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Theoretical Calculation and Experimental Verification for Dislocation Reduction in Germanium Epitaxial Layers with Semicylindrical Voids on Silicon
Published on: July 17, 2020
Confirmation of the random tiling hypothesis for a decagonal quasicrystal
Alexander Kiselev1, Michael Engel, Hans-Rainer Trebin
1Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany.
Physical Review Letters
|February 2, 2013
Summary
This study confirms the random tiling hypothesis for quasicrystals using atomistic models. It reveals that phason elastic constants soften near a phase transition to an approximant phase at lower temperatures.
Area of Science:
- Condensed matter physics
- Materials science
- Crystallography
Background:
- The mechanisms stabilizing quasicrystals are not fully understood.
- Quasicrystals exhibit unique atomic structures with long-range order but no translational symmetry.
Purpose of the Study:
- To confirm the random tiling hypothesis in a realistic quasicrystal model.
- To investigate the temperature-dependent behavior of quasicrystal stability.
- To calculate free energy and phason elastic constants.
Main Methods:
- Developed a fully atomistic decagonal quasicrystal model.
- Applied the Frenkel-Ladd method for phonon calculations.
- Utilized uncorrelated phason flips for configurational entropy calculations.
Main Results:
- Confirmed predictions of the random tiling hypothesis.
- Calculated free energy and phason elastic constants across a temperature range.
- Observed a phase transition to an approximant phase upon cooling.
- Found that a phason elastic constant softens near the transition temperature.
Conclusions:
- The random tiling hypothesis is validated for atomistic quasicrystals.
- Phason elasticity plays a critical role in quasicrystal stability and phase transitions.
- Softening of phason elastic constants indicates an approaching phase transition.
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