Phason softening and structural transitions in icosahedral quasicrystals

The structural instability driven by soft phason modes in icosahedral quasicrystals is investigated. It is found that, depending on the physical parameters, three distinct soft modes induce the structural instabilities associated with the symmetry changes, ${\mathit{I}}_{\mathit{h}}$→${\mathit{D}}_{5\mathit{d}}$, ${\mathit{I}}_{\mathit{h}}$→${\mathit{D}}_{3\mathit{d}}$, and ${\mathit{I}}_{\mathit{h}}$→${\mathit{C}}_{2\mathit{h}}$. The physical consequences of the phason softening, such as the characteristic diffuse scattering line shape and the temperature dependence of the Debye-Waller factor, are discussed for these three cases. It is shown that the onset of uniform phason strain fields always interrupts the growing of the soft-phason-mode fluctuations, leading to a first-order transition into a different strained phase if the system stays in equilibrium.