Alloy Quasicrystals: Perspectives and Some Open Questions at Forty Years

Abstract

Four decades have elapsed since the first quasiperiodic crystal was discovered in the Al-Mn alloy system, and many progresses have been made during this time interval in the science of quasicrystals (QCs). Notwithstanding this, a significant number of open questions still remain regarding both fundamental and technological aspects. For instance: What are QCs good for? How can we improve the current provisional QC definition? What is the role of the underlying quasiperiodic order and the characteristic inflation symmetry of these compounds in the emergence of their unusual physicochemical properties? or, What is the nature of chemical bonding in QCs formed in such different sorts of materials as alloys, oxides, or organic polymers? In this essay I will discuss these, and other closely related, issues from an interdisciplinary perspective and will comment on appealing prospectives in the field for the years to come.