Quasicrystal-related phases in tetrahedral semiconductors: Structure, disorder, andab initiocalculations

Abstract

We show that special structural changes (phason atomic jumps) can transform the BC8 and R8 phases, known to occur in Si and Ge, into a phase with tetrahedral coordination. These structural changes are analogous to the BC8-R8 transformation. The phase has the body-centered-tetragonal symmetry (the space group ${C}_{4h}^{6}\ensuremath{-}{I4}_{1}/a)$ with 16 atoms per unit cell or 8 atoms per primitive cell and will be referred to as BT8. All the atoms occupy equivalent general positions $x,y,z$ and there are three different tetrahedral bonds. It is shown that all three phases, BT8, BC8, and R8 may be considered as a result of phason-ordering transitions from a disordered phase with $\mathrm{Ia}3\ifmmode\bar\else\textasciimacron\fi{}d$ symmetry. An infinite number of other structures with tetrahedral bonding (ordered and disordered) can be constructed this way. The phason jumps are typical of these phases because they are related to hypothetical icosahedral quasicrystals. In particular, the BC8 and the recently suggested BC32 structure may be considered as $1/0$ and $1/1$ cubic approximants of the same quasicrystal. We present a detailed ab initio study of BT8 and BC32 phases in silicon within density-functional theory in the local-density approximation. Our results show that the energetics and diffraction patterns of the BT8 phase are very similar to those of the BC8 and R8 phases. We conclude that the available diffraction data do not exclude the existence of the BT8 phase. In contrast, the energy of the BC32 structure is significantly larger (for positive pressure), and the existence of this phase is therefore questionable. The pressure dependence of the bond lengths, angles, and the lattice parameters of the BT8 phase is investigated. Our estimation of the energy barrier for phason defect formation in the BC8 phase is about 0.12 eV per jumping atom and the energy of the defect is very small (less then 0.02 eV per jumping atom), therefore this type of defect could be present in real samples. Finally, we show that the computed elastic constants of the BC8 phase are almost isotropic as expected for the approximants of icosahedral quasicrystals.