‘‘Martensitic’’ instability of an icosahedral quasicrystal

A density-functional theory is developed to calculate the elastic moduli of crystals and quasicrystals. It is found that the nonaffine character of deformations below the unit-cell scale causes the Poisson ratio of a hard-sphere solid to be negative. An elastic instability is found for the icosahedral quasicrystals which lowers their symmetry to $D_3$ or $D_5$. The distortions of the diffraction pattern are in qualitative agreement with experiments.