Dynamics of Phason Fluctuations in the $i\mathrm{\text{−}}\mathrm{A}\mathrm{l}\mathrm{P}\mathrm{d}\mathrm{M}\mathrm{n}$ Quasicrystal

We report on the study of the dynamics of long wavelength phason fluctuations in the i-AlPdMn icosahedral phase using coherent x-ray scattering. When measured with a coherent x-ray beam, the diffuse intensity due to phasons presents strong fluctuations or speckles pattern. From room temperature to $500°\mathrm{C}$ the speckle pattern is time independent. At $650°\mathrm{C}$ the time correlation of the speckle pattern exhibits an exponential time decay, from which a characteristic time $\tau$ is extracted. We find that $\tau$ is proportional to the square of the phason wavelength, which demonstrates that phasons are collective diffusive modes in quasicrystals, in agreement with theoretical predictions.

Figure 1

Time dependence of the intensity correlation function measured at $400°\mathrm{C}$ for a phason wave vector equal to $0.17\mathrm{n}{\mathrm{m}}^{\mathrm{-}\mathrm{1}}$.

Figure 2

Time dependence of the intensity correlation function measured at $650°\mathrm{C}$ for two different phason wave vectors propagating along the $(\tau ,-1,0)$ direction. The solid line is an exponential time decay fit to the data. Corresponding $q$ and characteristic time $\tau$ values are indicated on the different panels.

Figure 3

Evolution of the characteristic time $\tau$ as a function of ${\lambda }^2$, measured at $650°\mathrm{C}$. There is a linear dependence from which the phason diffusion constant can be extracted.