Modeling growth and equilibrium form of α-SiO₂

The α phase of SiO₂ is known as a technologically important material. According to the Hartman–Perdok theory, so-called F forms are present: the hexagonal prism m {}, the major rhombohedron r {} and the minor rhombohedron z {}. F faces grow according to a two-dimensional growth mechanism and are the only forms to be expected on the growth form. Computation of attachment energies, which are considered to be directly related to the growth rates of the corresponding F faces, has been performed using an electrostatic point-charge model, taking into account Born repulsion and van der Waals contributions computed by means of the Gilbert equation or the van Beest and van Santen potential. All the theoretical growth forms are prismatic with the two aforementioned rhombohedra, which are almost equally important and independent of the corrections for the van der Waals and Born interactions. The equilibrium form is prismatic and shorter as a result of the hexagonal prism form being less important. On the atomic scale, the differences in surface topologies between the F forms depend on the variation in depth below the surface boundary of those central Si atoms that are partially unshielded because of the incomplete tetrahedral coordination.