Mechanical and Mathematical Properties of Quasicrystals
Military University of Technology, Warsaw, Poland
The discovery of quasicrystals in 1984 by D. Shechtman, destroyed the fundamental concepts of crystallography which relied on a traditional definition of the crystal as a periodic arrangement of identical unit cells. In his experiments with a rapidly cooled Al-Mn alloy, Shechtman obtained a sharp diffraction pattern with a rotational symmetry incompatible with periodicity. His findings forced the International Union of Crystallography to redefine the notion of the crystal as any solid having discrete diffraction diagram. Quasicrystals are a new class of materials which thanks to their unique properties such as electrical, optical, hardness and nonstick features are finding new and promising applications, e.g. in nonstick coatings, thermal barriers, infra red sensor etc. Two decades after the first publication on quasicrystals, a soft quasicrystal was found in nature and a number of materials including liquid crystals, polymers, nanoparticles and colloids enriched the family of soft quasicrystals, enhancing the potential applications of these quasi-periodic structures.
In my talk I will present a brief history of the discovery of quasicrystals and I will discuss some of the fascinating mechanical and mathematical properties of quasicrystals. In particular I will focus on elastic constitutive relations in which besides the phonon space there is also a contribution from the phason space. I will present the form of the energy density function in some of these quasi-periodic structures. Recent findings of natural quasicrystals will also be mentioned.
1979, M.S. in Mathematics, Department of Mathematics, Warsaw University, Poland;
1988, Ph. D. in Solid Mechanics, Institute of Fundamental Technological Research, Polish Academy of Science, Warsaw, Poland;
2008, Habilitation in Solid Mechanics, Institute of Fundamental Technological Research, Polish Academy of Science, Warsaw, Poland.
1980 - 2008 Assistant/Senior Assistant/Assistant Professor, Institute of Fundamental Technological Research, Polish Academy of Science, Warsaw, Poland;
1989 - 1990 Fulbright Postdoctoral Fellow, Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, USA;
1990 - 1991 Visiting Assistant Professor, Department of Mathematics and Statistics, University of Nebraska Lincoln, USA;
2001 - 2002 Visiting Associate Professor, Department of Mathematics and Statistics, University of Massachusetts, Amherst, USA;
2008- Professor of the Military University of Technology, Warsaw, Poland.
Lecture Series on Mechanics, Ningbo University