We use density functional theory to calculate the equilibrium isotopic fractionation factors of zirconium (Zr) in a variety of minerals including zircon, baddeleyite, Ca-catapleiite, ilmenite, geikielite, magnetite, apatite, K-feldspar, quartz, olivine, clinopyroxene, orthopyroxene, amphibole, and garnet. We also report equilibrium isotopic fractionation factors for Hf in zircons, Ca-catapleiite, and ilmenite. These calculations show that coordination environment is an important control on Zr and Hf isotopic fractionation, with minerals with Zr and Hf in low coordinations predicted to be enriched in the heavy isotopes of Zr and Hf, relative to those with Zr and Hf in high coordinations. At equilibrium, zircon, which hosts Zr and Hf in 8-fold coordination, is predicted to have low 94Zr/90Zr and 179Hf/177Hf ratios compared to silicate melt, which hosts Zr and Hf in 6-fold coordination. However, our modeling results indicate that little equilibrium isotopic fractionation for Zr is expected during magmatic differentiation and zircon crystallization. We show through isotopic transport modeling that the Zr isotopic variations that were documented in igneous rocks are likely due to diffusion-driven kinetic isotopic fractionation. The two settings where this could take place are (i) diffusion-limited crystallization of zircon (DLC model) and (ii) diffusion-triggered crystallization of zircon (DTC model) in the boundary layer created by the growth of Zr-poor minerals. Fractional crystallization of zircons enriched in light Zr isotopes by diffusion can drive residual magmas toward heavy Zr isotopic compositions. Our diffusive transport model gives the framework to interpret Zr isotope data and gain new insights into the cooling history of igneous rocks and the setting of zircon crystallization
