Silica or SiO$_2$, the main constituent of earths rocks has several 3D complex crystalline and amorphous phases, but it does not have a graphite like layered structure in 3D. Our theoretical analysis and numerical calculations from the first-principl
es predict a single-layer honeycomb like allotrope, h$alpha$-silica, which can be viewed to be derived from the oxidation of silicene and it has intriguing atomic structure with re-entrant bond angles in hexagons. It is a wide band gap semiconductor, which attains remarkable electromechanical properties showing geometrical changes under external electric field. In particular, it is an auxetic metamaterial with negative Poissons ratio and has a high piezoelectric coefficient. While it can form stable bilayer and multilayer structures, its nanoribbons can show metallic or semiconducting behavior depending on their chirality. Coverage of dangling Si orbitals by foreign adatoms can attribute new functionalities to h$alpha$-silica. In particular, Si$_2$O$_5$, where Si atoms are saturated by oxygen atoms from top and bottom sides alternatingly can undergo a structural transformation to make silicatene, another stable, single layer structure of silica.
The growth process of single layer graphene with and without substrate is investigated using ab initio, finite temperature molecular dynamic calculations within density functional theory. An understanding of the epitaxial graphene growth mechanisms i
n the atomic level is provided by exploring the transient stages which occur at the growing edges of graphene. These stages are formation and collapse of large carbon rings together with the formation and healing of Stone-Wales like pentagon-heptagon defects. The activation barriers for the healing of these growth induced defects on various substrates are calculated using the climbing image nudge elastic band method and compared with that of the Stone-Wales defect. It is found that the healing of pentagon-heptagon defects occurring near the edge in the course of growth is much easier than that of Stone-Wales defect. The role of the substrate in the epitaxial growth and in the healing of defects are also investigated in detail, along with the effects of using carbon dimers as the building blocks of graphene growth.
The Blume-Emery-Griffiths spin glass is studied by renormalization-group theory in d=3. The boundary between the ferromagnetic and paramagnetic phases has first-order and two types of second-order segments. This topology includes an inverted tricriti
cal point, first-order transitions replacing second-order transitions as temperature is lowered. The phase diagrams show disconnected spin-glass regions, spin-glass and paramagnetic reentrances, and complete reentrance, where the spin-glass phase replaces the ferromagnet as temperature is lowered for all chemical potentials.
