Phason softening in the AlPdMn icosahedral phase

The diffuse scattering located close to Bragg reflections has been studied as a function of the temperature on a single grain of the AlPdMn icosahedral phase. Between $600^\circ$C and $800^\circ$C there is a reversible and continuous transition. When the temperature increases, the diffuse scattering diminishes whereas high-$Q_\bot$ reflections have their intensity increased. All results are well interpreted within the elasticity theory of quasi-crystals: the changes in diffuse scattering shape and intensity when lowering the temperature are due to a softening of the K1 phason elastic constant. The time decay of these long-wavelength phason fluctuations is larger than 5 ns