The anisotropic glass-like properties of disordered crystals
The low temperature acoustic and thermal properties of amorphous, glassy materials are remarkably similar. All these properties are described theoretically with reasonable quantitative accuracy by assuming that the amorphous solid contains dynamical defects that can be described at low temperatures as an ensemble of two-level systems (TLS), but the deep nature of these TLSs is not clarified yet. Moreover, glassy properties were found also in disordered crystals, quasicrystals, and even perfect crystals with a large number of atoms in the unit cell. In crystals, the glassy properties are not universal, like in amorphous materials, and also exhibit anisotropy. Recently it was proposed a model for the interaction of two-level systems with arbitrary strain fields (Phys. Rev. B 75, 64202, 2007), which was used to calculate the thermal properties of nanoscopic membranes at low temperatures. The model is also suitable for the description of anisotropic crystals. We describe here the results of the calculation of anisotropic glass-like properties in crystals of various lattice symmetries.
Induced changes in the distribution of the tunneling states.
Ultrasonic attenuation measurements in neutron-irradiated quartz show distinct changes upon heat treatment in the behavior at the so-called plateau region. Since this plateau, observed in glasses and defective crystals such as neutron-irradiated quartz, is attributed to the specific distribution of the relaxation rates of the tunneling states (TS), the observations show that heat treatment can induce significant changes in this distribution, which provides an interesting tool to get more information about the nature of the tunneling states. The analysis in the framework of the tunneling model gives evidence that the TS with long relaxation times vanish upon heat treatment, which can be interpreted in terms of the disappearance of tunneling states with large mass.
Low-temperature thermal conductivity and acoustic attenuation in amorphous solids
In order to test whether the low-energy excitations explored extensively in amorphous solids are indeed universal, all measurements published on the low-temperature thermal conductivity and acoustic attenuation in these solids have been reviewed, on a total of over 60 different compositions. The ratio of the phonon wavelength \ensuremath{\lambda} to the phonon mean free path l has been found to lie between ${10}^{\ensuremath{-}3}$ and ${10}^{\ensuremath{-}2}$ in almost all cases, independent of chemical composition and frequency (wavelength) of the elastic waves, which varied by more than nine orders of magnitude in the different experiments. When the data were fitted with the tunneling model, which is based on the assumption of atomic or molecular tunneling states with a certain spectral distribution, the tunneling strength C, which describes their coupling to the lattice, was found to range from ${10}^{\ensuremath{-}4}$ to ${10}^{\ensuremath{-}3}$ in almost all cases. The only exceptions reported so far are certain films of amorphous silicon, germanium, and carbon. In these films, low-temperature acoustic attenuations over two orders of magnitude smaller have been observed compared to all other amorphous solids. Another remarkable observation is that a large number of disordered crystals, and even a thermally equilibrated quasicrystal, have low-energy lattice vibrations that are quantitatively indistinguishable from those of amorphous solids. Their tunneling strengths also range from ${10}^{\ensuremath{-}4}$ to ${10}^{\ensuremath{-}3}.$ These measurements have also been reviewed. It is concluded that the absence of long-range order is neither sufficient nor necessary for the existence of the low-energy excitations.