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Figure 2
Local free-energy densities [f(\phi)] used in this work: solid colored lines show the scaled (α = 1) quartic local free-energy function (7)[link] used by LP, for values of [\epsilon] above, equal to and below the spinodal value of [\epsilon] = 0. The full logarithmic local free-energy function fCG in equation (49)[link], as used by BDL, is shown with dashed lines for temperatures above, below and equal to the spinodal temperature, which is scaled to T = 1. The values of [\epsilon] and T are related by T = [4/(3\epsilon + 4)], as explained in Section 7[link]. In order to demonstrate visually the resulting fourth-order agreement, the solid lines have been stretched horizontally by 50% while the dashed lines have been compressed vertically by a factor of 27T/16. Note that the LP quartic free-energy density penetrates into the [\phi \,\lt\, -1] region and diverges from the BDL logarithmic free-energy density for [\phi \,\gt\, 1]. Finally, the solid black line shows the free-energy density used in Section 8[link] to stabilize 6n-fold quasicrystals with arbitrary n.

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