Three-wave vibrational mode broadening for Fibonacci one-dimensional quasicrystals

• Published in: Journal of physics. Condensed matter Vol. 17; no. 43; pp. 6849 - 6869
• Main Authors: Kats, E I, Muratov, A R
• Format: Journal Article
• Language: English
• Published: IOP Publishing 02.11.2005
• ISSN: 0953-8984; 1361-648X
• DOI: 10.1088/0953-8984/17/43/006

A one-dimensional Fibonacci chain is used to model vibrational mode broadening in icosahedral quasicrystals (i-QCs). All calculations are performed self-consistently for various finite size approximants at temperatures higher than the Debye temperature, TD. This approach is extended to three-dimensional systems as well. It is shown that vibrational spectra depend crucially on the Fibonacci chain mass ratio m. For m = 3, which roughly mimics AlPdMn i-QC, there are three almost dispersionless optic modes separated from the acoustic mode by three large gaps, and for m = 1/3, which mimics ZnMgY i-QC, there is one dispersionless optic mode and one acoustic mode. For the first time we provide a qualitative model which predicts experimentally observed phonon spectrum broadening of i-QC. It is shown that three wave broadening for both one-dimensional and three-dimensional Fibonacci i-QCs is the leading mechanism of spectrum broadening. For the intermediate range of mode coupling constants, it scales with the mode frequency as c1+c22 (where c1 and c2 are some numerical constants). For smaller values of the coupling constant, phonon broadening is proportional to 3. We conclude that for a system with a non-simple elementary cell, vibrational spectrum broadening is always larger than for a system with a primitive cell (provided all other characteristics are the same).