Phonon modes pressure dependence

Figures 5-6 show characteristic spectra at RT and the pressure dependence of the energy of the Ag-symmetry phonons for Y123 x 6.5 and x 7. The pressure dependence of the energy of the Big-like mode is almost linear for the yttrium-based compounds we have studied. As seen in Fig.6,...

Fig. 4 Phonon density of states at 180 K for the low-frequency modes of C60 at atmospheric pressure and at 0.5 GPa. Reprinted with permission from H Schober and B Renker, Pressure dependence of the external mode spectrum of solid C60 , Phys. Rev. B vol. 59 (1999) 3287-90 [39]. Copyright 1999 The American Physical Society...

The pressure-dependence of ZnO phonon-mode frequencies measured by Raman scattering was reported in [37, 130]. From that the Griineisen parameters 7j... 

The hydrostatic pressure dependence of the zone centre phonon modes has been determined in n-type bulk GaN [6,32] and GaN/sapphire (n = 9 x 10 16 cm 3) (TABLE 7) [33], Phonon modes and their hydrostatic pressure behaviour have been calculated in first-principles calculations [34],... 

For ice X and the (fee) antifluorite structure the quantification of various aspects of their structural and chemical character and their dependence with pressure was found using AIM in a novel approach. Metallic character was found to be present in the antifluorite structure, but did not persist with increased pressure since the BCPs then fell within the pseudopotential core radii. In future studies on the antifluorite structure it will be necessary to replace the core with the true all electron distribution. In addition we present a hypothesis for the physical meaning of the O—O bonding interactions, namely that they indicate the onset of, soft phonon modes that are known to accompany structural changes. The fact that there are no O—O interactions in the antifluorite structure is consistent with this hypothesis, since to date there aren t any higher pressure phases of ice than antifluorite ice and so no pressure induced phase change can occur in this structure. Thus our hypothesis would explain why there are no O—O interactions in the antifluorite structure. 

Elastic constants depend on pressure and temperature because of the anharmonicity of the interatomic potentials. From the dependence of bulk and shear moduli on hydrostatic and uniaxial pressure, third order elastic constants and Griineisen parameters may be determined. Griineisen parameter shows the effect of changing volume, V, on the phonon mode frequencies, co. 

How is the pressure inside the DAC determined Usually, this is achieved by adding to the sample a small amount of a pressure calibrant with a known vibrational or electronic spectroscopic response to changes in pressure. For the infrared, a material such as powdered NaNOs is normally used—the symmetric N—O stretching mode of the NOs group is located at 1,401.3 cm at ambient pressure and moves steadily to higher wavenumbers with increasing pressure. For the Raman, the most common pressure calibrant is a ruby chip—the Ri fluorescence of ruby at 694.2 nm has a well-established pressure dependence up to 160kbar. More recently, it has been shown that the t2g phonon mode of the diamonds in the DAC itself, located at 1,332.5 cm at ambient pressure, can be used as an in situ calibrant for pressures up to 50 kbar. ... 

Diminishing of the electron-hgand distance R under pressure, as well as the pressure-induced changes in the phonon energies, also influences the electron-lattice interaction Shm. When the interaction with a totally symmetric breathing mode is considered, the pressure dependence of the electron-lattice interaction is given by [76, 77] ... 

M. Kuball, J.M. Hayes, Y. Shi, J.H. Edgar, A.D. Prins, N.W.A. van Uden, D.J. Dunstan, Raman scattering studies on single-crystalline bulk AIN temperature and pressure dependence of the AIN phonon modes. J. Cryst. Growth 231(3), 391-396 (2001)... 

Figure 1.22 Top (Vio - Vjo) Ei phonon mode splitting versus pressure. Solid lines are linear least-square fits to the experimental points. Bottom Pressure dependence of the observed optical phonons. Open (full) symbols propagation of light perpendicular (parallel) to c-axis. (Courtesy of F. Decremps [92].)...

While there are no experimental data available for cubic ZnO at atmospheric pressure, ab initio calculations for phonon properties of cubic ZnO, which relied on experimental data of rocksalt ZnO studied under high pressures ( 8 GPa) as input parameters, have been undertaken [55]. The predictions by such an exercise for a>ro and cOlo lead to 235 cm and 528 cm, respectively, for cubic ZnO. The values are smaller than those obtained by extrapolating the IRSE analysis. However, it should be pointed out that both extrapolations follow the same trend in predicting phonon mode frequencies and that they are smaller than those of hexagonal ZnO. The width of phonon modes depends on sample quality and processes that lead to broadening. A discussion of phonon mode broadening parameters can be found in Ref. [26, 27]. 

Fig. 13. (a) Experimentally determined Raman spectra of Si-II and (b) their dependence on pressure (open circles) [101] together with theoretically predicted phonon frequencies for the TO and LO modes of Si-II (filled circles) [100]. The lines serve as guides to the eye. 

TP-BOLS matching of the measured and calculated size [144, 147], temperature [141, 148], and pressure [148] dependence of the B and Am [149] for Ti02 at room temperature, as shown in Hg. 27.14 allows us to verify the developed solutions and extract information as given in Table 27.5. Reproduction of TiOa phonons turns out m = 5.34 [ 150]. Reproduction of the Eg mode of Ti02, shown in Fig. 27.14, revealed that the respective phonon frequency is contributed by only one neighbor (z = 1). 

Fig. 27.13 Pressure and temperature-dependent Raman shift of (a, b) for AIN [126-129] (c, d) GaN[130-133], and (e, f) InN [134, 135], Extracted intrinsic phonon frequency co(l) and mode cohesive energies Ei,(0) for various modes are tabulated in Table 27.4 (reprinted with permission from [136])...

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