Libron model

Other more unusual pictures that have been proposed include the libron model [45], where librations (molecular rotations) are responsible for ph T). It was suggested that the T2 behavior arose from the dominance of two-libron processes, and that the first-order, single-libron contribution is small by symmetry. The T dependence of the spin susceptibility was discussed within the same framework, in terms of a band-narrowing effect [46]. However, this approach has been criticized [44], and furthermore, no evidence has been found that librations play any role in metal-semiconductor transitions [9]. 

Another significant source of variations in the local site energies of molecular ions and excitons in condensed media is the modulation of these energies by the thermal vibrations either of the medium (e.g., acoustical phonons and librons) or of the molecular ion (exciton) itself (intramolecular vibrations). A model Hamiltonian which incorporates electronic interactions with... 

Depending on the character of the molecular motions, one can distinguish several physical situations. In most cases, the molecules are trapped in relatively deep potential wells. Then, they perform small translational and orientational oscillations around well-defined equilibrium positions and orientations. Such motions are reasonably well described by the harmonic approximation. The collective vibrational excitations of the crystal, which are considered as a set of harmonic oscillators, are called phonons. Those phonons that represent pure angular oscillations, or libra-tions, are called librons. For some properties it turns out to be necessary to look at the effects of anharmonicities. Anharmonic corrections to the harmonic model can be made by perturbation theory or by the self-consistent phonon method. These methods, which are summarized in Section III under the name quasi-harmonic theories, can be considered to be the standard tools in lattice dynamics calculations, in addition to the harmonic model. They are only applicable in the case of fairly small amplitude motions. Only the simple harmonic approximation is widely used the calculation of anharmonic corrections is often hard in practice. For detailed descriptions of these methods, we refer the reader to the books and reviews by Maradudin et al. (1968, 1971, 1974), Cochran and Cowley (1967), Barron and Klein (1974), Birman (1974), Wallace (1972), and Cali-fano et al. (1981). 

D librons assemblies Properties, appUcations and modelling of three-dimensional textile strnctnres... 

When the MF model is further separated by Eq. (42) the MF excitations are either translational (T) or librational (L). The indices k and k which label the rows and columns of the matrix 0(q) run over both types of excitations. The elements 0 q) and 0 q) correlate the translational and rotational vibrations of the individual molecules the resulting lattice vibrations are the translational phonons and the librons. These are coupled by the elements and (g), which contain the translation-... 

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