Phonon experimental data

Fig. 5.37 Comparison of the calculated phonon dispersion curve for Al with the experimental values measured using neutron diffraction. (Figure redrawn from Michin Y, D Farkas, M ] Mehl and D A Papaconstantopoulos 1999. Interatomic Potentials for Monomatomic Metals from Experimental Data and ab initio Calculations. Physical Review 359 3393-3407.)...

Figure 7. Phonon dispersion including the electron-phonon interaction for bcc CuZn. Force constants have been obtained from ah initio calculations. Dashed line is the phonon dispersion without the V-i contribution. Diamonds mark experimental data. ...

It is interesting to note that the simple Morse potential model, when employed with appropriate values for the parameters a and D (a = 2.3 x 1010 m 1, D = 5.6 x 10 19 J as derived from spectroscopic and thermochemical data), gives fb = 6.4 nN and eb = 20%, which are quite comparable to the results obtained with the more sophisticated theoretical techniques [89]. The best experimental data determined on highly oriented UHMWPE fibers give values which are significantly lower than the theoretical estimates (fb 2 nN, b = 4%), the differences are generally explained by the presence of faults in the bulk sample [72, 90] or by the phonon concept of thermomechanical strength [15]. 

Figure 19. The predicted low T heat conductivity. The no coupling case neglects phonon coupling effects on the ripplon spectrum. The (scaled) experimental data are taken from Smith [112] for a-Si02 (AsTj/ScOd 4.4) and from Freeman and Anderson [19] for polybutadiene (ksTg/Hcao — 2.5). The empirical universal lower T ratio l /l 150 [19], used explicitly here to superimpose our results on the experiment, was predicted by the present theory earlier within a factor of order unity, as explained in Section lllB. The effects of nonuniversaUty due to the phonon coupling are explained in Section IVF.

Debye phonon velocity) and lower in the case of very dissimilar materials. For example, the estimated Kapitza resistance is smaller by about an order of magnitude due to the great difference in the characteristics of helium and any solid. On the other hand, for a solid-solid interface, the estimated resistance is quite close (30%) to the value given by the mismatch model. The agreement with experimental data is not the best in many cases. This is probably due to many phenomena such as surface irregularities, presence of oxides and bulk disorder close to the surfaces. Since the physical condition of a contact is hardly reproducible, measurements give, in the best case, the temperature dependence of Rc. 

The calculated Rayleigh mode (SJ, the lowest lying phonon branch, is in good agreement with the experimental data of Harten et al. for all three metals. Due to symmetry selection rules the shear horizontal mode just below the transverse bulk band edge can not be observed by scattering methods. The mode denoted by Sg is the anomalous acoustic phonon branch discussed above. Jayanthi et al. ascribed this anomalous soft resonance to an increased Coulomb attraction at the surface, reducing the effective ion-ion repulsion of surface atoms. The Coulomb attraction term is similar for all three metals... 

Experimental data of Gibson and Sibener appears to confirm qualitatively these predictions at least for monolayers. The phonon linewidths were broadened around T up to half of the Brillouin zone. The hybridization splitting could not be resolved, but an increase of the inelastic transition probability centered around the crossing with the Rayleigh wave and extending up to 3/4 of the zone has been observed and attributed to a resonance between the adatom and substrate modes. 

We can deduce the vibrational modes of atoms from experimental data on the interaction of radiation of various frequencies (photons and phonons) with the crystalline matter. 

Fig. 58. Composition dependence of the density of states N(E ) at the Fermi level ( ) of Y Lui-xl I C calculated by CPA, experimental data for the Sommerfeld parameter /n end the phenomenologically extracted values of the electron-phonon coupling constant Ae. ph (in this article usually written as Apt,), using eq. (9).

K. The transition time is 102 s at 1.3 K. Kapphan and Luty proposed a phonon-assisted tunneling mechanism for this process. Although the notion that a mass as heavy as Ag+ can tunnel 0.9 A through a 0.17-kcal/mol barrier at 1.3 K is quite surprising, the experimental data and analysis clearly support this conclusion. 

The most orthodox model involving a quasi-one-dimensional tight-binding band with electron scattering by acoustic phonons and molecular vibrations (one-phonon processes) has been analyzed carefully and in great detail [43,44]. Good agreement with experimental data is claimed by the proponents of this model. 

Whether conjugated polymers are best described by a band model, such as the SSH model, or an exciton model, will depend crucially on the relative strengths of the electron-phonon and electron-electron interactions. After the discovery of highly conductive polymers, the band model was widely accepted and applied to the interpretation of experimental data. Gradually since that time, evidence that suggests that an exciton picture is more appropriate has been accumulating. Comparison of experimental results with the models described above has been used to estimate the relative importance of the two types of interaction. This will be discussed in the following sections. 

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