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Figure 18
Free energies of the two-scale periodic and unstable quasiperiodic structures in the BDL model: plotted for comparison are the free energies of the uniform and single-scale hexagonal phases. q takes the values k4, k6, k8, k10 and [k_\infty], as labeled. As in the LP model, the free energies of the two-scale square (k4), hexagonal (k6), lamellar (q = [k_\infty]), decagonal (k5) and dodecagonal (k12) structures are lower than that of single-scale hexagonal structure, but unlike the LP model the decagonal structure remains the equilibrium phase down to zero temperature, without undergoing a second phase transition. On the other hand, still in line with the LP model, the free energies of the octagonal (k8) and decagonal (k10) quasicrystals are always higher than that of the single-scale hexagonal structure, and are therefore never the equilibrium phase.

IUCrJ
Volume 5| Part 3| May 2018| Pages 247-268
ISSN: 2052-2525
https://doi.org/10.1107/S2052252518001161