Continuous defect-free structural transformation of long-range order from quasiperiodic to translational

Abstract

We show that the perfect (defect-free) quasicrystalline order can be transformed continuously into a perfect crystalline one through a sequence of intermediate structures. The example of the pentagonal Penrose tiling is analyzed. The atomic positions in neighboring structures of the sequence either coincide or differ by one of 10 orientationally equivalent atomic jump vectors. Defect-free reconstruction is possible provided the linear phason strain is accompanied by a simultaneous shape variation of the atomic surface (AS). Two-step quasicrystal-to-crystal transformation is considered. In such a case the final crystalline state is obtained by two mutually orthogonal continuous phason distortions. The distortion of the first type results in a one-dimensional defect-free quasicrystal.