Hyperspace-Simulations of the Stability and Growth of Model Quasicrystals

• Applicant: Professor Dr. Michael Schmiedeberg
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 541211648

A fascinating feature of quasicrystals - structures with long ranged order but no translational symmetry - is the existence of additional degrees of freedom termed phasons, which are related to correlated rearrangements that in the long wavelength limit do not change the free energy. The occurrence of phasonic excitations or fluctuations affects a lot of properties of quasicrystals. For instance, the phasonic degrees of freedom lead to a larger entropy of a quasicrystal and thus contribute to its stability. Furthermore, the growth of a quasicrystal occurs in at least two stages and phasons are important in both: First, a quasicrystal often grows with a lot of phasonic excitations that are built into the structure (even if it growth without any dislocations). The resulting phasonic strain might be relaxed in a second step by phasonic rearrangements. Note that a similar strain with a subsequent repair mechanism is observed if the structure grows from multiple seeds. The details of the described phenomena and processes are still under investigation, especially because it is difficult to separate the phononic and phasonic contributions in conventional simulations which in addition usually are too inefficient to explore the slow relaxation processes of phasonic strain. In the proposed project we will implement and use Monte Carlo simulations in hyperspace where the actual (model) quasicrystal occurs as projection in the so-called physical space. Then phonons are given by the motion parallel to the physical space and phasonic rearrangements are triggered by displacements in perpendicular direction. In principle, a Monte Carlo simulation in hyperspace samples the same statistics as conventional simulations. However, by working in hyperspace, we will be able to switched on and off phasonic and phononic displacements independently as desired. As a consequence, we will be able to address open questions that rely on the understanding of phononic or phasonic contributions to a phenomena.The open questions and problems include: Concerning the stability of quasicrystals we will determine to what extend a given quasicrystal is stabilized by energy and to what extend by entropy. Furthermore, if a quasicrystal occurs on a periodic substrate (like two-dimensional oxide quasicrystals), how does the periodic substrate supports the quasicrystalline order what is the prize of this external stabilization in terms of built-in strain? Concerning the growth of quasicrystals we are interested in the role of phasons at all stages of the growth process. Finally, we will study quasicrystals with high rotational symmetries where there also is a large number of phasonic modes. We want to address the question whether statistical properties of quasicrystals with high rotational symmetries and their phasonic excitations are close to the properties of amorphous materials and their excitations (at least at length scales where long-ranged correlations are not yet important).

• DFG Programme: Research Grants