Zr. On the other hand, we show that diffusion, and in particular the development of Zr diffusive boundary layers in silicate magmas during fractional crystallization, provides a viable and most likely mechanism to produce permil-level, mass-dependent isotope fractionations similar to those observed in natural systems. We propose testable scenarii to explain the large and contrasting Zr isotopes signatures in different magmatic zircons, which underline the importance of magmatic composition, Zr diffusivity, and crystallization timescales.

中文翻译：

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含锆相和熔体中锆同位素分馏的驱动因素：振动、核场位移和扩散效应的作用

关于火成岩系统中 Zr 同位素分馏的机制、方向和大小，存在相互矛盾的结果。为了更好地理解在含锆的岩浆矿物和大块岩石中观察到的分馏的起源，我们从理论上研究了主要的潜在驱动过程：由（i）振动能或（ii）核体积驱动的热力学平衡效应，以及（iii）扩散驱动的动力学效应。估计了锆石 (^(VIII)ZrSiO₄)、斜锆石 (^(VII)ZrO2)、菱沸石 (^(VI)ZrCaSi2O₇)、sabinaite (Na₄^(VIII)Zr₂TiC₄O₁(Na₆) 的振动平衡分馏特性) VI)ZrSi₄O₁₁)。这些特性显示依赖于 Zr 配位，以及材料中强共价键的存在（CO、Si O 按递减效应）。更重要的是，尽管研究了各种各样的结构，但预测的质量相关平衡分馏（Δ⁹⁴/⁹⁰Zr ∼±0.05‰ 相对于 800 °C 的锆石）系统地比解释迄今为止在自然界中观察到的自然变异所需的数量级小一个数量级。设置（δ⁹⁴/⁹⁰Zr 从∼+1 到-5‰）。同样，对预期的核场位移 (NFS) 效应的仔细评估预测了 ∼0.08‰（在 800 °C 时）的分馏幅度，进一步支持了无法援引平衡效应来解释极端 δ⁹⁴/⁹⁰Zr 锆石值的结论。此外，锆石晶体中报告的所有 Zr 同位素比率的质量依赖性排除了 NFS 效应对 δ⁹⁴/⁹⁰Zr 的影响大于 ~0.01‰。另一方面，我们证明了扩散，尤其是在分步结晶过程中硅酸盐岩浆中 Zr 扩散边界层的发展，提供了一种可行且最可能的机制来产生类似于在自然系统中观察到的那些与质量相关的 permil 级同位素分馏。我们提出了可测试的情景来解释不同岩浆锆石中巨大且对比鲜明的 Zr 同位素特征，这强调了岩浆成分、Zr 扩散率和结晶时间尺度的重要性。