Transitions acoustic theory

A comparison of neutron spectra with theory was made by Danner et al. (7). These workers obtained data for Marlex 6050 at temperatures below and above the glass-transition interval and the melting point, and for samples of branched, irradiated, and quenched polyethylene at room temperature. The spectrum at 100 K (Fig. 3) showed two peaks with shapes characteristic of acoustic modes at 550 and 200 cm" (peaks C and E in Fig. 3). Five additional peaks were observed at 1360,750,340,... 

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This text of the two-volume treatment contains most of the theoretical background necessary to understand experiments in the field of phonons. This background is presented in four basic chapters. Chapter 2 starts with the diatomic linear chain. In the classical theory we discuss the periodic boundary conditions, equation of motion, dynamical matrix, eigenvalues and eigenvectors, acoustic and optic branches and normal coordinates. The transition to quantum mechanics is achieved by introducing the Sohpddingev equation of the vibrating chain. This is followed by the occupation number representation and a detailed discussion of the concept of phonons. The chapter ends with a discussion of the specific heat and the density of states. 

According to the BCS (Bardeen, Cooper and Schrieffer) theory, electrons form pairs below the critieal temperature T., stabilized by a decrease in energy A = kT. . Lattice vibrations, more precisely acoustic phonons, are mediators of the interaction. This interpretation is confirmed through different experimental observations when the transition temperature is low (T. < 30 0 K). For higher temperatures, and henee stronger interaetions, the mechanism of pair formation stated by BCS must be reexamined. Several proposals have been made but to date none have been impressive. The phase diagram in Figure 11.7 shows how superconductivity appears under extreme eonditions. 

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