Near-surface controls on the composition of growing crystals: Car-Parrinello molecular dynamics (CPMD) simulations of Ti energetics and diffusion in alpha quartz

Ab initio molecular dynamics simulations were used to explore changes in the vacancy-formation energy for Ti atoms and Ti-O bond characteristics in the outermost monolayers of the (1. 0. 0) and (0. 1. 0) prism faces of α quartz. Within 2 or 3 polyhedral layers of the crystal surface, the Ti vacancy-formation energy is substantially smaller than the bulk-lattice value of 11.8. eV. This is true of both oxygen-terminated surfaces and the geologically more realistic case in which the outermost oxygens are bonded to hydrogen. A key additional finding is that the Ti vacancy-formation energy near the H-terminated (1. 0. 0) surface differs by 1-2. eV from that near the H-terminated (0. 1. 0) surface. This difference means that the energy change accompanying Ti. ↔. Si exchange between the bulk lattice and the near surface is also different for (1. 0. 0) and (0. 1. 0). Ultimately, therefore, the equilibrium concentrations of Ti near these two prism faces will not be the same. During crystal growth, this compositional difference may be "captured" by the quartz lattice and preserved as sectoral variation in Ti content-a feature commonly observed in both synthetic and natural α quartz. In this respect, the MD simulations provide direct support for the growth entrapment model (GEM; Watson, 2004) for non-equilibrium uptake of trace elements.To complement the vacancy-formation energy results, we used the first-principles metadynamics method to calculate diffusion pathways and free energy barriers for Ti diffusion in the bulk α quartz lattice and in the near-surface region. The computed estimate of the bulk-lattice activation energy compares favorably with the experimentally determined value of 2.8. eV (Cherniak et al., 2007), lending credence to the method. Diffusion results for the near-surface reveal a steep decrease in the activation energy for Ti diffusion approaching the surface in the outermost 2-3 polyhedral layers of the crystal. This finding implies depth-dependent Ti diffusion in the near-surface (~0.5. nm), which is also a key aspect of the growth-entrapment model.Although our results are strictly applicable only to Ti in α quartz, the demonstration that impurity atom energetics and diffusion are functions of depth in the near-surface region may be broadly applicable, given the similarity in measured length scale of the near-surface relaxed region in a wide variety of minerals. Kinetic models of impurity uptake that do not consider these factors may be incomplete.