Two Level States and relaxation

A special feature of amorphous materials is the anomalous behaviour of several properties at very low temperatures, such as in the low temperature specific heats. Most of these anomalies are attributed to the presence of two-level states (TLS) separated by small barriers, which gives rise to tunneling excitations. These excitations are characterized by wide distribution of relaxation times and energies. Several ultrasonic and low temperature specific heat measurements have been performed to characterize the TLS but their physical nature such as their structures, etc. is far from having been understood. These are the ADWP states discussed earlier in Chapter 7 in some detail. 

Another important manifestation of TLS is the time-dependent excess specific heat. This specific heat C t) has been shown to be given by the relation 

The tunneling in two-level states takes place when both the barrier heights and the widths are very small and thus the barrier can be breached by heavy atoms, unlike in the case of electrons or protons, which involves only tunneling. It is not clear whether TLS is a distinct class of objects involved in relaxation or whether they are just the tail-end states of secondary relaxations with very broad distributions, which continue to be active down to cryogenic temperatures. Another remarkable feature of the low temperature specific heat is that its magnitude depends only weakly on chemical composition, implying that the TLS present in glasses is almost a universal feature. 

Cohen and Grest (1979) have assigned on the basis of their modified free volume model that the tunneling states arise at very low temperatures (T Tg) because the volume dependent free energies of the cell in their model (see Chapter 3) possess curvature, which lead to local free energy minima. These minima are separated by solid-like barriers of 

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