Structural model for octagonal quasicrystals derived from octagonal symmetry elements arising inβ-Mncrystallization of a simple monatomic liquid

Abstract

While performing molecular-dynamics simulations of a simple monatomic liquid, we observed the crystallization of a material displaying octagonal symmetry in its simulated diffraction pattern. Inspection of the atomic arrangements in the crystallization product reveals large grains of the $\ensuremath{\beta}\text{-Mn}$ structure aligned along a common fourfold axis, with $45\ifmmode^\circ\else\textdegree\fi{}$ rotations between neighboring grains. These $45\ifmmode^\circ\else\textdegree\fi{}$ rotations can be traced to the intercession of a second crystalline structure fused epitaxially to the $\ensuremath{\beta}\text{-Mn}$ domain surfaces, whose primitive cell has lattice parameters $a=b=c={a}_{\ensuremath{\beta}\text{-Mn}}$, $\ensuremath{\alpha}=\ensuremath{\beta}=90\ifmmode^\circ\else\textdegree\fi{}$, and $\ensuremath{\gamma}=45\ifmmode^\circ\else\textdegree\fi{}$. This secondary phase adopts a structure which appears to have no known counterpart in the experimental literature, but can be simply derived from the ${\text{Cr}}_{3}\text{Si}$ and ${\text{Al}}_{3}{\text{Zr}}_{4}$ structure types. We used these observations as the basis for an atomistic structural model for octagonal quasicrystals, in which the $\ensuremath{\beta}\text{-Mn}$ and the secondary phase structure unit cells serve as square and rhombic tiles (in projection), respectively. Its diffraction pattern down the octagonal axis resembles those experimentally measured. The model is unique in being consistent with high-resolution electron microscopy images showing square and rhombic units with edge-lengths equal to that of the $\ensuremath{\beta}\text{-Mn}$ unit cell. Energy minimization of this configuration, using the same pair potential as above, results in an alternative octagonal quasiperiodic structure with the same tiling but a different atomic decoration and diffraction pattern.