# Confirmation of the random tiling hypothesis for a decagonal quasicrystal.

@article{Kiselev2012ConfirmationOT, title={Confirmation of the random tiling hypothesis for a decagonal quasicrystal.}, author={Alexander V. Kiselev and Michael Engel and Hans-Rainer Trebin}, journal={Physical review letters}, year={2012}, volume={109 22}, pages={ 225502 } }

Mechanisms that stabilize quasicrystals are much discussed but not finally resolved. We confirm the random tiling hypothesis and its predictions in a fully atomistic decagonal quasicrystal model by calculating the free energy and the phason elastic constants over a wide range of temperatures. The Frenkel-Ladd method is applied for the phonon part, and an approach of uncorrelated phason flips is applied for the configurational part. When lowering the temperature, a phase transition to an…

## 17 Citations

Phasonic Diffusion and Self-confinement of Decagonal Quasicrystals in Hyperspace

- PhysicsJournal of Physics: Conference Series
- 2020

We introduce a novel simulation method that is designed to explore fluctuations of the phasonic degrees of freedom in decagonal colloidal quasicrystals. Specifically, we attain and characterise…

Non-close-packed three-dimensional quasicrystals

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2017

This work investigates the computational self-assembly of four quasicrystals in a single model system of identical particles interacting with a tunable isotropic pair potential.

On the stability of a quasicrystal and its crystalline approximant in a system of hard disks with a soft corona.

- PhysicsThe Journal of chemical physics
- 2015

The phase behavior of a model system of colloidal hard disks is studied and it is found that the random tiling dodecagonal quasicrystal is stabilised by entropy at finite temperatures with respect to the crystalline approximants that the authors considered, and its stability region seems to extend to zero temperature.

Quasicrystals in the Molecular Dynamic Model of Pure Aluminum

- Materials Science
- 2014

Growth and structures of crystals in the model of Al obtained in results of isothermal annealing after quick cooling to certain temperatures are studied by the method of molecular dynamics applying…

Phase behaviour of quasicrystal forming systems of core-corona particles.

- PhysicsThe Journal of chemical physics
- 2017

Using Monte Carlo simulations and free-energy calculations, a two-dimensional system of particles interacting with a hard core of diameter σHD and a repulsive square shoulder potential is studied and it is found that the system at all three shoulder widths forms hexagonal phases in two distinct density ranges due to the two characteristic length scales in the interaction potential.

Quasicrystal structure and growth models: discussion of the status quo and the still open questions

- Physics
- 2017

Where are we now in quasicrystal (QC) research more than three decades after Dan Shechtman’s discovery? Do we fully understand the origin of quasiperiodicity, the formation, growth, thermodynamic…

Self-assembly of two-dimensional binary quasicrystals: a possible route to a DNA quasicrystal

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2017

It is shown that binary solutions of penta- and hexavalent two-dimensional patchy particles can form thermodynamically stable quasicrystals even at very narrow patch widths, provided their patch interactions are chosen in an appropriate way.

Self-assembly of two-dimensional binary quasicrystals: a possible route to a DNA quasicrystal

- Physics
- 2016

We use Monte Carlo simulations and free-energy techniques to show that binary solutions of penta- and hexavalent two-dimensional patchy particles can form thermodynamically stable quasicrystals even…

High-temperature structural study of decagonal Al-Cu-Rh.

- Materials ScienceActa crystallographica Section B, Structural science, crystal engineering and materials
- 2014

The structure of decagonal Al-Cu-Rh has been studied as a function of temperature by in-situ single-crystal X-ray diffraction and a comparison of the high-temperature datasets suggests that the best quasiperiodic ordering should exist between 1083 and 1153 K.

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