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 much progress has been made during this time on 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? What is the nature of chemical bonding in QCs formed in different sorts of materials such as alloys, oxides, or organic polymers? Herein these and other closely related issues are discussed from an interdisciplinary perspective as well as prospective future work in the field in the years to come.

Eu Doping in the GdCd7.88 Quasicrystal and Its Approximant Crystal GdCd6

“…The DSC measurements were performed under an argon flow of 40 mL per min. The specific heat measurements were acquired by using a Bluefors dilution refrigerator equipped with a superconducting magnet with a maximum field of 12 T. A differential membrane-based nanocalorimeter with an operating range down to 100−200 mK was used for the data collection, with samples of typical dimensions 100 × 100 × 50 μm 3 . All of the dc magnetization data were acquired on single crystals of the various phases using an MPMS XL SQUID from Quantum Design, Inc.…”

“…Quasicrystals (QCs) constitute an unconventional state of matter that has been thoroughly researched since their discovery 40 years ago. − Tsai-type QCs are particularly well suited for understanding the interplay between magnetism and quasiperiodic lattices since they include lanthanide elements with strong spin moments associated with 4f magnetism and surrounded by nonmagnetic elements, such as Cd, or a mixture of monovalent and trivalent atoms. Stable examples of QCs can be obtained using the (Ag,In) pair, but metastable samples obtained from fast quenching have also been reported, using (Au,Al) or (Au,Ga) as the nonmagnetic elements.…”

From the Fibonacci Icosagrid to E8 (Part II): The Composite Mapping of the Cores

“…Quasicrystals, whose early study was inspired by decision theory [1,2] and simple mathematical curiostiy [3], later became a major area of research in material science [4][5][6][7][8][9] and have found applications in areas as wide-ranging as high-energy physics [10,11], conformal field theory [12] quantum computing [13][14][15], and biology [16][17][18]. Two of the most common methods for mathematically constructing quasicrystals, the dual multigrid (or generalized dual) method and the cut-and-project (or direct project, or model set) construction, provide theoretical foundations and many tools for their study [6,19].…”