Drivers of zirconium isotope fractionation in Zr-bearing phases and melts: The roles of vibrational, nuclear field shift and diffusive effects

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 (^VIIIZrSiO₄), baddeleyite (^VIIZrO₂), gittinsite (^VIZrCaSi₂O₇), sabinaite (Na₄^VIIIZr₂TiC₄O₁₆), and vlasovite (Na₂^VIZrSi₄O₁₁). These properties show dependency on Zr coordination, as well as the presence of strong covalent bonds (C[sbnd]O, Si[sbnd]O by order of decreasing effect) in the material. More importantly, despite the large variety of structures investigated, the predicted mass-dependent equilibrium fractionations (Δ^94/90Zr ∼±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 (δ^94/90Zr 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 δ^94/90Zr 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 δ^94/90Zr. 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.