Discussion on the surface science of quasicrystals

In search of multipolar order on the Penrose tiling

“…Further investigations are clearly necessary in order to seek out other possibilities of long-range multipolar order on the Penrose tiling. These should relax the m = 0 restriction imposed here, consider alternative forms of interparticle interaction, as well as explore other possibilities for the positions of particles on the quasiperiodic surface, such as those corresponding to the so-called "dark-stars" on the 5-fold surfaces of real icosahedral quasicrystals [16,17,18,48].…”

“…Hence, the knowledge of multipolar phase transitions and ground states is extremely important for a variety of applications as well as for fundamental understanding of physics and chemistry of solid state systems. With the recent ability to use the surfaces of real quasicrystals as templates upon which a variety of different particles can be adsorbed [16,17], it has become timely to study the ground states of multipoles on aperiodic substrates as well [18]. Yet, in contrast to the rather well-studied multipolar ground states on periodic lattices, the data for aperiodic tilings is quite limited [19,20,21,22], although there exists some group-theoretical analysis [23,24,25,26,27,28], describing the possible allowed symmetries of quasiperiodic multipolar arrangements, that may be used as a guide for our study.…”

Nanotechnology and Quasicrystals: From Self-Assembly to Photonic Applications

“…Nevertheless, other important questions have remained unanswered to this day. Many of these-such as the electronic and other physical properties of quasicrystals [46], the surface science of quasicrystals [47], and the importance of the phason degree of freedom [48]-were hotly debated at the "Silver Jubilee" conference [28], and continue to drive us forward. One particularly interesting set of questions, and the focus of this chapter, deals with metamaterials and soft-matter quasicrystals-the newly added members of the quasicrystal family.…”

“…For example, even the space groups of the observed phases have not been determined, although from the diffraction patterns of the dendrimer liquid crystals given by Zeng et al [50,51] it seems that they have a 12-fold screw axis, and therefore, most likely, the nonsymmorphic space group P 12 6 /mcm [37]. More generally, the same questions [46][47][48] concerning the thermodynamic stability, the role of clusters in formation and dynamics, and the importance of phasons, apply to soft quasicrystals as they do to hard quasicrystals.…”

Quasicrystals: diversity and complexity

“…Studies of the surfaces of quasicrystals have become a central component of quasicrystal research in the last decade or so [37,38]-a consequence of the availability of high-quality samples, discussed above, but also of the rapid development of sophisticated experimental techniques. Reports on surface studies at ICQ11 were numerous, providing important information not only on the surface structures but also, and maybe more importantly, on electronic, mechanical, tribological, and other physical properties of quasicrystals.…”