Cooperative Phonon Relaxation

N = 6 gives the three cage, book, and prism hexamer structures, all with nearly identical binding energy (Reprinted with permission from [11]). See appendix A4-2 for the optimal (H20)at configurations 

The trend of coh stiffening in Fig. 35.5b is consistent with experimental measurements (Fig. 35.3). For instances, the coh is stiffened from 3,200 to 3,650 cm when water cluster (H20)at drops from = 6 to 1 [39] and from 3,420 to 3,650 cm when the water (surface) becomes gaseous molecules [40]. IR measurements [38, 41] revealed that the coh shifts from 3,225, 3,350, 3,380 to 3,525 cm when Af drops from 6,5,4 to 3 of (H20)jvencapsuled in inert matrices. When the ice cluster reduces from 475 to 85 molecules, the o)h transits from 3,200 dominance to 3,500 cm [42], suggesting the shortening the real bond and stiffening the coh phonons when the cluster size is reduced. Coordination-reduction also stiffens the coh for H (H20)at n = 20 — 200) [65]. 

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Compression shortens and stiffens the softer 0 H bond, meanwhile, lengthens and softens the H-O bond through repulsion between electron pairs on adjacent O atoms, which results in the 0 H-0 length symmetrization, low compressibility, Tc depression, phonon cooperative relaxation. 

Figure 34.3 shows that MD-derived phonon relaxation trends agree with Raman and IR measurements of ice-VIII at 80 K [4, 6, 23]. As P increases, the calculated coh is softened from 3,520 to 3,320 cm and the cul is stiffened from 120 to 336 cm disregarding the possible phase change and other supplementary peaks nearby. The pressure-derived cooperative relaxation of the col and the cuh in both water [25] and ice [4-6] confirms the expectations that the longer and softer 0 H becomes shorter and stiffer, while the H-O does the otherwise. 

Fig. 36.6 Temperature-dependent Raman shifts of, (a) (o < 300 cm , (b) (Ofi > 3,000 cm in the regions of T > 273 K, 273 >T> 258 K, and T < 258 K, showing cooperative phonon-stiffness relaxation (Reprinted with permission from [45])...

Examples of two-body ET are shown in Figs. 24b,c. Migration, Fig. 24b, represents the case when the donor and acceptor are the same species. However, it can also occur nonresonantly since there may be a slight energy mismatch from the donor to the acceptor site, which can be compensated by acoustic phonons. In the second cross-relaxation mechanism, Fig. 24c, the emission from level / is quenched, and level i is populated. If the acceptor level is an excited state (often the same as the donor state, as in Fig. 24d), the process is called ET upconversion. The term cooperative ET upconver-... 

In general the Cooper pairs in conventional superconductors induced by phonons have. -symmetry where the gap opens uniformly on the Fermi surface and the temperature dependence of physical quantities below Tc is exponential. On the other hand, when the attractive force originates from spin or electron charge fluctuations, the Cooper pair has p- or d-wavc symmetry where the gap disappears on lines or points on the Fermi surface and the physical quantities have power-law temperature dependences. The quantities that are measured by NMR and nuclear quadrupole resonance (NQR) are the nuclear spin-lattice relaxation rate, 1 / T, the Knight shift, K, the spin echo decay rate, 1/T2 and the NQR frequency, vq. The most important quantities, K and 1/77 for the determination of the symmetry of the Cooper pairs are reviewed in the following sections. 

The question of the nature of the superconducting state in the radical-ion salts can still not be unambiguously answered even after more than 20 years of intensive research. In the conventional superconductors, the phenomenon can be explained through the BCS theory by the formation of Cooper pairs. Here, the attractive interaction between two electrons is mediated by phonons. The total spin of the Cooper pairs is S = 0, and their total orbital angular momentum is I = 0. The pair wave-function is an s-function. The concept of the Cooper pairs as spin singlets can evidently also be applied to the radical-ion salts. This can for example be shown by measurements of the NMR spin-lattice relaxation time in the superconducting state [3]. 

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