Elastic stability and diffuse scattering in icosahedral quasicrystals

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Abstract
Five elastic constants define the stiffness of coupled phonons and phasons in icosahedral quasicrystals. Requirements of elastic stability impose constraints (inequalities) on combinations of these elastic constants. This paper derives two sets of inequalities, one against the onset of spatially uniform strains, and a weaker set against the onset of spatially varying strains. When the elastic constants approach a violation of this weaker set of inequalities, Bragg peak intensities vanish continuously, while diffuse scattering intensities grow. Depending on which combination of elastic constants violates its stability condition, the diffuse scattering patterns peak in directions corresponding to icosahedron vertices, faces, or edges. Qualitative examination of diffuse scattering patterns therefore may yield an insight into the mechanism driving quasicrystal-to-crystal phase transitions, while quantitative studies may yield numerical values of the elastic constants.