Stable Ga–Mg–Zn quasi-periodic crystals with pentagonal dodecahedral solidification morphology

Abstract

The discovery in 1984 by Shechtman and co-workers of an Al–Mn alloy phase that exhibited a sharply peaked diffraction pattern with icosahedral point symmetry (m) was a major development in crystallography¹. It was the first demonstration that quasi-periodic structures with fivefold symmetry axes, which had been described in the mathematical literature and whose sharp reciprocal lattice peaks could be indexed with two sets of incommensurate basis vectors, did actually occur in nature. This discovery has been followed by intense experimental and theoretical work; many more icosahedral and decagonal crystals have been discovered, and the theory describing the quasi-periodic lattices and their defects was greatly developed^2–4. With one exception, all quasi-periodic crystals that have been discovered until now are metastable; they are produced by non-equilibrium methods, such as melt quenching, ion-beam mixing and sputtering, and upon heating they transform to phases with a periodic crystal structure. The only stable quasi-periodic crystal that was known is found in the Al–Li–Cu system, and has a striking rhombic triacontahedral solidification morphology^5–7. We report here the discovery in the Ga–Mg–Zn system of a second stable quasi-periodic crystal with a pentagonal dodecahedral solidification morphology.