Nucleation and growth of spherical water bubbles in hydrothermal grown quartz (A Review)

Abstract

Formation of water bubbles by precipitation of supersaturated water vapour and interactions of the bubbl-es with dislocations are fundamental for understanding the phenomenon of hydrolytic weakening of quartz during high temperature deformation. Annealing deformed synthetic quartz crystals at temperature in excess of 500 °C leads to phase-separation of grown-in water into hydroxyl (OH) species and molecular water (H₂Om). By homoge-neous inter-conversion hydroxyl reaction of H₂Om and O (anhydrous oxygen), the excess OH groups agglomerate into clusters to form embryos. Embryonic-nuclei of radii less than Gibbs critical size dissolve, while embryos of larger sizes grow to form stable nuclei in equilibrium with the supersaturated vapour. Ostwald ripening dissoluti-on-diffusion growth of nuclei at near critical state is limited by OH diffusion and surface vacancy kinetics. Chemi-cal potential difference of OH at the nucleus-bulk interface leads to changes in interfacial energy and higher OH concentration for growth of larger nucleus, as described by Gibbs-Thompson equation. For size evolution of nuclei, concentration gradients provide additional driving force for growth of larger nuclei at expense of smaller nuclei. La Mer model accounts for separation of nucleation and growth. Irreversible aggregation of stable nuclei form macrobubbles at the supercritical stage, which coalesce into spherical water bubbles of equilibrium sizes.

Hydroxyl groups of low solubility in quartz are considered as interstitial defects, which are primarily tra-pped by vacancies. The spherical bubbles consisting of OH-vacancy complexes grow by absorbing OH monomers and coalescing with other bubbles under annealing conditions. The rate-controlling steps for bubble growth are migration by volume, surface diffusion, and interaction with lattice defects. By coalescence events of random co-llisions and OH capture, the bubbles gain energy for growth due to reduction of surface energy, limited by vacancy relaxation of strain fields produced by excess pressure in the bubble.

The review examines mechanisms of nucleation and growth of water bubbles in quartz and presents com-prehensive models describing the processes occurring during bubble formation from evolution of clusters, embryonic-nuclei dissolution and growth, stable nuclei aggregation into nanobubbles, and coalescence to form macro-bubbles, which grow into equilibrium bubbles. The mathematical formulations governing clustering, dissolution-diffusion growth, coalescence events, interfacial hydroxyl mass diffusion, and surface adsorption kinetics for the physical processes of nucleation and growth of water-filled bubbles in quartz crystals are also presented.

Keywords: Embryonic-Nucleus, La Mer Model, Ostwald Ripening, Interfacial Energy, Chemical Potential, Coale-scence Event, Rate Theory