Debye-Waller factors in a quasicrystal

The mean-square vibrational amplitude 〈U²〉 for five reflections located on a twofold axis of an icosahedral quasicrystal Al71.0Pd20.5Mn8.5 have been determined between room temperature (RT) and below 20 K by x-ray diffraction. Their Q vectors (Q=2sinθ/λ) range from 1.278 ^-1 to 2.556 ^-1. For four reflections, the logarithm of the integrated intensity is linear, proportional to temperature, near and below RT, and tends to saturate to a constant value at low temperature (LT), an effect of the zero-point energy. All plots for these four reflections are indeed linear at RT and below, and saturate at LT to values that are different from those predicted by Debye theory. This behavior is reminiscent of that of layered crystals such as graphite or TaS₂, in which the anomaly could be explained by considering the effect of reduced dimensionality and anisotropy, none of which can be applied to icosahedral quasicrystals. The effect may be due to a change of Debye temperature below 100 K. The fifth reflection (Q=2.252^-1) displays a temperature dependence that does not lead to a single mean-square vibrational amplitude. The Debye temperature obtained from the first four plots is in the neighborhood of 312 K.